Delft3D FLOW User Manual FLOW_User_Manual

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3D/2D modelling suite for integral water solutions

DR
AF

Delft3D

Hydro-Morphodynamics

User Manual

DR
AF
T

DR
AF

Delft3D-FLOW

Simulation of multi-dimensional hydrodynamic flows
and transport phenomena, including sediments

User Manual

Hydro-Morphodynamics

Version: 3.15
SVN Revision: 54749
April 18, 2018

DR
AF

Delft3D-FLOW, User Manual

Published and printed by:
Deltares
Boussinesqweg 1
2629 HV Delft
P.O. 177
2600 MH Delft
The Netherlands

For sales contact:
telephone: +31 88 335 81 88
fax:
+31 88 335 81 11
e-mail:
software@deltares.nl
www:
https://www.deltares.nl/software

telephone:
fax:
e-mail:
www:

+31 88 335 82 73
+31 88 335 85 82
info@deltares.nl
https://www.deltares.nl

For support contact:
telephone: +31 88 335 81 00
fax:
+31 88 335 81 11
e-mail:
software.support@deltares.nl
www:
https://www.deltares.nl/software

Copyright © 2018 Deltares
All rights reserved. No part of this document may be reproduced in any form by print, photo
print, photo copy, microfilm or any other means, without written permission from the publisher:
Deltares.

Contents

Contents
List of Figures

xiii

List of Tables

xix

1 A guide to this manual
1.1 Introduction . . . . . . . . . . . . . . . .
1.2 Manual version and revisions . . . . . . .
1.3 Typographical conventions . . . . . . . .
1.4 Changes with respect to previous versions

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2 Introduction to Delft3D-FLOW
2.1 Areas of application . . . . . . . . . .
2.2 Standard features . . . . . . . . . . .
2.3 Special features . . . . . . . . . . . .
2.4 Coupling to other modules . . . . . .
2.5 Utilities . . . . . . . . . . . . . . . .
2.6 Installation and computer configuration

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3 Getting started
3.1 Overview of Delft3D . . . . .
3.2 Starting Delft3D . . . . . . .
3.3 Getting into Delft3D-FLOW .
3.4 Exploring some menu options
3.5 Exiting the FLOW-GUI . . .

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4 Graphical User Interface
4.1 Introduction . . . . . . . . . . . . . . . . . . .
4.2 MDF-file and attribute files . . . . . . . . . . .
4.3 Filenames and conventions . . . . . . . . . . .
4.4 Working with the FLOW-GUI . . . . . . . . . .
4.4.1 Starting the FLOW-GUI . . . . . . . . .
4.4.2 Visualisation Area window . . . . . . .
4.5 Input parameters of MDF-file . . . . . . . . . .
4.5.1 Description . . . . . . . . . . . . . . .
4.5.2 Domain . . . . . . . . . . . . . . . . .
4.5.2.1 Grid parameters . . . . . . .
4.5.2.2 Bathymetry . . . . . . . . . .
4.5.2.3 Dry points . . . . . . . . . .
4.5.2.4 Thin dams . . . . . . . . . .
4.5.3 Time frame . . . . . . . . . . . . . . .
4.5.4 Processes . . . . . . . . . . . . . . .
4.5.5 Initial conditions . . . . . . . . . . . .
4.5.6 Boundaries . . . . . . . . . . . . . . .
4.5.6.1 Flow boundary conditions . .
4.5.6.2 Transport boundary conditions
4.5.7 Physical parameters . . . . . . . . . .
4.5.7.1 Constants . . . . . . . . . .
4.5.7.2 Viscosity . . . . . . . . . . .
4.5.7.3 Heat flux model . . . . . . .
4.5.7.4 Sediment . . . . . . . . . . .
4.5.7.5 Morphology . . . . . . . . .
4.5.7.6 Wind . . . . . . . . . . . . .
4.5.7.7 Tidal forces . . . . . . . . . .

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iii

Delft3D-FLOW, User Manual

4.6
4.7

Numerical parameters . . . . . .
Operations . . . . . . . . . . . .
4.5.9.1 Discharge . . . . . . .
4.5.9.2 Dredging and dumping .
4.5.10 Monitoring . . . . . . . . . . . .
4.5.10.1 Observations . . . . . .
4.5.10.2 Drogues . . . . . . . .
4.5.10.3 Cross-sections . . . . .
4.5.11 Additional parameters . . . . . .
4.5.12 Output . . . . . . . . . . . . . .
4.5.12.1 Storage . . . . . . . .
4.5.12.2 Print . . . . . . . . . .
4.5.12.3 Details . . . . . . . . .
Save the MDF and attribute files and exit .
Importing, removing and exporting of data

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5 Tutorial
5.1 Introduction – MDF-file and attribute files
5.2 Filenames and conventions . . . . . . .
5.3 FLOW Graphical User Interface . . . . .
5.3.1 Introduction . . . . . . . . . . .
5.3.2 Saving the input data . . . . . .
5.4 Description . . . . . . . . . . . . . . .
5.5 Domain . . . . . . . . . . . . . . . . .
5.5.1 Grid parameters . . . . . . . .
5.5.2 Bathymetry . . . . . . . . . . .
5.5.3 Dry points . . . . . . . . . . .
5.5.4 Thin dams . . . . . . . . . . .
5.6 Time frame . . . . . . . . . . . . . . .
5.7 Processes . . . . . . . . . . . . . . .
5.8 Initial conditions . . . . . . . . . . . . .
5.9 Boundaries . . . . . . . . . . . . . . .
5.10 Physical parameters . . . . . . . . . .
5.10.1 Constants . . . . . . . . . . .
5.10.2 Roughness . . . . . . . . . . .
5.10.3 Viscosity . . . . . . . . . . . .
5.10.4 Wind . . . . . . . . . . . . . .
5.11 Numerical parameters . . . . . . . . .
5.12 Operations . . . . . . . . . . . . . . .
5.13 Monitoring . . . . . . . . . . . . . . .
5.13.1 Observation points . . . . . . .
5.13.2 Drogues . . . . . . . . . . . .
5.13.3 Cross-sections . . . . . . . . .
5.14 Additional parameters . . . . . . . . . .
5.15 Output . . . . . . . . . . . . . . . . .
5.16 Save MDF-file . . . . . . . . . . . . .
5.17 Additional exercises . . . . . . . . . . .
5.18 Execute the scenario . . . . . . . . . .
5.19 Inspect the results . . . . . . . . . . .

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4.5.8
4.5.9

6 Execute a scenario
155
6.1 Running a scenario . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.1.1 Parallel calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 155
6.1.1.1 DomainDecomposition . . . . . . . . . . . . . . . . . . . 155

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6.4
6.5

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7 Visualise results
7.1 Introduction . . . . . . . . . . . .
7.2 Working with GPP . . . . . . . .
7.2.1 Overview . . . . . . . . .
7.2.2 Launching GPP . . . . . .
7.3 Working with Delft3D-QUICKPLOT
7.4 GISVIEW interface . . . . . . . .

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6.2
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6.1.1.2 MPI-based parallel . . . . . .
6.1.1.3 Fluid mud . . . . . . . . . .
6.1.1.4 Mormerge . . . . . . . . . .
6.1.2 Running a scenario using Delft3D-MENU
6.1.3 Running a scenario using a batch script
Run time . . . . . . . . . . . . . . . . . . . .
Files and file sizes . . . . . . . . . . . . . . .
6.3.1 History file . . . . . . . . . . . . . . .
6.3.2 Map file . . . . . . . . . . . . . . . . .
6.3.3 Print file . . . . . . . . . . . . . . . .
6.3.4 Communication file . . . . . . . . . . .
Command-line arguments . . . . . . . . . . . .
Frequently asked questions . . . . . . . . . . .

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8 Manage projects and files
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8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
8.1.1 Managing projects . . . . . . . . . . . . . . . . . . . . . . . . . . 172
8.1.2 Managing files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
9 Conceptual description
9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.2 General background . . . . . . . . . . . . . . . . . . . . . . . . .
9.2.1 Range of applications of Delft3D-FLOW . . . . . . . . . . . .
9.2.2 Physical processes . . . . . . . . . . . . . . . . . . . . . .
9.2.3 Assumptions underlying Delft3D-FLOW . . . . . . . . . . . .
9.3 Governing equations . . . . . . . . . . . . . . . . . . . . . . . . .
9.3.1 Hydrodynamic equations . . . . . . . . . . . . . . . . . . .
9.3.2 Transport equation (for sigma-grid) . . . . . . . . . . . . . .
9.3.3 Coupling between intake and outfall . . . . . . . . . . . . . .
9.3.4 Equation of state . . . . . . . . . . . . . . . . . . . . . . .
9.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . .
9.4.1 Flow boundary conditions . . . . . . . . . . . . . . . . . . .
9.4.1.1 Vertical boundary conditions . . . . . . . . . . . .
9.4.1.2 Open boundary conditions . . . . . . . . . . . . .
9.4.1.3 Shear-stresses at closed boundaries . . . . . . . .
9.4.2 Transport boundary conditions . . . . . . . . . . . . . . . .
9.4.2.1 Open boundary conditions for the transport equation
9.4.2.2 Thatcher-Harleman boundary conditions . . . . . .
9.4.2.3 Vertical boundary conditions transport equation . .
9.5 Turbulence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5.1 Algebraic turbulence model (AEM) . . . . . . . . . . . . . .
9.5.1.1 Algebraic closure model (ALG) . . . . . . . . . . .
9.5.1.2 Prandtl’s Mixing Length model (PML) . . . . . . . .
9.5.2 k-L turbulence model . . . . . . . . . . . . . . . . . . . . .
9.5.3 k-eps turbulence model . . . . . . . . . . . . . . . . . . . .
9.5.4 Low Reynolds effect . . . . . . . . . . . . . . . . . . . . .

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Delft3D-FLOW, User Manual

Secondary flow; sigma-model only . . . . . . . . . . . . . . . . . .
Wave-current interaction . . . . . . . . . . . . . . . . . . . . . . .
9.7.1 Forcing by radiation stress gradients . . . . . . . . . . . . .
9.7.2 Stokes drift and mass flux . . . . . . . . . . . . . . . . . .
9.7.3 Streaming . . . . . . . . . . . . . . . . . . . . . . . . . .
9.7.4 Wave induced turbulence . . . . . . . . . . . . . . . . . . .
9.7.5 Enhancement of the bed shear-stress by waves . . . . . . .
9.8 Heat flux models . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.8.1 Heat balance . . . . . . . . . . . . . . . . . . . . . . . . .
9.8.2 Solar radiation . . . . . . . . . . . . . . . . . . . . . . . .
9.8.3 Atmospheric radiation (long wave radiation) . . . . . . . . . .
9.8.4 Back radiation (long wave radiation) . . . . . . . . . . . . .
9.8.5 Effective back radiation . . . . . . . . . . . . . . . . . . . .
9.8.6 Evaporative heat flux . . . . . . . . . . . . . . . . . . . . .
9.8.7 Convective heat flux . . . . . . . . . . . . . . . . . . . . .
9.8.8 Overview of heat flux models . . . . . . . . . . . . . . . . .
9.9 Tide generating forces . . . . . . . . . . . . . . . . . . . . . . . .
9.9.1 Tidal potential of Equilibrium tide . . . . . . . . . . . . . . .
9.9.2 Tidal potential of Earth tide . . . . . . . . . . . . . . . . . .
9.10 Hydraulic structures . . . . . . . . . . . . . . . . . . . . . . . . . .
9.10.1 3D gate . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.10.2 Quadratic friction . . . . . . . . . . . . . . . . . . . . . . .
9.10.3 Linear friction . . . . . . . . . . . . . . . . . . . . . . . . .
9.11 Flow resistance: bedforms and vegetation . . . . . . . . . . . . . .
9.11.1 Bedform heights . . . . . . . . . . . . . . . . . . . . . . .
9.11.1.1 Dune height predictor . . . . . . . . . . . . . . .
9.11.1.2 Van Rijn (2007) bedform roughness height predictor
9.11.2 Trachytopes . . . . . . . . . . . . . . . . . . . . . . . . .
9.11.2.1 Trachytope classes . . . . . . . . . . . . . . . . .
9.11.2.2 Averaging and accumulation of trachytopes . . . . .
9.11.3 (Rigid) 3D Vegetation model . . . . . . . . . . . . . . . . .

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9.6
9.7

10 Numerical aspects of Delft3D-FLOW
10.1 Staggered grid . . . . . . . . . . . . . . . . . . .
10.2 sigma-grid and Z-grid . . . . . . . . . . . . . . . .
10.3 Definition of model boundaries . . . . . . . . . . .
10.4 Time integration of the 3D shallow water equations .
10.4.1 ADI time integration method . . . . . . . .
10.4.2 Accuracy of wave propagation . . . . . . .
10.4.3 Iterative procedure continuity equation . . .
10.4.4 Horizontal viscosity terms . . . . . . . . . .
10.4.5 Overview time step limitations . . . . . . .
10.5 Spatial discretizations of 3D shallow water equations
10.5.1 Horizontal advection terms . . . . . . . . .
10.5.2 Vertical advection term . . . . . . . . . . .
10.5.3 Viscosity terms . . . . . . . . . . . . . . .
10.6 Solution method for the transport equation . . . . .
10.6.1 Cyclic method . . . . . . . . . . . . . . .
10.6.2 Van Leer-2 scheme . . . . . . . . . . . . .
10.6.3 Vertical advection . . . . . . . . . . . . . .
10.6.4 Forester filter . . . . . . . . . . . . . . . .
10.7 Numerical implementation of the turbulence models .
10.8 Drying and flooding . . . . . . . . . . . . . . . . .
10.8.1 Bottom depth at water level points . . . . .

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11 Sediment transport and morphology
11.1 General formulations . . . . . . . . . . . . . . . . . . . . .
11.1.1 Introduction . . . . . . . . . . . . . . . . . . . . . .
11.1.2 Suspended transport . . . . . . . . . . . . . . . . .
11.1.3 Effect of sediment on fluid density . . . . . . . . . .
11.1.4 Sediment settling velocity . . . . . . . . . . . . . . .
11.1.5 Dispersive transport . . . . . . . . . . . . . . . . .
11.1.6 Three-dimensional wave effects . . . . . . . . . . . .
11.1.7 Initial and boundary conditions . . . . . . . . . . . .
11.1.7.1 Initial condition . . . . . . . . . . . . . . .
11.1.7.2 Boundary conditions . . . . . . . . . . . .
11.2 Cohesive sediment . . . . . . . . . . . . . . . . . . . . . .
11.2.1 Cohesive sediment settling velocity . . . . . . . . . .
11.2.2 Cohesive sediment dispersion . . . . . . . . . . . .
11.2.3 Cohesive sediment erosion and deposition . . . . . .
11.2.4 Interaction of sediment fractions . . . . . . . . . . .
11.2.5 Influence of waves on cohesive sediment transport . .
11.2.6 Inclusion of a fixed layer . . . . . . . . . . . . . . .
11.2.7 Inflow boundary conditions cohesive sediment . . . .
11.3 Non-cohesive sediment . . . . . . . . . . . . . . . . . . . .
11.3.1 Non-cohesive sediment settling velocity . . . . . . . .
11.3.2 Non-cohesive sediment dispersion . . . . . . . . . .
11.3.2.1 Using the algebraic or k -L turbulence model
11.3.2.2 Using the k -ε turbulence model . . . . . .
11.3.3 Reference concentration . . . . . . . . . . . . . . .
11.3.4 Non-cohesive sediment erosion and deposition . . . .
11.3.5 Inclusion of a fixed layer . . . . . . . . . . . . . . .
11.3.6 Inflow boundary conditions non-cohesive sediment . .
11.4 Bedload sediment transport of non-cohesive sediment . . . .
11.4.1 Basic formulation . . . . . . . . . . . . . . . . . . .
11.4.2 Suspended sediment correction vector . . . . . . . .
11.4.3 Interaction of sediment fractions . . . . . . . . . . .
11.4.4 Inclusion of a fixed layer . . . . . . . . . . . . . . .
11.4.5 Calculation of bedload transport at open boundaries .
11.4.6 Bedload transport at U and V velocity points . . . . .
11.4.7 Adjustment of bedload transport for bed-slope effects .
11.5 Transport formulations for non-cohesive sediment . . . . . . .

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10.8.2 Total water depth at velocity points . . .
10.8.3 Drying and flooding criteria . . . . . . .
10.9 Hydraulic structures . . . . . . . . . . . . . . .
10.9.1 3D Gate . . . . . . . . . . . . . . . .
10.9.2 Quadratic friction . . . . . . . . . . . .
10.9.2.1 Barrier . . . . . . . . . . . .
10.9.2.2 Bridge . . . . . . . . . . . .
10.9.2.3 Current Deflection Wall . . . .
10.9.2.4 Weir . . . . . . . . . . . . .
10.9.2.5 Porous plate . . . . . . . . .
10.9.2.6 Culvert . . . . . . . . . . . .
10.9.3 Linear friction . . . . . . . . . . . . . .
10.9.4 Floating structure . . . . . . . . . . . .
10.10 Artificial vertical mixing due to sigma co-ordinates
10.11 Smoothing parameter boundary conditions . . .
10.12 Assumptions and restrictions . . . . . . . . . .

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Van Rijn (1993) . . . . . . . . . . . . . . . . . . . . . . . . . . .
Engelund-Hansen (1967) . . . . . . . . . . . . . . . . . . . . . .
Meyer-Peter-Muller (1948) . . . . . . . . . . . . . . . . . . . . .
General formula . . . . . . . . . . . . . . . . . . . . . . . . . .
Bijker (1971) . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5.5.1 Basic formulation . . . . . . . . . . . . . . . . . . . . .
11.5.5.2 Transport in wave propagation direction (Bailard-approach)
11.5.6 Van Rijn (1984) . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5.7 Soulsby/Van Rijn . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5.8 Soulsby . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5.9 Ashida–Michiue (1974) . . . . . . . . . . . . . . . . . . . . . . .
11.5.10 Wilcock–Crowe (2003) . . . . . . . . . . . . . . . . . . . . . . .
11.5.11 Gaeuman et al. (2009) laboratory calibration . . . . . . . . . . . .
11.5.12 Gaeuman et al. (2009) Trinity River calibration . . . . . . . . . . .
11.6 Morphological updating . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.6.1 Bathymetry updating including bedload transport . . . . . . . . . .
11.6.2 Erosion of (temporarily) dry points . . . . . . . . . . . . . . . . .
11.6.3 Dredging and dumping . . . . . . . . . . . . . . . . . . . . . . .
11.6.4 Bed composition models and sediment availability . . . . . . . . .
11.7 Specific implementation aspects . . . . . . . . . . . . . . . . . . . . . .
11.8 Validation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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11.5.2
11.5.3
11.5.4
11.5.5

12 Fixed layers in Z-model
12.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.2 Time integration of the 3D shallow water equations . . . . . . . . .
12.2.1 ADI time integration method . . . . . . . . . . . . . . . .
12.2.2 Linearisation of the continuity equation . . . . . . . . . . .
12.3 Bed stress term . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4 Horizontal viscosity terms . . . . . . . . . . . . . . . . . . . . . .
12.4.1 Overview time step limitations . . . . . . . . . . . . . . .
12.5 Spatial discretisations of 3D shallow water equations . . . . . . . .
12.5.1 Horizontal advection terms . . . . . . . . . . . . . . . . .
12.5.2 Vertical advection term . . . . . . . . . . . . . . . . . . .
12.5.3 Viscosity terms . . . . . . . . . . . . . . . . . . . . . . .
12.6 Solution method for the transport equation . . . . . . . . . . . . .
12.6.1 Horizontal advection . . . . . . . . . . . . . . . . . . . .
12.6.1.1 Van Leer-2 scheme . . . . . . . . . . . . . . . .
12.6.1.2 Implicit upwind scheme . . . . . . . . . . . . . .
12.6.2 Vertical advection . . . . . . . . . . . . . . . . . . . . . .
12.6.3 Forester filter . . . . . . . . . . . . . . . . . . . . . . . .
12.7 Baroclinic pressure term . . . . . . . . . . . . . . . . . . . . . .
12.8 Numerical implementation of the turbulence models . . . . . . . . .
12.9 Drying and flooding . . . . . . . . . . . . . . . . . . . . . . . . .
12.9.1 Bottom depth at water level points . . . . . . . . . . . . .
12.9.2 Bottom depth at velocity points . . . . . . . . . . . . . . .
12.9.3 Upwinding of the water level in defining the total water depth
12.9.4 Drying and flooding criteria . . . . . . . . . . . . . . . . .
12.10 Cut-cell and 45 degrees closed boundaries . . . . . . . . . . . . .
12.10.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . .
12.10.2 Cut Cells . . . . . . . . . . . . . . . . . . . . . . . . . .
12.10.3 45 degrees closed boundary . . . . . . . . . . . . . . . .
12.11 Hydraulic structures . . . . . . . . . . . . . . . . . . . . . . . . .
12.11.1 3D Gate . . . . . . . . . . . . . . . . . . . . . . . . . .
12.11.2 Quadratic friction . . . . . . . . . . . . . . . . . . . . . .

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12.11.3 Linear friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
12.11.4 Floating structure . . . . . . . . . . . . . . . . . . . . . . . . . . . 386
12.12 Assumptions and restrictions . . . . . . . . . . . . . . . . . . . . . . . . . 386
References

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Glossary of terms

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A Files of Delft3D-FLOW
A.1 MDF-file . . . . . . . . . . . . . . . . . . . . . . . . .
A.1.1 Introduction . . . . . . . . . . . . . . . . . . . .
A.1.2 Example . . . . . . . . . . . . . . . . . . . . .
A.1.3 Physical parameters . . . . . . . . . . . . . . .
A.1.3.1 Tide Generating Forces . . . . . . . .
A.1.3.2 Thatcher-Harleman Conditions . . . . .
A.1.4 Output options . . . . . . . . . . . . . . . . . .
A.1.4.1 Momentum terms output . . . . . . . .
A.2 Attribute files . . . . . . . . . . . . . . . . . . . . . . .
A.2.1 Introduction . . . . . . . . . . . . . . . . . . . .
A.2.2 Orthogonal curvilinear grid . . . . . . . . . . . .
A.2.3 Computational grid enclosure . . . . . . . . . . .
A.2.4 Bathymetry . . . . . . . . . . . . . . . . . . . .
A.2.5 Thin dams . . . . . . . . . . . . . . . . . . . .
A.2.6 Dry points . . . . . . . . . . . . . . . . . . . .
A.2.7 Time-series uniform wind . . . . . . . . . . . . .
A.2.8 Space varying wind and pressure . . . . . . . . .
A.2.8.1 Defined on the computational grid . . .
A.2.8.2 Defined on an equidistant grid . . . . .
A.2.8.3 Defined on a curvilinear grid . . . . . .
A.2.8.4 Defined on a Spiderweb grid . . . . . .
A.2.9 Initial conditions . . . . . . . . . . . . . . . . .
A.2.10 Open boundaries . . . . . . . . . . . . . . . . .
A.2.11 Astronomic flow boundary conditions . . . . . . .
A.2.12 Astronomic correction factors . . . . . . . . . . .
A.2.13 Harmonic flow boundary conditions . . . . . . . .
A.2.14 QH-relation flow boundary conditions . . . . . . .
A.2.15 Time-series flow boundary conditions . . . . . . .
A.2.16 Time-series correction of flow boundary conditions
A.2.17 Time-series transport boundary conditions . . . .
A.2.18 Time-series for the heat model parameters . . . .
A.2.19 Bottom roughness coefficients . . . . . . . . . .
A.2.20 Horizontal eddy viscosity and diffusivity . . . . . .
A.2.21 Discharge locations . . . . . . . . . . . . . . . .
A.2.22 Flow rate and concentrations at discharges . . . .
A.2.23 Dredge and dump characteristics . . . . . . . . .
A.2.24 Dredge and nourishment time-series . . . . . . .
A.2.25 Polygon file . . . . . . . . . . . . . . . . . . . .
A.2.26 Observation points . . . . . . . . . . . . . . . .
A.2.27 Moving observation points . . . . . . . . . . . .
A.2.28 Drogues . . . . . . . . . . . . . . . . . . . . .
A.2.29 Cross-sections . . . . . . . . . . . . . . . . . .
A.2.30 Fourier analysis . . . . . . . . . . . . . . . . . .
A.2.31 (Rigid) 3D vegetation model . . . . . . . . . . .
A.2.32 Space varying subsidence uplift definition . . . . .

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B Special features of Delft3D-FLOW
B.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.2 Decay rate constituents . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3 Hydraulic structures . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3.1 3D gates . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3.2 Quadratic friction . . . . . . . . . . . . . . . . . . . . . . . . .
B.3.2.1 Barrier . . . . . . . . . . . . . . . . . . . . . . . . .
B.3.2.2 Bridge . . . . . . . . . . . . . . . . . . . . . . . . .
B.3.2.3 Current deflection wall (CDW) . . . . . . . . . . . . .
B.3.2.4 Weirs (2D model) . . . . . . . . . . . . . . . . . . . .
B.3.2.5 Local weir . . . . . . . . . . . . . . . . . . . . . . .
B.3.3 Porous plate . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3.4 Culvert . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3.4.1 Definition of culvert in the discharge input file (<∗.src>)
B.3.4.2 Properties for culverts defined in INI file () .
B.3.4.3 Additional key-value pairs for culvert of type ‘c’ . . . . .
B.3.4.4 Additional key-value pairs for culvert of type ‘d’ or ‘e’ . .
B.3.4.5 Additional key-value pairs for culvert of type ‘f’ . . . . .
B.3.4.6 Additional key-value pairs for culvert of type ‘u’ . . . . .
B.3.4.7 More culverts . . . . . . . . . . . . . . . . . . . . . .
B.3.5 Linear friction . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.3.5.1 Rigid sheet . . . . . . . . . . . . . . . . . . . . . . .
B.3.6 Floating structure . . . . . . . . . . . . . . . . . . . . . . . . .
B.3.7 Upwind at Discharges . . . . . . . . . . . . . . . . . . . . . .
B.3.8 User defined discharge through a structure . . . . . . . . . . . .
B.4 Space varying Coriolis coefficients . . . . . . . . . . . . . . . . . . . .
B.5 Temperature modelling . . . . . . . . . . . . . . . . . . . . . . . . . .
B.5.1 Direct specification of net solar radiation . . . . . . . . . . . . .
B.5.2 Specification of the coefficient of free convection . . . . . . . . .
B.5.3 Output of computed heat fluxes . . . . . . . . . . . . . . . . . .
B.6 Evaporation and precipitation . . . . . . . . . . . . . . . . . . . . . . .
B.7 Space varying wind and pressure . . . . . . . . . . . . . . . . . . . . .
B.7.1 Space varying wind and pressure on an equidistant grid . . . . .
B.7.2 Space varying wind and pressure on a separate curvilinear grid . .
B.7.3 Space varying wind and pressure on a Spiderweb grid . . . . . .
B.8 Horizontal large eddy simulation . . . . . . . . . . . . . . . . . . . . .
B.9 Sediment transport and morphology . . . . . . . . . . . . . . . . . . .
B.9.1 Sediment input file . . . . . . . . . . . . . . . . . . . . . . . .
B.9.2 Morphology input file . . . . . . . . . . . . . . . . . . . . . . .
B.9.3 Sediment transport input file . . . . . . . . . . . . . . . . . . .
B.9.4 User defined transport routine for sand or bedload fractions . . . .
B.9.5 User defined transport routine for mud fractions . . . . . . . . . .
B.9.6 User defined routine for the settling velocity . . . . . . . . . . . .
B.9.7 Sediment transport and morphology boundary condition file . . . .
B.9.8 Morphological factor file . . . . . . . . . . . . . . . . . . . . .
B.9.9 Initial bed composition file . . . . . . . . . . . . . . . . . . . .
B.10 Fluid mud (2-layer approach) . . . . . . . . . . . . . . . . . . . . . . .
B.10.1 Two layer system . . . . . . . . . . . . . . . . . . . . . . . . .
B.10.1.1 Suspension layer . . . . . . . . . . . . . . . . . . . .
B.10.1.2 Fluid mud layer . . . . . . . . . . . . . . . . . . . . .
B.10.1.3 Mathematical modelling of fluid mud layer . . . . . . .
B.10.2 Applying fluid mud . . . . . . . . . . . . . . . . . . . . . . . .
B.10.2.1 DelftIO library . . . . . . . . . . . . . . . . . . . . .
B.10.2.2 Running a simulation in foreground . . . . . . . . . . .

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B.11

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B.12

B.10.2.3 Running a simulation in background . . . . . . . . . . .
B.10.2.4 Pitt falls . . . . . . . . . . . . . . . . . . . . . . . . .
B.10.3 Post-processing . . . . . . . . . . . . . . . . . . . . . . . . . .
Z-model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.11.1 Grid definition and construction . . . . . . . . . . . . . . . . . . .
B.11.2 Defining the keywords in the FLOW-GUI . . . . . . . . . . . . . .
B.11.3 Restrictions and limitations . . . . . . . . . . . . . . . . . . . . .
B.11.3.1 Defining Cut-cells and 45 degrees closed boundaries . . .
B.11.4 45 degrees staircase closed boundary points (Z -model only) . . . .
B.11.5 Cut-cell closed boundary points (Z -model only) . . . . . . . . . . .
Non-hydrostatic solver . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.12.1 The use of hydrostatic and non-hydrostatic models . . . . . . . . .
B.12.2 Governing equations . . . . . . . . . . . . . . . . . . . . . . . .
B.12.3 A pressure correction technique for computing the non-hydrostatic
pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.12.4 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . .
B.12.5 Conjugate gradient method (CG) . . . . . . . . . . . . . . . . . .
B.12.6 Practical aspects of using the non-hydrostatic flow module . . . . .
B.12.6.1 Switches in MDF-file . . . . . . . . . . . . . . . . . . .
B.12.6.2 Grid spacing . . . . . . . . . . . . . . . . . . . . . . .
B.12.6.3 Vertical mixing . . . . . . . . . . . . . . . . . . . . . .
B.12.6.4 Convergence criterion CG solver . . . . . . . . . . . . .
B.12.6.5 Defining the input (keywords) for the non-hydrostatic pressure approach . . . . . . . . . . . . . . . . . . . . . .
User defined functions . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.13.1 Boundary conditions for turbulence models . . . . . . . . . . . . .
B.13.2 Diagnostic mode . . . . . . . . . . . . . . . . . . . . . . . . . .
B.13.3 Particle wind factor . . . . . . . . . . . . . . . . . . . . . . . . .
Domain decomposition . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.14.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.14.2 Motivations for domain decomposition . . . . . . . . . . . . . . .
B.14.3 Local refinement horizontal and vertical . . . . . . . . . . . . . . .
B.14.4 Pre-processing, processing and post-processing . . . . . . . . . .
B.14.5 Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.14.6 How to set-up a domain decomposition model . . . . . . . . . . .
Surfbeat/roller model . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.15.1 Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.15.2 Formulations . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.15.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . .
B.15.4 Coupling with other modules . . . . . . . . . . . . . . . . . . . .
B.15.5 Modes of operation . . . . . . . . . . . . . . . . . . . . . . . . .
B.15.6 Input description . . . . . . . . . . . . . . . . . . . . . . . . . .
Bedform heights . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Trachytopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.17.1 Trachytope definition file . . . . . . . . . . . . . . . . . . . . . .
B.17.2 Area files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Creating D-Water Quality input files . . . . . . . . . . . . . . . . . . . . .
Dry run . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Reuse temporary files . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Change the update frequency of the nodal factors . . . . . . . . . . . . . .
Bubble screen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.22.1 Entrained water as function of the air injection . . . . . . . . . . .
B.22.1.1 Single nozzle bubble plume . . . . . . . . . . . . . . .
B.22.1.2 Bubble screen or line bubble plume . . . . . . . . . . . .

B.13

B.14

B.15

B.16
B.17

B.18
B.19
B.20
B.21
B.22

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Delft3D-FLOW, User Manual

B.24
B.25
B.26
B.27
B.28

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B.23

B.22.1.3 Bubble plume in stagnant stratified water . . . . . . . . . .
B.22.2 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.22.3 Numerical implementation . . . . . . . . . . . . . . . . . . . . . .
B.22.4 Input description . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.22.4.1 Generating a file with bubble screen locations . . . . . . .
B.22.4.2 Extending the discharge locations file with bubble screens .
B.22.4.3 Extending the time-series file (<∗.dis>) with amount of entrained water . . . . . . . . . . . . . . . . . . . . . . . .
B.22.5 Coupling with other models . . . . . . . . . . . . . . . . . . . . .
B.22.6 Model results . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1D–3D Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.23.1 Motivation for online Delft3D-SOBEK coupling . . . . . . . . . . . .
B.23.2 Implementation of Delft3D-SOBEK coupling . . . . . . . . . . . . .
B.23.3 Model setup and input (including best practise) . . . . . . . . . . . .
B.23.3.1 Preparation of the Delft3D-FLOW and SOBEK models . . .
B.23.3.2 Setup of the communication file used by coupling . . . . . .
B.23.3.3 Running of the coupled model system . . . . . . . . . . .
B.23.3.4 Best practice with regard to running coupled Delft3D-SOBEK
simulations . . . . . . . . . . . . . . . . . . . . . . . . .
B.23.4 Versions and limitations . . . . . . . . . . . . . . . . . . . . . . . .
Output of Courant number messages . . . . . . . . . . . . . . . . . . . . .
Initialisation of water depth in dry points . . . . . . . . . . . . . . . . . . . .
Remapping of near-bottom layers for accurate and smooth bottom shear stress
in Z -layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Slope Limiter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Real-time control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.28.1 Run procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.28.2 Time-series forcing of controlled structures . . . . . . . . . . . . . .
B.28.3 Data Locations layer . . . . . . . . . . . . . . . . . . . . . . . . .
B.28.4 Decision layer . . . . . . . . . . . . . . . . . . . . . . . . . . . .
B.28.5 Measures layer . . . . . . . . . . . . . . . . . . . . . . . . . . . .

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631
631
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632
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633
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640
640
641
642
642
643
643
646
646
659

C Astronomical constituents
663
C.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 663
C.2 List of astronomical constituents . . . . . . . . . . . . . . . . . . . . . . . 663
D Some modelling guidelines
D.1 Introduction . . . . . . . . . . . . . . .
D.2 Depth-averaged or 3D model . . . . . .
D.3 Selection of the vertical turbulence model
D.3.1 Well-mixed . . . . . . . . . . .
D.3.2 Partly mixed . . . . . . . . . .
D.3.3 Strongly stratified . . . . . . . .

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E Computational grid
F Delft3D-NESTHD
F.1 Introduction . . . . . .
F.2 How to use NESTHD1
F.3 How to use NESTHD2
F.4 Example . . . . . . .

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List of Figures

List of Figures
System architecture of Delft3D . . . . . . . . . . . . . . . . . . . . . . . .

3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
3.10
3.11

Title window of Delft3D . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Main window Delft3D-MENU . . . . . . . . . . . . . . . . . . . . . . . . . 12
Selection window for Hydrodynamics . . . . . . . . . . . . . . . . . . . . . 13
Select working directory window . . . . . . . . . . . . . . . . . . . . . . 13
Select working directory window to set the working directory to 13
The current working directory is not shown in the title bar due to its length . . . 14
Main window of the FLOW Graphical User Interface . . . . . . . . . . . . . . 14
Menu bar of the FLOW-GUI . . . . . . . . . . . . . . . . . . . . . . . . . . 15
File drop down menu . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
Data Group Domain selection and input fields . . . . . . . . . . . . . . . . . 16
Save changes window . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13

Main window of the FLOW-GUI . . . . . . . . . . . . . . . . . . . . . . .
Visualisation Area Window . . . . . . . . . . . . . . . . . . . . . . . . .
Possible selections of View → Attributes . . . . . . . . . . . . . . . . . .
Display symbols of all grid related quantities . . . . . . . . . . . . . . . .
Data Group Description . . . . . . . . . . . . . . . . . . . . . . . . . . .
Staggered grid of Delft3D-FLOW . . . . . . . . . . . . . . . . . . . . . .
Sub-data group Grid parameters . . . . . . . . . . . . . . . . . . . . . .
Definition sketch grid system to North orientation . . . . . . . . . . . . . .
Specifying the layers thickness . . . . . . . . . . . . . . . . . . . . . . .
Sub-data group Domain → Bathymetry . . . . . . . . . . . . . . . . . . .
Dry point at grid location (m, n) . . . . . . . . . . . . . . . . . . . . . .
Sub-data group Dry points . . . . . . . . . . . . . . . . . . . . . . . . .
Equivalence of v -type thin dams (left) and u-type thin dams (right) with the
same grid indices, (M−1 to M+1, N) . . . . . . . . . . . . . . . . . . . .
Sub-data group Thin dams . . . . . . . . . . . . . . . . . . . . . . . . .
Data Group Time frame . . . . . . . . . . . . . . . . . . . . . . . . . . .
Data Group Processes . . . . . . . . . . . . . . . . . . . . . . . . . . .
Sediment definition window . . . . . . . . . . . . . . . . . . . . . . . . .
Data group Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . .
Sketch of cross-section with 8 grid cells . . . . . . . . . . . . . . . . . . .
Main window for defining open boundaries . . . . . . . . . . . . . . . . .
Open and save window for boundary locations and conditions . . . . . . . .
Straight channel; location of open and closed boundaries . . . . . . . . . .
Specifying astronomical boundary conditions . . . . . . . . . . . . . . . .
Contents of a Component set with two tidal constituents having corrections .
Specifying harmonic boundary conditions . . . . . . . . . . . . . . . . . .
Specifying QH-relation boundary conditions . . . . . . . . . . . . . . . . .
Specifying time-series boundary conditions . . . . . . . . . . . . . . . . .
Transport conditions; Thatcher Harleman time lags . . . . . . . . . . . . .
Specifying transport boundary conditions . . . . . . . . . . . . . . . . . .
Specifying the physical constants . . . . . . . . . . . . . . . . . . . . . .
Examples of the wind drag coefficient . . . . . . . . . . . . . . . . . . . .
Sub-data group Roughness . . . . . . . . . . . . . . . . . . . . . . . . .
Defining the eddy viscosity and eddy diffusivity . . . . . . . . . . . . . . .
Window with HLES parameters . . . . . . . . . . . . . . . . . . . . . . .
Sub-data group Heat flux model . . . . . . . . . . . . . . . . . . . . . . .
Sub-data group Sediment, overall and cohesive sediment parameters . . . .
Sub-data group Sediment, cohesive sediment parameters (continued) . . .

DR
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2.1

4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
4.25
4.26
4.27
4.28
4.29
4.30
4.31
4.32
4.33
4.34
4.35
4.36
4.37

Deltares

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Delft3D-FLOW, User Manual

5.1
5.2
5.3
5.4
5.5
5.6
5.7
5.8
5.9
5.10
5.11
5.12
5.13
5.14
5.15
5.16
5.17
5.18
5.19
5.20
5.21
5.22
5.23
5.24
5.25
5.26
5.27
5.28
5.29
5.30

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Sub-data group Sediment, cohesive sediment parameters (continued)
Sub-data group Sediment, non-cohesive sediment parameters . . . .
Sub-data group Morphology . . . . . . . . . . . . . . . . . . . . .
Wind definition window . . . . . . . . . . . . . . . . . . . . . . . .
Nautical definition of the wind direction . . . . . . . . . . . . . . . .
Sub-window Tidal forces . . . . . . . . . . . . . . . . . . . . . . .
Data Group Numerical parameters . . . . . . . . . . . . . . . . .
Data Group Discharges . . . . . . . . . . . . . . . . . . . . . . . .
Sub-window to define the discharge rate and substance concentrations
Decomposition of momentum released by a discharge station in (m, n)
Sub-data group Dredging and dumping . . . . . . . . . . . . . . . .
Sub-window for Monitoring locations . . . . . . . . . . . . . . . . .
Sub-window for Observation points . . . . . . . . . . . . . . . . . .
Sub-data group Monitoring → Drogues . . . . . . . . . . . . . . . .
Sub-data group Monitoring → Cross-Sections . . . . . . . . . . . .
Data Group Additional parameters . . . . . . . . . . . . . . . . . .
Sub-data group Output storage . . . . . . . . . . . . . . . . . . . .
Sub-data group Output → Storage → Edit WAQ input . . . . . . . .
Sub-data group Output → Print . . . . . . . . . . . . . . . . . . .
Output Specifications window . . . . . . . . . . . . . . . . . . . .
File drop down menu . . . . . . . . . . . . . . . . . . . . . . . . .
Save changes window . . . . . . . . . . . . . . . . . . . . . . . .

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4.38
4.39
4.40
4.41
4.42
4.43
4.44
4.45
4.46
4.47
4.48
4.49
4.50
4.51
4.52
4.53
4.54
4.55
4.56
4.57
4.58
4.59

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80
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93
93
95
95
96
97
98
100
101
104
106
107
107
109

Starting window of the FLOW Graphical User Interface . . . . . . . . . . . . 114
Data Group Description sub-window . . . . . . . . . . . . . . . . . . . . . 115
Sub-data group Grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
Sub-data group Grid; filenames, type of co-ordinate system and grid dimensions116
Visualisation Area window . . . . . . . . . . . . . . . . . . . . . . . . . . 118
Staggered grid used in Delft3D-FLOW . . . . . . . . . . . . . . . . . . . . 118
Sub-data group Bathymetry . . . . . . . . . . . . . . . . . . . . . . . . . 119
Location of a dry point at grid indices (m, n) . . . . . . . . . . . . . . . . . 120
Sub-data group Dry Points . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Sets of thin dams blocking v -velocities (left) and blocking u-velocities (right) . . 122
Sub-data group Thin dams . . . . . . . . . . . . . . . . . . . . . . . . . . 122
Equivalence of v -type thin dams (left) and u-type thin dams (right) with the
same grid indices, (m − 1 to m + 1, n) . . . . . . . . . . . . . . . . . . . 123
Window Time frame . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
Processes window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
Processes: Pollutants and tracers sub-window . . . . . . . . . . . . . . . 126
Initial conditions sub-window . . . . . . . . . . . . . . . . . . . . . . . . 127
Boundaries sub-window . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
Open/Save Boundaries sub-window . . . . . . . . . . . . . . . . . . . . . 129
Harmonic boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . 131
Boundaries: Transport Conditions window . . . . . . . . . . . . . . . . . 131
Physical parameters sub-data groups . . . . . . . . . . . . . . . . . . . . 133
Physical parameters - Constants sub-window . . . . . . . . . . . . . . . . 134
Roughness sub-window . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Viscosity sub-window . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
Wind sub-window . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
Filled time table in the Wind sub-window . . . . . . . . . . . . . . . . . . . 136
Numerical parameters sub-window . . . . . . . . . . . . . . . . . . . . . 137
Data Group Operations; Discharges sub-window . . . . . . . . . . . . . . 138
Representation of a discharge in the Visualisation Area window . . . . . . . 139
Discharge Data sub-window . . . . . . . . . . . . . . . . . . . . . . . . . 139

Deltares

List of Figures

Observation points sub-window . . . . . . . . . . . . . . . . . . . . . .
Representation of an observation point in the Visualisation area window . .
Drogues sub-window . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Representation of a drogue in the Visualisation Area window . . . . . . .
Cross-sections sub-window . . . . . . . . . . . . . . . . . . . . . . . .
Representation of a v-cross-section in the Visualisation Area window . . .
Output sub-window . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
Output details sub-window . . . . . . . . . . . . . . . . . . . . . . . . .
Select scenario to be executed . . . . . . . . . . . . . . . . . . . . . . .
Part of the report file . . . . . . . . . . . . . . . . . . . . . .
Computed time-series of the water level, current and salinity in observation
point Obs4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.42 Computational grid with drogue Dr4, and contours of water level on 6 August
1990 01:00 hr . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5.43 Vector velocities and contours of salinity on 6 August 1990 01:00 hr . . . . .

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6.1
6.2
6.3
6.4

MENU-window for Hydrodynamics . .
Select the MDF-file to be verified . . .
Part of the report to the output window
Select a report file for inspection . . .

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157
157
158

7.1
7.2
7.3
7.4
7.5

Hierarchy of GPP . . . . . . . . . . . . . . . . . .
Main window of GPP . . . . . . . . . . . . . . . .
Parameters and locations in the file
Some options to change the plot attributes . . . . .
Delft3D-QUICKPLOT interface to Delft3D result . . .

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166
167
168
169
170

9.1
9.2
9.3
9.4

9.13
9.14

Definition of water level (ζ ), depth (h) and total depth (H ). . . . . . . . . . . 183
Example of σ - and Z -grid . . . . . . . . . . . . . . . . . . . . . . . . . . . 184
Examples wind drag coefficient depending on wind speed. . . . . . . . . . . 200
Hydrodynamic model of coastal area with three open boundaries with offshore
boundary (A–B at deep water) and two cross shore boundaries (A–A’, and B–B’)205
Illustration of memory effect for open boundary . . . . . . . . . . . . . . . . 209
Spiral motion in river bend (from Van Rijn (1990)) . . . . . . . . . . . . . . . 221
Vertical profile secondary flow (V ) in river bend and direction bed stress . . . 222
Vertical distribution of turbulent kinetic energy production . . . . . . . . . . . 230
Schematic view of non-linear interaction of wave and current bed shear-stresses
(from Soulsby et al. (1993b, Figure 16, p. 89)) . . . . . . . . . . . . . . . . . 232
Inter-comparison of eight models for prediction of mean and maximum bed
shear-stress due to waves and currents (from Soulsby et al. (1993b, Figure 17,
p. 90)) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 234
Overview of the heat exchange mechanisms at the surface . . . . . . . . . . 236
Co-ordinate system position Sun
δ : declination; θ: latitude; ωt: angular speed . . . . . . . . . . . . . . . . . 240
Effect of tide generating force on the computed water elevation at Venice . . . 250
Earth ocean tidal interaction (after Schwiderski (1980)) . . . . . . . . . . . . 251

10.1
10.2
10.3
10.4
10.5
10.6

Example of a grid in Delft3D-FLOW . . . . . . . . . . . . . .
Mapping of physical space to computational space . . . . . . .
Grid staggering, 3D view (left) and top view (right) . . . . . . .
Example of Delft3D-FLOW model area . . . . . . . . . . . . .
Example of Delft3D-FLOW grid . . . . . . . . . . . . . . . . .
Numerical region of influence for one time step, “Zig-zag channel”

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5.31
5.32
5.33
5.34
5.35
5.36
5.37
5.38
5.39
5.40
5.41

9.5
9.6
9.7
9.8
9.9

9.10

9.11
9.12

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149

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11.1
11.2
11.3
11.4

DR
AF

10.7 (a) Control Volume for mass for the Flooding scheme,
(b) Control Volume for momentum in horizontal and
(c) vertical direction for the Flooding scheme . . . . . . . . . . . . . . . .
10.8 Layer numbering in σ -model . . . . . . . . . . . . . . . . . . . . . . . .
10.9 Illustration of wiggles in vertical direction . . . . . . . . . . . . . . . . . .
10.10 Definition bottom depth on FLOW grid . . . . . . . . . . . . . . . . . . . .
10.11 Negative control volume with two positive flow-through heights, MEAN-option
10.12 Drying of a tidal flat; averaging approach. The flow-through height is based on
the average water level, see Equation (10.63), the velocity point is set dry. .
10.13 Overtopping of a river bank (weir); averaging approach. The flow-through
height is based on the average water level, see Equation (10.63), the velocity
point is set dry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.14 Drying of a tidal flat; upwind approach. The flow-through height is determined
by flow direction, see Equation (10.64), the velocity point remains wet. . . .
10.15 Overtopping of a river bank; upwind approach. The flow-through height is
based on the maximum water level, see Equation (10.64), the velocity point
remains wet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10.16 Special limiter for critical flow due to a sudden contraction (Flooding scheme
and increase in bottom larger than DGCUNI) . . . . . . . . . . . . . . . .
10.17 Example of a 3D Gate (vertical cross-section) . . . . . . . . . . . . . . . .
10.18 Computational layer partially blocked at bottom of gate . . . . . . . . . . .
10.19 Example of a hydrostatic consistent and inconsistent grid;
δx, (b) Hδσ < σ ∂H
δx . . . . . . . . . . . . . . . . . .
(a) Hδσ > σ ∂H
∂x
∂x
10.20 Finite Volume for diffusive fluxes and pressure gradients . . . . . . . . . .
10.21 Left and right approximation of a strict horizontal gradient . . . . . . . . . .
10.22 Cold start with damping of eigen oscillations due to bottom friction . . . . .
Sediment mixing coefficient in non-breaking waves (Source: Van Rijn (1993))
Selection of the kmx layer; where a is Van Rijn’s reference height . . . . . .
Schematic arrangement of flux bottom boundary condition . . . . . . . . .
Approximation of concentration and concentration gradient at bottom of kmx
layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
11.5 Setting of bedload transport components at velocity points . . . . . . . . .
11.6 Morphological control volume and bedload transport components . . . . . .
12.1 Irregular representation of bottom boundary layer in the Z -model . . . . . .
12.2 Vertical computational grid Z -model (left) and σ -model (right) . . . . . . . .
12.3 discretisation along streamlines. Grid points in difference stencil dependent
on flow direction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.4 Aggregation of Control volumes in the vertical due to variation position free
surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.5 Horizontal fluxes between neighbouring cells with variation in position free surface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.6 Definition bottom depth on Delft3D-FLOW grid . . . . . . . . . . . . . . .
12.7 The flow-through height is determined by the flow direction. The bottom is
represented as a staircase around the depth in water level points. . . . . . .
12.8 left: Cut Cell (definition) and right: defined by shifting (exaggerated) the corner
point to boundary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.9 Flow along staircase boundary. . . . . . . . . . . . . . . . . . . . . . . .
12.10 Reflection of velocities . . . . . . . . . . . . . . . . . . . . . . . . . . .
12.11 Example of a 3D Gate (vertical cross-section) . . . . . . . . . . . . . . . .
12.12 Computational layer partially blocked at the bottom of the 3D gate . . . . . .
A.1

xvi

Example of computational grid enclosures

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280
283
288
291
292

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. 293
. 294

. 294
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. 298
. 299
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308
309
310
312

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. 380
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384
384
384
385
385

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A.8
A.9

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419
420
421
424
469

. 473
. 473
. 474

Example of 3D gates in perspective view (left) and top view (right) . . . . . . 481
Barriers in model area . . . . . . . . . . . . . . . . . . . . . . . . . . . . 482
Example of CDW in perspective view (left) and top view (right) . . . . . . . . 484
Top view of 2D weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
Local weir . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 487
Top view of rigid sheets . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495
Cross-sectional view floating structure
The vertical lines are drawn through the velocity points . . . . . . . . . . . . 497
Illustration of the data to grid conversion for meteo input on a separate curvilinear grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 519
Wind definition according to Nautical convention . . . . . . . . . . . . . . . 522
Spiderweb grid definition . . . . . . . . . . . . . . . . . . . . . . . . . . . 522
Definition of truncation wave numbers due to resolution and numerical damping 528
Schematic representation of the governing processes between suspension
layer and fluid mud layer Winterwerp et al. (1999). . . . . . . . . . . . . . . 570
A schematic representation of two Delft3D-FLOW modules running simultaneously simulating a fluid mud problem . . . . . . . . . . . . . . . . . . . . . 573
Vertical grid construction, Z -model . . . . . . . . . . . . . . . . . . . . . . 578
Inserting appropriate keywords to switch on the Z -grid-model . . . . . . . . . 578
Defining cut-cell and 45 degree closed boundaries . . . . . . . . . . . . . . 579
45 degrees staircase closed boundary . . . . . . . . . . . . . . . . . . . . 580
Cut-cell closed boundary (not related to the data specified in the example above)581
Schematic representation of the free surface boundary condition for the pressure correction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 587
Area where a non-hydrostatic pressure is taken into account . . . . . . . . . 589
Defining the Non-hydrostatic solver using the Z -model in the FLOW-GUI . . . 591
Example of grid refinement . . . . . . . . . . . . . . . . . . . . . . . . . . 596
Example of coupling of models with a different dimension . . . . . . . . . . . 597
Schematised island without domain decomposition . . . . . . . . . . . . . . 597
Schematised island with domain decomposition . . . . . . . . . . . . . . . . 598
Example of grid refinement in the horizontal direction . . . . . . . . . . . . . 600
Problem layout sketch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 605
Schematic axisymmetric bubble plume with entrainment of water by the rising
bubbles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 622
Definition of near-, mid- and far-field of the circulation induced by a bubble
screen and the vertical profile of the vertical (downward) velocity in the midfield circulation cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 623
Flux of entrained water as function or air flow under atmospheric conditions
and height above the nozzle in stagnant non-stratified water based on experiments in (Milgram, 1983) The injected air flux is given in [Nm3 /s] where N
stands for normal atmospheric conditions. . . . . . . . . . . . . . . . . 624

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B.1
B.2
B.3
B.4
B.5
B.6
B.7

Example of thin dams in a model area . . . . . . . . . . . . . . . . . . .
Dry points in model area . . . . . . . . . . . . . . . . . . . . . . . . . .
Definition sketch of wind direction according to Nautical convention . . . . .
Definition wind components for space varying wind . . . . . . . . . . . . .
Cross-sections in model area . . . . . . . . . . . . . . . . . . . . . . . .
Example of the plant input file () where the areas are defined with
a polygon file, see section A.2.25 . . . . . . . . . . . . . . . . . . . . . .
Example of the plant input file () where the area is defined with
files according the depth-format, see section A.2.4 . . . . . . . . . . . . .
Example of the plant input file () where two different vegetation
types are defined. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

A.2
A.3
A.4
A.5
A.6
A.7

B.8

B.9
B.10
B.11
B.12
B.13
B.14
B.15
B.16
B.17
B.18
B.19

B.20
B.21
B.22
B.23
B.24
B.25
B.26
B.27
B.28
B.29

B.30

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E.1
E.2
E.3
E.4
E.5
F.1
F.2
F.3
F.4
F.5

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Steps to determine if a 3D model is required

. . . . . . . . . . . . . . . . . 670

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D.1

B.31 Schematic overview of the introduction of cold hypolimnion water into the lower
part of the warmer epilimnion by a bubble plume. Above the first plunge point
the second plunge point creates an intrusion and recirculation inside the epilimnion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 625
B.32 The mid field averaged heat equation with vertical distribution of sources/sinks
and vertical (downward) velocity profile and the model equation applied to a
single grid box. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 630
B.33 Initial temperature profile (blue) and after application of a bubble screen at
z = −16 m (red line). On horizontal axis the temperature (in ◦ C) and on the
vertical axis the vertical position in the water column (in m). . . . . . . . . . . 632
B.34 Explicit exchange of water levels and discharges between Delft3D-FLOW and
SOBEK. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634
B.35 Coupling of the Delft3D-FLOW and SOBEK grids. . . . . . . . . . . . . . . . 634
B.36 Enable Delft3D-FLOW in SOBEK settings and select MDF-file and communicationfile. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 637
B.37 Remapping of two near-bed layers to an equidistant layering. Figure from
Platzek et al. (2012). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641

Left: items with the same (array) number. Right: a computational control volume674
Lower-left (left) and lower right (right) computational grid cell . . . . . . . . . 674
Definition sketch of a (12 ∗ 7) staggered grid with grid enclosure (thick line)
and numerical grid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675
Location and combination of water level and velocity controlled open boundaries676
Straight channel with 10 ∗ 5 computational grid cells . . . . . . . . . . . . . 677
Hydrodynamics selection window with the Tools option . . . . . .
Additional tools window with the NESTHD1 and NESTHD2 options
Specification of input and output files for NESTHD1 . . . . . . . . .
Specification of input and output files for NESTHD2 . . . . . . . . .
Overview grids overall and nested models . . . . . . . . . . . . . .

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681
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List of Tables

List of Tables
4.1
4.2
4.3

Overview of the main attribute files . . . . . . . . . . . . . . . . . . . . . . 21
Time step limitations shallow water solver Delft3D-FLOW . . . . . . . . . . . 39
Definition of open and closed boundaries. . . . . . . . . . . . . . . . . . . . 51

5.1

Overview of attribute files. . . . . . . . . . . . . . . . . . . . . . . . . . . . 113

6.1

Simulation performance on different operating systems . . . . . . . . . . . . 159

9.2
9.3
9.4

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Overview of eddy viscosity options in Delft3D-FLOW . . . . . . . . . . . .
Overview of eddy diffusivity options in Delft3D-FLOW . . . . . . . . . . . .
Frequencies, phases and amplitude on alongshore waterlevel boundary and
corresponding frequenties, phases and amplitudes for the cross-shore Neumann boundaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9.5 Fitting coefficients for wave/current boundary layer model . . . . . . . . . .
9.6 Albedo coefficient and cloud function . . . . . . . . . . . . . . . . . . . .
9.7 Terms of the heat balance used in heat model 1 . . . . . . . . . . . . . . .
9.8 Terms of the heat balance used in heat model 2 . . . . . . . . . . . . . . .
9.9 Terms of the heat balance used in heat model 4 . . . . . . . . . . . . . . .
9.10 Terms of the heat balance used in heat model 5 . . . . . . . . . . . . . . .
9.11 Summary of time dependent input data of the heat flux models . . . . . . .
9.12 Constants of major tidal modes . . . . . . . . . . . . . . . . . . . . . . .

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234
241
247
247
248
248
249
251

10.1 Time step limitations shallow water solver Delft3D-FLOW . . . . . . . . . . . 278
11.1 Additional transport relations . . . . . . . . . . . . . . . . . . . . . . . . . 338
11.2 Overview of the coefficients used in the various regression models (Soulsby
et al., 1993a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 352
11.3 Overview of the coefficients used in the various regression models, continued
(Soulsby et al., 1993a) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353
12.1 Available advection and diffusion schemes in the Z -layer model (for comparison also the options available in the σ -model have been included). . . . . . . 368
12.2 Time step limitations shallow water solver Delft3D-FLOW . . . . . . . . . . . 371
A.2
A.3
A.3
A.4
A.5
A.5
A.6
A.7
A.8

Print flags for map-data . . . . . . . . . . . . .
Print flags for history-data . . . . . . . . . . . .
Print flags for history-data . . . . . . . . . . . .
Storage flags for map-data . . . . . . . . . . .
Storage flags for history-data . . . . . . . . . .
Storage flags for history-data . . . . . . . . . .
Optional output flags under Additional parameters
Dredge and dump input file with keywords . . . .
Vegetation input file with keywords . . . . . . .

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409
409
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471

B.1
B.1
B.2
B.3
B.4
B.5
B.5
B.6
B.7
B.7

Special features of Delft3D-FLOW . . . . .
Special features of Delft3D-FLOW . . . . .
Default parameter settings for the SGS model
Sediment input file with keywords . . . . . .
Options for sediment diameter characteristics
Sediment input file without keywords . . . .
Sediment input file without keywords . . . .
Morphological input file with keywords . . . .
Morphological input file without keywords . .
Morphological input file without keywords . .

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Additional transport relations . . . . . . . . . . .
Transport formula parameters . . . . . . . . . . .
Sediment transport formula input file with keywords
Initial bed composition file keywords . . . . . . .
Example of vertical grid refinement . . . . . . . .
Example of a file . . . . . . . . . .
Bedform keywords in mdf file . . . . . . . . . . .

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548
551
567
601
603
613

C.1

Astronomical constituents . . . . . . . . . . . . . . . . . . . . . . . . . . . 663

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B.8
B.9
B.10
B.11
B.12
B.13
B.14

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1 A guide to this manual
Introduction
This User Manual concerns the hydrodynamic module, Delft3D-FLOW, of the Delft3D software
suite. To make this manual more accessible we will briefly describe the contents of each
chapter and appendix.
If this is your first time to start working with Delft3D-FLOW we suggest you to read and practice
the getting started of chapter 3 and the tutorial of chapter 5. These chapters explain the user
interface options and guide you through the definition of your first simulation.

Chapter 2: Introduction to Delft3D-FLOW, provides specifications of Delft3D-FLOW, such
as the areas of applications, the standard and specific features provided, the required computer configuration and how to install the software.
Chapter 3: Getting started, explains the use of the overall menu program, which gives
access to all Delft3D modules and to the pre- and post-processing tools. Last but not least
you will get a first introduction into the FLOW Graphical User Interface (GUI), used to define
the input required for a flow simulation.

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1.1

Chapter 4: Graphical User Interface, provides practical information on the selection of all
parameters and the tuning of the model.
Chapter 5: Tutorial, emphasis at giving you some first hands-on experience in using the
FLOW-GUI to define the input of a simple problem, in verifying this input, in executing the
simulation and in inspecting the results.
Chapter 6: Execute a scenario, discusses how to verify and execute a scenario and provides
information on run times and file sizes.
Chapter 7: Visualise results, explains in short the visualisation of results. It introduces the
post processing program GPP to visualise or animate the simulation results.
Chapter 8: Manage projects and files, provides a detailed insight into the managing of
projects and scenarios.
Chapter 9: Conceptual description, describes the theoretical physics modelled in Delft3DFLOW.
Chapter 10: Numerical aspects of Delft3D-FLOW, discusses the various grids, grid-numbering
etc., as well as all practical matters about the implications of parameter selections.
Chapter 11: Sediment transport and morphology, describes the three-dimensional transport of suspended sediment, bedload transport and morphological updating of the bottom.
Chapter 12: Fixed layers in Z-model, the concept of fixed, horizontal layers in the vertical
grid are given.
References, provides a list of publications and related material on the Delft3D-FLOW module.
Glossary of terms, contains a list and explanations of the terms and abbreviations used in
this manual.

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Appendix A: Files of Delft3D-FLOW, gives a description of the files that can be used in the
input of Delft3D-FLOW. Generally, these files are generated by the FLOW-GUI and you need
not to be concerned about their internal details. However, in certain cases it can be useful to
know these details, for instance to generate them by means of other utility programs.
Appendix B: Special features of Delft3D-FLOW, gives an overview and description of the
additional functions provided by Delft3D-FLOW. An additional function provides specific functionalities which are not yet supported by the user interface, but which are recognised by a
keyword in the MDF-file with one or more values. This value can be a string of characters
referring to a file that contains additional input parameters for this function.

The available features are listed in Table B.1. They include e.g. decay rate for constituents,
hydraulic structures, space varying Coriolis coefficients, evaporation and precipitation, space
varying wind and pressure, horizontal large eddy simulation, 3D sediment and morphology,
fluid mud, Z -model, a non-hydrostatic module, user-defined functions, domain decomposition, surfbeat or roller model and trachytopes.

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Appendix C: Astronomical constituents, this appendix gives a complete overview of the
astronomical components supported by Delft3D-FLOW. For each component is given: its
name, angular frequency, amplitude in the equilibrium tide and the relation if an amplitude
coupling exists with other components.
Appendix D: Some modelling guidelines, this appendix discusses some guidelines to determine when you need a 3D computation and which vertical turbulence model you need,
given the type of modelling application.
Appendix E: Computational grid, discusses the location of open and closed boundaries
on the staggered grid used in Delft3D-FLOW. The definition and use of the grid enclosure is
discussed in detail. Reading this appendix is suggested when you want to know all the details
of the staggered grid and specific implementation aspects and consequences. For normal
use of Delft3D-FLOW you can skip this appendix.
Appendix F: Delft3D-NESTHD, discusses the steps to generate boundary conditions for a
nested Delft3D-FLOW model. In case the hydrodynamic and transport boundary conditions
of a Delft3D-FLOW model are generated by a larger (overall) model we speak of a nested
model. Nesting in Delft3D-FLOW is executed in three steps, using two separate utilities and
the Delft3D-FLOW program.
1.2

Manual version and revisions

This manual applies to Delft3D-FLOW version 6.00.00, and FLOW-GUI version 3.43.05.
1.3

Typographical conventions
Throughout this manual, the following conventions help you to distinguish between different
elements of text to help you learn about the FLOW-GUI.

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Description

Module
Project

Title of a window or a sub-window are in given in bold.
Sub-windows are displayed in the Module window and
cannot be moved.
Windows can be moved independently from the Module window, such as the Visualisation Area window.

Save

Item from a menu, title of a push button or the name of
a user interface input field.
Upon selecting this item (click or in some cases double
click with the left mouse button on it) a related action
will be executed; in most cases it will result in displaying
some other (sub-)window.
In case of an input field you are supposed to enter input
data of the required format and in the required domain.

<\tutorial\wave\swan-curvi>

Directory names, filenames, and path names are expressed between angle brackets, <>. For the Linux
and UNIX environment a forward slash (/) is used instead of the backward slash (\) for PCs.

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Example

“27 08 1999”

Data to be typed by you into the input fields are displayed between double quotes.
Selections of menu items, option boxes etc. are described as such: for instance ‘select Save and go to
the next window’.

delft3d-menu

Commands to be typed by you are given in the font
Courier New, 10 points.
In this User manual, user actions are indicated with this
arrow.

[m s−1 ] [−]

1.4

Units are given between square brackets when used
next to the formulae. Leaving them out might result in
misinterpretation.

Changes with respect to previous versions
Version

Description

3.15

Meteo input (wind, pressure, etc.) modified (FLOW v3.60.01.02 and higher),
see Appendices A.2.8 and B.7.
Bubble screen added.
1D–3D Coupling added.

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Description

3.14

Section 9.3.3: UNESCO formulation added.
Chapter 12.12, References: References on UNESCO formulation added.
Equation (9.173) corrected.
Equation (11.94): − before max changed to +.
Equation (11.97): V replaced by q .
Section A.2.15, example <∗.bct> file: time function should be time-function.
Section A.2.21, example <∗.dis> file: time function should be time-function.
Section B.8.4, example <∗.bcc> file: time function should be time-function.
Section B.8.5, example <∗.mft> file: time function should be time-function.
Section B.9.1.3, description of η and η added.
Section B13.4, runprocedure adjusted to use arguments for tdatom.exe and
trisim.exe.
Section 9.3.1: description horizontal viscosity extended taking
into account Subgrid scale viscosity and HLES viscosity. Momentum equation
adapted.
Section 9.3.2: description horizontal diffusivity extended taking
into account Subgrid scale viscosity and HLES diffusivity. Transport equation
adapted.

3.13

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Version

New keyword (IniSedThick) for Initial sediment layer thickness at the bed.
Unit is metre. GUI reads old keyword and converts data to new keyword.
New functionality: Neumann boundaries described.
New functionality: Time-varying morphological scale factor, see B.8.5.
New functionality: Maximum number of constituents (pollutants and/or sediments) increased to 99.
New functionality: if FLOW runs online with WAVE, and wind is active in the
FLOW simulation, this wind can be used in the WAVE simulation.
New functionality: Section 6.5 (Command-line arguments) added.
New functionality: Initial conditions from a map-file described.
Online Delft3D-WAVE and Online coupling is now possible.
GUI output file changed in with runid not
truncated.
Limitation of 4 Gb for NEFIS files added.
Maximum number of discharges increased to 500.
Units for reflection parameter at open boundaries added.
New functionality: reflection parameter for discharge boundaries implemented.
MENU screens updated.
Astronomical component A0 cannot be corrected by a <∗.cor> file.
New functionality: The name of the MDF-file may be up to 256 characters, i.e.
the runid is not limited anymore to 3 characters.
In Data Group Numerical parameters, Depth specified at cell corners or cell
centres introduced. Text adjusted accordingly.
Chapter 11 updated.
Appendix B.8 updated.
Appendix B.13: Before using you have to replace the grid
filenames by the MDF-filenames.
Appendix F.1: Restriction added: The boundaries of the nested model may not
consist of a single grid cell.

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A guide to this manual

Description

3.12

Chapter 4: the contribution from the HLES sub-grid model will be added to the
background values (FLOW v3.50.09.02 and higher).
Chapter 4 updated with online coupling, online Delft3D-WAVE.
Chapter 4 updated with latest GUI developments (Cartesian or spherical grids,
sediment and morphology, dredging and dumping, specification of astronomical flow boundary conditions changed, no slip condition added, Horizontal
Large Eddy Simulations, heat flux model parameters added, specification of
wind moved to Physical parameters, specification of tide generating forces
moved to Physical parameters, additional drying and flooding options, momentum solver options).
In chapter 4 emphasized that the stop time may not be too far ahead of the
Reference date.
Also in chapter 4 the description of In-out discharges improved.
In chapter 7 Delft3D-GIS updated to GISVIEW.
Theoretical background of Sediment and morphology updated and moved from
Appendix B.8 to a new chapter 11.
Inclusion of Z -model (horizontal layers) and Non-hydrostatic approach; Chapters 9 and 10 are amended. New Chapter, 12, is dedicated for specifics of the
Z -model.
C(urrent)D(eflection)W(all)-features added (for σ - and Z -model).
Special treatment for ‘staircase’ closed boundary added for Z -model.
Reference and Glossary updated and renamed to chapter 12.12 and 12.12 respectively.
Appendix B.10: Input description for Z -model.

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3.11

Update of MENU windows with second postprocessing tool Delft3DQUICKPLOT.
Operation of Change working directory updated in chapter 3.
In chapter 10: description of the Flooding Scheme.
Section 10.4.3: Description of AOI method removed.
Section 10.6.2: Equation (10.35) 0 and 1 interchanged.
Appendix B.8: Update of Sediment and Morphology latest developments.
Appendix B.14 added: Surfbeat/roller model.

3.10

Reference version for these change notes.

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2 Introduction to Delft3D-FLOW
Deltares has developed a unique, fully integrated computer software suite for a multi-disciplinary
approach and 3D computations for coastal, river and estuarine areas. It can carry out simulations of flows, sediment transports, waves, water quality, morphological developments and
ecology. It has been designed for experts and non-experts alike. The Delft3D suite is composed of several modules, grouped around a mutual interface, while being capable to interact
with one another. Delft3D-FLOW, which this manual is about, is one of these modules.

Delft3D-FLOW is a multi-dimensional (2D or 3D) hydrodynamic (and transport) simulation
program which calculates non-steady flow and transport phenomena that result from tidal and
meteorological forcing on a rectilinear or a curvilinear, boundary fitted grid. In 3D simulations,
the vertical grid is defined following the σ co-ordinate approach.
Areas of application
Tide and wind-driven flows (i.e. storm surges).
Stratified and density driven flows.
River flow simulations.
Simulations in deep lakes and reservoirs.
Simulation of Tsunamis, hydraulic jumps, bores and flood waves.
Fresh-water river discharges in bays.
Salt intrusion.
Thermal stratification in lakes, seas and reservoirs.
Cooling water intakes and waste water outlets.
Transport of dissolved material and pollutants.
Online sediment transport and morphology.
Wave-driven currents.
Non-hydrostatic flows.

2.2

Standard features
Tidal forcing.
The effect of the Earth’s rotation (Coriolis force).
Density driven flows (pressure gradients terms in the momentum equations).
Advection-diffusion solver included to compute density gradients with an optional facility
to treat very sharp gradients in the vertical.
Space and time varying wind and atmospheric pressure.
Advanced turbulence models to account for the vertical turbulent viscosity and diffusivity
based on the eddy viscosity concept. Four options are provided: k-ε, k-L, algebraic and
constant model.
Time varying sources and sinks (e.g. river discharges).
Simulation of the thermal discharge, effluent discharge and the intake of cooling water at
any location and any depth.
Drogue tracks.
Robust simulation of drying and flooding of inter-tidal flats.

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Overall Menu

Flow/Mor

Wave

Water Quality

Ecology

Particles/Oil

Tools
Figure 2.1: System architecture of Delft3D

Special features
Various options for the co-ordinate system (rectilinear, curvilinear or spherical).
Built-in automatic switch converting 2D bottom-stress coefficient to 3D coefficient.
Built-in anti-creep correction to suppress artificial vertical diffusion and artificial flow due
to σ -grids.
Built-in switch to run the model in either σ -model or in Z -model.
Various options to model the heat exchange through the free water surface.
Wave induced stresses and mass fluxes.
Influence of waves on the bed shear stress.
Optional facility to calculate the intensity of the spiral motion phenomenon in the flow (e.g.
in river bends) which is especially important in sedimentation and erosion studies (for
depth averaged — 2DH — computations only).
Optional facility for tidal analysis of output parameters.
Optional facility for special points such as 3D gates, Current Deflecting Wall (CDW) floating
structures, bridges, culverts, porous plates and weirs.
Optional facility to switch between a number of advection solvers.
Optional facility for user-defined functions.
Domain decomposition.

2.4

Coupling to other modules

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2.3

The hydrodynamic conditions (velocities, water elevations, density, salinity, vertical eddy viscosity and vertical eddy diffusivity) calculated in the Delft3D-FLOW module are used as input
to the other modules of Delft3D, which are (see Figure 2.1):
module

Delft3D-WAVE
D-Water Quality
D-Waq PART
Delft3D-ECO
Delft3D-SED

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description

short wave propagation
far-field water quality
mid-field water quality and particle tracking
ecological modelling
cohesive and non-cohesive sediment transport

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2.5

Utilities
For using Delft3D-FLOW the following utilities are important:
description

RGFGRID
QUICKIN

for generating curvilinear grids
for preparing and manipulating grid oriented data, such as
bathymetry or initial conditions for water levels, salinity or concentrations of constituents.
for performing off-line tidal analysis of time series generated
by Delft3D-FLOW
for performing tidal analysis on time-series of measured water
levels or velocities
for generating (offline) boundary conditions from an overall
model for a nested model
for visualisation and animation of simulation results
a second tool for visualisation and animation of simulation
results

Delft3D-TRIANA
Delft3D-TIDE
Delft3D-NESTHD

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GPP
Delft3D-QUICKPLOT

module

For details on using these utility programs you are referred to the respective User Manual.
2.6

Installation and computer configuration
See the Delft3D Installation Manual.

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3 Getting started
3.1

Overview of Delft3D
The Delft3D program suite is composed of a set of modules (components) each of which
covers a certain range of aspects of a research or engineering problem. Each module can be
executed independently or in combination with one or more other modules. The information
exchange between modules is provided automatically by means of a so-called communication
file; each module writes results required by another module to this communication file and
reads from the file the information required from other modules. Other, module-specific, files
contain results of a computation and are used for visualisation and animation of results.

Starting Delft3D
To start Delft3D:

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3.2

Delft3D is provided with a menu shell through which you can access the various modules. In
this chapter we will guide you through some of the input screens to get the look-and-feel of
the program. In chapter 5, Tutorial, you will learn to define and run a simple scenario.

On an MS Windows platform: select Delft3D in the Programs menu or click on the Delft3D
icon on the desktop.

On Linux machines: type delft3d-menu on the command line.
Next the title window of Delft3D is displayed, Figure 3.1:

Figure 3.1: Title window of Delft3D

After a short while the main window of the Delft3D-MENU appears, Figure 3.2.
Several menu options are shown. In Figure 3.2 all options are sensitive.
For now, only concentrate on exiting Delft3D-MENU, hence:

Click on the Exit push button.
The window will be closed and you are back in the Windows Desktop screen for PCs or on
the command line for Linux workstations.

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Figure 3.2: Main window Delft3D-MENU

Remark:
In this and the following chapters several windows are shown to illustrate the presentation of Delft3D-MENU and Delft3D-FLOW. These windows are grabbed from the PCplatform. For Linux workstations the content of the windows is the same, but the colours
may be different. On the PC-platform you can set your preferred colours by using the
Display Properties.
3.3

Getting into Delft3D-FLOW

To continue restart the menu program as indicated above.

Click the Flow button.

Next the selection window for Hydrodynamics is displayed for preparing a flow input (MDF-)file
or wave input (MDW-)file, to execute a computation in foreground (including online WAVE or
online coupling), to inspect the report files with information on the execution and to visualise
the results: Figure 3.3.
Before continuing with any of the selections of this Hydrodynamics (including morphology)
window, you must select the directory in which you are going to prepare scenarios and execute
computations:

Click the Select working directory button.

Next the Select working directory window, Figure 3.4, is displayed (your current directory
may differ, depending on the location of your Delft3D installation).

Browse to and open the sub-directory of your Delft3D Home-directory.
Open the directory.
Enter the sub-directory and close the Select working directory
window by clicking OK, see Figure 3.5.
Next the Hydrodynamics (including morphology) window is re-displayed, but now the

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Figure 3.3: Selection window for Hydrodynamics

Figure 3.4: Select working directory window

Figure 3.5: Select working directory window to set the working directory to

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Figure 3.6: The current working directory is not shown in the title bar due to its length

Figure 3.7: Main window of the FLOW Graphical User Interface

changed current working directory is displayed in the title bar (if the name is not too long),
see Figure 3.6.
Remark:
In case you want to start a new project for which no directory exists yet, you can select
in the Select working directory window to create a new folder.

In the main Hydrodynamics (including morphology) menu, Figure 3.3, you can define,
execute and visualise a scenario. In this guided tour through Delft3D-FLOW we limit ourselves
to inspecting some windows of the FLOW Graphical User Interface (GUI).
Hence:

Click on Flow input.

The FLOW-GUI is loaded and the primary input screen is opened, Figure 3.7.
The purpose of this FLOW-GUI is to create the input file of Delft3D-FLOW, also called the
“Master Definition Flow” file (MDF-file) which contains all information to execute a flow simulation.

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Figure 3.8: Menu bar of the FLOW-GUI

Exploring some menu options

The menu bar of the FLOW-GUI displays four options:
File
Table

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Figure 3.9: File drop down menu

View
About

select and open an MDF-file, save an MDF-file, save an MDF-file
under a different name, save attribute files or ‘exit’ the FLOW-GUI.
tool to change table oriented data by adding or deleting rows or values.
visualisation area or list of attribute files.
About information.

Each option provides one or more selections; for instance, clicking on File enables the selections:
New
Open
Save MDF
Save MDF As
Save All
Save All As
Exit

to clean-up the internal data structure and start with a new scenario.
to open an existing MDF-file.
to save the MDF-data under its current name.
to save the MDF-data under a new name.
to save all attribute data in the current attribute files + MDF-file.
to save all attribute data under a new name + MDF-file.
to exit the FLOW-GUI and return to the Hydrodynamics (including
morphology) window.

The input parameters that define a hydrodynamic scenario are grouped into Data Groups.
These Data Groups are represented by the large grey buttons at the left of the main window. Upon starting the FLOW-GUI, Figure 3.7 is displayed with the Data Group Description
selected and displayed. The area to the right of the Data Groups is called the canvas area.
This canvas area will be dynamically filled with input fields, tables, or list boxes to define the
various kinds of input data required for a simulation. In Figure 3.7 the Description text box is
displayed in the canvas area.
Click on a Data Group and see what happens. For example, clicking the Domain button and
next the sub Data Group Grid parameters, will result in the window shown in Figure 3.10. The
Tutorial in chapter 5 will make you become fully acquainted with the various input windows
that result from this main window.
You are encouraged to explore the various Data Groups and sub-windows to get a first impression on the items the Data Groups are composed of. Though several input items are

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Figure 3.10: Data Group Domain selection and input fields

Figure 3.11: Save changes window

related there is no fixed or prescribed order in defining the input data. Occasionally you might
get a warning or error message that some data is not saved or not consistent with earlier
defined data; during this introduction you can neglect these messages and press the Ignore
button if requested. No harm will be done on existing input files as you are not going to save
the input data of this exercise.
3.5

Exiting the FLOW-GUI
To exit the FLOW-GUI:

From the File menu, select Exit.
If you have made any change to any input field and have not explicitly saved both the attribute
data and/or the MDF-data Figure 3.11 is displayed.
In this case only the MDF-data was not saved; if you have changed data that must be saved
into a so-called attribute file, the unsaved attribute files will be listed.
Select one of the options displayed:
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YesAll
No
NoAll
Cancel

defined and proceed to the next unsaved data item.
save all unsaved data items and request a file name if not yet defined.
don’t save the first unsaved data item; proceed to the next unsaved
data.
exit without saving any unsaved data item.
abort this Exit action and return to the FLOW-GUI.

Neglect any unsaved data and exit:

Click NoAll.

Ignore all other options and just:

You will be back in the Hydrodynamics (including morphology) window of the Delft3DMENU program, Figure 3.3.

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Click Return to return to the main window of Delft3D-MENU, Figure 3.2.
Click Exit.

The window is closed and the control is returned to the desktop or the command line.
In this Getting Started session you have learned to access the FLOW-GUI and to load and
inspect an existing input (MDF-)file.
We encourage new users next to run the tutorial described in chapter 5.

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4 Graphical User Interface
4.1

Introduction
In order to set up a hydrodynamic model you must prepare an input file. All parameters to
be used originate from the physical phenomena being modelled. Also from the numerical
techniques being used to solve the equations that describe these phenomena, and finally,
from decisions being made to control the simulation and to store its results. Within the range
of realistic values, it is likely that the solution is sensitive to the selected parameter values, so
a concise description of all parameters is required. The input data defined is stored into an
input file which, as you may recall, is called the Master Definition Flow file or MDF-file.

If you have not used Delft3D-FLOW before, or if you are not familiar with the FLOW Graphical
User Interface (GUI) we suggest you to execute the tutorial given in chapter 5 first and then
return to this chapter.

4.2

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In section 4.2 we discuss some general aspects of the MDF-file and its attribute files. In
section 4.3 we discuss shortly the filenames and their extension. In section 4.4 we discuss
working with the FLOW-GUI and the Visualisation Area window. In section 4.5 we discuss all
input parameters, including their restrictions and their valid ranges or domain. In many cases
we give a short discussion on the criteria to determine a parameter or to select a certain
formulation, such as the turbulence closure model for the vertical turbulent eddy viscosity and
turbulent eddy diffusivity. In section 4.6 we discuss saving the MDF-file and exiting the FLOWGUI. Finally, we discuss in section 4.7 the aspect of importing, removing and exporting of data
and their references in the MDF-file.
MDF-file and attribute files

The Master Definition Flow file (MDF-file) is the input file for the hydrodynamic simulation
program. It contains all the necessary data required for defining a model and running the
simulation program. In the MDF-file you can define attribute files in which relevant data (for
some parameters) is stored. This will be particularly the case when parameters contain a large
number of data (e.g. time-dependent or space varying data). The MDF-file and all possible
user-definable attribute files are listed and described in Appendix A.
Although you are not supposed to work directly on the MDF-file it is useful to have some ideas
on it as it reflects the idea of the designer on how to handle large amounts of input data and
it might help you to gain a better idea on how to work with this file.
The basic characteristics of an MDF-file are:

It is an ASCII file.
Each line contains a maximum of 300 characters.
Each (set of) input parameter(s) is preceded by a (set of) keyword(s).
The MDF-file is an intermediate file between the FLOW-GUI and the hydrodynamic simulation program. Being an ASCII-file, it can be transported to an arbitrary hardware platform.
Consequently, the hydrodynamic simulation program and the FLOW-GUI do not necessarily
have to reside on the same hardware platform. Currently, Delft3D does not support remote
or distributed processing, but you can easily write a couple of scripts to run your pre- and
postprocessing on one hardware platform and run the computational intensive simulation at
an other hardware platform. The results of all modules are written to platform independent
binary files, so also these result files you can transfer across hardware platforms without any
conversion. Contact our support manager if you need remote or distributed computational

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functionalities.
The MDF-file is self contained, i.e. it contains all the necessary information about the model
concerned. It can therefore be used as model archive. To maintain a good overview of the
file, its length is restricted to 300 columns.
As you will see in chapter 5, after having specified certain types of input parameters you can
store them in attribute files. The MDF-file only contains permanent input parameters and
references to these attribute files. An overview of the attribute files is given in Section 4.3.

Filenames and conventions

The names of the MDF-file and its attribute files have a specific structure, some aspects are
mandatory while others are only advised or preferred.

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If you wish to create attribute files in advance, since supplying long time-series manually is
not very practical, you must make sure that the correct input formats are used. The formats
of all attribute files (and of the MDF-file itself) are described in detail in Appendix A.

MDF-file

The name of an MDF-file must have the following structure: .
The runid may consist of up to 256 alpha-numeric characters and may not contain blanks.
The runid part of the filename is used as a run-id in the names of the result files to safeguard
the link between an MDF-file and the result files. When you have many computations we
suggest to use a combination of one alpha- and two numeric-characters followed by a useful
name of your project.
Example: .

This file could indicate the flow-input file of the first calibration run of a project.
Result files

The results of a Delft3D-FLOW computation are stored in several types of files:

communication file: and .
history file: and .
map file: and .
drogue file: and .
restart files .

The result files are stored in the working or project directory.
Restrictions:
Each scenario must have a unique run-id; when you have many computations we suggest to use a character followed by a two digit number.
Avoid spaces in a filename, use an underscore instead, i.e. instead of
.
The extension mdf is mandatory.
The communication file contains results that are required by other modules, such as the water
quality module. The history file contains results of all computed quantities in a number of

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Table 4.1: Overview of the main attribute files

Filename and mandatory extension

Astronomic correction factors
Bathymetry or depth
Bottom roughness
Constituents boundary conditions
Cross-sections
Curvilinear grid
Discharge locations
Discharges rates
Dredge and dump characteristics
Drogues or floating particles
Dry points
Flow boundary conditions (astronomic)
Flow boundary conditions (harmonic)
Flow boundary conditions (QH-relation)
Flow boundary conditions (time-series)
Fourier analysis input file
Grid enclosure
Horizontal eddy viscosity and diffusivity
Initial conditions
Morphology characteristics
Observation points
Open boundaries
Sediment characteristics
Temperature model parameters
Thin dams
Wind

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Quantity

user-defined grid points at a user-defined time interval. The map file contains results of all
quantities in all grid points at a user-specified time interval.
Attribute files

Attribute files contain certain input quantities, such as monitoring points or time dependent
input data such as wind. The names of the main attribute files are basically free, but their
extension is mandatory as indicated in Table 4.1.
The name of an attribute file must have the following structure: .
Where:

may consist of up to 256 alpha-numeric characters and may contain
(sub-) directories, i.e. the full path.
There is no limitation other than the platform dependent limitations; you are referred to
your hardware platform manual for details. We suggest to add some continuation character, for instance -number to the name to distinguish between various updates or modifications of the file, i.e. .
The extension is mandatory as indicated in Table 4.1.

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Figure 4.1: Main window of the FLOW-GUI

4.4
4.4.1

Working with the FLOW-GUI
Starting the FLOW-GUI

The purpose of the FLOW-GUI is to provide a graphical user interface which simplifies the
preparation of an MDF-file. For your convenience, in this section we briefly recapitulate how
to work with the FLOW-GUI (alternatively, consult Chapters 3 and 5). With respect to the
parameters in the MDF-file, the FLOW-GUI follows either one of the following options:

A single parameter is updated and included in the MDF-file.
A reference to an attribute file is updated and included in the MDF-file. An attribute file
can be created by the FLOW-GUI if the required data was specified.

To start the FLOW-GUI you must in short execute the following commands, see chapter 3 for
details:
Click the Delft3D-MENU icon on the desktop (PC) or execute the command delft3d-menu
on the command line (Linux and UNIX).
Click the menu item FLOW.
Change to your project or working directory.
Click the menu item Flow input; the FLOW-GUI will be started and the main window will
be opened, see Figure 4.1.
You are now ready to start defining or modifying all input parameters grouped into so-called
data groups. In the menu bar you can choose from the following options:
File

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For opening and saving an MDF-file, or saving an MDF-file with another name, for saving attribute files under the same name or under
a new name, for cleaning up the internal data structure and for exiting the FLOW-GUI. Sub-menus are: New, Open, Save MDF, Save

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Figure 4.2: Visualisation Area Window

Table

View

Help

4.4.2

MDF As, Save All, Save All As and Exit.
To change attribute files by adding or deleting rows or values in table quantities. Sub-menus are: Insert row above, Copy row above,
Delete rowand Copy value to all rows.
For viewing the grid related parameters or for listing the attribute files
used (only their referenced name, not their contents). Sub-menus
are: Visualisation Area and Attribute files.
For getting online and context sensitive help. Sub-menus are: Contents and About. The first is not implemented yet.

Visualisation Area window

Most grid related data specified in the MDF-file can be visualised and defined in the Visualisation Area window. These grid related data are: dry points, thin dams, observation points,
drogues, discharges, cross-sections and open boundaries.
Upon selecting View → Visualisation Area the Visualisation Area window will pop up, Figure 4.2.
The visualisation area is still blank, but after you have defined or selected a grid it will display
the grid and several grid related quantities.
The main and sub-menus of the Visualisation Area window are:
File

Edit
Edit Mode

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To Open some of the grid defining files, to print (Print area) the Visualisation Area window or Exit (close) the Visualisation Area window.
To select one of the grid related quantities that can be visualised.
To Add, Delete, Modify (move) and View the quantities selected in

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Figure 4.3: Possible selections of View → Attributes

View

Fonts
Colors
Options
Help

Edit.
To Zoom In and Zoom Out the whole visualisation area, Zoom Box in
a user-defined area and Zoom Reset to return to the initial situation.
To switch on or off viewing attributes and/or attribute names. The
various selections of View → Attributes are displayed in Figure 4.3.
You can activate (display) or de-activate (hide) the various attributes.
To set the font, size, etc. of the attribute names.
To set the colours for visualising the bathymetry.
To select which quantities will be displayed in the visualisation area
and to refresh the display.
For online information of using the Visualisation Area window.

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Zoom

Remarks:
The Edit and Edit Mode options make it possible to graphically define, delete, modify
(move) or just view quantities of a certain type, without having to type locations manually.
If a quantity can have a user-defined name you can fill that in after having defined its
location graphically.
You can save the data in an attribute file before you change the quantity to be worked
on, but you can also postpone this until the end of your input session.
The Edit Mode remains in its selected mode as long as you are working in the Visualisation Area window. This allows you to define (Add) or delete (Delete) all kind of
quantities without having to set and reset the Edit Mode. The Edit Mode shifts back to
View mode as soon as you leave the Visualisation Area window, to prevent unintended
modifications of your grid related quantities.
Make sure the Edit Mode is selected properly, if not you might accidentally move a
quantity without notice!
To see how each quantity is represented in the Visualisation Area display the legend:
Select View → Legend
and next Figure 4.4 is displayed.
Remark:

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Figure 4.4: Display symbols of all grid related quantities

nition.
Input parameters of MDF-file

In this section all input parameters of the MDF-file will be described in the order as they appear
in the FLOW-GUI. After starting the FLOW-GUI data groups become available for defining or
changing the input parameters in the MDF-file.

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4.5

Symbols are grouped in colours, but with different representation to support easy recog-

A data group is a coherent set of input parameters that together define a certain type of input
data. For instance, in the Data Group Operations you can define all aspects related to a
discharge, such as its name, its location, its discharge rate, if the momentum of the discharge
is to be taken into account and if so in which direction and last but not least the concentration
of all substances released. Several of these items can be specified as a function of time,
where the time-series can be specified manually or read from a file.
Some data groups are organised in sub-data groups, such as the Data Group Domain, that
consists of four sub-data groups: Grid parameters, Bathymetry, Dry points and Thin dams.
We will now describe all data groups in consecutive order. For each input quantity we give:

A short description of its meaning. In many cases we add a more comprehensive discussion to put the quantity and its use in perspective.

The restrictions on its use.
The range of allowed values, called its domain, and its default value (if applicable).
Remark:
Before you can define grid related quantities, you must define or select the grid structure. When editing an existing input file there is no preferred or mandatory order in
which to address the various data groups.

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Figure 4.5: Data Group Description

4.5.1

Description

The Data Group Description is a text box of up to 10 lines of text, which you can use to
describe the purpose of the present model and for discriminating the present run from the
(possibly) other runs with the same model. The description is only used for reference. Upon
selecting the data group Figure 4.5 is displayed.

Domain:

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If you started from an existing MDF-file its name is displayed above in the title bar.

Parameter

Lower limit

Upper limit

Descriptive text

Any printable character

Default

Unit

Empty lines

none

Restriction:
10 lines of text each containing a maximum of 30 characters.
4.5.2

Domain

The Data Group Domain contains the following sub-data groups: Grid parameters, Bathymetry, Dry points and Thin dams.
4.5.2.1

Grid parameters

In the sub-data group Grid parameters you specify the grid used, the latitude of the model
area and the number of (vertical) layers.
Before continuing with discussing the Grid parameters you should familiarise yourself with the
concept of the staggered grid applied in Delft3D-FLOW.
In a staggered grid not all quantities, such as the water level, the depth, the velocity components or concentration of substances, are defined at the same location in the numerical grid
(and thus in the physical space).
The staggered grid applied in Delft3D is given in Figure 4.6.
Closed boundaries are defined through u- or v -points; open boundaries through either u-,
v - or water level (ζ -) points depending on the type of boundary condition such as velocity or
water level.

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Legend:

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full lines the numerical grid
grey area items with the same grid indices (m, n)
+ water level, concentration of constituents, salinity, temperature
− horizontal velocity component in ξ -direction (also
called u- and m-direction)
| horizontal velocity component in η -direction (also
called v - and n-direction)
• depth below mean (still) water level (reference level)

Figure 4.6: Staggered grid of Delft3D-FLOW

The location of other grid related quantities, such as discharges and observation points are
given when appropriate.
In Delft3D-FLOW we support two types of co-ordinate systems in the horizontal:

Cartesian: the co-ordinates are in metres
Spherical: the co-ordinates are in decimal degrees

For a Cartesian grid you have to specify the latitude of the model area; this will be used
to calculate a fixed Coriolis force for the entire area. For a spherical grid the Coriolis force is
calculated from the latitude co-ordinates in the grid file and thus varies in the latitude direction.
Typically, you use spherical co-ordinates for large areas, such as a regional model.
The type of co-ordinate system is stored in the grid file, together with the number of grid points
in both directions, and the co-ordinates of the grid points.
The construction of a suitable curvilinear grid is not a simple task, because the grid must fulfill
the following criteria:

It must fit as closely as possible to the land-water boundaries (in short land boundaries)
of the area to be modelled.
It must be orthogonal, i.e. grid lines must intersect perpendicularly.
The grid spacing must vary smoothly over the computational region to minimise inaccuracy
errors in the finite difference operators.
The Delft3D modelling suite contains the grid generator program RGFGRID that allows you to
generate a curvilinear grid (in Cartesian or spherical co-ordinates) with the required resolution
and properties. The actual construction of a grid is realised in an iterative procedure allowing

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for a stepwise generation of the model grid, working from a coarse version of the grid to finer
versions until the required resolution is achieved. RGFGRID provides all kind of features to
develop a grid, such as refine or de-refine the grid globally or locally, delete or add locally
individual grid cells, define separately a grid in a sub-area and glue it to the overall grid and
orthogonalise the grid. RGFGRID provides features to inspect the quality of the grid.
The quality of a grid is to a large extent determined by its orthogonality and the rate with
which certain properties change over the area to be modelled (smoothness). A measure for
the orthogonality is the angle, or the cosine of the angle, between the grid lines in ξ - and
η -direction. A measure for the grid smoothness is the aspect ratio of grid cells (ratio of the
grid cell dimension in ξ - and η -direction) and the ratio of neighbouring grid cell dimensions.
As a guideline we suggest the following overall quality criteria:

the grid lines.

Orthogonality: cos(ϕ) < 0.02, where ϕ is the angle between the grid lines.
Aspect ratio: must be in the range [1 to 2], unless the flow is predominantly along one of
Ratio of neighbouring grid cells: should be less than 1.2 in the area of interest up to 1.4

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far away.

You can use RGFGRID to inspect these and other properties graphically. For details see the
RGFGRID User Manual.
The horizontal resolution of the grid depends on the characteristic length scale of the bathymetry and the land-water boundary and of flow patterns you want to resolve. To resolve an
important geometrical or hydrodynamic phenomenon you will need at least 5 grid cells; to
resolve a horizontal circulation the grid size should be 1/10th or less of the size of the circulation.
Remark:
Flooding and drying is less accurate if the grid size increases.

Opening a grid and enclosure file
Select Grid parameters → Open grid, see Figure 4.7. A file window opens in which you
can browse to the required directory, and open a <∗.grd> file.
After the grid file has been opened, the co-ordinate system used is displayed, as well as the
number of grid points in both directions. Next
Select Grid parameters → Open grid enclosure, see Figure 4.7. A file window opens in
which you can browse to the required directory, and open the <∗.enc> file that belongs
to your grid file.
A grid enclosure is a closed polygon specified on a grid through the water level points. Its
purpose is to define the active or potentially active (i.e. wet) computational cells in the computational domain and the location of the open and closed boundaries. The grid enclosure is
generated by the grid generator RGFGRID; its use is under all practical conditions completely
transparent to you and you do not need to be aware of the definition and implementation
details.
However, if you want to inspect certain files, such as the grid file or the bathymetry file and
want to check all details in relation to values and locations, you must be aware of certain
details related to definition and implementation. You can find these details in chapter 10 as far

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Figure 4.7: Sub-data group Grid parameters

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as related to the numerical scheme, in section A.2.3 related to the file structure and content
and in Appendix E for a detailed discussion of the grid enclosure and the location of open and
closed boundaries.
Remarks:
We strongly suggest generating the grid and the grid enclosure in all cases with the
grid generator program RGFGRID.
If no grid enclosure is specified a default polygon is generated through the four corner
points of the numerical grid.
Latitude and orientation of the model area

If the grid is defined in Cartesian co-ordinates you have to specify the latitude and orientation
of the model:
Latitude

Latitude location of the model on Earth.

The Coriolis force is determined by the location of the model area on the Earth’s globe, i.e.
the angle of latitude (in degrees North). In the northern hemisphere you must enter a positive
value; in the southern hemisphere you must enter a negative value.
Remark:
The Coriolis force in a spherical model varies in the North-South direction and is determined by the actual latitude.
Orientation

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The model orientation is defined as the angle between the true North
and the y-axis of the Cartesian co-ordinate system. The angle is
positive if the rotation is clockwise, see Figure 4.8.

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Figure 4.8: Definition sketch grid system to North orientation

Number of layers

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For a depth-averaged computation you must set the Number of layers to 1. For a 3D computation, the Number of layers is larger than 1. Furthermore, you must specify the thickness of
the layers in the vertical. Upon setting the Number of layers larger than 1, an additional input
field Layer thickness is displayed, see Figure 4.9.

Figure 4.9: Specifying the layers thickness

In the vertical direction, two types of vertical grid with distinctive layer thickness characteristics
are supported:

With the σ -grid in the vertical the layer thickness varies with the depth, and the number of
active layers is constant (denoted in this manual as the σ -model) and
Z -grid; here the layer thickness is fixed and the number of active layers varies with the
depth. The layer thickness at the top is however determined by the actual water level
and at the bottom by the local topography. The model using this grid is referred to as the
Z -model.
To achieve a constant number of layers in the σ -model, a σ co-ordinate transformation in the
vertical is used. You can specify an arbitrary number or distribution as long as the total sum
of the layers is 100 %.
The thickness of a layer is defined as:

a percentage of the initial water depth for the Z -model and
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a percentage of the, time varying, water depth for the σ -model.
You can specify an arbitrary number or distribution as long as the total sum of the layers is
100 %. See Chapters 9, 10 and 12 for more details of the vertical co-ordinate system.
Remark:
In the σ -model layer 1 corresponds to the surface layer while in the Z -model layer 1
refers to the bottom layer.

To resolve the logarithmic profile of the horizontal velocity components in the vertical the
thickness of the bottom layer should be small. It is recommended to choose the bed layer
thickness to be about 2 % of the water depth. The variation in the layer thickness should not
be large, i.e. the layer thickness must have a smooth distribution. An indicative value for the
variation-factor for each layer is 0.7 to 1.4. Going from bottom to surface the suggested layer
thickness should not exceed 3 %, 4.5 %, 6.75 %, etc. of the water depth. For a ten σ -layers
example the suggested layer thickness is {2, 3, 4, 6, 8, 10, 12, 15, 20, 20} %.

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If wind is one of the important driving forces also the layer thickness near the surface should
not exceed 2 % of the water depth. Thus, going down from the surface the layer thickness
should not exceed 3 %, 4.5 %, 6.75 % etc. of the water depth.
A similar argument holds when you want to resolve sharp density gradients in the vertical:
you must have a sufficiently fine grid to resolve the vertical profile.
Domain:

Parameter

Lower limit

Upper limit

Default

Unit

Latitude

-90.0

90.0

0.0

degrees
North

Orientation

0.0

360.0

0.0

degrees

Number of layers

100

Thickness

0.01

100.0

% total
depth

Restrictions:
The direction of the line segments in the polygon of the grid enclosure must form a
multiple of a 45 degree angle with the numerical grid axis.
A line segment may not intersect or touch another line segment.
The grid enclosure (polygon) must be closed.
The sum of the layer thickness must be equal to 100 %.
The maximum number of layers is 100.

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Bathymetry

The depth schematisation may be uniform or non-uniform across the model area. A nonuniform (space-varying) bathymetry is given in an attribute file with the extension . For
a uniform bathymetry the sub-window is given in Figure 4.10.

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4.5.2.2

Figure 4.10: Sub-data group Domain → Bathymetry

You can either select:
Uniform
Depth

File
Open

Values specified at

Cell centre value
computed using

To enter a uniform depth value for the whole model area. Upon selecting Uniform an input field Depth is displayed.
To enter a uniform depth (positive downward).
Remark:
The reference level of the depth is a horizontal plane. A negative value defines a depth above the reference plane.
To specify a file with bathymetry data. Upon selecting File an Open
button is displayed.
To open and read the bathymetry file with extension ; see
Appendix A for its file format.
Select if the depth values have been generated at cell centres (Grid
cell centres) or at cell corners (Grid cell corners).
Remark:
Default QUICKIN generates data at the grid cell corners, but
you can also choose to generate data at cell centres.
You can either select (see also section 10.8.1):

Max The depth at the cell centre is the maximum of the 4 surrounding depths at the cell corners.

Mean The depth at the cell centre is the mean of the 4 surrounding depths at the cell corners.

Min The depth at the cell centre is the minimum of the 4 surrounding depths at the cell corners.
Domain:
Parameter

Lower limit

Upper limit

Default

Unit

Depth

-1,000

20,000

10.0

The task of assigning depth values to grid points can be split in two main components. The

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first one is the gathering of the raw bathymetric data, the second one is the actual interpolation
of these raw data on the structured grid.
You can obtain the bathymetric data by:

Digitising bathymetric charts (Admiralty Charts, Fair Sheets).
Extracting the bottom schematisation of the area to be modelled from the bottom schematisation of an overall coarser hydrodynamic model.
Using available measurements (echo-soundings).
Remark:
Do pay special attention to the reference levels of different raw bathymetric data sources.

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These options can be combined to obtain the most elaborate depth data. However, you
must be careful when combining depth data originating from different sources (different chart
datums). Corrections might be required to ensure that all depth values refer to only one
reference level. The combined bathymetric data may not all be of the same resolution, neither
of the same quality with respect to accuracy, nor may they cover the complete area of the
grid. If all data are simply stacked into one file, there will be the problem that high quality data
becomes contaminated with low quality data, thus spoiling interpolation results that might
have been good if properly dealt with. Hence, you must carefully evaluate the quality of the
various bathymetric data sets, before deciding to either include or discard it.
The interpolation of these data to the depth points of the grid should result in a bathymetry that
resembles the natural bathymetry as closely as possible. However, this does not mean that
the best bathymetry is obtained by always assigning the actual depths to all grid points. Since
the FLOW module calculates averaged flow velocities and water levels, equality of averaged
bathymetric features is more important than equality of bathymetric features at discrete grid
points. Therefore, you should adopt a volume-preserving interpolation method that uses all
data points if there is redundancy of data in a given grid cell.
In this way, the integral bathymetric features are best accounted for. In the opposite situation,
when there are less data points than grid points in a given area, you will apply some kind of
interpolation method on a triangulation network.
You can apply the utility program QUICKIN that enables you to select a sequence of data
files and to control the interpolation areas and the interpolation method. The triangulation
network is designed in such a way, that minimum triangle side lengths are achieved. Thus, a
maximum correlation between the numerical bathymetry and known bathymetric data points
is then obtained. The resulting bathymetry on the numerical grid is shown by way of iso-lines.
You can correct interactively depth values of individual samples or grid points.

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Bathymetry in relation to drying and flooding

Figure 4.11: Dry point at grid location (m, n)

4.5.2.3

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Drying and flooding is a discontinuous process. It may generate high frequency disturbances
in the results. In general, the magnitude of the disturbance will depend on the grid size and
the bottom topography. The disturbances are small if the grid size is small and the bottom
has smooth gradients. If the bottom has steep gradients across a large area on a tidal flat,
a large area may be taken out of the flow domain in just one half integration time step. This
can produce many (short wave length or wave period) disturbances (noise) in the simulation
results. You can avoid this by smoothing the bottom gradients. You should also pay attention
to the fact that depth values at points near closed boundaries are used in the drying and
flooding procedure. Finally, you must ensure that the topography for points near tidal flats in
general, and for discharge points near tidal flats in particular, are appropriately schematised
to prevent the cells to be set wet and dry at each integration time step. For details of the
numerical aspects of drying and flooding see chapter 10. Finally, you must avoid drying and
flooding at open boundaries.
Dry points

Dry points are grid cells centred around a water level point that are permanently dry during
a computation, irrespective of the local water depth and without changing the water depth as
seen from the wet points. Dry points are specified as a line of dry points; a single dry point is
specified as a line of unit length.
In Figure 4.11 a single dry point is defined at location (m, n). The depth at the corner points,
i.e. at (m, n), (m, n − 1), (m − 1, n − 1) and (m − 1, n) remain unchanged, i.e. as defined
by the bathymetry. As a result the water depth in the surrounding water level points (+) are
not influenced by the presence of the dry point.
You can specify dry points either manually, graphically in the Visualisation Area window or
by reading from an attribute file (file extension ).
Upon selecting the Data Group Dry points the sub-window of Figure 4.12 is displayed.
Dry points are characterised by their (m, n) grid indices. You can apply one or more of the
following options:
Add

To add one or a line of dry points either:
Click Add.

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Figure 4.12: Sub-data group Dry points

Specify the grid indices of the begin and end points, i.e. (m1, n1)
and (m2, n2).

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Delete

Use the Visualisation Area window (see section 4.4.2 on how
to use the Visualisation Area window).
To delete a single dry point or a line of dry points either:
Select the dry points to be deleted in the list box.
Click Delete.

Open

Save

Use the Visualisation Area window.
To read dry points from an attribute file with extension .
Remark:
If you want to combine dry points read from a file and inserted
manually you must read the file first and then add the manually
defined dry points. In reverse order the manually defined dry
points are overwritten by those of the file.
To save all dry points in the same or a new attribute file.
Remark:
You can save the dry points here or postpone it to the end of
the input definition when you save the MDF-file.

Domain:

Parameter

Lower limit

Upper limit

Indices (m, n)

Anywhere in the computational domain

Default

Unit

none

Restrictions:
Dry points may only be specified along line segments which form a 45 degrees angle,
or the multiple of it, with the computational grid axis.
If dry points are read from file and defined manually, the file must be read first. Upon
saving all dry points are stored in the (new) attribute file.

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Thin dams

Thin dams are infinitely thin objects defined at the velocity points which prohibit flow exchange
between the two adjacent computational cells without reducing the total wet surface and the
volume of the model. The purpose of a thin dam is to represent small obstacles (e.g. breakwaters, dams) in the model which have sub-grid dimensions, but large enough to influence the
local flow pattern. Thin dams are specified as a line of thin dams; a single thin dam is specified as a line of unit length. The line of thin dams is defined by its indices of begin and end
point, (m1, n1) and (m2, n2), respectively, and the direction of thin dam (u- or v -direction).
Thin dams can be specified either manually or via an imported file with mask .

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4.5.2.4

Figure 4.13: Equivalence of v -type thin dams (left) and u-type thin dams (right) with the
same grid indices, (M−1 to M+1, N)

In Figure 4.13 the location is shown for three single u-thin dams (left) and a line of three v thin dams (right). Note that these thin dams have the same grid indices; they only differ in the
direction.
Remark:
Thin dams separate the flow on both side, but they do not separate the bathymetry on
both sides. Depth points are located at the thin dam and so this depth is used on both
sides of the thin dam. If you need to apply a different depth on both sides you cannot
apply a thin dam, but you should use a line of dry points instead.
Upon selecting Thin dams the sub-window of Figure 4.14 is displayed.
You can apply one or more of the following selections:
Add

To add a single or a line of thin dams either:

Click Add.
Specify the grid indices of the begin and end point, i.e. (m1, n1)
and (m2, n2).

or
Delete

Use the Visualisation Area window, see section 4.4.2.
To delete a single or a line of thin dams either:
Select the thin dam to be deleted in the list box.
Click Delete.
or

Open

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Use the Visualisation Area window, see section 4.4.2.
To read thin dams from an attribute file with extension .

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Figure 4.14: Sub-data group Thin dams

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Save

Remark:
If you want to combine thin dams read from a file and inserted
manually you must read the file first and then add the manually
defined thin dams. In reverse order the manually defined thin
dams are overwritten by those of the file.
To save the thin dams to the same or a new attribute file.
Remark:
You can save the thin dams here or postpone it to the end of
the input definition when you save the MDF-file.
A thin dam can either be defined as blocking the flow in u- or v direction; select either direction.

Direction of Thin Dam

Domain:

Parameter

Lower limit

Upper limit

Indices (m, n)

Anywhere in the computational domain

Default

Unit

none

Restriction:
Thin dams can only be specified along lines parallel to one of the numerical grid axes
or along lines which form a 45 degrees angle with the numerical grid axis.
Remarks:
Defining thin dams at the grid boundaries (other then open boundaries) does not make
sense since these boundaries are already closed per definition.
Thin dams perpendicular to open boundaries are allowed.
Thin dams aligned along an open boundary section are strongly discouraged. You can
better subdivide such a section in sub-sections excluding the thin dams. If done so
these thin dams do not make sense anymore, see the first remark.

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Time frame

In the Data Group Time frame you define the relation between the time axis of the real world
and that of the simulation. All time dependent input is defined by the date and time as [dd mm
yyyy hh mm ss], but in the simulation a time is determined by its number of time steps after
the simulation reference date at time [00 00 00]. Upon selecting the Data Group Time frame
the sub-window given in Figure 4.15 is displayed.

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4.5.3

Figure 4.15: Data Group Time frame

You must specify the following input data:
Reference date

Simulation start time
Simulation stop time
Time step

The reference date of the simulation.
The reference date defines the (arbitrary) t = 0 point for all timeseries as used in the simulation. All time-series are specified in minutes after this t = 0 point. This reference date is also given in the
header of files containing time-series, such as boundary conditions
of type Time-Series, section A.2.15, or flow rate and concentrations
of discharges, section A.2.22. By default the reference date is set
equal to the current date.
The start date and time of the simulation.
The stop date and time of the simulation.
The time step used in the simulation in minutes.
Generally, you can choose the time step based on accuracy arguments only, in most cases stability is not an issue. The accuracy
is, among several other parameters, such as the reproduction of the
important spatial length scales by the numerical grid, dependent on
the Courant-Friedrichs-Lewy number (CFL), defined by:

√
∆t gH
CF L =
{∆x, ∆y}

(4.1)

where ∆t is the time step (in seconds), g is the acceleration of gravity, H is the (total) water depth, and {∆x, ∆y} is a characteristic
value (in many cases the minimal value) of the grid spacing in either
direction.
Generally, the Courant number should not exceed a value of ten, but
for problems with rather small variations in both space and time the
Courant number can be taken substantially larger. See section 10.4
for a discussion on the numerical scheme used in Delft3D-FLOW in
relation to stability and accuracy. For your convenience we repeat

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Table 4.2: Time step limitations shallow water solver Delft3D-FLOW

∆t ≤

Points per wave period T

1
T
40

Stability baroclinic mode

√
Ct = 2∆t gH ∆x1 2 + ∆y1 2 < 4 2
r

∆ρ
1
1
2∆t ρ gH ∆x2 + ∆y2 < 1

Explicit algorithm flooding

u∆t
∆x

Accuracy ADI for barotropic mode for
complex geometries

∆tνH

1
∆x2

1
∆y 2

Stability horizontal viscosity term

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the summary of that section. Let p
∆x and ∆y be horizontal
grid
p
Gξξ and ∆y = Gηη . In the
sizes. For a curvilinear grid ∆x =
time step limitations are given for the shallow water code Delft3DFLOW. Which of the limitations is most restrictive is dependent on
the kind of application: length scale, velocity scale, with or without
density-coupling etc.
For the Z -model the following additional limitations apply:

∆t ≤

min (∆x, ∆y)
max (|u|, |v|)

(4.2)

∆t ≤

min (∆x, ∆y)
q
∆ρ
gH
ρ

(4.3)

and

Local time zone

Remark:
You should check the influence of the time step on your results
at least once.
The time difference between local time and UTC.
The time zone is defined as the time difference (in hours) between
the local time (normally used as the time frame for Delft3D-FLOW)
and Coordinated universal time (UTC). The local Time Zone is used
for for two processes:

To determine the phases in local time of the tidal components
when tide generating forces are included in the simulation, see
Data Group Processes.
To compare the local time of the simulation with the times at
which meteo input is specified, e.g. wind velocities and atmospheric pressure. These can be specified in a different time zone.

If the Local Time Zone = 0.0 then the simulation time frame will refer
to UTC.

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Domain:

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Figure 4.16: Data Group Processes

Parameter
Date
Time

Lower limit

Upper limit

Default

Unit

Current date

none

00 00 00

23 59 59

00 00 00

hours
minutes
seconds

Time step

0.0

999.0

1.0

minutes

Local Time Zone

-12.0

12.0

0.0

hours

Restrictions:
If open boundaries are used with forcing type Astronomic then dates may not be before
1 January 1900.
The start and stop date must be equal to or larger than the reference date.
The start and stop time must be integer multiples of the time-step.
The simulation stop time must be equal to or larger than the simulation start time.
The time step must be positive.

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Processes
In the Data Group Processes you specify which processes or quantities that might influence
the hydrodynamic simulation are taken into account. Here you only define which processes
you are going to apply; the parameters required for these processes are defined in other Data
Groups, such as Initial conditions or Boundaries.
Click the Data Group Processes, upon which Figure 4.16 is displayed.
In Figure 4.16 the process Sediments has been selected; this enables the process Dredging
and dumping.

You can select any combination of the processes by:

Remarks:
To include Waves (offline) you need a communication file with wave data.
To run FLOW Online with WAVE you have to write the communication file, and you have
to prepare an MDW-file prior to execute these simulations
Secondary flow is only displayed for depth averaged computations using the σ -model,
but not for the Z -model
Tidal forces is only displayed if the grid is in spherical co-ordinates.

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4.5.4

Ticking off its check box and specifying names if required.
Salinity

Temperature

The salinity concentration will be taken into account including its influence on the water density and other processes.
The temperature is computed and the influence of the temperature
on the water density is taken into account. Several heat flux models
are available; see the sub-data group Physical parameters → Heat
flux model.

Salinity and temperature affect the density of the water. As a consequence, a horizontal
and vertical density gradient may occur which induces density driven flows. The density is
calculated at cell centres.
Pollutants and tracers

Sediments

Wind

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The spreading of up to 99 constituents (pollutants and/or sediments)
can be simulated simultaneously. If Pollutants are selected a window
appears to let you specify the names of the constituents applied. The
names of the constituents can be up to 20 characters long.
Remark:
You can specify a first order decay rate for each of the constituents. See section B.2 for a description on how to use this
option.
This functionality includes the transport of suspended sediments (cohesive and non-cohesive), bedloads and optionally updating the bathymetry. If Sediments are selected a window appears to let you specify
the names of the cohesive and/or non-cohesive sediments applied,
see Figure 4.17.
The names of sediment substances have to start with “Sediment”.
Furthermore, the tabs Sediment and Morphology are available in the
Data Group Physical parameters where you can define the sediment
and morphology characteristics.
Remark:
See chapter 11 and section B.9 for details on how to use the
Sediment and morphology functionality.
To include a wind field and its influence on the flow and spreading of

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Figure 4.17: Sediment definition window

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Wave

substances. If wind is selected a Wind tab is available in the Data
Group Physical parameters. There you can specify a global time
varying wind field, or read a time and space varying wind field and
pressure from a file. The latter is useful for the simulation of storm
surges or typhoons in a regional model.
Remark:
If FLOW runs online with WAVE, the wind specified in FLOW
can be used in WAVE.
To take into account the influence of short waves on the bed-stress
and the radiation stress on the overall momentum transport. See
section 9.7 for details on how to take the wave-current interaction
into account. For details of modelling waves you are referred to the
User Manual of Delft3D-WAVE.
Remark:
You first have to run the WAVE module to create a communication file with the required wave information.
Restriction:
The Wave process is only available for the σ -model.
You select the formulation for the influence of short waves on the
bottom roughness in the Data Group Physical parameters → Roughness.
An extension to the previous process is Online Delft3D-WAVE. In
this case there is a direct coupling with Delft3D-WAVE. Every time
the communication file is written, subsequently a WAVE simulation
is performed. Then FLOW resumes, using the latest WAVE results.
Prior to starting the FLOW simulation with online Delft3D-WAVE you
also have to prepare a WAVE input file. For details of modelling
waves you are referred to the User Manual of Delft3D-WAVE.
The process Secondary flow adds the influence of helical flow, such
as in river bends, to the momentum transport, see section 9.6 for
details of the formulations.
The influence of spiralling flow can either be taken into account through
an equilibrium formulation or as an evolutionary process by solving
an advection-diffusion equation.
Remark:
In 3D simulations the check box of Secondary flow is invisible,
i.e. cannot (and need not) be selected. The influence of helical

Online Delft3D-WAVE

Secondary flow

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flow is resolved in the 3D formulation itself.
Restriction:
Secondary flow is only available for the σ -model.
Tidal forces
To specify the parameters for tide generating forces. If tidal forces
is selected a tab Tidal forces is available in Data Group Physical
parameters. For details see section 9.9. Tidal forces can only be
specified for spherical co-ordinates.
Dredging and dumping When the process Sediments is switched on, you can use the functionality to dredge and dump sediments. This feature can also be
used for sand mining (only dredging, no associated dumping within
the model domain) and sediment nourishment (only dumping, no associated dredging within the model domain). The file with dredging and dumping sites and dredge characteristics must be opened
in the Data Group Operations → Dredging and dumping, see section 4.5.9.2.

4.5.5

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Restrictions:
The process Wave is not available for the Z -model.
Secondary flow is not available for the Z -model.
Tidal forces can only be applied for spherical grids.
Initial conditions

In the Data Group Initial conditions you can specify the initial values the computation will start
with.1 Initial conditions are required for all dependent variables, such as water level, flow velocity components, salinity and/or temperature in the case of an inhomogeneous computation,
and for the secondary flow and constituents if included in the simulation. The processes salinity, temperature, secondary flow and constituents are selected in the Data Group Processes.
Initial conditions can be very simple, such as a uniform value in the whole area, or more
complex as a space varying value obtained from ‘somewhere’ or taken from a previous run.
You can select the initial conditions arbitrarily within the domain specified below. The optimum
values depend on a combination of the values of the boundary conditions at the start time of
the simulation, the values of the variables in the (dynamic) equilibrium of the model and to
some extent the topography.
A large discrepancy between the initial condition and the boundary conditions at the simulation start time can result in short wave disturbances that propagate into the model area. If
the discrepancy is so large that the flow velocity becomes close to or above the critical flow
velocity the simulation might even become unstable. The time to reduce these short wave disturbances by internal dissipation such as bottom friction might be quite large, in tidal situations
one or even several tidal cycles.
The effects of a discrepancy between the initial condition and the boundary conditions at the
start time of the simulation can be substantially reduced by applying a transition period from
the initial condition to the actual boundary conditions and determine the intermediate values
by a smooth interpolation; see the Data Group Numerical parameters.
For complicated topographies with large drying and flooding areas we suggest to start at high
water and define an initial condition to this situation. Mismatches between the initial condition
and the boundary condition are washed out of the system instead of propagating inward.
1

Initial condition file is not yet available for the Z -model

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Figure 4.18: Data group Initial conditions

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If you do not use optimum initial conditions, the final results will be the same, but the transient
period to reach the (dynamic) equilibrium will increase.
To display the Initial conditions window:

Click the Data Group Initial conditions. Next, Figure 4.18 is displayed.
Remark:
For the layout to appear as displayed in Figure 4.18 we have selected a depth averaged
computation (Number of layers = 1 in the Data Group Domain → Grid parameters), selected all processes in the Data Group Processes, defined one pollutant, two sediments
and set the option in Figure 4.18 to Uniform. If you specify less processes less data
fields will be displayed.
You can select one of the following options:
Uniform

To specify a uniform initial condition for the water level and each of
the constituents defined in the Data Group Processes.
Remark:
The uniform initial condition for the velocity components is by
default set to zero.

For uniform initial conditions you must specify one or more of the following quantities, depending on the processes you have selected in the Data Group Processes:
Water level
Salinity
Temperature
Secondary flow

Constituents

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Specify the initial condition above the reference plane (i.e. the still
water level) in [m]. Above the reference plane is positive.
Specify the initial (sea)water salinity in [ppt].
Specify the initial water temperature in [◦ C].
Specify the initial secondary flow in [m/s]. This option can only be
applied when you have selected a depth averaged simulation (Number of layers = 1 in Data Group Domain → Grid parameters) and the
σ -model.
Specify the initial constituent (pollutant, sediment) concentrations in
[kg/m3 ].

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When you select either of the following options the input fields of the uniform values, displayed
in the lower half of Figure 4.18 are not displayed.
Initial conditions file

Restart file

Map file

The initial conditions are read from an attribute file that you some
how obtained, for instance from a previous run, created by a separate program or constructed from measurements. Upon selecting
this option you must specify the file.
The initial conditions are read from a restart file from a previous run.
To identify this file you must select either a or a file.
The initial conditions are read from a map file from a previous run.
To identify this file you must select a file.

Domain:
Lower limit

Upper limit

Default

Unit

Water level

-1,000

1,000

0.0

Salinity

0.0

100.0

31.0

ppt

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Parameter

Temperature

0.0

60.0

15.0

◦

Secondary flow

-10.0

10.0

0.0

m/s

Constituent

0.0

1,000

0.0

kg/m3

Restrictions:
The uniform initial conditions for the flow velocity components in both horizontal directions are zero by default and cannot be changed.
The initial conditions for salinity, temperature, secondary flow and constituents need
only be specified if the corresponding process is selected in the Data Group Processes.
For the Restart file and Map file options to work properly:

the restart-runid must differ from the current runid
the restart file or map file must reside in the current working
directory.
the simulation start time of the current scenario must coincide with the time instance
at which the restart file is written in the selected scenario; see Data Group Output
→ Storage; or, when using a map-file: the start time of the current simulation must
occur on the map file.
the same processes must be used in both computations.
in case of a 3D-application both computations must have the same number of layers
and layer thickness.

Remark:
Delft3D-FLOW does not check for all these requirements.

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Boundaries
In the Data Group Boundaries you can define the open boundaries, their location, type and
all input data related to driving the simulation. At an open boundary the flow and transport
boundary conditions are required. These conditions represent the influence of the outer world,
i.e. the area beyond the model area which is not modelled. The flow may be forced using water levels, currents, water level gradients, discharges (total or per grid cell) and the Riemann
invariant which is a combination of water level and current. The hydrodynamic forcing can be
prescribed using harmonic or astronomical components or as time-series. For water level forcing the boundary conditions can also be specified in terms of QH-relations. The transport of
salinity, temperature and/or constituents is prescribed by specifying the inflow concentrations.
You can specify the boundary conditions for these parameters as time-series only.

Depending upon the variability of the parameters along the open boundary, you can divide an
open boundary into sections. A boundary section is characterised by a name, indices of the
begin and end point of the boundary section, the type of boundary forcing and last but not
least the data itself.
The following types of boundary conditions are available:

Water level
Velocity
Neumann (water level gradient)
Discharge or flux (total or per grid cell)
Riemann or weakly reflective boundaries2

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4.5.6

The choice of the type of boundary condition used depends on the phenomena to be studied.
For instance, when you are modelling water levels at the inland side of an estuary, you will
prescribe the known water levels at the entrance of the estuary. However, the same internal
solution may be achieved by prescribing flow velocities, fluxes or weakly reflective conditions.
But, the latter three yield a much weaker control over the water level, since velocities are
only weakly coupled to water levels, especially for the more complex flow situations. Other
examples are:

When modelling river flow, the upstream flux is prescribed in combination with the downstream water level.
When modelling cross flow in front of a harbour, velocity components are prescribed.
The Neumann type of boundary is used to impose the alongshore water level gradient. Neumann boundaries can only be applied on cross-shore boundaries in combination with a water
level boundary at the seaward boundary, which is needed to make the solution of the mathematical boundary value problem well-posed.
The Riemann type of boundary is used to simulate a weakly reflective boundary. The main
characteristic of a weakly reflective boundary condition is that the boundary up to a certain
level is transparent for outgoing waves, such as short wave disturbances. Outgoing waves
can cross the open boundary without being reflected back into the computational domain as
happens for the other types of boundaries.
A weakly reflective form of the other boundary types is obtained by specifying a reflection
coefficient. This coefficient Alfa must be ≥ 0 (recommended value for tidal computations is
50 or 100). For more details about the weakly reflective boundary condition see Verboom and
2

This feature has only been tested for the σ -model

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Slob (1984), Verboom and Segal (1986) and chapter 9.
If there is more than one open boundary in the model area, you should avoid applying the
same type of boundary condition at all boundaries. For instance, two velocity boundaries at
both ends of a straight channel may lead to continuity problems, i.e. the channel will eventually
dry up or will overflow, if the fluxes that are a result of these velocity components and their
respective water levels are not compatible. In this case it is better to prescribe the normal
velocity component at one end of the channel and the water level at the other. A physically
stable result is then obtained. When modelling tidal flow in a large basin, forcing by prescribing
water levels only is generally a sound procedure.

In practice, the type of boundary condition applied often depends mainly on the available data.
For example, most of the larger sea models are likely driven by water level boundaries only
since these are the only quantities known with some accuracy.

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When prescribing water level boundaries, you should keep in mind that water level is a globally
varying quantity. There is a substantial correlation between water levels in locations being
not too far apart, meaning that a small error in the prescription of water levels can only be
compensated by a large response in the velocity components. The area of influence of this
phenomenon is not limited to a certain number of grid points near the boundary, but rather
to the entire physical area. Since we do not want small errors in the boundary conditions to
significantly influence the model results, we locate boundaries as far away from the areas of
interest as possible.
The boundary condition is prescribed at two so-called boundary support points (Begin or A,
and End or B), which divide a complete boundary into several segments. Points that lie in
between these two support points are calculated by linear interpolation of the forcing at both
ends. The actual signal at the support points may either be presented to the program as a
harmonic type of signal (frequencies, amplitudes and phases) or directly as a time-series.
Often, the signal itself will be a tidal signal composed of amplitudes and phases at astronomic
frequencies. For large area models (horizontal dimensions of the order of the tidal wave
length or larger), the amplitudes and phases can be interpolated from nearby ports. However,
the small relative error introduced by the interpolation procedure becomes more and more
significant and important when the method is applied for smaller area models (e.g. coastal
models). For these models, the boundary condition should be obtained by nesting the model
into a calibrated larger area model.
Remark:
The interpolation between the begin and end point of a boundary section are obtained
by linear interpolation of the values at these (support) points. For boundary conditions
expressed in amplitudes and phases the interpolation is executed on these quantities
(and not on the computed time dependent boundary values).

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Cross-section
Virtual line of grid points

-+-+-+- +- +-+- +- +- +
-+- + -+- +- +- +- +- +- +

Discharge
boundary

-+- + -+- +- +- +- +- +- +
Top view

Discharge per grid cell and total discharge

Figure 4.19: Sketch of cross-section with 8 grid cells

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To specify boundary conditions of type Discharge per cell you must apply a similar procedure
as for the other boundary types, i.e. the discharge is prescribed at both ends of a boundary
section and intermediate values are determined by linear interpolation. However, the discharge prescribed in an end point is the discharge through the grid cell related to that specific
end point. If you want to prescribe a certain discharge through the total cross-section you
must translate this total discharge into discharges at the end points. This is a rather difficult
task if the bathymetry changes appreciably over the cross-section. A better approach is to
define boundary sections of just one grid cell and to determine the boundary conditions per
grid cell (still given at its end points A and B, which now are the same) using the following
approach:
3/2

H
Qi = PN i

3/2

(4.4)

j=1 Hj

where Qi , Hi , Q and N are the discharge through section i, the average depth in section
i, the total discharge through the cross-section and the total number of sections in the crosssection, respectively.
Remark:
The depth is defined at the grid lines between the velocity, or discharge points, see
Figure 4.19 details.
In the present release of Delft3D-FLOW the procedure mentioned above is incorporated in
the FLOW-GUI, so you can prescribe the discharge through a cross-section using the type of
boundary Total discharge.
Upon selecting the Data Group Boundaries the following sub-window is displayed, see Figure 4.20. You can select one or more of the following options:
Add

To Add an open boundary section either:
Click Add. The section is given the default name “-Unnamed-”,
displayed in the Section name field.
Replace the name “-Unnamed-” by a useful name.
Specify the grid indices of the begin and end point given by (M1,
N1) and (M2, N2).
or

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Figure 4.20: Main window for defining open boundaries

Delete

Use the Visualisation Area window.
Remarks:
Open boundary sections typically extend over more than just
one grid cell, so you have to specify their begin and end point.
There is no preferred direction in the definition of a boundary
section.
Only an open boundary of the type Water level may be defined
along a diagonal grid line.
To Delete an open boundary section either:
Select the boundary section to be deleted in the list box.
Click Delete.

Open/Save

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Use the Visualisation Area window.
Open or Save the definitions (location, type of open boundary, reflection parameter, forcing type) of the open boundary sections in
an attribute file with extension bnd in the working directory. Upon
selecting Open / Save Figure 4.21 is displayed.

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Figure 4.21: Open and save window for boundary locations and conditions

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Figure 4.22: Straight channel; location of open and closed boundaries
Table 4.3: Definition of open and closed boundaries.

Indices of begin and end point

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Boundary

Displayed in FLOW-GUI

Used in computation

West boundary

(1, 2) and (1, 6)

South boundary

(2, 1) and (11, 1)

East boundary

(12, 2) and (12, 6)

(12, 2) and (12, 6) ζ -boundary
(11, 2) and (11, 6) u-boundary

North boundary

(2, 7) and (11, 7)

(2, 7) and (11, 7) ζ -boundary
(2, 6) and (12, 6) v -boundary

Discussion:

The location and numbering of open boundaries need some clarification and illustration. Both
open and closed boundaries are defined at the grid enclosure (through the water level points).
However, physically closed and open velocity controlled open boundaries are located at the
nearest velocity point inside the grid enclosure.
To illustrate this we take the example given in Appendix E for a straight rectilinear channel of
10 ∗ 5 grid cells or 11 ∗ 6 grid points, see Figure 4.22.
The definition of the boundary sections, both as displayed in the FLOW-GUI and as used in
the computation, are given in Table 4.3.
Remark:
Much confusion on the location and numbering of open and closed boundaries can be
avoided by thinking in terms of computational grid cells. Water level boundaries are
located just outside the first or last computational grid cell and velocity boundaries are
located at the edge of the first or last computation cell. See Appendix E for a discussion
and illustration.

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Domain:
Parameter

Lower limit

Name boundary

Upper limit

Default

Unit

Any printable character

-Unnamed-

none

(m, n)

At the grid enclosure

none

Alfa

0.0

none

10,000.0

Restrictions:
A boundary section name must be non-blank, and can contain up to 20 characters.
A boundary section must be located on the grid enclosure.
The number of boundary sections is limited to 300.
Next you must specify for each boundary section the type of forcing and the forcing itself.
Type of open boundary Select either one of the options:
Water level
Current
Neumann
Discharge per cell
Total discharge
Riemann

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Reflection parameter
Alfa

Forcing type

Remarks:
Riemann type of boundary has only been tested for the σ model.
Only an open boundary of the type Water level may be defined
along a diagonal grid line.
Specify the amount by which you to want to make the open boundary
less reflective for short wave disturbances that propagate towards
the boundary from inside the model.
Remark:
The reflection parameter does not apply for Neumann or Riemann controlled boundary sections.
Select either one of the options:

Astronomic, the flow conditions are specified using tidal constituents, amplitudes and phases. The nodal amplitude and phase
factors are determined at the start of the simulation and updated
after each NodalT time interval.
Harmonic, the flow conditions are specified using user-defined
frequencies, amplitudes and phases.
QH-relation, (only in combination with water level boundary type)
the water level is derived from the computed discharge leaving
the domain through the boundary.
Time-series, the flow conditions are specified as time-series.

Vertical profile for
hydrodynamics

The vertical profile does not apply for Water level or Neumann controlled boundary sections, neither for a 2D simulation. The profile
can be:

Uniform The velocity profile is uniform over the water depth.
Logarithmic The velocity profile is a logarithmic function over the

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water depth.
Per layer The velocity profile is embedded in the boundary condition file taken from a larger area model by nesting.
Remark:
This option is activated if you open a boundary location file with boundary type ‘3-d profile’. In the current implementation you must add this type manually in the -file;
see section A.2.10 and A.2.15 for details.

Edit transport
conditions

Edit flow conditions

Remark:
The Vertical profile for hydrodynamics forms also part of the
definition and it will be saved in the file as well.
To specify the boundary data for the hydrodynamic simulation. Details are specified in a separate window, see section 4.5.6.1.
To specify the boundary data for the constituents transported with
the flow and only for those constituents specified in the Data Group
Processes. Details are specified in a separate window, see section 4.5.6.2.

4.5.6.1

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To define the boundary condition data press the Edit flow conditions button. The sub-window
displayed depends on the Type of open boundary selected.
Flow boundary conditions

For flow boundary conditions you can either select:

Astronomic
Harmonic
QH-relation (for water levels only)
Time-series

The window to specify the boundary data depends on the forcing type selected.
Astronomic boundary conditions

You can specify the boundary conditions in terms of astronomical components. Specifying
astronomical components in a manner similar as harmonic components is a laborious activity,
as tens of components can be prescribed. These astronomical components are mostly obtained from some type of tidal analysis program, such as Delft3D-TIDE or Delft3D-TRIANA.
The boundary conditions are stored in an attribute file with extension .
The observed tidal motion can be described in terms of a series of simple harmonic constituent motions, each with its own characteristic frequency ω (angular velocity). The amplitudes A and phases G of the constituents vary with the positions where the tide is observed.
In this representation by means of the primary constituents, compound and higher harmonic
constituents may have to be added. This is the case in shallow water areas for example,
where advection, large amplitude to depth ratio, and bottom friction give rise to non-linear
interactions. For a list of primary and compound constituents, see Appendix C.
The general formula for the astronomical tide is:

H(t) = A0 +

k
X

Ai Fi cos (ωi t + (V0 + u)i − Gi )

(4.5)

i=1

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Figure 4.23: Specifying astronomical boundary conditions

in which:

H(t)
A0
k
i
Ai
Fi
ωi
(V0 + u)i
Gi

water level at time t
mean water level over a certain period
number of relevant constituents
index of a constituent
local tidal amplitude of a constituent
nodal amplitude factor
angular velocity
astronomical argument
improved kappa number (= local phase lag)

Fi and (V0 + u)i are time-dependent factors which, together with ω , can easily be calculated
and are generally tabulated in the various tidal year books. V0 is the phase correction factor
which relates the local time frame of the observations to an internationally agreed celestial
time frame. V0 is frequency dependent. Fi and ui are slowly varying amplitude and phase
corrections and are also frequency dependent. For most frequencies they have a cyclic period
of 18.6 years. A0 , Ai and Gi are position-dependent: they represent the local character
of the tide. You only have to provide the amplitudes, phases and frequencies (in terms of
constituent names). By default, Delft3D-FLOW re-calculates the nodal amplitude factors and
astronomical arguments every 6 hours. See section B.21 for changing this default.
Upon selecting Astronomic and next Edit flow conditions Figure 4.23 is displayed.
Each open boundary section has a begin (A) and an end (B) point. At each end you have
to assign a Component set. A Component set consists of a number of tidal constituents with
their Name, Amplitude and Phase.

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To add a Component set:
Click Add. The set is given the default name ‘-Unnamed-’.
Replace the name ‘-Unnamed-’ in the Selected set field by a useful name, reflecting the
boundary and the end point (A or B) for which this set will be used.
Remark:
When adding a Component set, this set will have the same tidal constituents as the first
set. The amplitudes will be 1 and the phases 0.
To add a tidal constituent to a Component set:

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Remark:
The mean value (A0) has no phase.

First select the required set from the list of available Component sets.
Click in the Amplitude or Phase field.
Use the menu item Table in the menu bar to insert, copy or delete a row, or to copy a
value.
In the Name field: select from the dropdown list the required tidal constituent.
Specify the Amplitude and Phase.

To assign a Component set to a boundary:

First select the required open boundary.
Click Edit flow conditions.
Under Selected component sets, select from the dropdown list the required set for End A.
Under Selected component sets, select from the dropdown list the required set for End B.
You can apply corrections to the defined astronomic components. These corrections can be
applied to a sub-set of the boundary sections and to a sub-set of the astronomic components
applied. These corrections are typically applied during the calibration phase of a model. Both
the amplitude (multiplicative) and the phase (additive) can be corrected, see Figure 4.24. This
attribute file has extension .
Remarks:
The correction does not apply for the A0 astronomic component.
If the type of open boundary is Total discharge, only one Component set is needed for
this open boundary. Specify the same set for End A and End B.
Be aware that amplitudes and phases for intermediate points at the open boundary are
linearly interpolated from the values at the end points. For instance, if you have a phase
of 1 degree at End A, and a phase of 359 degrees at End B, an intermediate point will
have a phase of 180 degrees. If you do not want this, you can specify 361 degrees at
End A.
To save the component sets, the corrections and the specification of the sets to boundary end
points:

Use Open / Save in Figure 4.20 to enter the Open/Save Boundaries window of Figure 4.21.
Remarks:
The components sets are stored in a file with extension .
The information about which set is assigned to which boundary end point is stored in
the file.

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Figure 4.24: Contents of a Component set with two tidal constituents having corrections

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You can import astronomic boundary conditions by selecting Open/Save in Figure 4.20 and
Open Astronomical flow conditions in Figure 4.21. In the window of Figure 4.23 the component
sets from the imported file are listed under Component sets. You can extend, delete or modify
them at will.
To assign a Component set to an end point of an open boundary section, follow the procedure
above.
Domain:

Parameter

Lower limit

Upper limit

Default

Unit

Water level

0.0

100.0

0.0

Neumann

0.0

100.0

0.0

Current

0.0

10.0

0.0

m/s

Discharge

0.0

1.0E+06

0.0

m3 /s

Riemann

0.0

100.0

0.0

m/s

Phase

-360.0

360.0

0.0

degrees

0.0

10,000

0.0

none

Alpha

Restrictions:
Astronomical forcing can not be mixed with harmonic forcing.
Boundary conditions of type Astronomic must precede boundary conditions of type QHtable and Time-series.
The maximum number of frequencies is 234.

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Figure 4.25: Specifying harmonic boundary conditions

Harmonic boundary conditions

Upon selecting Harmonic and next Edit flow conditions Figure 4.25 is displayed.
Remark:
If the type of open boundary is Total discharge, the amplitudes and phases for the whole
section are required.
The boundary signal F (t) is constructed by super-imposing the following individual components:

F (t) =

N
X

Ai cos (ωi t − ϕ)

(4.6)

i=1

where N is the number of frequency components. The unit of the amplitudes depends on the
quantity prescribed, they are respectively [m] for water elevations, [-] for Neumann, [m/s] for
velocities, [m3 /s] for fluxes, and [m/s] for Riemann boundaries.
For each of the boundary sections you can either import the boundary conditions by selecting
Open/Save, or specify the harmonic conditions manually in a table.
Open

Import the harmonic boundary conditions from an attribute file with
extension .
Remark:
The data you import here will be included in the attribute file when you save the boundary locations and conditions, see Figure 4.21.

In the table you must specify:
Frequency

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Amplitude

Phase

The amplitude of the harmonic component in [m], [-], [m3 /s] or [m/s]
at the Begin point A and at the End point B defined at grid indices
(M1, N1) and (M2, N2), respectively.
The phase of the harmonic component in [degrees] at the Begin
point A and at the End point B defined at grid indices (M1, N1) and
(M2, N2), respectively.

Use the menu item Table in the menu bar to insert, copy or delete a row, or to copy a value.

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Remarks:
The mean value is specified by zero frequency and zero phase. The mean value must
always be specified.
All boundaries with Harmonic forcing must have the same frequencies. If not taken care
of by you, the GUI will save the frequencies of the last Harmonic boundary.
Be aware that amplitudes and phases for intermediate points at the open boundary are
linearly interpolated from the values at the end points. For instance, if you have a phase
of 1 degree at End A, and a phase of 359 degrees at End B, an intermediate point will
have a phase of 180 degrees. If you do not want this, you can specify 361 degrees at
End A.
Restrictions:
Harmonic forcing may not be mixed with astronomical forcing and must precede QH
and time-series forcing.
The maximum number of frequencies is 234.
If you have defined all data for the currently selected boundary section:

Close the sub-window and select another boundary section to define its boundary conditions.
Domain:

Parameter

Lower limit

Upper limit

Default

Unit

Water level

0.0

100.0

0.0

Neumann

0.0

100.0

0.0

Current

0.0

10.0

0.0

m/s

Discharge

0.0

1.0E+06

0.0

m3 /s

Riemann

0.0

100.0

0.0

m/s

Phase

-360.0

360.0

0.0

degrees

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Figure 4.26: Specifying QH-relation boundary conditions

QH-relation boundary conditions (for water level boundaries only)
For QH-relations you must specify the relation between the outflowing discharge and the water
level at the boundary. Intermediate values are determined by linear interpolation. You cannot
change the type of interpolation. Above the highest specified discharge and below the lowest
specified discharge the water level is kept constant.
Upon selecting QH-relation and next Edit flow conditions Figure 4.26 is displayed.
The sub-window displayed has just one column for the discharge and one column for the water
level. Use the menu item Table in the menu bar to insert, copy or delete a row, or to copy a
value. First click in either the Discharge or Water level input field.
If you have defined all data for the currently selected boundary section:
Close the sub-window and select another boundary section to define its boundary conditions.
A relaxation parameter can be specified in the data group Numerical parameters.
Domain:
Parameter

Lower limit

Upper limit

Default

Unit

Discharge

-1.0E+6

1.0E+06

0.0

m3 /s

Water level

-100.0

100.0

0.0

Restrictions:
The discharges should be specified in increasing order. That is, for positive discharges
from small to large and for negative discharges from large to small.

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Figure 4.27: Specifying time-series boundary conditions

Intermediate values are determined by linear interpolation. Above the highest specified
discharge and below the lowest specified discharge the water level is kept constant.
Boundaries with forcing by a QH relation must precede time-series boundaries and they
must follow boundaries with harmonic and astronomical forcing.
Time-series boundary conditions

Upon selecting Time-series and next Edit flow conditions Figure 4.27 is displayed.
Remark:
If the type of open boundary is Total discharge, only one (1) discharge is required for
the whole section.
For time-series conditions you must specify the boundary conditions in terms of values of
the selected kind, i.e. water level, Neumann, current, discharge or Riemann, at time breakpoints for both the Begin point A and the End point B, respectively. Intermediate values are
determined by linear interpolation. You cannot change the type of interpolation.
Use the menu item Table in the menu bar to insert, copy or delete a row, or to copy a value.
If you have defined all data for the currently selected boundary section:

Close the sub-window and select another boundary section to define its boundary conditions.

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Figure 4.28: Transport conditions; Thatcher Harleman time lags

Domain:
Lower limit

Upper limit

Default

Unit

Water level

-100.0

100.0

0.0

Neumann

-100.0

100.0

0.0

Current

-10.0

10.0

0.0

m/s

Discharge

-1.0E+6

1.0E+06

0.0

m3 /s

Riemann

-100.0

100.0

0.0

m/s

Alfa

0.0

10,000

0.0

none

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Parameter

Restrictions:
The time breakpoints must differ from the simulation start time by an integer multiple of
the time-step (Data Group Time frame).
The first time breakpoint must be before or equal to the simulation start time, and the
last time breakpoint must be equal or later than the simulation stop time (see Data
Group Time frame).
Time breakpoints must be given in ascending order.
Intermediate values are determined by linear interpolation.
Time-series forcing must follow astronomic, harmonic or QH forcing when these type of
boundary conditions are applied in the same model area.
4.5.6.2

Transport boundary conditions

To specify the boundary conditions for all quantities defined in the Data Group Processes you
must for each boundary section:

Select the boundary section in the list box, see Figure 4.20.
Specify if required Thatcher Harleman time lags, see Figure 4.28.
Thatcher-Harleman
time lag

The return time for concentrations from their value at outflow to their
value specified by the boundary condition at inflow. For 3D simulations you can specify different values at the surface and at the bottom
to represent the influence of stratification and the different flow conditions above and below the interface.

At the sea-side boundary a common problem for numerical models of estuarine areas is encountered when the boundary conditions for a constituent are to be prescribed. In a physical
(unbounded) world, the inflowing water mass immediately after low water slack originates from
the outflowing water mass a moment earlier. Consequently, the concentration of the inflowing

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Figure 4.29: Specifying transport boundary conditions

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water is commonly not equal to the concentration Cmax which has been prescribed along
this open boundary. It will take some time before the concentration along this open boundary
reaches the Cmax value. In numerical models, this time lag (return time) is often modelled
by means of a “Thatcher-Harleman” boundary condition (Thatcher and Harleman, 1972). The
return time depends on the flow conditions outside the estuary. If there is a strong circulation
the return time is short. The return time must be specified for each open boundary section,
one for the top layer and the other for the bottom layer. The return times for the layers in
between will be determined through a linear interpolation of these two values.
Select Edit transport conditions.

Next the window Boundaries: Transport Conditions is displayed, see Figure 4.29. The
window displayed is for a 3D simulation; for a 2D simulation all input fields related to 3D are
either absent or insensitive. In a 3D simulation you can specify a surface and a bottom value,
in a 2D simulation you need to specify only the surface value (applied over the whole depth).
Transport boundary conditions always are specified as time-series.

You can specify one or more of the following options, depending whether you have a 2D or a
3D simulation; for each of the quantities selected in the Data Group Processes you must:
Constituent

Select the quantity to be defined next in the table.

In the table you must specify time breakpoints and concentrations at the Surface and Bottom
layer for the Begin point A and the End point B of the current boundary section, defined at
grid indices (m1, n1) and (m2, n2), respectively. Use the menu item Table in the menu bar
to insert, copy or delete a row, or to copy a value.
Vertical profile

To specify the vertical profile of the concentration at the current boundary section. You can either select:

Uniform The value is applied over the whole water depth; only
the surface values need to be specified.
Linear Surface and bottom values are linearly interpolated for
intermediate depth.
Step You can define a jump in the vertical profile.
Upon selecting this option you can specify the depth (Profile
jump) below the free surface at which the profile jump occurs.
The surface value is maintained down to this depth and the bottom value is used from the jump depth down to the bottom.

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Per layer The vertical profile is embedded in the boundary condition file taken from a larger area model by nesting.
If a constituent (i.e. salinity or temperature, etc) is included in a 3D model then the vertical
profiles for these quantities must be prescribed, besides the usual boundary condition values.
The options for the vertical profile for these quantities are respectively: Uniform, Linear and
Step (discontinuous profile). In the last case the location of the profile jump, measured in metres from the water surface, must be prescribed. During initialisation the jump in the profile will
be translated into a layer number. Once determined, this layer number will be fixed throughout
the simulation; so this layer number depends on the initial water level.

Remark:
When the initial conditions are read from a restart file (hot start), the position of the
jump will be determined using the water elevation read from this file. Consequently,
a mismatch between your boundary condition and the concentration distribution in the
vertical, just inside the open boundary, may occur. This mismatch can produce spurious
oscillations in your result.

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If you have defined all data for the currently selected boundary section:

Close the sub-window and select another boundary section to define its transport boundary conditions.
Domain:

Parameter

Lower limit

Upper limit

Default

Unit

Salinity

0.0

100.0

0.0

ppt

Temperature

0.0

60.0

0.0

◦

Pollutant or sediment

0.0

1,000

0.0

kg/m3

Physical parameters

In the Data Group Physical parameters you can select or specify a number of parameters
related to the physical condition of the model area. The physical parameters can be split into
several classes; some are always needed and some are related to the processes switched on
or off.
The Data Group Physical parameters contains several tabs. The tabs for Constants, Roughness and Viscosity are always visible. The other tabs are only available if the associated
processes are switched on:

Heat flux model (requires Temperature process activated)
Sediment and Morphology (requires Sediments process activated)

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Figure 4.30: Specifying the physical constants

Wind (requires Wind process activated)
Tidal forces (requires grid in spherical co-ordinates and Tidal forces process activated)
4.5.7.1

Constants

Upon selecting Physical parameters → Constants the sub-window given by Figure 4.30 is
displayed. You can specify one or more of the following constants:
Gravity
Water density

Air density
Temperature

Salinity

Beta_c

Equilibrium state

The gravitational acceleration in [m/s2 ].
The background water density in [kg/m3 ].
This value is only required for a homogeneous simulation, i.e. the
processes temperature and salinity are not selected.
The density of air in [kg/m3 ], used in the wind stress formulation.
The background water temperature in [◦ C], used in the equation of
state. This value is only required if the process Temperature is not
selected, and the process Salinity is.
The background water salinity in [ppt], used in the equation of state.
This value is only required if the processes Salinity is not selected,
and the process Temperature is.
Fraction of the shear stress due to secondary flow taken into account
in the momentum equation.
Tick off if you want to apply the equilibrium state for the secondary
flow process (only for depth-averaged flow):

Yes Apply the equilibrium state.
No Compute the secondary flow as a dynamical process.
The flow in a river bend is basically three-dimensional. The velocity has a component in the
plane perpendicular to the river axis. This component is directed to the inner bend along the
river bed and directed to the outer bend near the water surface. This so-called ‘secondary
flow’ (spiral motion) is of importance for the calculation of changes of the river bed in morphological models. This spiral motion is automatically taken into account in a 3D simulation,

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Figure 4.31: Examples of the wind drag coefficient

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but in 2D simulations the flow equations must be extended to take this effect into account.
The intensity of the secondary flow is a measure for the magnitude of the component of the
secondary flow normal to the depth averaged flow. The vertical distribution of this horizontal
velocity component is assumed to be a universal function of the vertical co-ordinate. The
actual local velocity distribution originates from a multiplication of this function with the spiral
motion intensity. The spiral motion intensity, I , can be used to determine the deviation of the
direction of the bed shear stress from the direction of the depth-averaged flow; this is done in
the morphological module if the secondary flow is included as a process. The βc parameter
described here influences the extent to which the effect of spiral motion in a depth-averaged
model is accounted for. The secondary flow may be computed from a local equilibrium approach or from an advection/diffusion equation. The parameter Beta_c specifies to which
extent the shear stresses due to the secondary flow are included in the momentum equation
(Beta_c = 0 means no inclusion). See section 9.6 for full details.
Remark:
You do not need (can not) prescribe boundary conditions for the transport equations
that describe the secondary flow. The underlying assumption is that the secondary flow
is locally determined inside the model area and not transported into the model area
through the open boundaries. This assumption might be violated in models that cover
only a very small area.
Wind drag

You can specify three Wind drag coefficient values and three Wind
speed values at which these coefficients apply.

The wind drag coefficient may be linearly dependent on the wind speed, reflecting increasing
roughness of the water surface with increasing wind speed. The three wind drag coefficients
determine three breakpoints in the piece-wise linear function of wind drag coefficient and wind
speed, see Figure 4.31. The first two coefficients, Breakpoint (A), determine the constant wind
drag coefficient from zero wind speed up to the wind speed specified. The last two coefficients,
Breakpoint (C), specify the constant wind drag coefficient from the specified wind speed and
higher. Inbetween the breakpoints there is a linear interpolation applied. As a result, you
can specify a constant wind drag coefficient, a linearly increasing wind drag coefficient or a
piece-wise linear function of wind speed, as shown in Figure 4.31.

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Domain:
Parameter

Lower limit

Upper limit

Default

Unit

Gravity

9.5

12.0

9.81

m/s2

Water density

900.0

1,500

1,000

kg/m3

Air density

0.5

1.5

1.0

kg/m3

Temperature

0.0

60.0

15.0

◦

Salinity

0.0

100.0

31.0

ppt

Beta_c

0.0

1.0

0.5

none

Coefficient A

0.0

0.1

Coefficient B

0.0

0.1

Coefficient C

0.0

0.1

none

0.00723

none

0.00723

none

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0.00063

Wind speed A

0.0

100.0

0.0

m/s

Wind speed B

0.0

100.0

m/s

Wind speed C

0.0

100.0

m/s

Roughness

In the sub-data group Roughness you can specify the bottom roughness and the roughness
of the side walls.
The bottom roughness can be computed with several formulae and you can specify different
coefficients for x- (or ξ -) and y - (or η -) direction; either as a uniform value in each direction,
or space-varying imported from an attribute file.
Upon selecting Physical parameters → Roughness the window given by Figure 4.32 is displayed.
Bottom roughness

You can select and define the following options and parameters:
Roughness formula

The bottom roughness can be computed according to:

Manning.
White-Colebrook.
Chézy.
Z0 (for 3D simulations only).

In the Manning formulation the Manning coefficient, n, must be specified. The Chézy friction coefficient is calculated from:

H 1/6
n

(4.7)

where H is the water depth. A typical Manning value is 0.02 [s/m1/3 ].

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Figure 4.32: Sub-data group Roughness

In the White-Colebrook formulation you must specify the equivalent
geometrical roughness of Nikuradse, ks [m]. The Chézy friction coefficient is calculated from:
10

C = 18 log

12H
ks

(4.8)

A first estimate of the bed roughness length z0 [m] in 3D computations can be derived from the equivalent geometrical roughness of
Nikuradse, ks :

z0 =

ks
30

(4.9)

Typical values of ks range from 0.15 [m] for (river) beds with sediment
transport down to 0.01 [m] or less for (very) smooth surfaces; see
section 9.4.1 for more details.
A first estimate of the Chézy friction coefficient is given by:

C = 25 + H

Uniform
File

Stress formulation due
to wave forces

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(4.10)

Remark:
The Chézy friction coefficient discussed above applies to a
depth averaged computation.
Specify the values in u- and v -direction in the input fields.
Select the space varying coefficients in u- and v -direction from an
attribute file (extension ). See section A.2.19 for a format
description of the roughness file. The file is not read.
The bottom stress due to wave forces can be computed with several
formulae. You can select one of the following formulae, see also
section 9.7.5:

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Fredsøe (1984)
Myrhaug and Slaattelid (1990)
Grant and Madsen (1979)
Huynh-Thanh and Temperville (1991)
Davies et al. (1988)
Bijker (1967)
Christoffersen and Jonsson (1985)
O’ Connor and Yoo (1988)
Van Rijn et al. (2004)

Wall roughness
The friction of side walls is computed from a ‘law of the wall’ formulation if selected:
You can select one of the following:

Slip condition

Free; zero tangential shear stress
Partial; specify the roughness length (m).
No; zero velocity at the wall assumed.

Domain:

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In large-scale hydrodynamic simulations, the tangential shear stress for all lateral boundaries
or vertical walls can be safely neglected (free slip). For simulations of small-scale flow (e.g.
laboratory scale) the influence of the side walls on the flow can be significant and this flag can
be activated. The partial slip only applies to the side walls of permanently dry areas, including
dry points. The tangential shear stress is calculated based on a logarithmic law of the wall
where the roughness length needs to be specified. See chapter 9 for details.

Parameter

Lower limit

Upper limit

Default

Unit

Manning

0.0

0.04

65.0

m−1/3 s

White-Colebrook

0.0

10.0

65.0

Chézy

0.0

1,000

65.0

m1/2 /s

0.0

1.0

65.0

Remark:
The default value is set for the Chézy-formulation.
4.5.7.2

Viscosity

The background horizontal eddy viscosity and horizontal eddy diffusivity are user-defined. The
viscosity and diffusivity calculated with the Horizontal Large Eddy Simulation (HLES) sub-grid
model will be added to the background values (for FLOW v3.50.09.02 and higher).
Remark:
If you use an older version of FLOW, or if you re-run an old MDF-file with FLOW
v3.50.09.02 or higher, be aware of this adding operation.
The user-defined parameters can be entered as one uniform value for each quantity (uniform
for both directions) or as non-uniform values read from a user-specified file with file extension
.

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Figure 4.33: Defining the eddy viscosity and eddy diffusivity

If the model is 3D, you may specify constant background values for the turbulent vertical eddy
viscosity. If constituents are modelled you may also specify a constant background value for
the vertical turbulent eddy diffusivity and the Ozmidov length scale.
Finally the model for 3D turbulence can be specified. For details see section 9.5.
Upon selecting Physical parameters → Viscosity Figure 4.33 will be displayed.
Horizontal eddy viscosity and diffusivity

You can select or specify the following parameters:
Background values
Uniform
Horizontal eddy
viscosity
Horizontal eddy
diffusivity
File

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A uniform horizontal eddy viscosity and eddy diffusivity. The values
are defined in the separate input fields.
Specify a uniform horizontal eddy viscosity in [m2 /s].
Specify a uniform horizontal eddy diffusivity in [m2 /s].
Select the horizontal eddy viscosity and eddy diffusivity from an attribute file with extension . The data is not read.

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Figure 4.34: Window with HLES parameters

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Model for 2D turbulence
Subgrid scale HLES
Upon selecting Figure 4.34 will be displayed. Details about the input
parameters and theory can be found in section B.8.
Remarks:
The contribution from the HLES model will be added to the background values.
If the relaxation time is less than 0.0, the high-pass filtering operation will be cancelled.

Background vertical eddy viscosity and diffusivity
You can select or specify the following parameters:

Vertical eddy viscosity Specify a uniform vertical turbulent eddy viscosity in [m2 /s].
Vertical eddy diffusivity Specify a uniform vertical turbulent eddy diffusivity in [m2 /s].
The resulting viscosity is the maximum of the user-defined background value and the calculated value from the turbulence model. Similar for the diffusivity.
Ozmidov length scale

The Ozmidov length scale determines the minimal value for the vertical diffusivity from the calculated vertical diffusivity and the equation
using Brunt-Väisälä frequency and Ozmidov length scale; see chapter 9 for details.

Model for 3D turbulence
Turbulence Model
For a 3D simulation you can select the type of turbulence formulation
used to determine the vertical turbulent eddy viscosity and the vertical turbulent eddy diffusivity additional to the background values.
You can select from:

Constant Only the background values will be applied.
Algebraic The coefficients are determined by algebraic equations
for the turbulent energy and the mixing length.

k-L The coefficients are determined by a transport equation for
the turbulent kinetic energy k and mixing length L.
k-epsilon The coefficients are determined by transport equations
for both the turbulent kinetic energy and the turbulent kinetic energy dissipation.

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Remark:
You do not need (can not) prescribe boundary conditions for the transport equations
used in the selected turbulence model. The underlying assumption is that the turbulence is mainly generated inside the model area and not transported into the model
area through the open boundaries. For very small area models this assumption might
be violated and a special add-on to the flow module can be provided to prescribe the
required boundary conditions.
In 3D-simulations the vertical turbulent eddy viscosity and turbulent diffusivity are computed
using a turbulence closure model. The four models differ in their prescription of the turbulent
kinetic energy, the dissipation of energy and/or the mixing length.

Constant eddy viscosity and diffusivity: you must specify background values that are used
in both (horizontal) directions.
Algebraic model: the first closure model uses an algebraic formula for k and L.

k depends on the (friction) velocities, whereas for the mixing length L a function following

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Bakhmetev (1932) is used. In the case of vertical density gradients, the turbulent exchanges
are limited by buoyancy forces and the mixing length L must be corrected. This correction
involves a so-called damping function. The approach is sufficiently accurate to be applied in
cases where weakly stratified flow conditions exist. See section 9.5.1 for full details.
k -L model: the second closure model is a first-order turbulence closure model.
In this model an identical approach is applied for the mixing length L. To find the turbulent
kinetic energy k a transport equation is solved. See section 9.5.2 for full details.
k -ε model: the third model is a k -ε model which is a second-order turbulence closure model.
Here, both the turbulent kinetic energy k and the turbulent kinetic dissipation ε are prescribed
by a transport equation. From k and ε the mixing length and the vertical turbulent eddy
viscosity value are determined. The mixing length is now a property of the flow, and in the
case of stratification no damping functions are needed. The eddy diffusivity is derived from
the eddy viscosity. See section 9.5.3 for full details.
Remark:
Both parameters, the vertical eddy viscosity and eddy diffusivity, are defined at the layer
interfaces. Therefore, when you plot or print these values you will obtain one value more
than the number of layers.
The value for both the horizontal eddy viscosity and the horizontal eddy diffusivity depends
on the flow and the grid size used in the simulation. For detailed models where much of the
details of the flow are resolved by the grid, grid sizes typically tens of metres or less, the values
for the eddy viscosity and the eddy diffusivity are typically in the range of 1 to 10 [m2 /s]. For
large (tidal) areas with a coarse grid, grid sizes of hundreds of metres or more, the coefficients
typically range from 10 to 100 [m2 /s]. Both coefficients are so-called calibration parameters;
their value must be determined in the calibration process.
The use of the uniform vertical eddy viscosity and eddy diffusivity coefficient depends on the
selected turbulence closure model:

If a constant turbulence closure model is selected the prescribed (constant) background

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values are applied.
In all other cases the uniform values are used as a background (minimum) value for the
turbulent contribution. The molecular viscosity and diffusivity are added to the turbulent
part.
In case of strongly stratified flow, a background vertical eddy viscosity may be needed to damp
out short oscillations generated by e.g. drying and flooding, boundary conditions, wind forcing
etc. Without this background eddy viscosity these short oscillations will only be damped in
the bottom layer. The layers behave as if they were de-coupled. The value suggested for the
background eddy viscosity depends on the application. The value must be small compared to
the vertical eddy viscosity calculated by the turbulence closure model. Our experience is that
for stratified estuaries and lakes a value of 10−4 to 10−3 [m2 /s] is suitable.

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Domain:

For the eddy diffusivity similar arguments hold as for the eddy viscosity with one exception.
Actually, a background eddy diffusivity is not necessary and will generate additional vertical
mixing of matter through the pycnocline. However, the access to this value is retained for
reason of compatibility with the eddy viscosity and for experimental purposes.

Parameter

Lower limit

Upper limit

Default

Unit

Horizontal eddy viscosity

0.0

100.0

10..0

m2 /s

Horizontal eddy diffusivity

0.0

1,000

10.0

m2 /s

Vertical eddy viscosity

0.0

100.0

1.0E-6

m2 /s

Vertical eddy diffusivity

0.0

1,000

1.0E-6

m2 /s

Ozmidov length scale

0.0

Max. number

0.0

Restriction:
Due to the manner in which the horizontal shear stresses containing cross derivatives
are numerically implemented (explicit integration) the, otherwise unconditionally stable,
numerical scheme for the viscosity term will become conditionally stable. Please check
the stability criterion in chapter 10.
4.5.7.3

Heat flux model

If you have switched on the Temperature process, you can specify how the exchange of heat
through the free surface is modelled.
Upon selecting the tab Heat flux model in the Data Group Physical parameters the window
given by Figure 4.35 is displayed.
In Figure 4.35 the Ocean heat flux model is selected. Depending on the selected heat flux
model parameters are displayed or not.

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Figure 4.35: Sub-data group Heat flux model

Heat flux model

You can select one of the following options:
No flux
Absolute flux, total
solar radiation

The background temperature is used throughout the model area.
The absolute temperature is computed. The relative humidity, air
temperature and the (short wave) solar radiation for a clear sky have
to be prescribed. The net atmospheric (long wave) radiation and the
heat losses due to evaporation and convection are computed by the
model.
Absolute flux, net solar The absolute temperature is computed. The relative humidity, air
radiation
temperature and the combined net (short wave) solar and net (long
wave) atmospheric radiation have to be prescribed. The terms related to heat losses due to evaporation and convection are computed
by the model.
Excess temperature
The heat exchange flux at the air-water interface is computed; only
the background temperature is required.
Murakami
The relative humidity, air temperature and the net (short wave) solar
radiation have to be prescribed. The effective back radiation, and the
heat losses due to evaporation and convection are computed by the
model. The incoming radiation is absorbed as a function of depth.
The evaporative heat flux is calibrated for Japanese waters.
Ocean
The relative humidity, air temperature and the fraction of the sky covered by clouds is prescribed (in %). The effective back radiation and
the heat losses due to evaporation and convection are computed by
the model. Additionally, when air and water conditions are such that
free convection occurs, free convection of latent and sensible heat
is computed by the model and added to the forced convection. This
model formulation typically applies for large water bodies.

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The absolute temperature models compute the heat fluxes through the water surface by considering incoming radiation, back radiation, evaporation and convection. Evaporation and
convection depend on air temperature, water temperature, relative humidity and wind speed.
When modelling the effect of a thermal discharge, it is often enough to compute the excess
temperature distribution and decay. Excess heat is transferred from the water surface to
the atmosphere by evaporation, long-wave radiation and convection. This total heat flux is
proportional to the excess temperature at the surface. The heat transfer coefficient depends
mainly on the water temperature and the wind speed.

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Remarks:
If you have selected a heat flux model which includes evaporation, you can specify if
the evaporated water should be taken into account. Specify Maseva = #Y# in Data
Group Additional parameters.
Precipitation and evaporation is an add-on of FLOW independent if you model temperature or not. See section B.6 for how you can use this add-on. If you use this add-on
together with the process Temperature, then the user-defined evaporation overrules the
computed evaporation from the heat flux model. The user-defined evaporated water is
always included in the continuity equation.
Global parameters for the heat flux models
You can define:

Water surface area

The water area exposed to wind in [m2 ]. Required for heat flux models 1, 2 and 3.

A secondary effect is included in the heat models by taking into account the surface area of
the water body exposed to the wind. Wind strongly affects the evaporation and convection
process. The value for the surface area can differ from the effective water surface in the
model. Its value depends on the model geometry and on the direction of the wind (Sweers,
1976). Effectively, the surface area can be regarded as a calibration parameter.
Sky cloudiness

The fractional blocking of the solar radiation by clouds in [%]. Required by heat flux models 1, 4 and 5.

The incoming solar and atmospheric radiations are affected by clouds. The Sky cloudiness
parameter describes the percentage of the solar radiation blocked by the clouds; 0 % refers
to clear sky condition whereas a value equal to 100 % implies that most of the solar radiation
will be absorbed by the atmosphere. Only 35 % (excluding the reflection) of the specified
solar radiation will reach the water surface. Consequently, due to increased absorption the
atmosphere will ultimately radiate more energy.
Secchi depth
Dalton number
Stanton number

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Required by heat flux models 4 and 5.
for evaporative heat flux. Required by heat flux models 4 and 5.
for heat convection. Required by heat flux model 5.

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Time dependent heat flux model input
Interpolation
The type of interpolation used for the time-series at intermediate time
instances. You can select either Linear or Block interpolation.
Open / Save
To open and read or save the time-series from or to an attribute file
with extension .
In the table you must specify time-series for the following parameters:

Incoming solar radiation for a clear sky in J/(m2 s) (only for heat flux model 1)
Net (short wave) solar radiation in J/(m2 s) (heat flux model 4)
Combined net (short wave) solar and net (long wave) atmospheric radiation in J/(m2 s)
(heat flux model 2)
Background temperature in ◦ C (Excess heat flux model)
Air temperature in ◦ C (all heat flux models except the Excess model)
Relative humidity in % (all heat flux models except the Excess model)
Fraction of the sky covered by clouds (in %) (Ocean heat flux model)

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The background temperature used in the excess temperature heat model is already prescribed in Data Group Physical parameters → Constants.
Domain:

Parameter

Lower limit

Upper limit

Default

Unit

Water surface

0.0

Max. Number

0.0

Sky cloudiness

0.0

100.0

0.0

Secchi depth

0.0

2.00

Dalton number

0.0

1.0

0.00130

Stanton number

0.0

1.0

0.00130

Temperature

0.0

60.0

0.0

◦

Humidity

0.0

100.0

0.0

Solar radiation

0.0

Max. Number

0.0

W/m2

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4.5.7.4

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Figure 4.36: Sub-data group Sediment, overall and cohesive sediment parameters

Sediment

Sediment transport offers the following functionalities (for details see chapter 11):

Cohesive sediment transport, including the effect of salinity on flocculation.
Non-cohesive suspended sediment (sand) transport.
Bedload transport, including effect of wave asymmetry.
Influence of waves and hindered settling.
Updating the bed-level and feedback to the hydrodynamics.
Up to 99 fractions of sand or combination of sand and mud.
Numerous sediment transport formulations

If you have switched on the Sediments process, you can specify the characteristics of the
(non-) cohesive sediments, the critical shear stresses for sedimentation and erosion (for cohesive sediments) and the initial sediment at the bed.
Upon selecting the tab Sediment in the Data Group Physical parameters the window given
by Figure 4.36 is displayed.
Open / Save

The sediment characteristics can be read from or saved to the file
<∗.sed>. See section B.9 for a detailed description.

Overall sediment data
Reference density for
In high concentration mixtures, the settling velocity of a single parhindered settling
ticle is reduced due to the presence of other particles. In order to
account for this hindered settling effect Richardson and Zaki (1954)
are followed. The reference density is a parameter in their formulation. See section 11.1.4.

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For sediment transport the Eckart relation is extended to include the
density effect of sediment fractions in the fluid mixture, see section 11.1.3. The specific density of each sediment fraction is part
of this formulation.
The thickness of the sediment above the fixed layer is calculated
by dividing the mass of sediment available at the bed by the user
specified dry bed density.
The settling velocity of the cohesive sediment.
Remarks:
The settling velocity has to be specified in mm/s in the GUI but
is written in [m/s] to the <∗.sed> file
In salt water cohesive sediment tends to flocculate to form sediment “flocs”, with the degree of flocculation depending on the
salinity of the water. This has been implemented, see section 11.2.1. Though the GUI does not support this formulation,
you can still edit the <∗.sed> file to use this functionality.

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Cohesive sediment
Specific density

Figure 4.37: Sub-data group Sediment, cohesive sediment parameters (continued)

Dry bed density

Settling velocity

Press Next to browse to the next cohesive input parameters, showing Figure 4.37.
For cohesive sediment fractions the fluxes between the water phase and the bed are calculated with the well-known Partheniades-Krone formulations (Partheniades, 1965):
Critical bed shear
stress for
sedimentation
Critical bed shear
stress for erosion

If the bed shear stress is larger than the critical stress, no sedimentation takes place. If the bed shear stress is smaller than the flux is
calculated following Partheniades-Krone, see section 11.2.3.
If the bed shear stress is smaller than the critical stress, no erosion
takes place. If the bed shear stress is larger than the flux is calculated following Partheniades-Krone, see section 11.2.3.

Space-varying shear stress files can be made with QUICKIN.
Press Next to browse to the next cohesive input parameters, showing Figure 4.38.
Sediment erosion rate
Initial sediment layer
thickness at bed

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Erosion parameter in the formulation of Partheniades-Krone, see
section 11.2.3.
The initial sediment layer thickness at the bed in metre.
Remarks:

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Figure 4.38: Sub-data group Sediment, cohesive sediment parameters (continued)

The initial bed composition should be specified at the cell centres. You can use QUICKIN with the Operations → Data in

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Cell Centre option on to prepare the file with space-varying initial sediment layer thickness at the bed.
GUI v3.39.25 and higher writes a new keyword (IniSedThick)
to the <∗.sed> file. The sediment now is in metre, before it
was in kg/m2 . Old <∗.sed> files will be converted by the GUI.

Non-cohesive sediment

If you have defined a non-cohesive sediment fraction, you have to specify the following parameters, see Figure 4.39.
Specific density

Dry bed density

Median sediment
diameter

Initial sediment layer
thickness at bed

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For sediment transport the Eckart relation is extended to include the
density effect of sediment fractions in the fluid mixture, see section 11.1.3. The specific density of each sediment fraction is part
of this formulation.
The thickness of the sediment above the fixed layer is calculated
by dividing the mass of sediment available at the bed by the user
specified dry bed density.
The settling velocity of a non-cohesive (“sand”) sediment fraction is
computed following the method of Van Rijn (1993). The formulation
used depends on the diameter of the sediment in suspension: See
section 11.3.1.
Remark:
The sediment diameter has to be specified in µm in the GUI
but is written in m to the <∗.sed> file.
The initial available sediment at the bed.
Remarks:
The initial bed composition should be specified at the cell centres. You can use QUICKIN with the Operations → Data in
Cell Centre option on to prepare the file with space-varying initial sediment layer thickness at the bed.
GUI v3.39.25 and higher writes a new keyword (IniSedThick)
to the <∗.sed> file. The sediment now is in metre, before it
was in kg/m2 . Old <∗.sed> files will be converted by the GUI.

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Figure 4.39: Sub-data group Sediment, non-cohesive sediment parameters

Domain:
Parameter

Lower limit

Upper limit

Default

Unit

Reference density

100.0

Max. Number

1600.0

kg/m3

100.0

4000.0

2650.0

kg/m3

Dry bed density

mud: 100.0
sand: 500.0

3000.0
3000.0

mud: 500.0
sand: 1600.0

kg/m3
kg/m3

Settling velocity

> 0.0

30.0

0.25

mm/s

Median sediment diameter

64.0

2000.0

200

µm

Critical shear stress for sedimentation

0.0

1000.0

N/m2

Critical shear stress for erosion

0.001

100.0

0.5

N/m2

Sediment erosion rate

0.0

1.0

0.0001

kg/(m2 s)

Initial sediment layer at bed

0.0

mud: 10.0
sand: 50.0

mud: 0.05
sand: 5.0

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Specific density

Remarks:
The settling velocity value is written in [m/s] to the file <∗.sed>.
The mean sediment diameter value is written in [m] to the file <∗.sed>.
4.5.7.5

Morphology

With the feedback of bottom changes to the hydrodynamic computation you can execute a full
morphodynamic computation. You can include the influence of waves by running this version
of Delft3D-FLOW in combination with the Delft3D-WAVE module. See section 11.6 for details.
Selecting the tab Morphology in the Data Group Physical parameters opens Figure 4.40.
Open / Save

The morphology characteristics can be read from or saved to the file
<∗.mor>. See section B.9 for a detailed description.

General

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Figure 4.40: Sub-data group Morphology

Update bathymetry
If you want to take into account the feedback of bottom changes on
during FLOW
the hydrodynamics, tick off this option.
simulation
Remark:
The use of this update option only affects the updating of the depth values (at ζ and
velocity points) used by flow calculations at subsequent time-steps; the quantity of sediment available at the bed will still be updated, regardless of the state of this flag.
Include effect of
You can include or neglect the effect of sediment on the fluid density
sediment on fluid
by setting this option accordingly.
density
For coarser non-cohesive material you can specify that, at all open inflow boundaries, the flow
should enter carrying all “sand” sediment fractions at their equilibrium concentration profiles.
This means that the sediment load entering through the boundaries will be near-perfectly
adapted to the local flow conditions, and very little accretion or erosion should be experienced
near the model boundaries.
Equilibrium sand
Tick off to use this option. When not activated the inflow concenconcentration profile at trations specified in Data Group Boundaries → Transport conditions
inflow boundary
will be used.
One of the complications inherent in carrying out morphological projections on the basis of
hydrodynamic flows is that morphological developments take place on a time scale several

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times longer than typical flow changes (for example, tidal flows change significantly in a period
of hours, whereas the morphology of a coastline will usually take weeks, months, or years to
change significantly). One technique for approaching this problem is to use a Morphological
time scale factor whereby the speed of the changes in the morphology is scaled up to a rate
that it begins to have a significant impact on the hydrodynamic flows.
Morphological scale
The above can be achieved by specifying a non-unity value.
factor
Remark:
The Morphological scale factor can also be time-varying, see section B.9.8. This feature
is not yet supported by the GUI. You have to edit the <∗.mor> file manually.

The implementation of the Morphological time scale factor is achieved by simply multiplying
the erosion and deposition fluxes from the bed to the flow and vice-versa by this scale factor, at
each computational time-step. This allows accelerated bed-level changes to be incorporated
dynamically into the hydrodynamic flow calculations.

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Frequently, a hydrodynamic simulation will take some time to stabilise after transitioning from
the initial conditions to the (dynamic) boundary conditions. It is likely that during this stabilisation period the patterns of erosion and accretion that take place do not accurately reflect the
true morphological development and should be ignored.
Spin-up interval before Specify a time interval (in minutes after the start time) after which the
morphological changes morphological bottom updating will begin. During this time interval all
other calculations will proceed as normal (sediment will be available
for suspension for example) however the effect of the sediment fluxes
on the available bottom sediments will not be taken into account.
Minimum depth for
In the case of erosion near dry points a threshold depth for computsediment calculation
ing sediment transport can be used, see section 11.6.2.
Sediment transport parameters

The following parameters are only relevant for non-cohesive sediments.
van Rijn’s reference
height factor

For non-cohesive sediment (e.g. sand), we follow the method of Van
Rijn (1993) for the combined effect of waves and currents, see section 11.3. The reference height formulation contains a proportionality
factor called van Rijn’s reference height factor.

Because of the more complex, partly explicit — partly implicit, erosive flux terms used for
“sand” type sediments it is not possible to use the simple source limitation technique used for
cohesive sediments. Instead, you must specify a Threshold sediment thickness.
Threshold sediment
thickness

At each time-step the thickness of the bottom sediments is calculated. If the remaining sediment thickness is less than the userspecified threshold and erosive conditions are expected then the
source and sink sediment flux terms, see Eq. (??), are reduced in
the following manner:
Estimated ripple height In case of waves, the wave related roughness is related to the estifactor
mated ripple height, see section 11.3.3.

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Multiplication (calibration) factors
The following parameters are only relevant for non-cohesive sediments.
In the case of erosion near a dry beach or bank, the standard scheme will not allow erosion
of the adjacent cells, even when a steep scour hole would develop right next to the beach.
Therefore a scheme has been implemented, where for each wet cell, if there are dry points
adjacent to it; the erosion volume is distributed over the wet cell and the adjacent dry cells.
Factor for erosion of
adjacent dry cells

The distribution is governed by a user-specified factor for erosion
of adjacent dry cells, which determines the fraction of the erosion
to assign (evenly) to the adjacent cells; if this factor equals zero,
the standard scheme is used; if this factor equals 1, all erosion that
would occur in the wet cell is assigned to the adjacent dry cells.
The reference concentration is calculated in accordance with Van
Rijn et al. (2000), see section 11.3.3.

Current-related
reference
concentration factor
Only Van Rijn (1993) and Van Rijn et al. (2004) compute explicitly a wave-related transport
component.

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Stotal = BED · Sbedload current + BEDW · Sbedload waves + SUSW · Ssuspended waves (4.11)

dDP S
= Stotal out − Stotal in + SUS · (Entrainment − Deposition)
dt

(4.12)

where Sbedload current , Sbedload waves , Ssuspended waves , Entrainment, and Deposition depend on
the sediment transport formula used. In most cases it holds Sbedload waves = 0 and Ssuspended waves =
0.
Current-related transport vector magnitude factor : —
Wave-related suspended transport factor : The wave-related suspended sediment transport is modelled using an approximation method proposed by Van Rijn (2001), see section 11.5.1.
Wave-related bedload transport factor : —

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Domain:
Parameter

Lower limit

4.5.7.6

Default

Unit

during

yes or no

yes

none

Include effect of sediment on
fluid density

yes or no

none

Equilibrium sand concentration
profile at inflow boundary

yes or no

yes

none

Morphological scale factor

0.0

1.0

Spin-up interval

0.0

720.0

min

Minimum depth for sediment
calculation

0.1

10.0

0.1

Van Rijn’s reference height

0.4

2.0

1.0

Threshold sediment thickness

0.005

10.0

0.05

10000.0

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Update bathymetry
FLOW simulation

Upper limit

Estimated ripple height factor

1.0

5.0

2.0

Factor for erosion of adjacent
dry cells

0.0

1.0

0.0

Current-related reference concentration factor

0.0

100.0

1.0

Current-related transport vector magnitude factor

0.0

100.0

1.0

Wave-related
transport factor

suspended

0.0

100.0

1.0

Wave-related bedload transport factor

0.0

100.0

1.0

Wind

When the Wind process is activated in Data Group Processes, see Figure 4.16, the tab Wind
is available in the Data Group Physical parameters. Selecting this tab displays Figure 4.41.
Wind fields can be specified as uniform but time dependent or as a space and time varying
wind (and pressure) field. In the Wind tab you can select:
Space varying wind
and pressure
Uniform

To define a space and time varying wind and pressure field. Open
the file with wind and pressure data.
To define a wind field that is time dependent but uniform in space.

Upon selecting Uniform you can either specify the wind data or read an attribute file.

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Figure 4.41: Wind definition window

Uniform wind

For a uniform wind you can specify:
Open
Save

Interpolation Type

Time-Series

To read an attribute file with a uniform but (potentially) time dependent wind field; file extension .
To save the manually defined or modified wind field to a file. If you
want to combine wind data read from a file and defined manually you
must first import the file and then add, delete or modify the imported
data; reversing this order will overwrite your manually defined data.
Time dependent data is specified at time instances called breakpoints; to determine the value at intermediate times you can apply a
linear or a block type of interpolation.
Specify the time breakpoints in [dd mm yyyy hh mm ss], the wind
speed in [m/s] and the wind direction in degrees (nautical definition).

The wind direction is defined according to the nautical definition, i.e. relative to true North and
positive measured clockwise. In Figure 4.42 the wind direction is about +60 degrees, i.e. an
East-North-East wind.
Remark:
The wind direction is measured (clockwise) starting from true North. East-North-East
wind thus has a direction of +67.5 degrees.
Domain:
Parameter

Lower limit

Upper limit

Default

Unit

Wind speed

0.0

100.0

0.0

m/s

Wind direction

0.0

360.0

0.0

degrees
North

Restrictions:

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North
Wind direction

West

East

South

Figure 4.42: Nautical definition of the wind direction

The time breakpoints must differ from the simulation start time by an integer multiple of
the time-step (see Data Group Time frame).

The first time breakpoint must be before or equal to the simulation start time, and the

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last time breakpoint must be equal or later than the simulation stop time (see Data
Group Time frame).
Time breakpoints must be given in ascending order.
Space varying wind and pressure

For a space varying wind and pressure you can specify:
Select file

Interpolation Type

To select an attribute file with space and time varying wind and pressure data. The file is not read.
Time dependent data is specified at time instances called breakpoints; to determine the value at intermediate times you can apply a
linear or a block type of interpolation.

Remarks:
The space varying wind and pressure selected in this sub-data group must be defined
on the hydrodynamic grid.
It is also possible to use space varying wind and pressure defined on an independent
wind grid. See section A.2.8.2 and section B.7 for details.
When using space varying wind and pressure, the input is applied at the interior of the
domain. On open boundaries this can cause a pressure gradient, which in turn causes
a water level gradient. To reduce this effect, it is possible to apply a pressure correction
on open boundaries. This functionality is described in section B.7.1.
4.5.7.7

Tidal forces
When the process Tidal forces is selected (see Figure 4.16), the tab Tidal forces is available
in Data Group Physical parameters. Selecting this tab Figure 4.43 is displayed.
You can select the components that are taken into account by the tidal force generating routine
by ticking off the check box. See section 9.9 for details of tide generating forces.

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4.5.8

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Figure 4.43: Sub-window Tidal forces

Numerical parameters

In the Data Group Numerical parameters you can specify parameters related to drying and
flooding and some other advanced options for numerical approximations.
Several drying/flooding procedures are available in Delft3D-FLOW, see chapter 10. By default
the water depth in each of the grid cell faces (velocity points) of a computational grid cell is
determined to decide if the flow should be blocked by a (temporary) thin dam. If the flow at
the four faces of a computational grid cell is blocked this grid cell is set dry. Note that this
does not guarantee the water depth at the grid cell centre (water level point) to be positive
definite. An additional check can be done on the water depth at the centre (water level point).
The bottom depth in the cell centre (water level point) is not uniquely defined, several options
are available. In combination with the water level in the cell centre it is determined if the cell
is being dried or flooded; see section 10.8 for more details on drying and flooding.
Click the Data Group Numerical parameters. This results in Figure 4.44. Note: if your model
is not 3D, or you have not modelled salinity or another constituent, then you will see less input
parameters.
You must select or define one or more of the following parameters:
Drying and flooding
check

Determine if you want to apply an additional check on the water
depth at the cell centres (water level points); or only a check at the
cell faces (velocity points).
Depth at grid cell faces You can either select (see also section 10.8.2):

Mean The depth at the cell face is the mean of the depths at the
cell corners (m,n) and (m,n+1).

Min The depth at the cell face is the minimum of the depths at
the water level points (m,n) and (m+1,n).

Upwind The depth at the u-velocity point is the depth at water
level point (m,n) if the u-velocity is larger than 0, the depth at
water level point (m+1,n) if the u-velocity is less than 0, and the
average if the u-velocity is 0.
Mor The Mor option is the same as Min.

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Figure 4.44: Data Group Numerical parameters

Remark:
Depth specified at grid cell centres (section 4.5.2.2) and Depth at grid cell faces is
Mean, can not be used together.
Threshold depth

The threshold depth above which a grid cell is considered to be wet.
The threshold depth must be defined in relation to the change of
the water depth per time step in order to prevent the water depth to
become negative in just one time step. This would result in iterations
in the computation and thus a larger computational time.
As a rule of thump you can use:

δ≥

2π|a|
∂ζ
2π|a|
∆t ≈
∆t =
∂t
T
N

(4.13)

∂ζ

Marginal depth

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where δ is the threshold depth, ∂t is a measure for the change of
the water level as a function of time with a as characteristic amplitude, T is the tidal period, ∆t is the time step of the computation
and N is the number of time steps per tidal period.
Example:
With a tidal amplitude of 2 m and time step of 1 minute (N = 720)
we find δ ≥ 0.017 m.
For the water level at the velocity points as default the mean value is
used. It is also possible to determine the water levels at the cell faces
with a so-called upwind approach: initially the water depth is the
bottom depth at the velocity point plus the water level at the velocity
point.
If this water depth is less than the marginal depth then:

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The water depth equals the bottom depth plus the water level at
(m,n) if the u-velocity is larger than 0.
The water depth equals the bottom depth plus the water level at
(m+1,n) if the u-velocity is less than 0.
The water depth equals the bottom depth plus the maximum of
the water levels at (m,n) and (m+1,n) if the u-velocity is 0.
The time interval used at the start of a simulation for a smooth transition between initial and boundary conditions.
In some cases, the prescribed initial condition and the boundary
values at the start time of the simulation do not match. This can
introduce large spurious waves that enter the model area. Subsequently, the wave will be reflected at the internal boundaries and
along the open boundaries of the model until the wave energy is
dissipated completely by bottom or internal (eddy viscosity) friction
forces. These reflections can be observed as spurious oscillations
in the solutions and they will enhance the spin-up (warming-up) time
of the model. To reduce this time, a smooth transition period can
be specified, during which the boundary condition will be adapted
gradually starting from the prescribed initial condition value.

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Smoothing time

For the spatial discretization of the horizontal advection terms, three options are available in
Delft3D-FLOW. The first and second option use higher-order dissipative approximations of
the advection terms. The time integration is based on the ADI-method. The first scheme
is denoted as the Cyclic method; see Stelling and Leendertse (1992). The second scheme
is denoted as the WAQUA-scheme, see Stelling (1984) and Stelling and Leendertse (1992).
The WAQUA-scheme and the Cyclic method do not impose a time step restriction. The third
scheme can be applied for problems that include rapidly varying flows for instance in hydraulic
jumps and bores (Stelling and Duinmeijer, 2003). The scheme is denoted as the Flooding
scheme and was developed for 2D simulations with a rectilinear grid of the inundation of dry
land with obstacles such as road banks and dikes. The integration of the advection term is
explicit and the time step is restricted by the Courant number for advection. See section 10.4.1
for more details.
Advection scheme for
momentum

Select the type of numerical method for the advective terms in the
momentum equation.
Currently, the following numerical schemes are supported:

the Cyclic scheme
the Waqua scheme
the Flood scheme

Default the standard Cyclic method is applied; see chapter 10.

For the Flooding scheme the accuracy in the numerical approximation of the critical discharge
rate for flow with steep bed slopes, can be increased by the use of a special approximation
(slope limiter) of the total water depth at a velocity point downstream, see section 10.8 for
details.
Threshold depth for
critical flow limiter
Advection scheme for
transport

For the Flood scheme you have to specify a threshold depth which
determines how the water depth is calculated.
Select the type of numerical method for the advective terms in the
advection-diffusion equation for constituents.
Currently, two numerical schemes are supported:

theCyclic method (accurate, but positive definite results are not

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guaranteed).
Van Leer-2 method (less accurate, but positive definite results
guaranteed).

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Relaxation factor
QH-forcing

Default the standard Cyclic method is applied; see chapter 10. However, when a monotonous solution (no over- and undershoots) in the
horizontal is required, then the slightly less accurate but monotonous
Van Leer-2 method can be applied (see chapter 10). It might still
be necessary to remove wiggles generated by the central difference
scheme in the vertical.
Remark:
The continuity equation is solved iteratively, see section 10.4.4.
The default number of iterations is 2. With the keyword and
value Iter = #, where # is the required number of iterations,
you can specify the number of iterations. You can add this keyword and value manually to the MDF-file or specify them under
Additional parameter, see section 4.5.11.
This factor only applies if QH-forcing is used at open boundaries. In
some cases, when discharge fluctuates quickly, under-relaxation is
necessary to stabilise the forcing by a QH-relation. This parameter in
the range between 0 and 1 specifies the amount of under-relaxation.
If no relaxation is required, this parameter should be set to 0.
Activate or de-activate a Forester filter in the horizontal or in the vertical direction.
In the horizontal direction numerical diffusion is added in points where
the quantity (concentration) is negative. The diffusion is two-dimensional
along σ -planes. The horizontal Forester filter acts on the salinity, the
temperature and the concentrations of dissolved substances, including suspended sediments. The horizontal Forester filter is not applied to the spiral motion intensity, as this quantity can be negative
by its nature.
In the vertical direction the solution is made monotone for salinity and
temperature only; i.e. the vertical filter is not applied to constituents
or suspended sediments. Wiggles, generated by the central differences in the vertical, are smoothed.
When the Forester filter is applied in both directions, the horizontal
filter is applied first, followed by the filter in the vertical direction.
Remark:
In 3D sediment transport computations, see section B.9, small
negative sediment concentrations (smaller than 1.10−3 kg/m3 )
can be found. These negative concentrations can be suppressed
by applying a horizontal Forester filter. However, the penalty
can be a substantially larger computational time.
Activate or de-activate an anti-creep correction. σ co-ordinates have
a slight disadvantage in case large bottom gradients exist in the
model. Owing to truncation errors, artificial vertical diffusion and artificial flow may occur in this case. A counter measure (a so-called
anti-creep approach) can be activated to suppress this phenomenon.

Forester filter

Correction for sigma
co-ordinates

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Domain:
Lower limit

Drying and flooding check

Upper limit

Default

Unit

At cell faces always; optional at
cell centres

at both

Depth specified at

grid cell corners or centres

cell corners

Depth at grid cell centres

Max, Mean, Min

Max

Depth at grid cell faces

Mean, Min, Upwind, Mor

Mean

Threshold depth

0.0

0.1

Marginal depth

-999.999

Smoothing time

0.0

n.a.

Advection scheme momentum

Cyclic, Waqua, Flood

Threshold depth flow limiter

0.0

Advection scheme transport

Cyclic, Van Leer-2

Relaxation factor QH

0.0

Forester filters

Parameter

min

Cyclic

none

0.0

Cyclic

none

0.0

on or off

off

none

on or off

off

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0.0

Correction
ordinates

for

sigma

co-

1.0

Remark:
A warning will be issued if the Threshold depth exceeds 1.0 m.
4.5.9

Operations

Upon selecting the Data Group Operations the sub-window of Figure 4.45 is displayed. The
tab Dredging and dumping is only available if the Sediments process has been selected and
the man-made process Dredging and dumping has been switched on.
4.5.9.1

Discharge

In Delft3D-FLOW intake stations and waste-water outfalls can be considered as localised discharges of water and dissolved substances. A discharge (or source) in the model domain is
characterised by a name which serves as identification, and its position in the grid (respectively m, n and k). If the discharged effluent is to take place at one point in the vertical, then
the layer number k has to be specified. However, if the discharged flow is to be distributed
uniformly over all layers (taking into account the layer thickness), then the layer number K
must be set to 0.
In addition to the discharge rate the concentration of the constituents released and the temperature and/or the salinity, depending on the selections made in the Data Group Processes
must be specified.
Upon selecting the tab Discharges the sub-window of Figure 4.45 is displayed.

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Figure 4.45: Data Group Discharges

Remarks:
You can model a river as an open boundary or as a discharge.
The discharge rate is communicated to the water quality and particle tracking modules
WAQ and PART, respectively, but not the concentrations, temperature or salinity. These
quantities are computed in the WAQ and PART module in combination with the other
water quality processes.
The various input items you can select are discussed below.
Add

To Add a discharge either:

Click Add.
Specify the grid indices and the layer of the release point, i.e. (M,
N, K). K only if you have a 3D model.

Use the Visualisation Area window.
and
Delete

Specify the name of the discharge in the Name input field.
To Delete a discharge either:
Select the discharge to be deleted in the list box.
Click Delete.
or

Open/Save

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Use the Visualisation Area window.
Open or save the discharge data to attribute files; the locations to a

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file with extension , the discharge rates to a file.
Remark:
If you want to combine discharges read from an attribute file and inserted manually you
must read the file first and then add the manually defined discharges. In reverse order
the manually defined discharges are overwritten by those of the file.
Type

The discharge can be of type:

Normal: the discharge rate is released without taking specific
aspects into account.

Momentum: the momentum of the discharge is taken into ac-

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count. When prescribing the data the momentum and its direction relative to the North must be specified; for more details see
below under specify v -direction.
Walking: the discharge moves to the nearest wet grid cell if the
cell in which the discharge is released becomes dry. It moves
back to its original position when the grid cell is flooded again.
In-out: intake and outlet are on different locations. The intake
and outlet discharge rates are the same; the concentration of
a constituent at the outlet equals the concentrations at the inlet
plus the user-defined concentration (when applicable).

Interpolation

The interpolation of time dependent input data can be either

Linear : intermediate values are determined by linear interpolation.

Block : the last value is repeated until the next value is defined.

Outlet location

Edit data

You define the grid indices (M, N, K) of the outlet related to the just
defined inlet. These indices are only required and accessible for the
discharge Type = In-out.
To specify the discharge rate and the concentration of the discharged
substances. Upon selecting Edit data a sub-window is displayed,
see Figure 4.46.

The time dependent data are defined at time breakpoints and their intermediate value is determined by either linear or block wise interpolation as defined under Interpolation. Depending
on the selections made in the Data Group Processes you must specify more or less quantities.
In the most complete case you must specify:
Time
Flow

v -magnitude
v -direction

Date and time of the time breakpoints.
The discharge rate in [m3 /s].
Remark:
A positive rate indicates discharging into the model, except for
an In-out discharge: a positive rate means withdrawal at the
intake. The same amount of water is discharged into the model
at the outlet.
The speed with which the discharge is released in [m/s]. Only for
discharge Type = Momentum.
The direction in which the momentum is delivered to the flow. The
direction is defined similar to the wind direction, i.e. measured (clockwise) from the North. Only for discharge of Type = Momentum.

The momentum released to the flow due to a discharge is distributed over the velocity points

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Figure 4.46: Sub-window to define the discharge rate and substance concentrations

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that bound the quadrant in which the discharge is released.

Example: the momentum of a discharge released in the first quadrant as seen from the discharge location (water level point), is decomposed over the u- and v -velocity point with grid
indices (m, n). The momentum of a discharge released in the third quadrant is decomposed
over the u- and v -velocity points with grid indices of respectively, (m − 1, n) and (m, n − 1),
see Figure 4.47. The mass (of water and constituents) is released in the (water level) point
with grid indices (m, n).
North

West

East

South

(a) Direction of the discharge with momentum
vector.

(b) The ξ - and η -components of the discharge
momentum vector are shifted to the downstream velocity points.

Figure 4.47: Decomposition of momentum released by a discharge station in (m, n)

Salinity
Temperature
Pollutants and
sediments

The salinity concentration in [ppt]. Only if Salinity is selected in the
Data Group Processes.
The temperature of the discharge in [◦ C]. Only if Temperature is selected in the Data Group Processes.
The concentration of the constituents released in [kg/m3 ]. Only if Pollutants and/or Sediments are defined in the Data Group Processes.

Remarks:
Layer 1 corresponds to the surface layer.

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If the discharge is to be distributed uniformly over the layers, you must enter K = 0.
A positive discharge represents an inflow into the model area; a negative discharge
represents an outflow from the area; for Type = Normal, Walking and Momentum.

For Type = In-out, a positive discharge represents withdrawal at the intake. The same
amount is an inflow at the outlet. Furthermore, the specified concentration is added to
the concentration of the water withdrawn.
A discharge can be located in an area that becomes temporarily dry during the simulation. In such a case there will be no intake, unless you have specified the discharge to
be of Type = Walking.
Walking discharges move to the nearest wet grid cell by looking at the steepest descent
of the surrounding bathymetry.
Domain:
Lower limit

Upper limit

Default

Unit

Location

Anywhere in the grid, within the computational domain
and not at the model boundaries.

Flow

-10,000

Parameter

0.0

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+10,000

m3 /s

v -magnitude

0.0

100.0

0.0

m/s

v -direction

-360.0

360.0

0.0

degree

Salinity

0.0

100.0

0.0

ppt

Temperature

0.0

60.0

0.0

◦

Concentration

0.0

10,000

0.0

kg/m3

Restrictions:
The discharge name must be non-blank, and contains up to 20 characters.
The discharge must be located within the grid enclosure.
The number of discharges is limited to 5000, including the automatically generated
discharges when using bubble screens, see section B.22.4.2.
If discharges are specified both through an attribute file and interactively, then the attribute file must be read first. Reversing this order will overwrite the interactively defined
discharges.
The time breakpoints specified for time-series must differ from the simulation start time
by an integer multiple of the time-step (Data Group Time frame).
The first time breakpoint must be before or equal to the simulation start time, and the
last time breakpoint must be equal or later than the simulation stop time (see Data
Group Time frame).
Time breakpoints must be given in ascending order.

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Figure 4.48: Sub-data group Dredging and dumping

Figure 4.49: Sub-window for Monitoring locations

4.5.9.2

Dredging and dumping

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When sediments are modelled and the man-made process Dredging and dumping is switched
on (see Data Group Processes), the tab Dredging and dumping is available, see Figure 4.48.
Click Select file and specify the file <∗.dad> with dredging and dumping data.
Remark:
See the QUICKIN User Manual on how to define dredging and dumping areas.
4.5.10

Monitoring

Computational results can be monitored as a function of time by using observation points,
drogues or cross-sections. Monitoring points are characterised by a name and the grid indices
of its location in the model area.
4.5.10.1

Observations

Observation points are used to monitor the time-dependent behaviour of one or all computed
quantities as a function of time at a specific location, i.e. water elevations, velocities, fluxes,
salinity, temperature and concentration of the constituents. Observation points represent an
Eulerian viewpoint at the results. Observation points are located at cell centres, i.e. at water
level points. Upon selecting the data and sub-data group Monitoring → Observations the
sub-window of Figure 4.50 is displayed.
You can apply one or more of the following options:
Add

To Add an observation point either:
Click Add.
Replace the name “-Unnamed-” by a useful name in the Name
input field.
Specify the grid indices of the observation point, i.e. (m, n).
or

Delete

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To Delete an observation point either:

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Figure 4.50: Sub-window for Observation points

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Select the observation point to be deleted in the list box.
Click Delete.

Open

Save

Use the Visualisation Area window.
Open and read observation points defined in an attribute file.
Remark:
If you want to combine observation points read from an attribute
file and inserted manually you must read the file first and then
add the manually defined observation points. In reverse order the manually defined observation points are overwritten by
those of the file.
Save the observation points defined in an attribute file with extension
.

The domain and restrictions for Observation points, Drogues and Cross-sections are very
similar and are discussed at the end of this section.
4.5.10.2

Drogues

Drogues are used to monitor the path of a particle moving with the flow. In the horizontal:
drogues can be released anywhere in the grid, this means you can release them at fractional
grid cell positions. In the vertical: drogues are released in the surface layer. Drogues are only
transported due to the velocities in the surface layer. There is no diffusion or random process
involved. When wind applies, the wind affects the velocities in the surface and thus the path
of drogues. You can release and recover them at any time during the simulation (provided the
time complies with the restrictions for time instances).
Upon selecting the data and sub-data group Monitoring → Drogues the sub-window of Figure 4.51 is displayed.
You can apply one or more of the following options:
Add

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To Add a drogue either:

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Figure 4.51: Sub-data group Monitoring → Drogues

Click Add.
Replace the name “-Unnamed-” by a useful name in the Name
input field.
Specify the grid indices of the drogue release point, i.e. (m, n).

Delete

Use the Visualisation Area window.
Remark:
Drogues can be released inside grid cells, i.e. their grid indices
M and N can have fractional values. When using the visualisation area you can only specify release points at the grid centres;
so if other fractional values are required you have to specify
them manually.
To Delete a drogue point either:
Select the drogue to be deleted in the list box.
Click Delete.

Open

Save

Use the Visualisation Area window.
Open and read drogues defined in an attribute file.
Remark:
If you want to combine drogues read from an attribute file and
inserted manually you must read the file first and then add the
manually defined drogues. In reverse order the manually defined drogues are overwritten by those of the file.
Save the drogues defined in an attribute file with extension .

The domain and restrictions for Drogues, Observations points and Cross-sections are very
similar and are discussed at the end of this section.

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4.5.10.3

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Figure 4.52: Sub-data group Monitoring → Cross-Sections

Cross-sections

Cross-sections are used to store the sum of computed fluxes (hydrodynamic), flux rates (hydrodynamic), fluxes of matter (if existing) and transport rates of matter (if existing) sequentially
in time at a prescribed interval. A cross-section is defined along a constant m- or n- grid index
and it must include at least two grid points. To define a cross-section, you must specify an
arbitrary section name, the begin indices (M1, N1) and end (M2, N2) indices of the section.
Upon selecting the data and sub-data group Monitoring → Cross-sections the sub-window of
Figure 4.52 is displayed.
You can apply one or more of the following options:
Add

To Add a cross-section either:

Click Add.
Replace the name “-Unnamed-” by a useful name in the Name
input field.
Specify the grid indices (M1, N1) and (M2, N2).

Delete

Use the Visualisation Area window.
Remark:
Cross-sections typically extent over more than just one grid
cell, so you have to specify their start and end point.
To Delete a cross-section either:
Select the cross-section to be deleted in the list box.
Click Delete.
or

Open
Save

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Use the Visualisation Area window.
Open and read cross-sections defined in an attribute file.
Save the cross-sections in an attribute file with extension .

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If you want to combine cross-sections read from an attribute file and inserted manually you
must read the file first and then add the manually defined cross-sections. In reverse order the
manually defined cross-sections are overwritten by those of the file.
All cross-sections must be saved in an attribute file upon leaving the sub-data group.
Domain:
Parameter

Lower limit

Upper limit

Default

Unit

Location

Anywhere in the grid, within the computational domain
and not at the model boundaries, i.e. 2 ≤ M ≤ Mmax−1;
2 ≤ N ≤ Nmax−1.

4.5.11

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Restrictions:
The release time and the recovery time of drogues must comply with the definition of
time parameters.
Drogues must be released in an active grid point; this point may become dry during the
computation.
A cross-section must extend over at least two grid points.
If observation points are read from an attribute file and defined interactively, the file must
be read first; reversing the order will overwrite the manually defined observation points.
When saving the results as time-series, you have to define at least 2 obsservation
points.
When using cross-sections, you should define at least 2 sections.
Additional parameters

Through the use of an Additional parameter you have access to additional functionalities that
are not yet fully supported by the FLOW-GUI. The option of Additional parameters has been
introduced to be more flexible in providing special functionality in the computational code
without changing the FLOW-GUI. After thorough testing it will be released to all users. If you
have access to an option, you can specify the required parameters in a separate input file.
Upon selecting this data group Figure 4.53 is displayed.

Each Additional parameter is characterised by a keyword and a value:
Remarks:
Keywords are CASE-sensitive!
The value is often the name of an attribute file and must be enclosed between #’s.
See Appendix B for full details of the currently available Add-ons, their keywords, values, file
format and file contents.
Example:
Keyword

Value

Fillwl

#ex-001.lwl#

Iter

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Figure 4.53: Data Group Additional parameters

The first keyword refers to local weirs and the value is the filename in which the location and
other properties of the local weir(s) are defined; for details see section B.3.
The second keyword redefines the number of iterations used when computing the continuity
equation to be 4 (instead of the default value 2); for details see section A.1.
4.5.12

Output

In the Data Group Output you can specify which computational results will be stored for further
analysis or for other computations and which output shall be printed. Though the printing
option is hardly used it is a useful option when numerical output values are required.
Before defining the various input fields we want to explain in short the use of the various data
files used to store the results.
Delft3D modules use one or more Map, History, Communication and Restart files to store the
simulation results and other information needed to understand and interpret what is on the
files:
Maps are snap shots of the computed quantities of the entire area. As you (can) save all
results in all grid points a typical Map file can be many hundreds of MB large. So typically
Map results are only stored at a small number of instances during the simulation.
In a History file you store all results as function of time, but only in the specified monitoring
points. The amount of data is usually much smaller than for a Map file, and you typically store
history data at a small time interval to have a smooth time function when plotting the results.
In the Communication file you store data required for other modules of Delft3D, such as the
hydrodynamic results for a water quality simulation or the wave forces for a wave-current interaction. As the results must be stored in all grid points a Communication file can typically be
as large as or even larger than a Map file. So, you only store the results in the Communication
file as far as needed for the other simulations. For water quality simulations you typically store
the results of the last day or a (couple of) tidal cycles and use this data cyclic to make a water

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Figure 4.54: Sub-data group Output storage

quality simulation over many days or weeks.

In order not to waste computing time you can restart a simulation at a predefined time of a
previously executed simulation. For this you specify the restart interval at which all information
required to restart the simulation, are stored in a so-called Restart file. Typically, you select a
large restart interval in order not to waste disk space.
Remark:
The restart file is not platform independent. This means you can not use directly, i.e.
without some kind of conversion, a restart file from a simulation executed on another
hardware platform. You can also restart from a map-file which is platform independent.
Click the Data Group Output.

The data group Output is organised in three sub-data groups:

Storage, to define the time intervals to various file used.
Print, to define if, when and which data will be printed.
Details, to make a selection of all possible data to be stored in the files or to be printed.

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Storage
The sub-data group Output storage is displayed in Figure 4.55.
In the top of the Output storage sub-window the simulation start and stop time and the timestep used in the simulation are displayed for your convenience, but they cannot be changed
in this data group (see the Data Group Time frame).
You can apply one or more of the following options:

Store history results
History interval

Date and time to start storing the results in the Map file.
Date and time to stop storing the results in the Map file.
Time interval, in minutes, to write the Map file.

Store map results
Start time
Stop time
Interval

Time interval, in minutes, to write the History file for the whole simulation.

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4.5.12.1

Store communication file
Start time
Date and time to start storing the results in the Communication file.
Stop time
Date and time to stop storing the results in the Communication file.
Interval
Time interval, in minutes, to write the Communication file.
Write restart files
Restart interval

Time interval, in minutes, to write the Restart file.

Perform Fourier analysis
Fourier Analysis
To activate the Fourier analysis on computational results. Upon ticking off this option you can select a file with the time period and the
frequencies you want to apply, see below for a short description and
section A.2.30 for details of the file format.
For large scale tidal flow models, Delft3D-FLOW is equipped with
a facility to perform online Fourier analysis on computational results.
This enables the generation of computed co-tidal maps. These maps
can be compared with co-tidal maps from literature, a very convenient way to check if the tidal wave propagation is simulated correctly by the model. Upon selecting Fourier analysis you specify
the time period to use, the variable(s) to analyse, the layer number,
the frequencies to use and some other more special items (see Appendix A). When you specify a zero frequency the minimum, mean
and maximum level of the variable is computed in the model area
over the specified time period. You can select one or more of the
following parameters:

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Water level.
Velocity components.
Mass fluxes of water.
Temperature.
Salinity.
Constituent(s).

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This option creates by default output in ascii format. The output format can be switched to NetCDF by means of the FlNcdf keyword
under Additional parameters. For spherical models we recommend
the NetCDF format since the latitude and longitude are written to the
ascii file with only three digits behind the decimal point.
View results during the simulation
Online visualisation
When selecting this option you can inspect the results during the
computation.

The option of Online visualisation lets you monitor the results during the simulation as an
animation. You can select the type of parameter displayed, the type of view used, such as
iso-lines and vector plots in plain view per layer, or as cross-section, and per layer. You can
store the results to file and run this file afterwards as an animation. During the simulation
you can change your selection of parameter(s) displayed. Online animation is a very powerful
tool to let you inspect the behaviour of your model; this will help you to see anomalies in the
results much better and in a much earlier stage than when using plots and figures.

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Built-in coupling with D-Water Quality
Export WAQ input
When continuing with the Water Quality modules, you can either couple the com-file after the FLOW simulation has ended, or do it via the
built-in option.
The D-Water Quality input files can either be generated using a coupling program that runs
concurrently with the Delft3D-FLOW simulation or they can be written by Delft3D-FLOW directly. The latter approach is the preferred approach (i.e. the built-in option). See section B.18
for details of the file format.
Export WAQ input window

In the top of the Output storage sub-window, frame WAQ simulation times (Figure 4.55), the
start and stop time and the time-step used for hydro-morphodynamic simulation are displayed
for your convenience, but they cannot be changed in this window (see the Data Group Time
frame).
Store results for WAQ

To store results for use in D-Water Quality you can edit the following options:
Start time
Stop time
Time step [min]

Date and time to start storing the results in files suitable for D-Water
Quality.
Date and time to stop storing the results in files suitable for D-Water
Quality.
Time interval, in minutes, to write files suitable for D-Water Quality.

In the frame WAQ aggregation you can specify the horizontal aggregation and the vertical
aggregation.

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Figure 4.55: Sub-data group Output → Storage → Edit WAQ input

Horizontal aggregation
Horizontal aggregation When selecting this option you can select a file defining the horizontal aggregation. This file can be made with the program D-Waq
DIDO.
To make a horizontal aggregation with the program D-Waq DIDO, save first the MDF-file without a check on Use horizontal aggregation. Now a hydro-morphodynamic simulation without
horizontal aggregation could be made. Start the program D-Waq DIDO and load the just
saved MDF-file, define your horizontal aggregation (see DIDO UM (2013)). Save the aggregation file in D-Waq DIDO and select this file in the FLOW-GUI. Go to data group Output →
Storage → Edit WAQ input, check mark Use horizontal aggregation and select the just saved
aggregation file.

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Vertical aggregation
For convenience the number of layers in the hydrodynamic simulation is given. You are able
specify the number of layers needed for the D-Water Quality simulation. If this number is
less then the number of hydrodynamic layers you have to specify which layers should be
aggregated to one WAQ layer.
Example: In the example 5 WAQ layers with aggregation “1 2 2 3 2” in table # aggr. FLW layers
are specified, which means that hydrodynamic layers 2/3, 4/5, 6/7/8 and 9/10 are aggregated
(see Figure 4.55).

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Remarks:
No Map, History, Communication or Restart file is written if you set the interval to write
the data equal to zero. When verifying the MDF-file a warning will be issued that the
time definition is not correct and that the corresponding file will not be created. If you
did not want to create this file, you can ignore this warning.
By default the start time to store the hydrodynamic results is used as the simulation
start time of the far- and mid-field water quality scenarios using these hydrodynamic
results.
Drogues are written to a separate drogue-file for each time step between the release
and recovery time. You can not specify the interval to write the drogue-file.
Domain:

Parameter

Lower limit

Date and time

Interval

Upper limit

Default

Unit

Reference date

Simulation
date and time

Valid
date and
time

0.0

0.00

minutes

Restriction:
The start and stop time must differ an integer multiple from the Reference date and
the time interval for storing results must be an integer multiple of the Time step, both
specified in the Data Group Time frame.
4.5.12.2

In the sub-data group Output → Print you can specify which results will be printed. The
selected results are printed to a file; the name of the file is composed using the prefix of the
name of the MDF-file: .
Upon selecting the sub-data group Output → Print a sub-window is displayed, see Figure 4.56.
You can apply one or more of the following options:
Print history results
Start time
Stop time
Interval

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Date and time to start writing the history data to a print file.
Date and time to stop writing the history data to a print file.
Time interval, in minutes, to write the history data to a print file.

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Figure 4.56: Sub-data group Output → Print

Print Map Results
Add
Delete

Add the map time, specified in the input field below the list box, to
the list of time instances to be written to the print file.
Select a time instance from the list box and press Delete to remove
a time instance from the list box.

A warning is issued if the maximum number of time instances is reached. The print times
may be specified in ascending order; the computed water elevations, flows and transported
quantities at all points are stored in an ASCII-formatted file for printing.
4.5.12.3

Details

In the sub-data group Output → Details you can make a selection of all possible data to be
stored in the files or selected for printing. Upon selecting the sub-data group Figure 4.57 is
displayed.
By ticking the check boxes you can specify which items you want the program to store on file
or to print and which not.

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Figure 4.57: Output Specifications window

Figure 4.58: File drop down menu

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Save the MDF and attribute files and exit
To save the MDF-file or any of the attribute files:
Click File in the menu bar of the FLOW-GUI window and select any of the Save or Save
As options, see Figure 4.58.
For saving the files and exiting the FLOW-GUI only the last five options in the file drop down
menu are relevant.
Select:

Save MDF to save the MDF-data under its current name.
Save MDF As to save the MDF-data under a new name.
Save All to save all attribute data in the current attribute files.
Save All As to save all attribute data under a new name.
Exit to exit the FLOW-GUI and return to the Hydrodynamics window.

Upon selecting Save MDF or Save MDF As the MDF-file is save with a reference to the
attribute files as they existed at the time you started the edit session or after the last save
command. Changes to attributes are ignored if you have not explicitly saved them. These
Save MDF and Save MDF As options allows you to ignore some or all of the changes you
have made to some or all attribute data and restore the last saved situation. The non-saved
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If you want to save the changes to the attribute files as well, you must select Save All or Save
All As. Existing files are overwritten when you select Save All; you are requested to specify
a filename if the attribute file does not yet exist. With Save All As you must specify a (new)
filename for all the files, including the MDF-file, which must be saved.
To exit the FLOW-GUI:
Click File → Exit.

If all data items, including the MDF-file, have been saved, the FLOW-GUI is closed and the
Hydrodynamics (including morphology) window of Delft3D-MENU is redisplayed.
However, if not all data items have been saved yet a list of all non-saved (attribute) data
will be displayed and you can select for each non-saved data item the required action, see
Figure 4.59. In this case none of the data items nor the MDF-file itself has been saved yet.
Select one of the options displayed:
Yes
YesAll
No
NoAll
Cancel

Save the first unsaved data item, request for a filename if not yet
defined and proceed to the next unsaved data item.
Save all unsaved data items and request a filename if not yet defined.
Don’t save the first unsaved data item; proceed to the next unsaved
data item.
Exit without saving any unsaved data.
Abort this Exit action and return to the FLOW-GUI.

After you have worked through all unsaved data items the FLOW-GUI will be closed and the
Hydrodynamics (including morphology) window of Delft3D-MENU will be displayed.

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Figure 4.59: Save changes window

4.7

Importing, removing and exporting of data

When starting a scenario definition session from an existing MDF-file, all attribute files are
imported automatically. If the reference to an attribute file does not exist, or if you wish to
apply a different attribute file you can apply the Open or Select file option.
Warnings:
If you want to combine attribute data from an existing file with manually defined data,
you must open the existing data before you add new data items.
If you want to concatenate data items from two files you must do so offline with your
favourable editor.
The reference to an empty attribute file (because you have deleted all data items) is automatically removed from the MDF-file upon saving the MDF-file.
Most attribute files are ASCII-files and free formatted; you are referred to Appendix A for
details on their format and contents.

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5 Tutorial
Introduction – MDF-file and attribute files
In this Tutorial we will guide you through the process of creating a simple example of a flow
simulation. All information for a flow simulation, also called scenario, is stored in an input
file, also known as Master Definition Flow file (MDF-file). However, before starting this input
definition process we want to explain in short the basics of a model definition, the structure of
an MDF-file and the basic steps you are supposed to execute.

To execute a flow simulation for a specific area we need various kinds of information, such
as the extent of the model area, (i.e. both the boundary between wet and dry areas and
the location of the open boundaries where water level or flow conditions are prescribed), the
bathymetry, geometrical details of the area such as breakwaters, structures, discharges and
the definition of which and where results of the simulation need to be stored for later inspection
or for other simulations. Finally, a numerical grid must be defined on which all location related
parameters are being defined. So, the basic steps that precede the definition of an input file
can be summarised as:

Selection of the extent of the area to be modelled.
Definition of location and extent of open boundaries and the type of boundary conditions

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5.1

to be prescribed, i.e. water level, velocities or discharges.
Definition of the land(-water) boundary.
Generation of a numerical grid.
Generation of the bathymetry defined on the numerical grid.
Definition of many different grid related quantities, such as open boundaries, monitoring
points, discharge locations, release points of drogues.
Definition of the time frame of your scenario, i.e. start and stop time and various time
functions, such as the open boundary conditions, wind speed and direction, discharges
and salinity concentrations or other substances transported by the flow.

Most activities, but the last two, must be executed before starting the FLOW Graphical User
Interface (GUI). They result in most cases in one or more files that are to be located in the
project directory to be defined when starting the project (see chapter 8). The project directory
is also referred to as the working directory. The first two steps are based on experience
in solving similar problems and on engineering judgement, no tools are available to support
these steps others than (GIS-based) maps and (digitised) charts.
Delft3D supports the use of a rectilinear, a curvilinear and a spherical grid. Rectilinear and
spherical grids are generated automatically given the grid dimensions and sizes, and no tool
is required. To generate a curvilinear grid you can use the grid generator program RGFGRID,
provided with Delft3D. To generate a curvilinear body fitted grid you need a file with the land
boundary and preferably the bathymetry. The land boundary is obtained from digitising a map
or from GIS and the bathymetry is obtained upon using the tool QUICKIN. For details you
are referred to the User Manuals of RGFGRID and QUICKIN. For the file formats of the land
boundary, the bathymetry and other files, see Appendix A. For this tutorial these files are
provided.
The data of the land boundary, the bathymetry and the numerical grid, but also information
on boundary conditions, discharges and grid related quantities such as monitoring points,
discharges etc. are stored in separate, so-called attribute files. In the MDF-file only a reference
is made to these files instead of including all data in the MDF-file itself. The big advantage of
using attribute files is that the data can be used in many scenarios but is stored only once on
the system disks.

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In this tutorial we provide an existing MDF-file with attribute files for a specific example called
‘fti’. The area modelled concerns the entrance between two islands in the northern part of
The Netherlands and is called “Friesian Tidal Inlet”. On the outer side of the area the flow
is driven by a semi-diurnal tide, while the inner side the area enclosed by land. We use this
basic example to guide you through most of the input definition part of a flow simulation.

To create or modify an MDF-file you use the FLOW-GUI you became acquainted with in chapter 3. Furthermore, two attribute files are provided for use in this tutorial, viz. the curvilinear
grid file called and the grid enclosure file . The grid enclosure describes the extent of the numerical model; points outside the grid enclosure will not take part
in the simulation (are outside the open boundaries or are always on-land). While using the
FLOW-GUI you will create new attribute files which contain data like locations of monitoring
points or time-series needed for the computation. The complete MDF-file and all attribute files
created in this tutorial are also provided in the Tutorial directory, but instead of using them you
will build your own attribute files and MDF-file.

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Remarks:
The choices you are going to make are not based on physical relevance or other practical considerations, but merely to show a number of features of the FLOW-GUI and to
make you familiar with it.
You will start with a new (empty) input file, so all input fields when displayed are empty or
only have default values. But, the screens displayed in this tutorial display the situation
after you have typed in the required data.
Filenames and conventions

The names of the MDF-file and of attribute files have a specific structure, some aspects are
obliged while others are only advised or preferred.
MDF-file

The name of an MDF-file must have the following structure: . The name may
consist of up to 252 alpha-numeric characters and may contain (sub-)directories: .
The runid of the filename is used in the names of the result files to safeguard the link between
an MDF-file and the result files. We suggest to use a combination of one alpha- and two
numeric-characters followed by a useful name of your project.
Example:

This file could indicate the flow-input file of the first calibration run of a project named Panama
in the directory .
The extension is mandatory.

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Table 5.1: Overview of attribute files.

Filename and mandatory extension

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Quantity

Result files

The results of a Delft3D-FLOW computation are stored in four types of files:

History file: and .
Map file: and .
Drogues file: and .
Communication file: and .

The result files are stored in the working or project directory.

The history file contains results of all computed quantities in a number of user-defined grid
points at a user-defined time interval. The map-file contains results of all quantities in all grid
points at a user-specified time interval. The drogues file contains the positions of all drogues
released as a function of time. The communication file contains results that are required by
other modules, such as the water quality module.

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Figure 5.1: Starting window of the FLOW Graphical User Interface

Attribute files

Attribute files contain certain input quantities, such as monitoring points or time dependent
input data such as wind. The names of attribute files are basically free, but their extension is
mandatory as indicated below.
5.3
5.3.1

FLOW Graphical User Interface
Introduction

To start the FLOW Graphical User Interface (GUI) you must execute the following commands,
see chapter 3 for details:
Click the Delft3D-MENU icon on the desk-top (Windows) or execute the delft3d-menu
command on the command line (Linux).
Select the menu item FLOW, see Figure 3.2.
Change, i.e. go to the working directory <..\tutorial\flow\friesian_tidal_inlet>.
Select the menu item Flow input, Figure 3.3.
Next the main window of the FLOW-GUI is displayed, see Figure 5.1.
To open an existing input file:
Select File → Open.
By selecting an existing MDF-file all attribute files and their related data are loaded into memory and displayed in the input fields.
Instead, you are going to define all input data from scratch and save your data into an input
file called .

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Figure 5.2: Data Group Description sub-window

If you have selected File → Open you can return to the initial situation right after starting the
FLOW-GUI by selecting File → New. This will reset the internal data structure.

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You are now ready to start defining your own scenario, but before doing so you will learn how
to save your input data, even if the input data is incomplete.
Saving the input data

Initially, this tutorial may be somewhat tedious to work with. Rather then going on until the end
you may want to stop somewhere during the exercise. In order to save you from re-entering
again all the data another time up to the moment where you had stopped, you should save
the just entered data, so that later on you can pick up the thread where you left it.
To save your data:

Select File → Save All. This option is enabled when necessary.
For each Data Group with changed data for which you have not yet defined an attribute
filename and for the MDF-data (if you have not yet defined an MDF-filename) a file selection window will be opened, enabling you to save the unsaved data in an existing or in a
new file.
Next select Exit to close the FLOW-GUI or continue with your data definition.
Neglect the other options of the File drop down menu; they will be discussed later on.
5.4

Description

In the Data Group Description you can identify the scenario you are going to define by giving
a comprehensive description of the project, the application domain and the specific selections
to be made in this scenario. The description is only used for identification and has no influence
on the simulation itself. Type the description as displayed in, Figure 5.2.
5.5

Domain
The Data Group Domain supports four sub-data groups:

Grid, to define the numerical grid.
Bathymetry, to define the bottom topography.
Dry points, to define grid points that are excluded from being flooded during a simulation.
Thin dams, to define dams along grid lines that block the flow but have no influence on the
storage.

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Figure 5.3: Sub-data group Grid

Figure 5.4: Sub-data group Grid; filenames, type of co-ordinate system and grid dimensions

5.5.1

Grid parameters

In the sub-data group Grid you can open the grid to be used, its location and the number and
thickness of the vertical layers.
Click on Domain and then on Grid.

The resulting window is given in Figure 5.3.
There are two Open buttons, one for the grid and one for the grid enclosure.
Click Open grid. A file selection window is displayed.
Select the folder <..\tutorial\flow\friesian_tidal_inlet> if not already selected at the start of
this tutorial, see section 5.3.1.
Select the file and open it.
The file selection window is closed and the filename appears to the right of the
Open grid button, see Figure 5.4.

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Furthermore, the type of co-ordinate system (Cartesian or Spherical) is displayed together
with the grid dimensions. This information is contained in the grid file.
Repeat the same actions for the grid enclosure file .
Set the Latitude to: “55.00” [degrees N].
Orientation is the angle (clockwise is positive) between true North and the y -direction; its
default value is zero and can be left unchanged. For the current purpose the grid is ready for
use.

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Remarks:
You cannot modify the Grid Dimensions after loading a grid file. The dimensions of the
grid Mmax (number of grid points in ξ -direction) and Nmax (the number of grid points
in η -direction) have been set (in this case to 15 and 22) in the grid generation program
and cannot be changed. However, you can still select the number of vertical layers.
Maintain the currently inserted value 1 (for a depth averaged computation).
Many of the data items to be specified in the coming windows are related to and defined
at a numerical grid. It is therefore obvious first to select or define the grid you are going
to use.
A warning will be displayed when you try to define a grid related quantity before you
have defined your grid.
Before you continue with the other sub-data groups, you should visualise and inspect the area
to be modelled and the numerical grid used.
Click the item View in the menu bar and select the item Visualisation Area in the drop
down list. This will result in the window as shown in Figure 5.5.
Move the Visualisation Area window to the right of the screen, to keep it (at least partly)
uncovered.
In Figure 5.5 the numerical grid is shown with the active grid cells enclosed by the grid enclosure. In the Visualisation Area window all grid related quantities can be viewed, defined,
moved and deleted, but as no quantities are yet defined only the grid is displayed. Select the
menu items in the menu bar of the Visualisation Area window to inspect the various options.
For the tutorial we leave the Visualisation Area window, this window is described in more
details in chapter 4.
Before continuing with the sub-data group Bathymetry you should make yourself acquainted
with the concept of the staggered grid applied in Delft3D.
In Delft3D-FLOW we apply a staggered grid, i.e. not all quantities are defined at the same
location in the numerical grid. When defining grid related quantities it is important you have
familiarised yourself with the concept of staggered grids.
The staggered grid applied in Delft3D is given in Figure 5.6, with the following legend:
full lines
the numerical grid
grey area items with the same grid indices (m, n)
+
water level, concentration of constituents, salinity, temperature
−
horizontal velocity component in x- or ξ -direction (also called u- and m-direction)
|
horizontal velocity component in y - or η -direction (also called v - and n-direction)
•
depth below mean (still) water level (reference level). Depth is defined positive
downward.
Closed boundaries are defined through u- or v -points; open boundaries through u-, v - or

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Figure 5.5: Visualisation Area window

Figure 5.6: Staggered grid used in Delft3D-FLOW

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Figure 5.7: Sub-data group Bathymetry

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water level (zeta-)points depending on the type of boundary condition such as velocity or
water level. The location of other grid related quantities are given when appropriate.
Bathymetry

The next step in preparing the MDF-file is to set up the bathymetry of the area for which you
just have loaded the grid:
Click the sub-data group Bathymetry.
Activate the File option.
Select the file after pressing the Open button.
Behind Values specified at, select radio button Grid cell corners.
The Cell centre values computed using is set to MAX by default.
The sub-window should look like Figure 5.7.

Another option would have been to Open a (free or unformatted) bathymetry file.
Remark:
The bathymetry is defined relative to the reference level and is counted positive downward to the bottom. The tool QUICKIN provides an option to compose a bathymetry
from measured (sampled) data and to reverse the sign of grid related data in case the
data is provided with the opposite sign.
5.5.3

Dry points

Dry points are grid cells that are permanently dry during a computation, irrespective of the
local water depth. Dry points are located at the water level point, Figure 5.8.
Click the sub-data group Dry points.
Next the Dry points sub-window is displayed, Figure 5.9.
You will see the layout of Figure 5.9 in several other sub-data groups, so it is worthwhile to
discuss this window in some more details. In this window you can see the following items:

A list box with the names of the quantities defined so far. The name of a dry point is
composed of its grid indices, but for other quantities (such as discharges) you can specify
a name. You can select an item by clicking on its name in the list box.

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Figure 5.8: Location of a dry point at grid indices (m, n)

items to an attribute file.

Buttons Add and Delete for adding or deleting items from the list box.
Buttons Open and Save for opening the items from an existing attribute file or saving the
A couple of input fields to specify the location (and for some quantities a name field). For
some quantities you can specify only one item at a time, so only one pair of (m, n) indices

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needs to be specified. For other quantities you can specify a line of quantities and then
the indices of the start and end point must be specified.
To add a dry point:
Click Add.

In the list box a dry point with default name –Unnamed– appears.

As dry points can be defined as a line of dry points you must specify the indices of the start
and end point of the line, or set the indices the same for a single dry point.
Select and enter one after the other the following values: M1 = “2”, N1 = “13”, M2 = “7”,
and N2 = “13”.
Click in the list box to confirm the input.
Now, you have defined a line of dry points along the grid line N=13 and extending over several
M-grid points, i.e. M=2, . . . , M=7. In the list box the name of the line of dry points is changed
to (2,13)..(7,13); note the name is composed of the grid indices of start and end point.
To see the just defined dry points:

Select in the GUI menu View → Visualisation Area.

In the Visualisation Area window you can see the indicated fields light up in red; this implies
that dry points have been defined at these locations and are selected.
Remain in the Visualisation Area window and select View → Legend.
A window is displayed with a legend of the symbols that can be displayed in the Visualisation
Area window. Minimise this window after inspection to keep it near by.
You can also define dry points by means of point-and-click in the Visualisation Area window.
Please note that while moving the cursor over the visualisation area the position of the cursor
is displayed just below the menu bar in both world coordinates and grid indices.

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Figure 5.9: Sub-data group Dry Points

To add a dry point by point-and-click in the Visualisation Area window:

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Select Edit Mode → Add and select Edit → Dry Point in the menu bar.
Move the mouse pointer to the grid cell with indices M=13 and N=2.
Select this point.

Remark:
Selecting a menu item or a grid related quantity actually consists of two actions: the
first action is to move the cursor to the required item or position and next confirm the
selection with clicking the left mouse. In short this process will be called selecting.
As a result the earlier defined six dry points in the grid have turned yellow, the newly defined
dry point is displayed in red and in the Dry points list box the indices of the newly defined dry
point is given. Now, before you move on to the next item you will delete the six defined dry
points and single dry point, hence:
Select the dry points (2,13)..(7,13) and click Delete; the dry points are removed from the
list (and from the Visualisation Area).
Click Save next to the list box.
Specify the name in the working directory of the opened file selection
window and save the file. If the file already exists the program will ask you whether you
wish to overwrite the old file . Please confirm.
Below Save the filename appears, see Figure 5.9.

Remark:
You don’t need to save the data in each sub-data group. The FLOW-GUI keeps track
of all changed data fields. When selecting File → New, or when exiting the FLOW-GUI
you will be notified that not all data has not been saved and you can either continue and
discard this data or save the data to an existing or new file. However, a preferred way
of working is to save data items when defined.

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Figure 5.10: Sets of thin dams blocking v -velocities (left) and blocking u-velocities (right)

Figure 5.11: Sub-data group Thin dams

5.5.4

Thin dams

Next you are going to define a Thin dam. Thin dams are infinitely thin objects defined along
the grid lines, which prohibit flow exchange between two computational cells at the two sides
of the dam without reducing the total wet surface and the volume of the model. The purpose
of a thin dam is to represent small obstacles (e.g. breakwaters or dams). See Figure 5.10 for
the location of u- and v-thin dams.
The Thin dams sub-window is displayed in Figure 5.11.

Click the sub-data group Thin dams in the Domain window. Similar to what happened in
the previous section, there appears a sub-window for Thin dams.
Define a line of thin dam points who block the flow in v -direction by entering the indices
M1 = “14”, N1 = “4”, M2 = “14” and N2 = “3”.
The selected grid section turns red in the visualisation area to indicate thin dams have
been defined and are currently selected.
Save the thin dams in the file .
You have just defined two thin dams with a length of one grid cell each. In the list box a name
composed of the indices of start and end point is displayed. The selected direction of the thin
dam is indicated in the check box of u- or v -direction.
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sation Area window:

Figure 5.12: Equivalence of v -type thin dams (left) and u-type thin dams (right) with the
same grid indices, (m − 1 to m + 1, n)

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Select Edit Mode → Add and Edit → Thin Dams in the Visualisation Area menu bar.
Click a grid location, but keep the mouse button pressed.
Move the mouse pointer to the required length and release the mouse button.
The selected grid line section turns yellow, thus indicating a thin dam has been defined.
Remark:
You can define lines or sets of thin dams along the grid lines but also at angles of a
multiple of 45 degrees with the grid.
Add a couple of more thin dams, change the direction in which the thin dam is defined by clicking the u- or v -direction check box and see how the change is visualised in the Visualisation
Area window. Familiarise yourself with this, understand why a line of thin dams along one grid
line changes to a set of single thin dams along the other grid direction when changing from uto v -direction and vice versa. See Figure 5.12 for u- and v -types of thin dams with the same
grid indices.
Before you go on to the next data group you should undo the random changes; the easiest
way to do this is to neglect the additional thin dams and go on to the next data group, as
you already have saved the firstly defined thin dams. However, this would stimulate a wrong
working habit and so you are advised to delete all the additional thin dams before you leave
the data group, or to overwrite the currently defined thin dams by the saved thin dams in
. So:
Open the thin dam file .

You have defined all the required items in the Domain window, so you can move on to the
next data group.

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Time frame

In the Data Group Time frame you can specify the time frame of your computation composed
of the reference date, the simulation start time, the simulation stop time and the time step
used in the numerical simulation.

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5.6

Figure 5.13: Window Time frame

Click the Data Group Time frame. In the canvas area the following sub-window is displayed, Figure 5.13:
Remark:
When this window is first activated it always shows the current calendar date of your
computer.
The Reference date prescribes the (arbitrary) t = 0 point for all time-series as used in the
simulations. However, in the FLOW-GUI all time related input is specified in a real time format,
i.e. [dd mm yyyy] for the date and [hh mm ss] for the time.
Click the Reference date input field and type the date “05 08 1990”.
Set the Simulation start time to “05 08 1990 00 00 00”.
Set the Simulation stop time to “06 08 1990 01 00 00”.
Set the time step to “5” minutes.

The simulation time thus covers exactly 25 hours, or about two semi-diurnal tidal cycles.
Neglect the other input field.

Remarks:
All data items of the Data Group Time frame are stored in the MDF-file and not in an
attribute file. In fact all single data items are stored in the MDF-file.
The maximum Courant number given the grid, depth and time step is about 11.

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Processes
In the Data Group Processes you specify which processes or quantities that might influence
the hydrodynamic simulation are taken into account. You can select constituents:

Salinity
Temperature
Pollutants and tracers
Sediments

Wind
Wave
Secondary flow (2D mode only and no Z -model)
Online Delft3D-WAVE
Tidal Forces (spherical co-ordinates only)

or man-made processes:

or physical processes:

Dredging and dumping (only if sediments are selected)

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5.7

To select the required processes:

Click the Data Group Processes.

The Processes sub-window is displayed with the list of possible constituents and processes,
see Figure 5.14. The buttons Edit are only displayed after you have selected the constituents
Pollutants and tracers or Sediments.

Figure 5.14: Processes window

Activate the required processes by ticking off their check box; in this tutorial we select the
constituents:
Salinity and
Pollutants and tracers,

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Figure 5.15: Processes: Pollutants and tracers sub-window

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Immediately after ticking off the Pollutants and tracers checkbox or when the Edit is
pressed (if enabled), the Processes: Pollutants and tracers window is displayed, see
Figure 5.15.
And tick off the physical process
Wind.

Now type into the Name input field the words “Conservative Spill” and click Add.
Close the sub-window.
You have just defined one conservative constituent that is transported by the flow.
Remarks:
The first time you select Processes - Pollutants and tracers, Figure 5.14 is automatically
displayed. For changing the constituent names later on you must click the aforementioned Edit button.
You can specify a simple decay rate for each of the substances. It is currently implemented as a special feature, see section B.2 for details. For interacting constituents you
have to apply the water quality module D-Water Quality.
See chapter 11 for the use of cohesive and non-cohesive sediments.
5.8

Initial conditions

In the Data Group Initial conditions you can specify the initial values used when starting the
computation. The initial conditions can be very simple, such as a uniform value in the whole
area or taken from a previous computation.
Click the Data Group Initial conditions.
The sub-window Initial conditions is displayed, Figure 5.16.
Shown are some option boxes and input fields. In the dropdown list Uniform values has
already been set. If not:
Select Uniform values.
Input fields are shown for the processes selected in the Data Group Processes, so in this case
for the processes water level (by default), salinity and one constituent.

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Figure 5.16: Initial conditions sub-window

Enter the values: Water Level: “1.9” m; Salinity: “30.0” ppt and Conservative Spill: “1.0”
kg/m3.

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The initial conditions are stored in the MDF-file when saving the input.
Boundaries

In the Data Group Boundaries you can define the open boundaries, their location, type and all
input data related to forcing the simulation. Open boundaries are defined in sections of one
or more grid cells. Boundary conditions are prescribed at both ends of a section, called begin
and end, or, A and B. Boundary conditions for intermediate points along a boundary section
are determined by linear interpolation. Boundary sections may not be overlapping, so if you
define two boundary sections along an open boundary, end-point B of section one and start
point A of section two are located in consecutive grid cells.
Firstly, you are going to define the location and extent of the open boundaries:
Click the Data Group Boundaries.
Click Add to the right of the list box.

In the input field Section name appears the word –Unnamed–.
Enter instead: “Sea Boundary”.

Remark:
Values are read from the input field upon losing the focus, i.e. when you select another
input field or select a boundary section in the list box.
Now define the begin and end point of the open boundary:
Type the following values of the grid indices in the appropriate input fields: M1 = “2”, N1 =
“22”, M2 = “14” and N2 = “22”.
Retain the value 0.0 in the Reflection parameter alpha input field.
In the Visualisation Area window the open boundary just defined is displayed as a thick red
line.
To save these settings:

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Figure 5.17: Boundaries sub-window

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Figure 5.18: Open/Save Boundaries sub-window

Click Open/Save in the Boundaries sub-window.
Click Save (Boundary definitions) in the pop-up sub-window, Figure 5.18.
Enter the filename in the working directory and close the Open/Save
Boundaries menu window.
Remarks:
After pressing Open/Save a sub-window is displayed with references to all type of attribute files related to open boundaries. Concentrate for the moment on the Boundary
Definitions attribute file and discard the others.
You can define an open boundary in the Visualisation Area window in the same way
as you define a line of thin dams or a line of dry points, i.e. select the begin point, keep
the mouse button pressed, drag the mouse pointer to the end point of the boundary
section along the grid line, and release the mouse button.
For open boundaries there is one additional condition, i.e. the open boundary must be
defined at the edge of the grid as shown in the Visualisation Area. To define an open
boundary by point-and-click: select the Edit Mode → Add and Edit → Open Boundaries in the menu bar of the Visualisation Area window and continue as prescribed.
Make sure you undo all changes; the easiest way is to import the previously saved open
boundary locations.
In the visualisation area all open boundaries are visualised at grid lines, i.e. at the edge
of computational grid cells. The (M, N) indices displayed in the Visualisation Area
refers to the computational grid cell. This grid cell number differs by one in M or N
depending on the location of the boundary (left, lower, right or upper) from the grid line.

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This rule also applies to open boundaries in side the computational domain. For a detailed
discussion on the computational grid and the location of open and closed boundaries see
Appendix E.
To define an open boundary by point and click you should select and drag inside the first
(or last) grid cell so as to select the first (or last) water level or velocity point.
In this tutorial you will use the default type of open boundary i.e. Water level and the Harmonic
type of forcing (the default is Astronomic).

Set the forcing type to Harmonic.
Click Edit flow conditions.
In this tutorial we are going to specify harmonic boundary conditions for a depth averaged
computation (only one layer in the vertical, see Data Group Domain → Grid), so several
options are either invisible or insensitive.

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The harmonic components must be specified for both ends of an open boundary section. The
begin and end point are referred to as ‘Begin’ or ‘point A’ and ‘End’ or ‘point B’. The Begin
point has the indices (M1, N1) and the End point has the indices (M2, N2); see Figure 5.17.
You are going to prescribe a semi-diurnal tide with amplitude of 1.1 m and phase 0 degrees
at the Begin point and amplitude 1.1 m and phase -34.26 degrees in the End point.
After filling the input fields the table should look like Figure 5.19.

Remark:
The frequency is specified in degrees per hour. Hence, 360/12.5 = 28.8 for the semidiurnal tide. A mean sea level is defined with a frequency of 0 degrees/hr.
Now save the data to the attribute file:

Close the Boundaries - Flow Conditions sub-window.
Select Open/Save in the Boundaries window.
Save the harmonic flow conditions into file .
Close the Open/Save Boundaries window.

You are back in the Boundaries window. Next you will provide time-series for the concentrations of the constituent and salinity at the open boundary.
Set the Thatcher-Harleman time lag to “100” minutes, see Figure 5.17.
Click Edit transport conditions.
To define the boundary conditions for the process salinity:
Select from the Constituents dropdown list: Salinity.
Next, fill out the table form with the following time breakpoints and parameter values at both
ends (Begin and End):

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Figure 5.19: Harmonic boundary conditions

Figure 5.20: Boundaries: Transport Conditions window

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Date and time

Begin

End

05 08 1990 00 00 00

30.0

06 08 1990 01 00 00

30.0

Next select from the dropdown list the constituent Conservative Spill.

Date and time

Begin

End

05 08 1990 00 00 00

1.0

06 08 1990 01 00 00

1.0

and fill out the table with the following time breakpoints and parameter values at both ends.

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For this constituent you set all concentrations to 1.0, representing a tracer that is present in
the inflowing sea water. For a tracer to be washed out of the system you should enter the
sea-background concentration, for instance zero or a small value. Recall you have specified
the initial condition (Data Group Initial conditions) to 1.0 for this constituent.
Remarks:
The time breakpoints for Salinity and the constituent Conservative Spill and for any
other process selected can be different; they do not need to be the same.
In Figure 5.20 only the input data for Salinity is visible; you must use the Constituents
drop down list to select the other selected constituents.
Remark:
In a 3D model you can specify a profile. To inspect this you can go back to the Data
Group Domain → Grid and increase the number of layers to two (with a distribution of
50 % for each layer) and return to the current window (Data Group Boundaries - Edit
transport conditions - Constituents - Salinity ). Ignore all warnings and error messages
that might be displayed (remember you might not have specified all kind of data required
for a real 3D simulation). After inspection make sure to return the number of layers to
one.
You have now finished the boundary conditions for all processes and constituents and you are
ready to save the data.
Close this window to return to the Boundaries window.
Select in the Boundaries window Open/Save - Transport conditions - Save and save the
transport boundary conditions in the working directory in the file .
Close the Open/Save Boundaries window.

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Figure 5.21: Physical parameters sub-data groups

5.10

Physical parameters
In this Data Group you can define a number of physical parameters, grouped in several subdata groups.
Click the Data Group Physical parameters.

Next the sub-data groups Constants, Roughness, Viscosity and Wind are displayed as tabs;
Figure 5.21. As temperature was not selected in the Data Group Processes the sub-data
group Heat flux model is invisible.
In the next sections the other sub-data groups will be treated.
Constants

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5.10.1

The sub-data group Constants concerns items such as the acceleration of gravity, the water
and air density and constants that determine the wind drag force. To specify the constants:
Click the tab Constants, see Figure 5.22.

Set the values by entering into their respective input fields:
Gravity : “9.81” m/s2 (default value).
Water density : “1024.0” kg/m3 .
Air density : “1.00” kg/m3 .
Temperature: “10.0” ◦ C.
There are three Wind drag coefficients:

Type into the input fields of the first line “0.0025” [-] and “0.00” [m/s].
Type into the input fields of the second line “0.0025” [-] and “100.00” [m/s].
Type into the input fields of the third line “0.0025” [-] and “100.00” [m/s].
The three wind drag coefficients determine breakpoints in the piece-wise linear function of
wind drag and wind speed:

The first two coefficients determine the wind drag value that is used from zero wind speed
up to the wind speed specified by the second constant.

The third two coefficients specify the wind drag used from the specified wind speed and
higher.

As a result you can specify a constant wind drag, a linearly increasing wind drag or a piecewise linear function of wind speed.

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Figure 5.22: Physical parameters - Constants sub-window

Figure 5.23: Roughness sub-window

5.10.2

Roughness

In the sub-data group Roughness you can specify the bed roughness and for specific situations the roughness of the side walls.
Click the tab Roughness, next Figure 5.23 is displayed.

Three different friction formulations are given, i.e. Manning, White-Colebrook or Chézy :
Select White-Colebrook.
The bottom roughness can be specified as a constant value over the whole area or as a space
varying value (read from an attribute file). The option Uniform has already been activated by
default, you only have to specify the constant value that is to be used.
Enter the value “0.05” for both U- and V-direction.
Ignore the Slip condition dropdown box (and the roughness value related to it).

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5.10.3

Viscosity

Figure 5.24: Viscosity sub-window

In the sub-data group Viscosity you can specify the eddy viscosity and the eddy diffusivity in
the horizontal and vertical directions.

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Click the tab Viscosity, next Figure 5.24 is displayed.

As this is a depth averaged model, only the background Horizontal eddy viscosity and the
background Horizontal eddy diffusivity are displayed and require a value:
Set the horizontal eddy viscosity to “2.0” m2 /s. and the horizontal eddy diffusivity to “10.0”
m2 /s, respectively.
Remark:
You specify one value for both the Horizontal Eddy Viscosity and the Horizontal Eddy
Diffusivity in U- and V-direction. Space varying values can be read from a file; these
files must be prepared offline using some kind of editor or a program, such as the tool
QUICKIN provided with Delft3D.
The model for 2D turbulence computes viscosities and diffusivities which will be added to the
background values. In this tutorial we will not use this model.
5.10.4

Wind

Next you are going to specify the wind speed and direction:
Click the Wind tab.

Next Figure 5.25 is displayed. The check box Uniform is set, indicating you are specifying a
uniform, but possibly time dependent wind field. Now for the sake of curiosity, select Space
varying wind and pressure, and see what happens next. But then go back by activating again
the Uniform check box.
You are going to define a linearly increasing wind speed from 0 m/s to 10 m/s during the first
12:30 hour of the simulation, the direction changing from 0 to 90 degrees in the same time
interval, and keeping that value for the rest of the computation.
For operations on a table use the menu item Table in the menu bar. To add or insert (before
the current row) a row:
Select Table → Copy row above.

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Figure 5.25: Wind sub-window

Figure 5.26: Filled time table in the Wind sub-window

A new row has been inserted and you can modify the data.
In the time table, fill in the following data:
“05 08 1990 00 00 00”, “0”, “0”
“05 08 1990 12 30 00”, “10”, “90”
“06 08 1990 01 00 00”, “10”, “90”

After editing, the table should look like Figure 5.26.
Now save the wind data:

Save the wind data in the working directory in the file .

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Figure 5.27: Numerical parameters sub-window

5.11

Numerical parameters

In the Data Group Numerical parameters you can specify parameters related to drying and
flooding and some other advanced options for numerical approximations.
Although drying and flooding will not take place in this model, for the sake of getting a good
overview of what is going on, you will include a drying and flooding procedure.
Click the Data Group Numerical parameters, next Figure 5.27 is displayed.
The first selection to be made concerns drying and flooding. The options for Drying and
flooding check at determine where the check should be performed:

at grid cell centres (water level points) and grid cell faces (velocity points),
or at only grid cell faces (velocity points).
A grid cell is flooded if the water depth is larger than the specified Threshold depth and dried
if the water depth is smaller than half this value. See chapter 10 for details of this drying and
flooding procedure. The Marginal depth is used to change the approximation of the convective
terms in the momentum equations to allow for local super-critical flows. Skip for this tutorial
the Marginal depth input field.
Set the Threshold depth to “0.05” m.
The Smoothing time determines the time interval in which the open boundary conditions are
gradually applied, starting at the specified initial condition to the specified open boundary
conditions. This smoothing of the boundary conditions prevents the introduction of short wave
disturbances into the model.
Set the Smoothing time to “60” minutes.
Ignore the other options or input fields.

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Figure 5.28: Data Group Operations; Discharges sub-window

5.12

Operations

In the Data Group Operations you can specify the location and all related properties of discharges. For this tutorial we have introduced one constituent (Conservative Spill); its release
rate must be defined.
Click the Data Group Operations.

The Discharges tab, Figure 5.28, has a similar layout as the Dry points or Thin dams subwindow, but in addition you must specify the rate and concentrations of the discharged substances.
To add a discharge by point-and-click in the Visualisation Area window:

Select Edit Mode → Add and select Edit → Discharges in the menu bar.
Define the discharge location by point-and-click in the Visualisation Area window at grid
cell M = “14” and N = “2”.
Replace the text (14,2) in the Name input field with “Outfall”.
In the Visualisation Area window discharges are represented by a lozenge at a water level
point, see Figure 5.29.
The discharge is located at the centre of the computational cell (m, n).
To save the discharge location:
Click Open/Save to open the Open/Save Discharges window.
Click Save in group Discharge definitions to save the discharge location in the file

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Figure 5.29: Representation of a discharge in the Visualisation Area window

Figure 5.30: Discharge Data sub-window

in the working directory.
Close the Open/Save Discharges window.

Next you must define the time dependent discharge data:
Click Edit data.

The table to define the discharge rate and concentrations is displayed in Figure 5.30.
Specify the following data in this table:
Date and time

Flow
m3 /s

Salinity
ppt

Cons.Spill
kg/m3

05 08 1990 00 00 00

3.0

0.0

1.0

06 08 1990 01 00 00

3.0

0.0

1.0

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Remarks:
The data specified represents a fresh water discharge (salinity = 0 ppt) of 3 m3 /s.
Obviously, the time breakpoints are the same for all time dependent quantities related
to the discharge.
Scroll the table horizontally, if needed, to display the Conservative Spill data input fields.
Close the window if all input is specified.
Click Open/Save and click on Save in datagoup Discharge data to save the discharge data
in the attribute file in the working directory.
Close the Open/Save Discharges window.
5.13

Monitoring

Observation points

Observation points are grid locations where all quantities computed during the simulations are
stored at a user-defined time interval (Data Group Output → Storage). Observation points
are located at the computational grid cell centres, i.e. at the water level points.

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5.13.1

The Data Group Monitoring consists of three sub-data groups, i.e. Observations, Drogues
and Cross-sections.

Click the sub-data group Observations, Figure 5.31 is displayed.
To add an observation point:

Select from the menubar Edit mode →Add and Edit →Observation Point.
Select the location (M = 4, N = 17) in the Visualisation Area window.
Replace the text (4,17) with “Obs1”.
Repeat this for the observation points Obs2 to Obs5 as specified in the table below:
Name
Obs1
Obs2
Obs3
Obs4
Obs5

M index

N index

4
9
12
9
9

17
17
17
11
7

Save the Observation Points just defined in the file in the working directory.
In the Visualisation Area window observation points are represented by a cross through the
computational grid cell centre, Figure 5.32.
The observation point is defined at (m, n).

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Figure 5.31: Observation points sub-window

Figure 5.32: Representation of an observation point in the Visualisation area window

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Figure 5.33: Drogues sub-window

Drogues

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5.13.2

Drogues are floats that move with the flow. They are released and recovered at a userspecified time. Their location is stored at the same time interval as the computational time
step (see Data Group Time frame). Drogues can be located anywhere in a grid cell, i.e. a
drogue can be released at decimal indices. However, in the Visualisation Area window you
can only select grid centre location, so if other decimal values are required you must enter
these indices manually in the FLOW-GUI.
Click the sub-data group Drogues, Figure 5.33 is displayed.
To add drogues:

Click Add and enter the following drogues:
Name
Dr1
Dr2
Dr3
Dr4
Dr5

M index

N index

3.50
8.50
11.50
8.50
8.50

16.50
16.50
16.50
10.50
6.50

The Release Time and Recovery Time are by default the same as the start and stop times
of the simulation. For all drogues change them to:
Release Time : “05 08 1990 12 30 00”
Recovery Time : “06 08 1990 01 00 00”
Save the drogue data in the file in the working directory.
In the Visualisation Area window drogues are represented by a ‘+’ through the computational
grid centre, Figure 5.34.
The drogue is located at (m, n).

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Figure 5.34: Representation of a drogue in the Visualisation Area window

Figure 5.35: Cross-sections sub-window

5.13.3

Cross-sections

Cross-sections are sections along one of the grid directions through which the various kinds of
transport fluxes are determined and stored as a function of time. For defining cross-sections
you can apply the same procedures as for Thin dams or Dry points in the Data Group Domain.
Cross-sections are defined along the grid lines, either as U- or as V-cross-section. To enter
the sub-data group Cross-sections:
Click Cross-sections, next Figure 5.35 is displayed.
To add a cross-section:

Click Add.
Type in the Name field the word “CS1” to replace –Unnamed–.
Enter the indices M1 = “2”, N1 = “11”, M2 = “14” and N2 = “11”.

In the Visualisation Area window a cross-section is represented by a thick line along one of
the grid lines, Figure 5.36.
In Figure 5.36 the V-cross-section runs from (m−1, n) to (m+1, n).
Remark:
Cross-sections must have a minimum length of two grid cells.

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To save the just defined cross-section:

Figure 5.36: Representation of a v-cross-section in the Visualisation Area window

Click Save.
Save the data in file in the working directory.

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Remark:
You are encouraged to define a cross-section along either of the grid lines by pointdrag-and-click. Make sure to undo the additional definitions (for instance by opening
the just saved attribute file) before you move on to the next data group.
Additional parameters

In the Data Group Additional parameters you can specify keywords and their value, often the
name of an attribute file, which are not yet supported by the FLOW-GUI. For details you are
referred to Appendix B, but for this tutorial we ignore this Data Group.
5.15

Output

In the Data Group Output you can specify which computational results will be stored for further
analysis or other computations and which output shall be printed. Though the printing option
is hardly used it is a useful option when numerical output values are required.
To enter the data group:

Click the Data Group Output.

The Data Group Output supports three sub-data groups:

Storage: to define the time interval to store results to disk.
Print: to define the time interval to store results to a printable file.
Details: to define which quantities will be stored or printed.

Upon selecting Storage the sub-window, Figure 5.37, will be displayed.
Before defining the various input fields we want to explain in short the use of the various files
used to store the results. Basically, Delft3D-FLOW uses four types of files to store results:

History file
The history file contains all quantities as a function of time, but only in the specified Monitoring Points and Cross-Sections. The amount of data is usually much smaller than for
a map file, and you typically store history data at a small interval to have a smooth time

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Figure 5.37: Output sub-window

function when plotting the results.

Map file

The map file contains snap shots of the computed quantities of the entire area. As you
save all results in all grid points a typical Map file can be many hundreds of Mbytes large.
So typically map results are only stored at a small number of instances during the simulation.
Drogue file
The drogue file contains the (x, y)-position of all drogues at each computational time step
in the time interval between release and recovery time.
Communication file
The communication file contains results required by other modules of Delft3D, such as the
hydrodynamic results for a water quality simulation or the wave forces for a wave-current
interaction. As the results must be stored in all grid points a communication file can be
as large as or even larger than a Map file. So typically you only store the results in the
Communication file as far as needed for the other simulations; for water quality simulations
you typically store the results of the last day or a (couple of) cyclic tidal cycle and use this
data repeatedly to make a water quality simulation over many days or weeks.
In order not to waste computing time you can restart a simulation at a predefined time of a
previously executed simulation (Data Group Initial conditions). For this you specify the Restart
Interval at which all information required to restart the simulation. Typically you select a large
restart interval in order not to waste disk space.
Now continue to define the various times and time intervals:

Set Store map results to:
Start time: “05 08 1990 00 00 00”
Stop time: “06 08 1990 01 00 00”
Interval time: “150” min.
Set Store communication file to:
Start time: “05 08 1990 12 30 00”
Stop time: “06 08 1990 01 00 00”

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Figure 5.38: Output details sub-window

Interval time: “15” min

Set History interval to: “5” minutes.
Set Restart int.: “1500” min

Remarks:
The interval to write the various files must be an integral multiple of the computational
time step, defined in the Data Group Time frame.
The history, map, and drogue data is stored by default in binary NEFIS files. This file
format is best suited for further post-processing using Deltares software. For interoperability with other software you may want to use the binary NetCDF file format instead.
The file format can be changed by means of the FlNcdf keyword; see section A.1.4.
The restart interval as set results in a restart file at the end of the simulation.
For this tutorial we ignore the item Fourier analysis, it is discussed in detail in chapter 4.
Tick off Online visualisation, this results in viewing the results during the simulation.
To control the quantities that are actually stored on files or printed:

Click the sub-data group Details, next Figure 5.38 is displayed.

By ticking the check boxes you can specify which items you want the program to store on
file or to print and which not; details of the quantities covered by each group are given in
chapter 4.
For this tutorial we ignore the sub-data group Print.
You have now gone through all Data Groups and you have defined in most of them one or
more data items. Before continuing you should save this data to make sure you can always
return to this status of the FLOW-GUI.

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Save MDF-file
In the preceding sections you have entered many data items, some of which are already saved
in attribute files.
To summarise:
Dry Points
Thin Dams
Open Boundaries definitions
Wind
Flow boundary conditions (harmonic)
Transport boundary conditions
Discharge locations
Discharge rates
Observation points
Drogues
Cross sections

1
2
3
4
5
6
7
8
9
10
11

In addition you have used three predefined attribute file:

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5.16

1 Curvilinear Grid
2 Grid Enclosure
3 Bathymetry

To save the reference to all these attribute files and other (single) input data in the MDF-file:
Click File → Save MDF As in the menu bar of the FLOW-GUI.
Save the MDF-data in the file in the working directory.
Remarks:
Do not use blanks in the name of the MDF-file.
All attribute data is saved in attribute files (if they exist) and the references to existing
attribute files are stored in the new MDF-file.
If you have defined all attribute files in their respective Data Group, the MDF-file is
complete.
All unsaved Data Groups are ignored.
Upon selecting File → New, File → Open or Exit you will be notified if some data is not
saved and you can choose to ignore the data, or to save the data.
In previous versions of the FLOW-GUI you were obliged to save the attribute data in
their respective Data Group. A warning was issued on leaving a Data Group without
saving its related attribute file(s). Starting this version of the FLOW-GUI you can save
attribute data in their respective Data Group, but you can postpone it to the moment
when you save the MDF-data. You will be prompted for unsaved data.
To exit the program:
Click File → Exit.

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Figure 5.39: Select scenario to be executed

5.17

Additional exercises

Execute the scenario

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5.18

You are encouraged to go back to the start of the tutorial and explore some of the options
not used or discussed in this first example. A very worthwhile exercise is to define, delete or
modify the definition of grid related quantities using the Visualisation Area window only. With
the menu item Edit Mode → Modify you can drag-and-drop (i.e. move) any of the grid related
quantities.

If you have an error free scenario you can start the simulation:

Select Start in the Delft3D-MENU to start the computation in foreground. In Figure 5.39
the selection window is displayed for the scenario to be executed (i.e. MDF-file).
If is not selected already, use Select file to navigate to the working directory
and select .
Confirm your selection with OK.
In foreground the status of the simulation and possible messages are displayed in the active
window.
After the simulation is finished you are strongly advised to inspect at least some of the report
files generated during the simulation to check if all went according to plan. This concerns
especially the file (located in the working directory). To see this report:
Select Reports in the Hydrodynamics (including morphology) window.
Select Flow to inspect the report file.
Especially the end of this file is of importance as it summarises errors, warnings and information of the simulation, see Figure 5.40.
The simulation is executed without errors or warnings.

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Figure 5.40: Part of the report file

5.19

Inspect the results

In Figure 5.41 to Figure 5.43 some results are shown of the simulation just finished. To
reproduce these plots you should start the general post processing program GPP (see the
GPP User Manual GPP UM (2013)).
Select GPP in the Hydrodynamics (including morphology) window or Utilities - GPP in
the main Delft3D-MENU.
In the main window of GPP select Session → Open.
Copy the file to the working directory<.\tut_fti.ssn>.
In the file selection menu select and open the file .
In the main window of GPP select Plots and select from the list of possible plots the one
you would like to inspect.
In a <∗.ssn> file the references are stored to data sets, in this case the result files of the
tut_fti-scenario, and the definition of earlier defined plots and their layout. By calling this
scenario file you can inspect the same plots after repeating the simulation with (other input
data) of the FLOW scenario tut_fti. For details of using GPP you are referred to the User
Manual of GPP.
To return to the main window of GPP while viewing a plot:
Select Plot → Close.
You can select another plot as described above.
To close GPP and return to Delft3D-MENU:
Select in the main window of GPP Session → Exit.
To close Delft3D-MENU:
Select Return.

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Select Exit.

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Figure 5.41: Computed time-series of the water level, current and salinity in observation
point Obs4

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Figure 5.42: Computational grid with drogue Dr4, and contours of water level on 6 August
1990 01:00 hr

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Figure 5.43: Vector velocities and contours of salinity on 6 August 1990 01:00 hr

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6 Execute a scenario
6.1

Running a scenario
After defining the input for the Delft3D-FLOW hydrodynamic simulation, the computation can
be executed either via Delft3D-MENU or using a batch script. Via Delft3D-MENU, the status
of the computation and possible messages are displayed in a separate window. When using
a batch script, all messages are written to a file and you can continue working in the current
window.

Parallel calculations

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6.1.1

Using MPI to run in parallel
Using mormerge
Using fluid mud
Using some queueing mechanism on a cluster

Not all functionality is available when using Delft3D-MENU to start a calculation. Use a batch
script (see section 6.1.3) in the following cases:

This section is an overview of all techniques where parallel calculations are involved.
6.1.1.1

DomainDecomposition

See section B.14. An example is at https://svn.oss.deltares.nl/repos/delft3d/
trunk/examples/02_domaindecomposition. Each subdomain runs in a separate
thread, inside one executable.

Multiple cores will be used automatically when available on the executing machine.
DomainDecomposition calculations can not be executed using multiple machines.
Does not work in combination with MPI-based parallel calculations
MPI-based parallel

Example scripts are inside https://svn.oss.deltares.nl/repos/delft3d/trunk/
examples/01_standard. The domain is split automatically in stripwise partitions.

Can not be started via Delft3D-MENU
Does not work in combination with:

6.1.1.2

DomainDecomposition
Fluid mud
Coup online
Drogues and moving observation points
Culverts
Power stations with inlet and outlet in different partitions
Non-hydrostatic solvers
Walking discharges
2D skewed weirs
max(mmax,nmax)/npart ≤ 4
Roller model
Mormerge
Mass balance polygons

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6.1.1.3

Fluid mud
See section B.10. An example is at https://svn.oss.deltares.nl/repos/delft3d/
trunk/examples/04_fluidmud. The two calculations run in separate executables.

Multiple cores will be used automatically when available on the executing machine.
Fluid mud calculations can not be executed using multiple machines.
Does not work in combination with MPI-based parallel calculations
6.1.1.4

Mormerge
An example is at https://svn.oss.deltares.nl/repos/delft3d/trunk/examples/
05_mormerge. A script, written in the language "Tcl" is used to start all executables:.

Running a scenario using Delft3D-MENU
To start Delft3D-FLOW:

Select Start, see Figure 6.1.

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6.1.2

Multiple cores will be used automatically when available on the executing machine.
Does not work in combination with MPI-based parallel calculations

Figure 6.1: MENU-window for Hydrodynamics

A new window is displayed in which you can select the input file to be used, Figure 6.2.

Apply Select file to select the required MDF-file.
After pressing OK the simulation will start and a window will appear. In foreground the status
of the simulation and possible messages are displayed in the active window, see Figure 6.3
After the simulation is finished you are strongly advised to inspect at least some of the report
files generated during the simulation to check if all went according to plan. To see which

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Figure 6.2: Select the MDF-file to be verified

Figure 6.3: Part of the report to the output window

reports are generated:

Select Reports in the Hydrodynamics (including morphology) window, upon which Figure 6.4 is displayed.
Select either one to inspect:

The report file of the simulation: .
The print file with printed output results: .
The report file of the WAVE simulation (if applicable): .
The report file of the Hydrodynamic coupling (if applicable): .
A random file, upon selecting this option an editor window is opened that allows you to
inspect or modify a file without having to leave the FLOW-GUI.

The report file contains information on the total simulation time, the time spent in
certain parts of the simulation and an indication of the performance (seconds processor time
per grid point per time step). In the next section we shall give some guidelines to estimate the
simulation time and the required disk space for the various result files.

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Figure 6.4: Select a report file for inspection

6.1.3

Running a scenario using a batch script

Batch scripts can be generated in two ways:

Delft3D-MENU can generate batch scripts (not for all functionality)
Copy an existing script and adapt it for your purpose. Examples are available at https:
//svn.oss.deltares.nl/repos/delft3d/trunk/examples
Separate scripts are needed for Windows (with extension "bat") and Linux (with extension
"sh"). See section 6.4 for the command-line arguments.
The easiest Windows script (assuming Delft3D is installed properly, assuming a correct
is available, compare with example "01_standard"):
set PATH=%D3D_HOME%\%ARCH%\flow2d3d\bin;%PATH%
%D3D_HOME%\%ARCH%\flow2d3d\bin\d_hydro.exe config_d_hydro.xml

The easiest Linux script (assuming Delft3D is installed properly, assuming a correct
is available, compare with example "01_standard"):
export LD_LIBRARY_PATH=$D3D_HOME/$ARCH/flow2d3d/bin:$LD_LIBRARY_PATH
$D3D_HOME/$ARCH/flow2d3d/bin/d_hydro.exe config_d_hydro.xml

6.2

Run time
The actual run time of a model can vary considerably depending on a variety of factors such
as:

The problem being solved, characterised by the number of active grid points, the number
of layers in the vertical or the number of processes taken into account.

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Table 6.1: Simulation performance on different operating systems

Computation

WIN

LINUX

Without Domain decomposition

0.5E-05

0.4E-05

With Domain decomposition

0.5E-04 to 0.1E-03

The length of the simulation in time and the time step being used.
The hardware configuration that is used and the work load of the processor.

For this reason, only some general considerations are given to determine the run time of a
hydrodynamic simulation. On a PC or a workstation without separate I/O-processors the CPU
time is the sum of the processor time and the I/O time.
The processor time required for a simulation is primarily determined by:

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The model definition, i.e. the number of active grid points and the number and type of the
processes taken into account.

The length of the simulated period in terms of the number of time steps executed.
The I/O time is determined by:

The number of times the computed data are written to history, map, print and communication files.

The number of observation points, cross-sections and the number of output parameters.
The simulation performance is defined as the CPU time per grid point per time step per constituent:

simulation performance =

CPU time

N · Mmax · Nmax · Kmax · Lmax

[system seconds]

where:

N
Mmax
Nmax
Kmax
Lmax

is the number of time steps executed
is the number of grid points in x-direction
is the number of grid points in y -direction
is the number of layers in the vertical
is the number of constituents

In Table 6.1 the simulation performance is given for a PC with a Windows and a Linux operating system respectively. The Windows and Linux PC have similar processors (AMD Athlon
64 X2 Dual Core Processor 4200+, 2.19GHz).
Remarks:
The simulation performance is almost linearly dependent on the processor speed.
The simulation performance can be improved with about 20 % by minimizing the output
written to the result files.
The simulation performance is written to the diagnosis file at the end of a calculation.

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When using Domain decomposition, each domain produces its own simulation performance index. The difference between these indexes will become very large when the
domain load is unbalanced.
To improve the time estimates we suggest to keep record of the simulation performance
on your hardware environment including all site specific aspects. In case the simulation
performance is very bad on similar hardware and the workload is not excessively high,
you are advised to contact your system manager to check the general settings of your
hardware such as swap and stack space. For system requirements you are referred to
the Installation Manual.
6.3

Files and file sizes

history file
map file
print file
communication file
drogues file

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For estimating the required disk space the following files are important:

Remark:
Drogues files are generally small and are not discussed further.
6.3.1

History file

The size of the history file is determined by:

The number of monitoring points (observation points + cross-sections): H1.
The number of quantities stored: H2.
The number of additional process parameters, such as salinity, temperature, constituents
and turbulence quantities, taken into account in the simulation: H3.

The number of time the history data is written to the history file: H4.

You can estimate the size of a history file (in bytes) from the following equation:
size history file = H1 · (H2 + H3) · H4 · 4 bytes.
As a first approximation you can use H2 = 15.
Example

For a 2D simulation with density driven currents (salinity and temperature), a simulated period
of 12 hrs 30 min, a time integration step of 5 minutes, 30 monitoring points and each time
step being stored, the size of the history file will be of the order of 360 kBytes. For the same
model but now with 10 layers in the vertical the file size will increase to about 4 MBytes. These
estimates show that history files are rather small. Unless the number of monitoring points is
excessively large the history files are typically much smaller than the map output files.

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6.3.2

Map file
The size of the map file is determined by:

The size of the model, i.e. the number of active grid cells multiplied by the number of layers
(Mmax · Nmax · Kmax): M1.
The number of quantities stored: M2.
The number of process parameters taken into account, such as salinity, temperature,
constituents and turbulence quantities: M3.

The number of time steps for which the map file is written: M4.

Remark:
For a more refined estimate you should distinguish between parameters that depend
or not on the number of layers used (such as the water level). For a 3D simulation the
latter quantities can be neglected, for a 2D simulation they must be accounted for. As a
first estimate we double the number of quantities M2 in a 2D simulation.

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As a first approximation you can use M2 = 15 for a 3D simulation and M2 = 30 for a 2D
simulation.
You can estimate the size of a map file (in bytes) from the following equation:
size map file = M1 · (M2 + M3) · M4 · 4 bytes.
Example

For a 3D simulation with 50 by 50 points and 5 layers, simulated with density driven currents
(salinity and temperature), simulation results stored for a period of 12 hours and 30 minutes,
and the file is written with an interval of 30 minutes the size of the map file will be about 31
MBytes. For larger models the map file can easily become excessively large, as result the
map file is less frequently written, for instance every 2 or 3 hours.
6.3.3

Print file

The print file is a formatted ASCII file with a size that can be large, varying from hundreds of
Kbytes to hundreds of Mbytes. Its size depends on:

The number of grid points: P1.
The number of layers in the vertical: Kmax.
The print flags for the map data requested: P2.
The number of times the map data is written to the file: P3.
The number of monitoring stations: P4.
The print flags for the history data requested: P5.
The number of times the history data is written to the file: P6.

You can estimate the size of a print file (in bytes) from the following equation:
size print file = 2 · (P1 · Kmax · P2 · P3 + P4 · P5 · P6) · 4 bytes
The factor of 2 is applied for all explaining text included in the file.

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Example
For a similar simulation as in the former section and all print flags checked, i.e. roughly 15
items, the print file is found to be in the order of 36 MBytes; its size is found to be determined
by the map data.
6.3.4

Communication file
The size of the communication or COM-file (e.g. for the other Delft3D modules, such as the
water quality module WAQ) from the hydrodynamic simulation is determined by:

The number of grid cells in horizontal and vertical direction, i.e. Mmax · Nmax · Kmax: C1.
The number of quantities stored: C2.
The number of process parameters taken into account, such as salinity, temperature,
constituents and turbulence quantities: C3.

The number of time steps, for which the communication file is written: C4.

You can estimate the size of a communication file (in bytes) from the following formula:

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size communication file = C1 · (C2 + C3) · C4 · 4 bytes.
As a first approximation you can use C2 = 15.
Example

A COM-file size of 20 MBytes should be expected for a model containing 50 by 50 points by 5
layers, simulated with density driven currents and simulation results stored for a period of 12
hrs 30 min, and the file is written with an interval of 15 minutes.
For a more refined estimate you should account for parameters that are stored only once and
parameters that are stored for each layer. However, the contribution of the latter to the file size
easily dominates by far the contribution of the other parameters.
Remark:
The file sizes given are indicative and the figures may not be linearly extrapolated to
determine the file size when the number of grid points is enlarged.
6.4

Command-line arguments

When using Delft3D-MENU to start a Delft3D-FLOW calculation, an XML-formatted configuration file will be generated automatically named . The calculation
itself is started by executing:
d_hydro.exe

With:

d_hydro.exe
The name of the executable to be started
The (only) command-line argument with default name
When using a script to start a Delft3D-FLOW calculation, the XML-formatted configuration file
has to be generated manually. There are three ways to do this:
1 Use one of the examples at https://svn.oss.deltares.nl/repos/delft3d/
trunk/examples as a start, both for example configuration files and for run scripts.

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2 Use the tcl script <.../menu/bin/create_config_xml.tcl> inside the Delft3D installation directory.
3 Use a text editor and write the file from scratch. Use the following (minimum) example as
a start:

flow2d3d
f34.mdf

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Remarks:
The automatically generated XML configuration file contains comments about optional
parameters.
The automatically generated XML configuration file itself is generated using the script
<.../menu/bin/create_config_xml.tcl> mentioned above.
The site http://oss.deltares.nl/web/delft3d contains a lot of information
about running a calculation.
Frequently asked questions

This chapter aims to help you with common questions that may arise while using Delft3DFLOW.
1 Question
What to do if the message No convergence in UZD appear often in the diagnostic file
Answer
In general this message appear in the beginning of your simulation and it means that the
Red-Black Jacobi iteration is not converged. If this iteration process is not converged the
computed momentum has not reached the desired accuracy, after the maximum number
of iterations (i.e. hard coded on 50 iterations). As no convergence is reported for the
first few time steps (tidal cycles) there is no need to adjust the input parameters of your
simulation.
The simulations of Delft3D-FLOW are boundary driven and the mismatch of momentum
should disappears after a few tidal cycles. But if the message No convergence in UZD still
appears after a few tidal cycles you have to decrease the timestep.
2 Question
What to do if the message Water level gradient too high > x m (per 0.5 DT) after nst
timesteps in the following points: m, n appear in the diagnostic file
Answer
In general this message appear in the beginning of your simulation and it means that the
water level changes are too high for the given time step (nst) and at location (m, n).
The simulations of Delft3D-FLOW are boundary driven and the mismatch should disappears after a few tidal cycles. But if the message Water level gradient too high . . . still
appears after a few tidal cycles you have to decrease the timestep.

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7 Visualise results
7.1

Introduction
Visualisation and animation of results is an essential part of presenting the results of your
project. In Delft3D-FLOW you have several options:

Online Visualisation: to inspect your results during the computation, see section 4.5.12.
GPP: to display and print a large variety of graphs, store the defined sets of figures in a
session file and use the same definitions in a next computation.

Delft3D-QUICKPLOT: to display quickly and print a large variety of graphs, save the defined sets of figures, etc.

Delft3D-MATLAB1 interface: to load, process or display your results in the MATLAB envi-

ronment.
GISVIEW interface: to load, process or display your results in the ArcGIS2 environment.
The interfaces to MATLAB and ArcGIS are additional utilities in Delft3D and must be acquired
separately.

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In the following sections we will briefly discuss each of these options; for full details you are
referred to the respective User Manuals.
Working with GPP

GPP offers a comprehensive selection and plotting facility to visualise or animate simulation
results, to import and visualise other data such as measurements, or to export selected data
sets of the results for use in other programs. You can define a single figure or a set of figures
and inspect it on screen or make a hardcopy of it on one of the supported hard copy devices.
The figures can be processed in an interactive manner or in the background (batch) mode.
In this section we only give a very concise description of the post-processor. For a detailed
description of its use and functionalities you are referred to the GPP User Manual.
7.2.1

Overview

When executing a project with many simulations the amount of data from which a set will be
visualised can be enormously large; also the files in which the data are stored can be very
large. Therefore it is not optimal to search the original result files over and over again for each
parameter or for each new figure. GPP, instead, provides a mechanism to make a selection of
the various results and parameters before starting the actual visualisation process and makes
a kind of reference list to these sets of data. Next you can define one or more graphs and
fill them with data from these data sets. As GPP knows were to find this data, retrieving the
data is executed very efficiently. This efficiency is further increased by the option to select all
observation points for a certain quantity or to select all time instances at which a quantity is
stored in the map file and let you make the final selection when producing the figure.
GPP has access to the communication file and to the result files of all Delft3D modules and
in fact to many other programs of Deltares, so you can combine almost any kind of data in a
figure.
GPP uses a certain hierarchy in the data and the meta-data, see Figure 7.1.
1
2

MATLAB is software for PC desktop and is a trademark of The MathWorks, Inc, Natick, MA, USA.
ArcGIS is GIS-software for desktop and is a trademark of ESRI, Inc. Redlands, CA, USA.

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M eta-data

Data

m odels

file types

files

presentation

data sets

plots

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layouts

Session file

Figure 7.1: Hierarchy of GPP

We distinguish meta-data to specify the definitions of a figure at a high level of abstraction
(left part of Figure 7.1) and the actual data (right part of Figure 7.1).
Meta-data:
models

file types

presentations
layouts

Data:
files
data sets
plots

session file

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Defines the set of models the results of which can be visualised.
You can change this set of models to limit the options presented in
GPP menus.
Defines the set of file types that can be used.
You can change this set of file types to limit the options presented in
GPP menus.
Defines the set of data-presentation methods, such as contour maps
or xy-graphs.
Defines the set of layouts that can be used in a figure.
You specify the general set-up of a figure by defining the appropriate
layout, the size of the graph, the plot areas, their position, additional
text etc.

The actual files to be used in your plot session.
The actual data sets selected from the files and to be used in the
visualisation.
The actual figures, including the data, which will be presented on
your monitor or printed on paper.
An ASCII file containing all information that defines the figures. For
the data only the references to the data is stored in the session file,
not the data itself.

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Figure 7.2: Main window of GPP

7.2.2

Launching GPP
To start GPP:

Select from the Delft3D-MENU FLOW - GPP and next Figure 7.2 is displayed.
The basic functions are shortly described below; for full details you are referred to the GPP
User Manual.
Session

Description
Datasets

Plots

Add
Preview
Combine

Export
Delete

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To load an existing session file or to save the settings and selections
of the current session in a session file for later use.
To give a short description of a session file; this information is used
only for reference.
List of pre-selected data sets to be used in the current plot session.
You can give selected data sets a useful name. At start-up the selections are displayed of the previous plot session in the current directory.
List of pre-selected plot layouts to be used in the current plot session.
At start-up the selections are displayed of the previous plot session
in the current directory.
To add a data set or plot layout, depending which function on the left
side of the list box has been selected.
To preview a selected data set or plot layout from the list displayed
in the list box.
To combine any of the available (single) data sets to a new data set,
such as multiply, divide, take the maximum value etc. and save the
new data set under a unique name.
To export the selected single or combined data set to an ASCII file
or GIS-file (for single data sets only).
To delete the selected data set or plot layout.

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Figure 7.3: Parameters and locations in the file

To add a data set of a specific result file to the Available data sets in Figure 7.2:
Select Datasets - Add in Figure 7.2.
Click Select File in the Add dataset window, Figure 7.3.
Select the required data file in the file selection window that is being displayed.
The parameters and locations (or time in case of map-results) available in a selected result
file are displayed in the Add dataset window, see Figure 7.3.
You can make as many selections from a specific result file, or from different results files (to
combine results from different computations or models) as you like.
To have a quick view on a data set:
Select in Figure 7.2 the required data set and click Preview.
The selected data set and a default plot layout will be displayed in the Plot window, see
Figure 7.3.
Remark:
GPP recognises the type of data selected and uses an appropriate default presentation
method to display the results.
In Figure 7.4 some of the options are displayed to change attributes of the figure.

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Figure 7.4: Some options to change the plot attributes

You are referred to the User Manual of GPP for full details on how to use GPP.
7.3

Working with Delft3D-QUICKPLOT

A graphical interface, Delft3D-QUICKPLOT, see Figure 7.5, is provided to make a basic graphical representation of the data or make a quick animation. The interface can be started from
the Delft3D-MENU or by typing d3d_qp at the MATLAB command prompt.
The interface allows to open the binary Delft3D output files (both NEFIS and NetCDF) and to
select data fields. After making a selection of time steps, stations and (m, n, k) indices, you
can either load the data (Open a data file button) or plot the data (Quick View button). See the
Delft3D-QUICKPLOT User Manual for full details and a description of the routines and their
use.
7.4

GISVIEW interface

To access, visualise and process Delft3D map-results in a GIS-environment, an interface
between Delft3D and ArcGIS was developed. This interface is provided as an extension to
ArcGIS. From a user point of view three menu-options are added to the standard menu-bar of
ArcGIS.
For full details of the GISVIEW interface you are referred to the GISVIEW User Manual
(Delft3D-GISVIEW UM, 2013).

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Figure 7.5: Delft3D-QUICKPLOT interface to Delft3D result

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8 Manage projects and files
Introduction
When executing a project generally a large number of files are created. Typically, some of
these files have a rather general use and will not or hardly change during the project, such
as the curvilinear grid, while other files may change appreciably for each simulation, such as
the bed stress or wind field during a calibration phase. Organising the files in your project in a
logical sense is important to keep track of all simulations and changes you have investigated.
We suggest to organise your project directory along the hierarchy of steps typical for your
project.

Hydrodynamics:

A typical hierarchy of steps for a hydrodynamic – water quality assessment study might be:

Inspection and analysis of the problem to be solved, of the available data and information
of the area and of the processes involved.

Setting up of the hydrodynamic model, i.e. definition of the model extent, the grid size, the

number of layers (in case of a 3D simulation), generation of the land boundary outline and
the curvilinear grid.
Collecting and processing the bathymetric data and generating the model bathymetry.
Preparing boundary conditions.
Processing field measurements for calibration and verification data in stations, crosssections and verticals, both as time-series and as maps.
Defining a couple of simulations to make a first assessment of the model behaviour.
Defining the calibration runs to be executed.
Accessing the results, performing a (in most cases several) sensitivity analysis and iterating on the calibration process if necessary.
Determining and executing the verification runs and accessing the final accuracy of the
simulations.
Determining the simulation period to be stored for the water quality study and generating
the hydrodynamic database for the water quality simulations.

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8.1

Water quality:

A similar set of steps can be defined for the water quality assessment study.
Determining if the same or a coarser grid shall be used for the water quality simulations
and transfer the hydrodynamics defined on the hydrodynamic grid to the water quality grid.

Determining the water quality processes and parameters that must be involved.
Remark:
The number of water quality computations can be very large due to the number of processes that must be simulated and the number of parameters that must be investigated
in a sensitivity analysis.
This hierarchy of steps, the related computations each with its specific input, attribute and
results files must be organised in some way to control the large amounts of files. This is
necessary to guarantee the quality of the results and the consistency between input data and
result.

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8.1.1

Managing projects
It is of utmost importance to structure your project in a logical way. This will make it easy to
understand its structure by colleagues working on the same project. Furthermore, it helps to
retrieve results when after some time you have to answer additional questions.
There are many ways to structure a project and there is probably not just one best way. The
structure you want to apply may depend on company rules or personal preferences. Below
we give some general ideas to structure your projects.
To manage your projects you might apply the following steps:

Define for each project a separate directory or file system.
Organise the directory in-line with the various steps mentioned in the introduction, i.e. pre-

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pare sub-directories for preparing the boundary conditions, the field data, the bathymetry,
the grid, etc. and give them useful names.
Execute each dominant step in the project, such as preliminary assessment, calibration
and verification in separate sub-directories and execute sensitivity studies within these
steps in sub-sub-directories.
Remark:
Never combine the program files with project data; define a project directory.
Currently, the FLOW Graphical User Interface (GUI) only supports short file names in a working directory, i.e. all files used in a scenario must be in the current working directory. Organising your project as sketched above means that many unchanged files must be copied to each
(sub-)directory and so will reside many times on your file system, thereby increasing your disk
requirements. However, the alternative of ‘all scenarios in one and the same directory’ is not
attractive either as you easy will have hundreds of files. You are advised to prefer the structuring of your simulations above optimising the amount of disk space used for the attribute
files. This problem is solved to a large extent if the FLOW-GUI can handle long file names and
paths. This option will be available in a next release.
A probably more urgent problem is to handle the large result files; they may easily result in
full file systems. An option in case of a full file system is to move the large result files to a
background storage facility and only load them back on the file system when necessary. The
result files are usually the real big ones so the storage problem is relieved quite a bit by moving
these files. Online compression is only a partial solution as a typical compression factor for
result files is only 2 or 3. Fortunately, the costs or mass storage devices is decreasing at a
rapid rate.
8.1.2

Managing files

The length of the MDF-file name is limited to 256 characters, and has the form .
Do not use blanks in the runid.

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9 Conceptual description
9.1

Introduction
Increasing awareness of environmental issues has focused the attention of scientists and engineers on the problem of predicting the flow and dispersion of contaminants in water systems.
Reliable information on water flow, waves, water quality, sediment transport and morphology
can be obtained from appropriate mathematical models. In general the first step in such modelling activities concerns the simulation of the flow itself. Whether the problem is related, for
example, to the stability of a hydraulic structure, to salt intrusion, to the dispersion of pollutants or to the transport of silt and sediment, flow simulations usually form the basis of the
investigations to be carried out.

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Delft3D is the integrated flow and transport modelling system of Deltares for the aquatic environment. The flow module of this system, viz. Delft3D-FLOW, provides the hydrodynamic
basis for other modules such as water quality, ecology, waves and morphology. For steady and
non-steady modelling of the far-field water quality and ecology, it is coupled with the far-field
water quality module D-Water Quality. Non-steady modelling of the mid-field water quality
is performed by coupling the flow module to the particle tracking simulation module D-Waq
PART. For the interaction between waves and currents the flow module may be coupled with
the short-waves model Delft3D-WAVE.
In the vertical direction Delft3D-FLOW offers two different vertical grid systems: a so-called σ
co-ordinate system (σ -model) introduced by Phillips (1957) for ocean models and the Cartesian Z co-ordinate system (Z -model).
This chapter gives some background information on the conceptual model of the Delft3DFLOW module. The numerical algorithms are described in chapter 10. Most of the concepts
and algorithms are applicable to both the σ -model and Z -model. However, the specifics of
the Z co-ordinate system will be presented in more detail in chapter 12.
9.2
9.2.1

General background

Range of applications of Delft3D-FLOW

The hydrodynamic module Delft3D-FLOW simulates two-dimensional (2DH, depth-averaged)
or three-dimensional (3D) unsteady flow and transport phenomena resulting from tidal and/or
meteorological forcing, including the effect of density differences due to a non-uniform temperature and salinity distribution (density-driven flow). The flow model can be used to predict
the flow in shallow seas, coastal areas, estuaries, lagoons, rivers and lakes. It aims to model
flow phenomena of which the horizontal length and time scales are significantly larger than
the vertical scales.
If the fluid is vertically homogeneous, a depth-averaged approach is appropriate. Delft3DFLOW is able to run in two-dimensional mode (one computational layer), which corresponds
to solving the depth-averaged equations. Examples in which the two-dimensional, depthaveraged flow equations can be applied are tidal waves, storm surges, tsunamis, harbour
oscillations (seiches) and transport of pollutants in vertically well-mixed flow regimes.
Three-dimensional modelling is of particular interest in transport problems where the horizontal flow field shows significant variation in the vertical direction. This variation may be
generated by wind forcing, bed stress, Coriolis force, bed topography or density differences.
Examples are dispersion of waste or cooling water in lakes and coastal areas, upwelling and
downwelling of nutrients, salt intrusion in estuaries, fresh water river discharges in bays and

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thermal stratification in lakes and seas.
Physical processes
The numerical hydrodynamic modelling system Delft3D-FLOW solves the unsteady shallow
water equations in two (depth-averaged) or in three dimensions. The system of equations
consists of the horizontal equations of motion, the continuity equation, and the transport
equations for conservative constituents. The equations are formulated in orthogonal curvilinear co-ordinates or in spherical co-ordinates on the globe. In Delft3D-FLOW models with
a rectangular grid (Cartesian frame of reference) are considered as a simplified form of a
curvilinear grid. In curvilinear co-ordinates, the free surface level and bathymetry are related
to a flat horizontal plane of reference, whereas in spherical co-ordinates the reference plane
follows the Earth’s curvature.

The flow is forced by tide at the open boundaries, wind stress at the free surface, pressure
gradients due to free surface gradients (barotropic) or density gradients (baroclinic). Source
and sink terms are included in the equations to model the discharge and withdrawal of water.
The Delft3D-FLOW model includes mathematical formulations that take into account the following physical phenomena:

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9.2.2

Free surface gradients (barotropic effects).
The effect of the Earth’s rotation (Coriolis force).
Water with variable density (equation of state).
Horizontal density gradients in the pressure (baroclinic effects).
Turbulence induced mass and momentum fluxes (turbulence closure models).
Transport of salt, heat and other conservative constituents.
Tidal forcing at the open boundaries.
Space and time varying wind shear-stress at the water surface.
Space varying shear-stress at the bottom.
Space and time varying atmospheric pressure on the water surface.
Time varying sources and sinks (e.g. river discharges).
Drying and flooding of tidal flats.
Heat exchange through the free surface.
Evaporation and precipitation.
Tide generating forces.
Effect of secondary flow on depth-averaged momentum equations.
Lateral shear-stress at wall.
Vertical exchange of momentum due to internal waves.
Influence of waves on the bed shear-stress (2D and 3D).
Wave induced stresses (radiation stress) and mass fluxes.
Flow through hydraulic structures.
Wind driven flows including tropical cyclone winds.

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Conceptual description

Assumptions underlying Delft3D-FLOW
In Delft3D-FLOW the 2D (depth-averaged) or 3D non-linear shallow water equations are
solved. These equations are derived from the three dimensional Navier-Stokes equations for
incompressible free surface flow. The following assumptions and approximations are applied:

In the σ co-ordinate system the depth is assumed to be much smaller than the horizontal

length scale. For such a small aspect ratio the shallow water assumption is valid, which
means that the vertical momentum equation is reduced to the hydrostatic pressure relation. Thus, vertical accelerations are assumed to be small compared to the gravitational
acceleration and are therefore not taken into account. When this assumption is not valid
then Delft3D provides an option to apply the so-called Non-hydrostatic pressure model in
the Z -model. For details, we refer to chapter 12 and section B.12 of this User Manual.
The effect of variable density is only taken into account in the pressure term (Boussinesq
approximation).
In the σ co-ordinate system, the immediate effect of buoyancy on the vertical flow is not
considered. In Delft3D-FLOW vertical density differences are taken into account in the
horizontal pressure gradients and in the vertical turbulent exchange coefficients. So the
application of Delft3D-FLOW is restricted to mid-field and far-field dispersion simulations
of discharged water.
For a dynamic online coupling between morphological changes and flow the 3D sediment
and morphology feature is available.
In a Cartesian frame of reference, the effect of the Earth’s curvature is not taken into
account. Furthermore, the Coriolis parameter is assumed to be uniform unless specifically
specified otherwise.
In spherical co-ordinates the inertial frequency depends on the latitude.
At the bottom a slip boundary condition is assumed, a quadratic bottom stress formulation
is applied.
The formulation for the enhanced bed shear-stress due to the combination of waves and
currents is based on a 2D flow field, generated from the velocity near the bed using a
logarithmic approximation.
The equations of Delft3D-FLOW are capable of resolving the turbulent scales (large eddy
simulation), but usually the hydrodynamic grids are too coarse to resolve the fluctuations.
Therefore, the basic equations are Reynolds-averaged introducing so-called Reynolds
stresses. These stresses are related to the Reynolds-averaged flow quantities by a turbulence closure model.
In Delft3D-FLOW the 3D turbulent eddies are bounded by the water depth. Their contribution to the vertical exchange of horizontal momentum and mass is modelled through
a vertical eddy viscosity and eddy diffusivity coefficient (eddy viscosity concept). The
coefficients are assumed to be proportional to a velocity scale and a length scale. The
coefficients may be specified (constant) or computed by means of an algebraic, k -L or
k -ε turbulence model, where k is the turbulent kinetic energy, L is the mixing length and
ε is the dissipation rate of turbulent kinetic energy.
In agreement with the aspect ratio for shallow water flow, the production of turbulence is
based on the vertical (and not the horizontal) gradients of the horizontal flow. In case
of small-scale flow (partial slip along closed boundaries), the horizontal gradients are included in the production term.
The boundary conditions for the turbulent kinetic energy and energy dissipation at the free
surface and bottom assume a logarithmic law of the wall (local equilibrium).
The eddy viscosity is an-isotropic. The horizontal eddy viscosity and diffusivity coefficients
should combine both the effect of the 3D turbulent eddies and the horizontal motions that
cannot be resolved by the horizontal grid. The horizontal eddy viscosity is generally much
larger than the vertical eddy viscosity.
For large-scale flow simulations, the tangential shear-stress at lateral closed boundaries
can be neglected (free slip). In case of small-scale flow partial slip is applied along closed

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boundaries.
For large-scale flow simulations, the horizontal viscosity terms are reduced to a bi-harmonic
operator along co-ordinate lines. In case of small-scale flow the complete Reynold’s stress
tensor is computed. The shear-stress at the side walls is calculated using a logarithmic
law of the wall.
In the σ co-ordinate system, Delft3D-FLOW solves the so-called long wave equation. The
pressure is hydrostatic and the model is not capable of resolving the scales of short waves.
Therefore, the basic equations are averaged in analogy with turbulence introducing socalled radiation stresses. These stresses are related to the wave quantities of Delft3DWAVE by a closure model.
It is assumed that a velocity point is set dry when the actual water depth is below half
of a user-defined threshold. If the point is set dry, then the velocity at that point is set to
zero. The velocity point is set wet again when the local water depth is above the threshold.
The hysteresis between drying and flooding is introduced to prevent drying and flooding in
two consecutive time steps. The drying and flooding procedure leads to a discontinuous
movement of the closed boundaries at tidal flats.
A continuity cell is set dry when the four surrounding velocity points at the grid cell faces
are dry or when the actual water depth at the cell centre is below zero (negative volume).
The flux of matter through a closed wall and through the bed is zero.
Without specification of a temperature model, the heat exchange through the free surface
is zero. The heat loss through the bottom is always zero.
If the total heat flux through the water surface is computed using a temperature excess
model the exchange coefficient is a function of temperature and wind speed and is determined according to Sweers (1976). The natural background temperature is assumed
constant in space and may vary in time. In the other heat flux formulations the fluxes
due to solar radiation, atmospheric and back radiation, convection, and heat loss due to
evaporation are modelled separately.
The effect of precipitation on the water temperature is accounted for.

Governing equations

In this section, we will present in detail the governing equations. Below an overview of the
symbols that are used in the equations is presented.
List of Symbols
Symbol

Units

Meaning

A(m,n)
Âδ
a
α
Bk

area of computational cell at location (m, n)

m
m
m2 /s3

near-bed peak orbital excursion
reference height as defined by Van Rijn
artificial compression coefficient
buoyancy flux term in transport equation for turbulent kinetic
energy
buoyancy flux term in transport equation for the dissipation of
turbulent kinetic energy
2D Chézy coefficient
3D Chézy coefficient
wind drag coefficient
mass concentration
mass concentration at reference height a

m2 /s4

C, C2D
C3D
Cd
c
ca

m1/2 /s
m1/2 /s
kg/m3
kg/m3

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Units

Meaning

cp
cµ
c0µ
D
D
DP SED
D∗
d
Ds
D50
D90
E
E
ea
es
Fc
Fx
Fy
Fξ
Fη
f
f (Fc )

J/(kg◦ C)
kg/s3
kg/(m2 s)
m
m
m
m
m
m/s
kg/(m2 s)
mbar
mbar
m/s2
m/s2
m/s2
m/s2
1/s
-

fFIXFAC
fMORFAC
fw
fw0
fwind
p
Gξξ
p
Gηη

constant relating mixing length, turbulent kinetic energy and
dissipation in the k -ε model
specific heat of sea water
calibration constant
constant in Kolmogorov-Prandtl’s eddy viscosity formulation
dissipation rate wave energy
deposition rate cohesive sediment
depth of sediment available at the bed
non-dimensional particle diameter
depth below some horizontal plane of reference (datum)
representative diameter of suspended sediment
median diameter of sediment
sediment diameter
evaporation
erosion rate cohesive sediment
vapour pressure at a given air temperature
saturated vapour pressure at a given temperature
cloudiness factor
radiation stress gradient in x-direction
radiation stress gradient in y -direction
turbulent momentum flux in ξ -direction
turbulent momentum flux in η -direction
Coriolis parameter (inertial frequency)
attenuation function for the solar and atmospheric (long wave)
radiation
fixed layer proximity factor
user-defined morphological acceleration factor
total wave friction factor
grain-related wave friction factor
dependency of λ of the wind speed in temperature excess
model
coefficient used to transform curvilinear to rectangular coordinates
coefficient used to transform curvilinear to rectangular coordinates
acceleration due to gravity
total water depth (H = d + ζ ; d positive downward)
root-mean-square wave height
spiral motion intensity (secondary flow)
equilibrium intensity of spiral motion due to curvature of stream
lines
equilibrium intensity of spiral motion due to Coriolis
turbulent kinetic energy
increased (apparent) bed roughness height felt by the current
in the presence of waves
Nikuradse roughness length
current related bed roughness height
wave number
wave related bed roughness height
mixing length

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Symbol

m
m

g
H
Hrms
I
Ibe

m/s2
m
m
m/s
m/s

Ice
k
ka

m/s
m2 /s2
m

ks
ks,c
kx , ky
ks,w
L

m
m
1/m
m
m

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Units

Meaning

`
MxS
MyS
Mξ
Mη
n
P
P
Pk

kg m/s
kg m/s
m/s2
m/s2
m−1/3 s
kg/(ms2 )
m/s
m2 /s3

Pξ
Pη
Pε

kg/(m2 s2 )
kg/(m2 s2 )
m2 /s4

Q
Qa
Qan
Qbr
Qco
Qev
Qs
Qsc
Qsn
Qtot
qin
qout
R
Ri
Rs
r

m/s
J/(m2 s)
J/(m2 s)
J/(m2 s)
J/(m2 s)
J/(m2 s)
J/(m2 s)
J/(m2 s)
J/(m2 s)
J/(m2 s)
1/s
1/s
m
m
-

index number of sediment fraction
depth-averaged mass flux due to Stokes drift in x-direction
depth-averaged mass flux due to Stokes drift in y -direction
source or sink of momentum in ξ -direction
source or sink of momentum in η -direction
Manning’s coefficient
hydrostatic water pressure
precipitation
production term in transport equation for turbulent kinetic energy
gradient hydrostatic pressure in ξ -direction
gradient hydrostatic pressure in η -direction
production term in transport equation for the dissipation of turbulent kinetic energy
global source or sink per unit area
atmospheric radiation (long wave radiation)
net atmospheric radiation
back radiation (long wave radiation)
heat loss due to convection
heat loss due to evaporation
solar radiation (short wave radiation)
solar radiation with a clear sky
net solar insolation
heat flux through free surface
local source per unit volume
local sink per unit volume
radius of the Earth
gradient Richardson’s number
radius of curvature of a streamline in the secondary flow model
reflection coefficient for solar and atmospheric (long wave) radiation
relative air humidity at a given temperature
salinity
representative surface area in heat model
maximum salinity for flocculation calculations
additional bedload transport vector. The direction of this vector
is normal to the unadjusted bedload transport vector, in the
down slope direction
magnitude of the unadjusted bedload transport vector (adjusted for longitudinal bed slope only)
mass bedload transport rate
magnitude of the bedload transport vector

|Sb0 |

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rhum
S
Sarea
Smax
Sb,n

Symbol

%
ppt
m2
ppt

Sb00
|Sb00 |
(m,n)
Sb,uu

kg/(ms)

s
S
T
T̄
T

ppt
◦
C
K
-

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kg/(ms)
kg/(ms)

computed bedload sediment transport vector in u-direction,
held at the u-point of the computational cell at location (m, n)
relative density of sediment fraction (= ρs /ρw )
salinity
temperature (general reference)
temperature (general reference)
non-dimensional bed-shear stress

Deltares

Conceptual description

Units

Meaning

Ta
Ta
Tback
Tp
TTHbottom
TTHsurface
Ts
Tξξ , Tηη ,
Tξη
t
U
Û
Ûδ
u
ub,cr
ub
u∗
u0∗
u∗
u∗b
ub∗
us∗
~
U

C
C
s
s
s
◦
C
kg/(ms2 )

non-dimensional bed-shear stress for reference concentration
air temperature
natural background temperature of water in the model area
peak wave period
Thatcher Harleman return time for the bed layer
Thatcher Harleman return time for the surface layer
water temperature at free surface
contributions secondary flow to shear stress tensor

s
m/s

time
depth-averaged velocity in ξ -direction

m/s

velocity of water discharged in ξ -direction

m/s
m/s
m/s
m/s
m/s
m/s
m/s
m/s
m/s
m/s

peak orbital velocity at the bed
flow velocity in the x- or ξ -direction
critical (threshold) near-bed fluid velocity
near-bed fluid velocity vector
friction velocity due to currents or due to current and waves
effective bed shear velocity
vertically averaged friction velocity
friction velocity at the bed
modified friction velocity near bed
friction velocity at the free surface

◦

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◦

Symbol

m/s

magnitude of depth-averaged horizontal velocity vector

(U, V )T

U10
Û
Û orb
uS
ũ
v
vb
V
V̂
vS
ṽ
w
ws,0
ws
x, y, z
z0
z̃0
z0n
∂zb
∂s
∂z(u)
∂x

m/s

averaged wind speed at 10 m above free surface

m/s

velocity of water discharged in x- or ξ -direction

m/s
m/s
m/s
m/s
m/s
m/s

amplitude of the near-bottom wave orbital velocity
Stokes drift in x- or ξ -direction
total velocity due to flow and Stokes drift in x- or ξ -direction
fluid velocity in the y - or η -direction
velocity at bed boundary layer in y - or η -direction
depth-averaged velocity in y - or η -direction

m/s
m/s
m/s
m/s
m/s
m/s
m
m
m
m
-

velocity of water discharged in y - or η -direction
Stokes drift in y - or η -direction
total velocity due to flow and Stokes drift in y - or η -direction
fluid velocity in z -direction
particle settling velocity in clear water (non-hindered)
particle (hindered) settling velocity in a mixture
Cartesian co-ordinates
bed roughness length
enhanced bed roughness length due to current and waves
roughness length normal to the boundary
bed slope in the direction of bedload transport

∂z(v)
∂y

∂zb
∂n

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bed slope in the positive x-direction evaluated at the downwind

u-point
bed slope in the positive y -direction evaluated at the downwind

v -point
bed slope in the direction normal to the bedload transport vector

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Symbol

Units

Meaning

αbn
β
βc

δm
δw
χ
∆r
(m,n)
∆SED
∆t
∆x(m,n)
∆y (m,n)
∆zb
∆zs
∆σb
εε

m
m
deg
m

user-defined coefficient
ratio of sediment and fluid mixing
coefficient to account for secondary flow in momentum equations
thickness of wave boundary mixing layer
thickness of wave boundary layer
astronomical argument of a tidal component
ripple height

change in quantity of bottom sediment at location (m, n)
computational time-step
cell width in the x-direction, held at the v -point of cell (m, n)
cell width in the y -direction, held at the u-point of cell (m, n)
thickness of the bed layer
thickness of the surface layer
thickness of the bed boundary layer in relative co-ordinates
dissipation in transport equation for dissipation of turbulent kinetic energy
dissipation in transport equation for turbulent kinetic energy
emissivity coefficient of water at air-water interface
fluid diffusion in the z -direction
fluid diffusion coefficients in the x, y, z -directions, respectively

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kg/m2
s
m
m
m
m
m2 /s4

ε
ε
εf
εf,x , εf,y ,
εf,z
εs
εs,x , εs,y ,
εs,z
γ
γ
φ
φ

m2 /s3
m2 /s
m2 /s

φ
ϕ
ϕe
ϕeo
ϕo
λ
λd
νmol
back
νH
νVback
back
DH
DVback
νV
ν2D
ν3D

deg
m
m
m
m
deg
1/s
m2 /s
m2 /s
m2 /s
m2 /s
m2 /s
m2 /s
m2 /s
m2 /s

η
µc
ρ

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m2 /s
m2 /s

m−1
mbar/◦ C
deg
J/(sm2◦ C)

–
–
kg/m3

sediment diffusion in the z -direction
sediment diffusion coefficients in the x, y, z -directions, respectively
extinction coefficient (measured)
Bowen’s constant
latitude co-ordinate in spherical co-ordinates
exchange coefficient for the heat flux in excess temperature
model
internal angle of friction of bed material (assumed to be 30◦ )
equilibrium tide
perturbation of the equilibrium tide due to earth tide
perturbation of the equilibrium tide due to tidal load
perturbation of the equilibrium tide due to oceanic tidal load
longitude co-ordinate in spherical co-ordinates
first order decay coefficient
kinematic viscosity (molecular) coefficient
background horizontal eddy viscosity (ξ - and η -direction)
background vertical eddy viscosity for momentum equations
background horizontal eddy diffusivity (ξ - and η -direction)
background vertical eddy diffusivity for transport equation
vertical eddy viscosity
part of eddy viscosity due to horizontal turbulence model
part of eddy viscosity due to turbulence model in vertical direction
relative availability of the sediment fraction in the mixing layer
efficiency factor current
density of water

Deltares

Conceptual description

Units

Meaning

ρa
ρ0
σ
σ

kg/m3
kg/m3
J/(m2 s K4 )
–

σc
σc0

–
–

σmol

–

τb
τbξ
τbη
τc
τw
τm

N/m2
kg/(ms2 )
kg/(ms2 )
kg/(ms2 )
kg/(ms2 )
kg/(ms2 )

density of air
reference density of water
Stefan-Boltzmann’s constant
z−ζ
scaled vertical co-ordinate; σ = d+ζ ;
(surface, σ = 0; bed level, σ = −1)
Prandtl-Schmidt number
Prandtl-Schmidt number for constituent (0.7 for salinity and
temperature, 1.0 for suspended sediments)
Prandtl-Schmidt number for molecular mixing
(700 for salinity, 6.7 for temperature)
bed shear stress due to current and waves
bed shear stress in ξ -direction
bed shear stress in η -direction
magnitude of the bed shear stress due to current alone
magnitude of the at bed shear stress due to waves alone
magnitude of the wave-averaged at bed shear stress for combined waves and current
bed shear stress due to current
critical bed shear stress
bed shear stress due to current in the presence of waves
bed shear stress due to waves
critical bed shear stress
user-defined critical deposition shear stress
user-defined critical erosion shear stress
mean bed shear stress due to current and waves
maximum bottom shear stress with wave-current interaction
mean (cycle averaged) bottom shear stress with wave-current
interaction
shear stress at surface in ξ -direction
shear stress at surface in η -direction
velocity in the σ -direction in the σ -co-ordinate system
angular frequency waves
angular frequency of tide and/or Fourier components
heat flux through free surface
horizontal, curvilinear co-ordinates
water level above some horizontal plane of reference (datum)
bottom tide
earth tide
tidal loading

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Symbol

τb,c
τb,cr
τb,cw
τb,w
τcr
τcr,d
τcr,e
τcw
τmax
τmean

N/m2
N/m2
N/m2
N/m2
N/m2
N/m2
N/m2
N/m2
N/m2
N/m2

τsη
τsη
ω
ω
ω
ψ
ξ, η
ζ
ζb
ζe
ζ eo

kg/(ms2 )
kg/(ms2 )
m/s
1/s
deg/hour
J/(m2 s)
m
m
m
m

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Hydrodynamic equations
Delft3D-FLOW solves the Navier Stokes equations for an incompressible fluid, under the shallow water and the Boussinesq assumptions. In the vertical momentum equation the vertical
accelerations are neglected, which leads to the hydrostatic pressure equation. In 3D models
the vertical velocities are computed from the continuity equation. The set of partial differential
equations in combination with an appropriate set of initial and boundary conditions is solved
on a finite difference grid, see chapter 10 for the numerical aspects.
In the horizontal direction Delft3D-FLOW uses orthogonal curvilinear co-ordinates. Two coordinate systems are supported:

Cartesian co-ordinates (ξ, η)
Spherical co-ordinates (λ, φ)
The boundaries of a river, an estuary or a coastal sea are in general curved and are not
smoothly represented on a rectangular grid. The boundary becomes irregular and may introduce significant discretization errors. To reduce these errors boundary fitted orthogonal
curvilinear co-ordinates are used. Curvilinear co-ordinates also allow local grid refinement in
areas with large horizontal gradients.

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9.3.1

Spherical co-ordinates are a special case of orthogonal curvilinear co-ordinates with:

ξ = λ,
p η = φ,
p Gξξ = R cos φ,
Gηη = R,

(9.1)

in which λ is the longitude, φ is the latitude and R is the radius of the Earth (6 378.137 km,
WGS84).
In Delft3D-FLOW the equations are formulated in orthogonal curvilinear co-ordinates. The
velocity scale is in physical space, but the components are perpendicular to the cell faces of
the curvilinear grid. The grid transformation introduces curvature terms in the equations of
motion.
In the vertical direction Delft3D-FLOW offers two different vertical grid systems: the σ coordinate system (σ -model) and the Cartesian Z co-ordinate system (Z -model). The hydrodynamic equations described in this section are valid for the σ co-ordinate system. The equations for the Z co-ordinate system are similar. Equations or relations that are fundamentally
different will be discussed separately and in detail in chapter 12.
The σ co-ordinate system
The σ -grid was introduced by Phillips (1957) for atmospheric models. The vertical grid consists of layers bounded by two σ -planes, which are not strictly horizontal but follow the bottom
topography and the free surface. Because the σ -grid is boundary fitted both to the bottom and
to the moving free surface, a smooth representation of the topography is obtained.
The number of layers over the entire horizontal computational area is constant, irrespective of
the local water depth (see Figure 9.2). The distribution of the relative layer thickness is usually
non-uniform. This allows for more resolution in the zones of interest such as the near surface
area (important for e.g. wind-driven flows, heat exchange with the atmosphere) and the near
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The σ co-ordinate system is defined as:

with:

z
ζ
d
H

z−ζ
z−ζ
=
,
d+ζ
H

(9.2)

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σ=

Figure 9.1: Definition of water level (ζ ), depth (h) and total depth (H ).

the vertical co-ordinate in physical space.
the free surface elevation above the reference plane (at z = 0).
the depth below the reference plane.
the total water depth, given by d + ζ .

At the bottom σ = −1 and at the free surface σ = 0 (see Figure 9.1). The partial derivatives
in the original Cartesian co-ordinate system are expressed in σ co-ordinates by the chain rule
introducing additional terms (Stelling and Van Kester, 1994). The flow domain of a 3D shallow
water model consists in the horizontal plane of a restricted (limited) area composed of open
and closed (land) boundaries and in the vertical of a number of layers. In a σ co-ordinate
system the number of layers is the same at every location in the horizontal plane, i.e. the layer
interfaces are chosen following planes of constant σ , see Figure 9.2. For each layer a set of
coupled conservation equations is solved.
Cartesian co-ordinate system in the vertical (Z -model)

In coastal seas, estuaries and lakes, stratified flow can occur in combination with steep topography. Although the σ -grid is boundary fitted (in the vertical), it will not always have enough
resolution around the pycnocline. The co-ordinate lines intersect the density interfaces that
may give significant errors in the approximation of strictly horizontal density gradients (Leendertse, 1990; Stelling and Van Kester, 1994). Therefore, recently a second vertical grid coordinate system based on Cartesian co-ordinates (Z -grid) was introduced in Delft3D-FLOW
for 3D simulations of weakly forced stratified water systems.
The Z -grid model has horizontal co-ordinate lines that are (nearly) parallel with density interfaces (isopycnals) in regions with steep bottom slopes. This is important to reduce artificial
mixing of scalar properties such as salinity and temperature. The Z -grid is not boundaryfitted in the vertical. The bottom (and free surface) is usually not a co-ordinate line and is
represented as a staircase (zig-zag boundary; see Figure 9.2).
Continuity equation
The depth-averaged continuity equation is derived by integration the continuity equation for
u = 0) over the total depth, taken into account the kinematic
incompressible fluids (∇ • ~

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Figure 9.2: Example of σ - and Z -grid

boundary conditions at water surface and bed level, and is given by:

p
Gηη

∂ (d + ζ) V
∂η
Gηη

Gξξ

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with U and V the depth averaged velocities

1
p

1
U=
d+ζ

1
V =
d+ζ

= (d + ζ)Q,

(9.3)

u dz =

u dσ

(9.4)

v dσ

(9.5)

−1
Z 0

v dz =

p
Gξξ

∂ (d + ζ) U
∂ζ
1
+p p
∂t
∂ξ
Gξξ Gηη

−1

and Q representing the contributions per unit area due to the discharge or withdrawal of water,
precipitation and evaporation:

(qin − qout ) dσ + P − E,

(9.6)

−1

with qin and qout the local sources and sinks of water per unit of volume [1/s], respectively, P
the non-local source term of precipitation and E non-local sink term due to evaporation. We
remark that the intake of, for example, a power plant is a withdrawal of water and should be
modelled as a sink. At the free surface there may be a source due to precipitation or a sink
due to evaporation.
Momentum equations in horizontal direction

The momentum equations in ξ - and η -direction are given by:

p
∂ Gηη
∂u
u ∂u
v ∂u
ω ∂u
v2
+p
+p
+
−p p
+
∂t
Gξξ ∂ξ
Gηη ∂η d + ζ ∂σ
Gξξ Gηη ∂ξ
p
∂ Gξξ
uv
1
+p p
− fv = − p
Pξ + F ξ +
Gξξ Gηη ∂η
ρ0 Gξξ

1
∂
∂u
+
νV
+ Mξ , (9.7)
∂σ
(d + ζ)2 ∂σ

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Conceptual description

and

p
∂ Gηη
∂v
u ∂v
v ∂v
ω ∂v
uv
+p
+p
+
+p p
+
∂t
Gξξ ∂ξ
Gηη ∂η d + ζ ∂σ
Gξξ Gηη ∂ξ
p
∂ Gξξ
u2
1
−p p
Pη + F η +
+ fu = − p
Gξξ Gηη ∂η
ρ0 Gηη

1
∂
∂v
+
νV
+ Mη . (9.8)
∂σ
(d + ζ)2 ∂σ

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The vertical eddy viscosity coefficient νV is defined in Equation (9.20). Density variations are
neglected, except in the baroclinic pressure terms, Pξ and Pη represent the pressure gradients. The forces Fξ and Fη in the momentum equations represent the unbalance of horizontal
Reynold’s stresses. Mξ and Mη represent the contributions due to external sources or sinks
of momentum (external forces by hydraulic structures, discharge or withdrawal of water, wave
stresses, etc.). The effects of surface waves on the flow as modelled in Delft3D-FLOW are
described in section 9.7.
Vertical velocities

The vertical velocity ω in the adapting σ -co-ordinate system is computed from the continuity
equation:

∂ (d + ζ) u
∂ζ
1
+p p
∂t
∂ξ
Gξξ Gηη

p
Gηη

p
∂ (d + ζ) v Gξξ
1
+p p
+
∂η
Gξξ Gηη
∂ω
+
= (d + ζ) (qin − qout ) . (9.9)
∂σ

At the surface the effect of precipitation and evaporation is taken into account. The vertical
velocity ω is defined at the iso σ -surfaces. ω is the vertical velocity relative to the moving
σ -plane. It may be interpreted as the velocity associated with up- or downwelling motions.
The “physical” vertical velocities w in the Cartesian co-ordinate system are not involved in
the model equations. Computation of the physical vertical velocities is only required for postprocessing purposes. These velocities can be expressed in the horizontal velocities, water
depths, water levels and vertical ω -velocity according to:

p
p
∂H ∂ζ
∂H ∂ζ
1
+
+ v Gξξ σ
+
+
w=ω+p p
u Gηη σ
∂ξ
∂ξ
∂η
∂η
Gξξ Gηη

∂H ∂ζ
+ σ
+
. (9.10)
∂t
∂t

Hydrostatic pressure assumption (for σ -grid)
Under the shallow water assumption, the vertical momentum equation is reduced to a hydrostatic pressure equation. Vertical accelerations due to buoyancy effects and due to sudden
variations in the bottom topography are not taken into account. So:

∂P
= −gρH.
∂σ

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(9.11)

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After integration, the hydrostatic pressure is given by:

Z
P = Patm + gH

ρ (ξ, η, σ 0 , t) dσ 0 .

(9.12)

Firstly, we consider water with a constant density and next with a non-uniform density.
For water of constant density and taking into account the atmospheric pressure, the pressure
gradients read:

1
g ∂ζ
1
∂Patm
p
Pξ = p
+ p
,
ρ0 Gξξ
Gξξ ∂ξ ρ0 Gξξ ∂ξ
1
1
g ∂ζ
∂Patm
p
+ p
.
Pη = p
ρ0 Gηη
Gηη ∂η ρ0 Gηη ∂η

(9.13)

(9.14)

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The gradients of the free surface level are the so-called barotropic pressure gradients. The
atmospheric pressure is included in the system for storm surge simulations. The atmospheric
pressure gradients dominate the external forcing at peak winds during storm events. Space
and time varying wind and pressure fields are especially important when simulating storm
surges.
In case of a non-uniform density, the local density is related to the values of temperature and
salinity by the equation of state, see section 9.3.4. Leibniz rule is used to obtain the following
expressions for the horizontal pressure gradients:

1
g ∂ζ
d+ζ
p
Pξ = p
+g p
ρ0 Gξξ
Gξξ ∂ξ
ρ0 Gξξ

g ∂ζ
d+ζ
1
p
Pη = p
+g p
ρ0 Gηη
Gηη ∂η
ρ0 Gηη

∂ρ ∂ρ ∂σ
+
∂ξ ∂σ ∂ξ

∂ρ ∂ρ ∂σ
+
∂η ∂σ ∂η

dσ 0

(9.15)

(9.16)

The first term in Eqs. (9.15) and (9.16) represents the barotropic pressure gradient (without
atmospheric pressure gradients) and the second term the baroclinic pressure gradient. In the
horizontal gradient a vertical derivative is introduced by the σ co-ordinate transformation. In
estuaries and coastal seas the vertical grid may deteriorate strongly in case of steep bottom
slopes. In order to avoid artificial flow the numerical approximation of the baroclinic pressure terms requires a special numerical approach. The discretisations of Delft3D-FLOW are
discussed in Section 10.10, see also Stelling and Van Kester (1994).
Floating structures
To simulate the influence of floating structures, such as ships or pontoons, both the pressure
term in the momentum equations and the continuity equation are modified.
The pressure of a floating structure at the free surface is dependent on the draft of the structure, generically called ’ship’ (dship ):

Patm = gρ0 dship
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(9.17)

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If the free surface is covered by a floating structure, the free surface cannot move freely. The
water level should be fixed, using a “rigid lid” boundary condition. This boundary condition
is implemented by reducing the storage area of the grid cell with a factor α (the parameter
Riglid in section B.3.6):

∂ζ
∂t

(9.18)

with 0 < α ≤ 1. The wave speed below the floating structure increases to
gH/α. To
prevent numerical inaccuracy for wave propagation α must be larger than zero. We suggest
α ≈ 0.1.
Coriolis force

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Reynold’s stresses

The Coriolis parameter f depends on the geographic latitude and the angular speed of rotation of the earth, Ω: f = 2Ω sin φ. For a curvilinear grid you should specify the space
varying Coriolis parameter, using a suitable projection.

The forces Fξ and Fη in the horizontal momentum equations represent the unbalance of
horizontal Reynolds stresses. The Reynolds stresses are modelled using the eddy viscosity
concept, (for details e.g. Rodi (1984)). This concept expresses the Reynolds stress component as the product between a flow as well as grid-dependent eddy viscosity coefficient and
the corresponding components of the mean rate-of-deformation tensor. The meaning and the
order of the eddy viscosity coefficients differ for 2D and 3D, for different horizontal and vertical
turbulence length scales and fine or coarse grids. In general the eddy viscosity is a function
of space and time.
For 3D shallow water flow the stress tensor is an-isotropic. The horizontal eddy viscosity
coefficient, νH , is much larger than the vertical eddy viscosity νV (νH νV ). The horizontal
viscosity coefficient may be a superposition of three parts:
1 a part due to “sub-grid scale turbulence”,
2 a part due to “3D-turbulence” see Uittenbogaard et al. (1992) and
3 a part due to dispersion for depth-averaged simulations.

In simulations with the depth-averaged momentum and transport equations, the redistribution
of momentum and matter due to the vertical variation of the horizontal velocity is denoted
as dispersion. In 2D simulations this dispersion is not simulated as the vertical profile of the
horizontal velocity is not resolved. Then this dispersive effect may be modelled as the product
of a viscosity coefficient and a velocity gradient. The dispersion term may be estimated by the
Elder formulation.
If the vertical profile of the horizontal velocity is not close to a logarithmic profile (e.g. due to
stratification or due to forcing by wind) then a 3D-model for the transport of matter is recommended.
The horizontal eddy viscosity is mostly associated with the contribution of horizontal turbulent
motions and forcing that are not resolved by the horizontal grid (“sub-grid scale turbulence”) or
by (a priori) the Reynolds-averaged shallow-water equations. For the former we introduce the
sub-grid scale (SGS) horizontal eddy viscosity νSGS and for the latter the horizontal eddy visback
cosity νH
. Delft3D-FLOW simulates the larger scale horizontal turbulent motions through a
methodology called Horizontal Large Eddy Simulation (HLES). The associated horizontal vis-

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Table 9.2: Overview of eddy viscosity options in Delft3D-FLOW

νSGS

back
νH
(represents)

ν3D

νVback

2D, no HLES

2D-turbulence +
dispersion coefficient

2D, with HLES

computed
by HLES

3D-turbulence +
dispersion coefficient

3D, no HLES

2D-turbulence

computed by vertical
turbulence
model.

background
vertical
viscosity

3D, with HLES

computed
by HLES

computed by vertical
turbulence
model.

background
vertical
viscosity

model description

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cosity coefficient νSGS will then be computed by a dedicated SGS-turbulence model, including
the Elder contribution if requested. For details of this approach, see section B.8.
The background horizontal viscosity, user-defined through the input file is represented by
back
. Consequently, in Delft3D-FLOW the horizontal eddy viscosity coefficient is defined by
νH
back
νH = νSGS + νV + νH
.

(9.19)

The 3D part νV is referred to as the three-dimensional turbulence and in 3D simulations it is
computed following a 3D-turbulence closure model.
For turbulence closure models responding to shear production only, it may be convenient to
specify a background or “ambient” vertical mixing coefficient in order to account for all other
forms of unresolved mixing, νVback . Therefore, in addition to all turbulence closure models in
Delft3D-FLOW a constant (space and time) background mixing coefficient may be specified
by you, which is a background value for the vertical eddy viscosity in the momentum Eqs. (9.7)
and (9.8). Consequently, the vertical eddy viscosity coefficient is defined by:

νV = νmol + max(ν3D , νVback ),

(9.20)

with νmol the kinematic viscosity of water. The 3D part ν3D is computed by a 3D-turbulence
closure model, see section 9.5. Summarizing, since in Delft3D-FLOW several combinations
of horizontal and vertical eddy viscosity are optional, Table 9.2 presents an overview of these
combinations.
Remarks:
We note that the “background horizontal eddy viscosity” represents a series of complicated hydrodynamic phenomena. Table 9.2 shows that this background horizontal eddy
back
viscosity νH
either contains zero, one or two contributions.
back
The background horizontal eddy viscosity νH
has to be specified by you in the GUI in
addition to the Elder formulation for 3D-turbulence and dispersion in 2D simulations.
For the description of the (vertical) turbulence models for 3D simulations, we refer to
section 9.5.
It is important to emphasize that the lower limit of vertical eddy viscosity νVback is only
used in the momentum equations (see Eqs. (9.7) and (9.8)) and is not used in the
vertical turbulence models (see for example Eqs. (9.115), (9.127) and (9.128)). For the
transport equation there is similar lower limit.

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For the sake of completeness; to model secondary flow in river bends in depth-averaged simulations, Delft3D-FLOW contains a formulation to account for the effect of this spiral motion.
Then, the horizontal stress tensor is extended with additional shear stresses, see section 9.6.
The σ co-ordinate system rotates the Cartesian stress tensor and introduces additional derivatives (Stelling and Van Kester, 1994). In Delft3D-FLOW, the stress tensor is redefined in the
σ co-ordinate system assuming that the horizontal length scale is much larger than the water
depth (Blumberg and Mellor, 1985) and that the flow is of boundary-layer type. The horizontal
gradients are taken along σ -planes. This approach guarantees a positive definite operator,
also on the numerical grid (Beckers et al., 1998). Thus, the forces Fξ and Fη are of the form:

1 ∂τξη
1 ∂τξξ
+p
,
Fξ = p
Gξξ ∂ξ
Gηη ∂η

(9.21)

1 ∂τηξ
1 ∂τηη
Fη = p
+p
.
Gξξ ∂ξ
Gηη ∂η

(9.22)

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For small-scale flow, i.e. when the shear stresses at the closed boundaries must be taken into
account, the shear stresses τξξ , τξη , τηξ and τηη are determined according to:

2νH
τξξ = p
Gξξ

∂u ∂u ∂σ
+
∂ξ ∂σ ∂ξ
(

τξη = τηξ = νH

τηη

2νH
=p
Gηη

1
p
Gηη

∂u ∂u ∂σ
+
∂η ∂σ ∂η

∂v ∂v ∂σ
+
∂η ∂σ ∂η

1
+p
Gξξ

∂v ∂v ∂σ
+
∂ξ ∂σ ∂ξ

(9.23)

)
,

(9.24)

(9.25)

For large-scale flow simulated with coarse horizontal grids, i.e. when the shear stresses along
the closed boundaries may be neglected, the forces Fξ and Fη are simplified. The horizontal
viscosity terms in Delft3D-FLOW are then reduced to the Laplace operator along grid lines:

F ξ = νH

1
∂ 2u
1
∂ 2u
p p
p
p
+
Gξξ Gξξ ∂ξ 2
Gηη Gηη ∂η 2

F η = νH

1
1
∂2 v
∂2 v
p p
p
p
+
Gξξ Gξξ ∂ ξ 2
Gηη Gηη ∂ η 2

(9.26)

!
,

(9.27)

where the eddy viscosity has been assumed to be a constant.
The choice between the formulations represented by Eqs. (9.21) to (9.25), or Eqs. (9.26) and
(9.27) depends on the application (velocity scales) and can be specified by you. Eqs. (9.21)
to (9.25) are used in combination with rough side walls (partial slip). Their numerical implementation is explicit and this introduces a stability condition, see chapter 10.

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In the expressions for the horizontal viscosity terms, the curvature of the grid in the horizontal
and vertical plane has been neglected.
In strongly stratified flows, the turbulent eddy viscosity at the interface reduces to zero and
the vertical mixing reduces to molecular diffusion (laminar flow). This is physically not realistic because in strongly stratified flow random internal waves exist. These internal waves are
generated continuously by various sources; they increase the production of turbulence and
generate vertical mixing of momentum. Because the effect of internal waves is not explicitly
taken into account in the present implementation of the turbulence models, the effect of internal waves may be assigned to a constant (in space and time) background eddy viscosity at
input, which is added to the momentum equations only.
Discharge or withdrawal of momentum

Mξ = qin (Û − u)

(9.28)
(9.29)

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Mη = qin (V̂ − v)

The discharge of water, when momentum is taken into account, gives an additional term in
the U and V momentum equation:

with Û and V̂ the velocity components of the momentum discharged in ξ - and η -direction,
respectively. If Û and V̂ are set to zero, then the flow is decelerated.
9.3.2

Transport equation (for σ -grid)

The flows in rivers, estuaries, and coastal seas often transport dissolved substances, salinity
and/or heat. In Delft3D-FLOW, the transport of matter and heat is modelled by an advectiondiffusion equation in three co-ordinate directions. Source and sink terms are included to
simulate discharges and withdrawals. Also first-order decay processes may be taken into
account. A first-order decay process corresponds to a numerical solution which is exponentially decreasing. For more complex processes e.g. eutrophication, biological and/or chemical
processes the water quality module D-Water Quality should be used.
The transport equation here is formulated in a conservative form in orthogonal curvilinear
co-ordinates in the horizontal direction and σ co-ordinates in the vertical direction:

( p
p

)
∂
Gηη (d + ζ) uc
Gξξ (d + ζ) vc
∂
1
∂ωc
∂ (d + ζ) c
+p p
+
+
=
∂t
∂ξ
∂η
∂σ
Gξξ Gηη
(
!
!)
p
p
Gηη ∂c
Gξξ ∂c
d+ζ
∂
∂
p p
DH p
+
DH p
+
∂η
Gξξ Gηη ∂ξ
Gξξ ∂ξ
Gηη ∂η

1 ∂
∂c
+
DV
− λd (d + ζ) c + S, (9.30)
d + ζ ∂σ
∂σ
with DH the horizontal diffusion coefficient, DV the horizontal diffusion coefficient, λd representing the first order decay process and S the source and sink terms per unit area due to
the discharge qin or withdrawal qout of water and/or the exchange of heat through the free
surface Qtot :

S = (d + ζ) (qin cin − qout c) + Qtot .

(9.31)

The total horizontal diffusion coefficient DH is defined by
back
DH = DSGS + DV + DH

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(9.32)

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Conceptual description

with DSGS the diffusion due to the sub-grid scale turbulence model (Equation (B.4)). We
remark that in Equation (9.32) a user defined diffusion coefficient for the horizontal is used
back
DH
. The reason is that you may use this horizontal diffusion coefficient for calibration
independent of the horizontal eddy viscosity. This eddy diffusivity depends on the constituent.
The vertical diffusion coefficient DV is defined by

DV =

νmol
+ max D3D , DVback ,
σmol

(9.33)

with D3D the diffusion due to turbulence model in vertical direction (Equation (9.103)) and
with νmol the kinematic viscosity of water and σmol is either the (molecular) Prandtl number
for heat diffusion or the Schmidt number for diffusion of dissolved matter.

For vertical mixing, the eddy viscosity νV is defined by you at input via the GUI (e.g. in
case of a constant vertical eddy viscosity) or computed by a 3D-turbulence model, see Equation (9.20). Delft3D-FLOW will also compute the vertical diffusion coefficients by taking into
account the turbulence Prandtl-Schmidt number.

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For shallow-water flow, the diffusion tensor is an-isotropic. Typically, the horizontal eddy diffusivity DH exceeds the vertical eddy diffusivity DV . The horizontal diffusion coefficient is
assumed to be a superposition of three parts:
1 The 2D part DSGS (sub-grid scale turbulence), due to motions and mixing that are not
resolved by the horizontal grid.
2 The contribution due to 3D turbulence, D3D , which is related to the turbulent eddy viscosity and is computed by a 3D turbulence closure model, see Uittenbogaard et al. (1992).
back
representing the Reynolds-averaged equations and/or accounting for other unre3 DH
solved horizontal mixing.
For depth-averaged simulations, the horizontal eddy diffusivity should also include dispersion
by the vertical variation of the horizontal flow (so-called Taylor-shear dispersion). Delft3DFLOW has an option (so-called HLES approach) solving explicitly the larger scale horizontal
turbulent motions. Then the 2D part DSGS is associated with mixing by horizontal motions and
forcing that cannot be resolved on the grid. For details of the HLES-approach, see section B.8.
back
The horizontal background diffusion coefficient is represented by DH
and it is specified by
you at input and it should account for all other forms of unresolved mixing (in most cases it is
a calibration parameter).
Remark:
We remark that for small scale applications the default value set by the GUI of 10 m2 /s
is too large.
In addition to the vertical eddy diffusivity estimated by a 3D turbulence model you may specify
a background or “ambient” vertical mixing coefficient accounting for all other forms of unresolved mixing. In strongly stratified flows, breaking internal waves may be generated which are
not modelled by the available 3D turbulence models of Delft3D-FLOW. Instead, you can specify the so-called Ozmidov length scale Loz , see section 9.5 for a more detailed description.
Then, the 3D-turbulence part D3D is defined as the maximum of the vertical eddy diffusivity
computed by the turbulence model and the Ozmidov length scale (see also Equation (9.101)):

s
D3D = max D3D , 0.2L2oz

Deltares

g ∂ρ
−
ρ ∂z

!
.

(9.34)

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Table 9.3: Overview of eddy diffusivity options in Delft3D-FLOW

DSGS

back
DH
(represents)

D3D

back
DV

2D, no HLES

2D-turbulence +
dispersion coefficient

2D, with HLES

computed
by HLES

3D-turbulence +
dispersion coefficient

3D, no HLES

2D-turbulence

maximum
of
value of turbulence model and
the
Ozmidov
length scale.

background
eddy
diffusivity

3D, with HLES

computed
by HLES

maximum
of
value of turbulence model and
the
Ozmidov
length scale.

background
eddy
diffusivity

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model description

For all turbulence closure models in Delft3D-FLOW a vertical background mixing coefficient
DVback has to be specified by you via the GUI, Equation (9.33)
back
For two-dimensional depth-averaged simulations, the horizontal eddy diffusivity DH
should
also contain a contribution due to the vertical variation of the horizontal flow (Taylor shear
dispersion). This part is discarded by depth averaging the 3D advection diffusion equation.
For the application of a depth-averaged transport model, the water column should be wellmixed and the Taylor shear dispersion should be of secondary importance, otherwise a 3D
model should be used for the simulation of the transport of matter.

Summarizing, in Delft3D-FLOW many options are available for the eddy diffusivity; Table 9.3
presents an overview of these options. We note that this is rather similar to the eddy viscosity
options (see Table 9.2).
Remarks:
back
The horizontal background diffusion-type coefficient is represented by DH
and pre2
scribed by you in the GUI. The default value of 10 m /s is too large for small scale
applications.
The vertical eddy diffusivity D3D is the maximum value of the Ozmidov length scale and
the vertical eddy viscosity computed by the turbulence model. If you have not switched
on the Ozmidov length scale, which is the case in most of the simulations, then the
Ozmidov length scale is equal to zero.

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Artificial vertical diffusion
The σ co-ordinate system rotates the Cartesian stress tensor and introduces additional derivatives (Stelling and Van Kester, 1994). In Delft3D-FLOW the diffusion tensor is redefined in the
σ co-ordinate system assuming that the horizontal length scale is much larger than the water
depth (Blumberg and Mellor, 1985) and that the flow is of boundary-layer type. The horizontal
gradients are taken along σ -planes. This approach guarantees a positive definite operator,
also on the numerical grid (Beckers et al., 1998).

9.3.3

Coupling between intake and outfall

For steep bottom slopes in combination with vertical stratification, the horizontal diffusion
along σ -planes introduces artificial vertical diffusion (Huang and Spaulding, 1996). Strict
horizontal diffusion along Z -planes gives a more realistic description of the physical transport
process. Numerical implementation of the complete transformation behaved poorly (Blumberg
and Mellor, 1985). Stelling and Van Kester (1994) developed an algorithm to approximate the
horizontal diffusion along Z -planes in a σ -co-ordinate framework, see Section 10.10.

For a power plant, the discharge at the outfall is set equal to the inflow at the intake, i.e.:

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qout = qin .

(9.35)

The temperature, salinity and concentrations of substances prescribed as a function of time
for the Intake - Outfall combination are added to the values at the intake, i.e. they represent
the influence of the power plant on their value or concentration:

Tout = Tin + ∆Tdischarge ,
Sout = Sin + ∆Sdischarge ,
Cout = Cin + ∆Cdischarge ,

(9.36)
(9.37)
(9.38)

where the increase in temperature, salinity or concentration due to the power plant can be
negative.
Remark:
The temperature, salinity, or concentration at the outfall is set to zero when its value
would become negative. The computation is continued, but a warning is written to the
diagnostic file.
9.3.4

Equation of state

The density of water ρ is a function of salinity (s) and temperature (t). In Delft3D-FLOW you
can choose between two different formulations for the equation of state (Eckart or UNESCO).
The first empirical relation derived by Eckart (1958) is based on a limited number of measurements dating from 1910 (only two salinities at 5 temperatures). In the original equation the
pressure is present, but at low pressures the effect on density can be neglected.
Eckart formulation
The Eckart formulation is given by (Eckart, 1958):
Range: 0 < t < 40 ◦ C, 0 < s < 40 ppt

ρ=

Deltares

1, 000P0
,
λ + α0 P 0

(9.39)

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where:

λ = 1779.5 + 11.25t − 0.0745t2 − (3.80 + 0.01t) s,
α0 = 0.6980,
P0 = 5890 + 38t − 0.375t2 + 3s.

(9.40)
(9.41)
(9.42)

with the salinity s in ppt and the water temperature t in ◦ C.

UNESCO formulation

For fresh water the Eckart formulation does not give the maximum density at the temperature
of 4 degrees Celsius. This is an important physical aspect when simulating the thermocline
formation in lakes or stagnant basins. Therefore also the so-called UNESCO formulation is
implemented in Delft3D-FLOW.

The UNESCO formulation is given by (UNESCO, 1981a):
Range: 0 < t < 40 ◦ C, 0.5 < s < 43 ppt

where

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ρ = ρ0 + As + Bs3/2 + Cs2

ρ0 = 999.842594 + 6.793952 · 10−2 t − 9.095290 · 10−3 t2 +
+ 1.001685 · 10−4 t3 − 1.120083 · 10−6 t4 + 6.536332 · 10−9 t5
A = 8.24493 · 10−1 − 4.0899 · 10−3 t + 7.6438 · 10−5 t2 +
− 8.2467 · 10−7 t3 + 5.3875 · 10−9 t4
B = −5.72466 · 10−3 + 1.0227 · 10−4 t − 1.6546 · 10−6 t2
C = 4.8314 · 10−4

(9.43)

(9.44)

(9.45)
(9.46)
(9.47)

Remarks:
Equation (9.45) is known as the International Equation of State for Seawater (EOS80)
and is based on 467 data points. The standard error of the equation is 3.6 · 10−3 kg/m3
(Millero and Poisson, 1981).
The Practical Salinity Scale (UNESCO, 1981b, Par. 3.2) and the International Equation
of State are meant for use in all oceanic waters. However, these equations should be
used with caution in waters that have a chemical composition different from standard
seawater. In such waters, densities derived with the methods based on practical salinity
measurements and the International Equation of State may deviate measurably from
the true densities. However, in water masses different in composition from standard
seawater the differences in densities derived by the new equations involve only very
small errors.
Recommendation
The UNESCO formulae serve as an international standard. Further, the UNESCO formulae
show the correct temperature of 4 degrees Celsius where fresh water has its maximum density. The latter is of importance for thermal stratification in deep lakes in moderate climate
zones. Therefore we recommend the application of the UNESCO formulae and to select the
Eckart formulation only for consistence with previous projects in which it has been used. At
this moment the default is UNESCO.

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Nevertheless, the UNESCO formulae have their limitations as they are based on the general
properties of seawater mixed with fresh water. Particularly in cases where marginal density
differences play a role, typically lakes, a variable mineral content of the water may create density differences not detected by just temperature and salinity. For such dedicated cases, you
are warranted to check the accuracy of the UNESCO formulae against experimental densityrelations derived from the (lake) water. In case of deviations or other constituents determining
the water density, we then recommend to contact the Helpdesk for further assistance such as
the implementation of a more dedicated density formulation.
How to specify the equation of state
The equation of state cannot yet be specified from the FLOW-GUI. You have to edit the MDFfile yourself:

If you want to apply the Eckart formulation, add DenFrm = #Eckart#.

9.4

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If you want to apply the UNESCO formulation you do not need to change the MDF-file, since
the default formulation is UNESCO. However, you may add DenFrm = #UNESCO# if you
want to.
Boundary conditions

The 3D and 2D depth-averaged shallow water or long-wave equations applied in Delft3DFLOW represent a hyperbolic (inviscid case) or parabolic (viscid case) set of partial differential
equations. To get a well-posed mathematical problem with a unique solution, a set of initial and
boundary conditions for water levels and horizontal velocities must be specified. The contour
of the model domain consists of parts along “land-water” lines (river banks, coast lines) which
are called closed boundaries and parts across the flow field which are called open boundaries.
Closed boundaries are natural boundaries. The velocities normal to a closed boundary are set
to zero. Open boundaries are always artificial “water-water” boundaries. In a numerical model
open boundaries are introduced to restrict the computational area and so the computational
effort. They are situated as far away as possible from the area of interest. Long waves
propagating out of the model area should not be hampered by the open boundaries. The
reflection should be minimal.
The solution of the shallow water equations can be split in a steady state solution and a transient solution. The steady state solution depends on the boundary conditions and the forcing
terms while the transient solution follows from the deviation between the initial condition and
the steady state solution at the start of the simulation, the reflection at the open boundaries
and the amount of dissipation.
Usually it is assumed that initially the model is at rest (“cold start”). The start of the simulation
will generate short progressive waves with a wavelength coupled with the length of the model
area (eigen oscillations). When disturbances are reflected at the open boundaries and are
trapped in the model area, a standing wave may be generated. A water level boundary acts
as a nodal point and a velocity or closed boundary acts as an anti-nodal point. The transient solution may propagate out of the model area through the open boundaries (Riemann
boundary condition) or be reduced at the open boundaries (low pass filter) by use of the αcoefficient, Eqs. (9.74) and (9.75), or die out due to bottom friction and viscosity. The spin-up
time of a model is dependent on the time-scale with which the transient solution dies out.
The steady state solution is completely dependent on the boundary conditions. It is reached
after the transient solution died out. The number of boundary conditions specified at any
particular point of the boundary should be equal to the number of characteristics entering the

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region at that point, see Courant and Hilbert (1962) or Vreugdenhil (1989). Delft3D-FLOW
assumes that the flow at the open boundaries is sub-critical, which means that the magnitude
of the flow is smaller than the velocity of wave propagation. Sub-critical flow means that the
Froude number, which is defined by:

|U |
Fr = √ ,
gH

(9.48)

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is smaller than one. For sub-critical flow we distinguish two situations, viz. inflow and outflow.
At inflow, we have to specify two boundary conditions and at outflow we have to specify one
boundary condition. For tidal flow the number of required boundary conditions varies between
ebb and flood. The first boundary condition is an external forcing by the water level, the normal
velocity, the discharge rate or the Riemann invariant specified by you. The second boundary
condition is a built-in boundary condition. At inflow the velocity component along the open
boundary is set to zero. The influence of this built-in boundary condition is in most cases
restricted to only a few grid cells near the open boundary. It would be better to specify the tangential velocity component. The tangential velocity may be determined from measurements
or from model results of a larger domain (nesting of models). In the present implementation
of the open boundary conditions in Delft3D-FLOW it is not possible yet to specify the tangential velocity component at input. To get a realistic flow pattern near the open boundary, it is
suggested to define the model boundaries at locations where the grid lines of the boundary
are perpendicular to the flow.
For modelling the region outside the computational domain, incident waves should be known
and are prescribed at the open boundaries. To reduce the reflections at the open boundaries
a so-called weakly reflecting boundary condition may be applied. This boundary condition is
derived using the Riemann invariants of the linearised shallow water equations without Coriolis and bottom friction (Verboom and Slob, 1984). The boundary condition is non-reflective
for waves, which pass normal to the boundary (wave front parallel with open boundary). If we
do not prescribe exactly the incoming Riemann invariants at an open boundary, the outgoing
wave will reflect at the boundary and propagate back as a disturbance into the model area.
Usually information on both water level and velocity is not available and consequently we cannot specify the Riemann invariant. A water level or velocity boundary condition can be made
weakly reflective for short wave components originating from the initial conditions or the eigen
frequencies by adding the time derivative of the Riemann invariant see Eqs. (9.74) and (9.75).
If these Riemann invariants are not used then these short wave components may disturb the
solution for a long time.
In the vertical direction the momentum equations are parabolic. The vertical velocity profile is
determined by the vertical eddy viscosity and the boundary conditions at the bed (bed stress)
and at the free surface (wind stress). The spin-up time of the vertical profiles is dependent on
the vertical eddy viscosity.
When the grid size near the boundaries is larger than the thickness of the boundary layers
occurring in the flow, the shear-stresses along the lateral boundaries can be neglected. A
so-called free slip boundary condition is applied at all lateral boundaries. For the simulation
of laboratory flumes the effect of side wall friction can be added to the system of equations in
Delft3D-FLOW by a so-called partial slip boundary condition.
9.4.1
9.4.1.1

Flow boundary conditions
Vertical boundary conditions

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Kinematic boundary conditions
In the σ co-ordinate system, the free surface (σ = 0, or z = ζ ) and the bottom (σ = −1,
or z = −d) are σ co-ordinate surfaces. ω is the vertical velocity relative to the σ -plane. The
impermeability of the surface and the bottom is taken into account by prescribing the following
kinematic conditions:

ω|σ=−1 = 0 and ω|σ=0 = 0

(9.49)

For the Z -grid the kinematic conditions read:

w|z=−d = 0 and w|z=ς = 0

Bed boundary condition

(9.50)

At the seabed, the boundary conditions for the momentum equations are:

1
τbξ ,
ρ0

=
σ=−1

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νV ∂u
H ∂σ
νV ∂v
H ∂σ

1
τbη ,
ρ0

σ=−1

(9.51)

(9.52)

with τbξ and τbη the components of the bed stress in ξ - and η -direction, respectively. The bed
stress may be the combined effect of flow and waves. In this section we restrict ourselves
to the resistance due to flow only. For the parameterisations for the combination of flow and
waves, see section 9.7. At first we discuss the formulations for 2D depth-averaged flow,
followed by the formulations for 3D flow.
Depth-averaged flow

For 2D depth-averaged flow the shear-stress at the bed induced by a turbulent flow is assumed
to be given by a quadratic friction law:

~ U
~
ρ0 g U

~τb =

2
C2D

(9.53)

~ is the magnitude of the depth-averaged horizontal velocity.
where U
The 2D-Chézy coefficient C2D can be determined according to one of the following three
formulations:

Chézy formulation:
C2D = Chézy coefficient [m1/2 /s].
Manning’s formulation:
√
6
H
C2D =
n

(9.54)

(9.55)

where:

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H
n

is the total water depth [m].
is the Manning coefficient [m−1/3 s].
White-Colebrook’s formulation:
10

C2D = 18 log

12H
ks

(9.56)

where:

H
ks

is the total water depth
is the Nikuradse roughness length.

Three-dimensional flow

Alluvial bed properties and land use data can be used to determine the roughness and flow
resistance. Specific functionality has been implemented to make the translation of bed and
land use properties into roughness and flow resistance characteristics. See section 9.11.2 for
details.

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For 3D models, a quadratic bed stress formulation is used that is quite similar to the one for
depth-averaged computations. The bed shear stress in 3D is related to the current just above
the bed:

~τb3D =

gρ0~ub |~ub |
,
2
C3D

(9.57)

with |~
ub | the magnitude of the horizontal velocity in the first layer just above the bed. The contribution of the vertical velocity component to the magnitude of the velocity vector is neglected.
The first grid point above the bed is assumed to be situated in the logarithmic boundary layer.
Let ∆zb be the distance to the computational grid point closest to the bed, so:

~u∗
∆zb
~ub =
ln 1 +
,
κ
2z0

(9.58)

where z0 is user-defined. In the numerical implementation of the logarithmic law of the wall for
a rough bottom, the bottom is positioned at z0 . The magnitude of the bottom stress is defined
as:

|~τb | = ρ0~u∗ |~u∗ | .

(9.59)

Using Eqs. (9.57) to (9.59), C3D can be expressed in the roughness height z0 of the bed:

√

C3D

g
∆zb
ln 1 +
.
=
κ
2z0

(9.60)

The parameter z0 can be linked to the actual geometric roughness as a fraction of the RMSvalue of the sub-grid bottom fluctuations. For rough walls Nikuradse (1933) found:

z0 =

ks
,
30

(9.61)

where ks is known as the Nikuradse roughness length scale and has been determined experimentally.

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Often a 3D-calculations are preceded by depth-averaged calculations. Then, the Chézycoefficients C2D may be used for calibration of the 3D model. Under the assumption of
a logarithmic velocity profile Equation (9.54), equality of bottom stress and the assumption
z0 H , the magnitude of the depth-averaged velocity is given by:

|~u∗ |
H
~
U =
ln 1 +
.
κ
ez0

(9.62)

The Chézy coefficient C2D can be converted into the bed roughness height z0 using the
relation:

H
e

κC
1+ √2D
g

(9.63)

−e

z0 =

The depth H in Eqs. (9.62) and (9.63) denotes the actual water depth. As a result the roughness height z0 depends on the horizontal co-ordinates ξ , η and time t. Equality of the bed
stress in 2D leads to the relation:

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AF

√

C2D

g
H
=
ln 1 +
.
κ
ez0

(9.64)

Note: that the difference between the 2D- and the 3D-Chézy coefficient (9.64) and (9.60)
depends on the relative thickness of the computational bed layer. Using a 2D simulation for
the calibration of waterlevels is only accurate if the vertical velocity profile of the horizontal
velocity is almost logarithmic. Examples are discharge waves in rivers, tidal flows in estuaries
and seas. The method is not accurate for stratified flows and wind driven flows, because in
these cases the vertical profile will deviate a lot from the logarithmic profile Equation (9.54),
so also Equation (9.58) is not correct.
Surface boundary condition

At the free surface the boundary conditions for the momentum equations are:

νV ∂u
H ∂σ
νV ∂v
H ∂σ

1
|~τs | cos (θ) ,
ρ0

(9.65)

1
|~τs | sin (θ) ,
ρ0

(9.66)

σ=0

where θ is the angle between the wind stress vector and the local direction of the grid-line η
is constant. Without wind, the stress at the free surface is zero. The magnitude of the wind
shear-stress is defined as:

|~τs | = ρ0~u∗s |~u∗s | .

(9.67)

The magnitude is determined by the following widely used quadratic expression:
2
|~τs | = ρa Cd U10

(9.68)

where:

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Figure 9.3: Examples wind drag coefficient depending on wind speed.

ρa
U10

the density of air.
the wind speed 10 meter above the free surface (time and space
dependent).
the wind drag coefficient, dependent on U10 .

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Delft3D-FLOW offers the possibility to prescribe either global or local wind. Global wind corresponds to uniform in space and varying in time. Local winds vary both in space and time.
Local wind is applied in combination with space and time varying atmospheric pressure.
The wind drag coefficient may be dependent on the wind velocity, reflecting increasing roughness of the sea surface with increasing wind speed, see Smith and Banke (1975). You may
specify an empirical relation following:

 A
Cd ,



A

U10 − U10


,
CdA + CdB − CdA
B
A
U10
− U10
Cd (U10 ) =
B


B
C
B U10 − U10

C
+
C
,
−
C

d
d
d

C
B

U10
− U10

 C
Cd ,
where:

Cdi
i
U10

A
U10 ≤ U10
,

B
A
,
≤ U10 ≤ U10
U10

B
U10

≤ U10 ≤

(9.69)

C
U10
,

C
U10
≤ U10 ,

are the user-defined wind drag coefficients at respectively the wind
i
speed U10
(i = A, B, C ).
are user-defined wind speeds (i = A, B, C ).

With Equation (9.69) several relations for the wind drag coefficient are possible, see Figure 9.3.
9.4.1.2

Open boundary conditions
Open boundaries are virtual “water-water” boundaries. They are introduced to obtain a limited computational area and so to reduce the computational effort. In nature, waves can cross
these boundaries unhampered and without reflections. At an open boundary the water level,
the normal velocity component or a combination should be prescribed to get a well-posed
mathematical initial-boundary value problem. For an inflow boundary, also the tangential velocity component should be specified. In the present implementation, the tangential velocity
component is set to zero. It is assumed that the flow is normal to the open boundary. The data
needed for the boundary conditions can be obtained from measurements, tide tables or from

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a larger model, which encloses the model at hand (nesting). If we do not prescribe exactly
the incoming waves at an open boundary, the outgoing waves will reflect at the boundary and
propagate as a disturbance into the area.
To reduce the reflections at the open boundary (Verboom and Slob, 1984; Verboom and Segal,
1986) derived a so-called zero and first order weakly reflecting boundary condition based on
the work of Engquist and Majda (1977, 1979). Assuming zero flow along the boundary, the
zero order boundary condition may also be obtained using the so-called Riemann invariants
for the linearised 1D equation normal to the open boundary:

p
R = U ± 2 gH.

(9.70)

The two Riemann√invariants are two waves moving in opposite direction with propagation
speed R = U ± gH . The sign is dependent on the direction of propagation. At the open
boundary, the incoming wave should be specified. We restrict ourselves to the positive sign
(left boundary). The linearised Riemann invariant is given by:

|ζ|
1.
(9.71)
d
pg
The boundary condition which should be specified by you is: f (t) = U + ζ d , the term
√
2 gd is computed from the known depth-field and added in the computational part. It is
p
p
gH = U + 2 g (d + ζ) ≈ U + 2 gd + ζ

g
,
d

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U +2

assumed that the reference plane is chosen such that the mean water level is zero.
The boundary condition based on the Riemann invariant is weakly reflective in 1D. But in 2D
this boundary condition is only weakly reflective for waves which pass normal to the boundary
and if the Coriolis force and the bottom friction are negligible. Nevertheless, in practice it
reduces the reflection also for waves, which have an oblique incidence. Usually we do not
have information on both water level and velocity so we do not know the incoming Riemann
invariant and another type of boundary should be chosen. A water level or velocity boundary
condition can be made weakly reflective for short wave components originating from the initial
conditions or the eigen frequencies by adding the time derivative of the Riemann invariant see
Eqs. (9.74) and (9.75).
In the computational part the following type of boundary conditions are distinguished (for the
sake of simplicity only a description for the U -direction is given here):

Water level: ζ = Fζ (t) + δatm ,
Velocity (in normal direction): U = FU (t),
Discharge (total and per cell): Q = FQ (t),
∂ζ
∂~
n

= f (t),
pg
Riemann invariant U ± ζ d = FR (t).
Neumann

If measured elevation data is not available, the barotropic forcing at the open boundaries is
approximated by a linear superposition of:

Free surface gradient for long-term circulation (geostrophic currents).
Tidal fluctuations.
Meteorological forcing (wind set-up).
Waves (wave set-up).

In general, the boundary conditions are specified in a limited number of boundary points.
Linear interpolation is used to generate the boundary conditions at the intermediate points
along the boundary. This interpolation can generate physical unrealistic flows in the region

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close to the open boundary. The boundary conditions should allow these disturbances to
propagate out of the area or the number of points where the boundary condition is specified
should be extended.

δatm =

On water level boundaries, an input signal is prescribed that is consistent with some average
pressure. Usually the signal corresponds to Mean Sea Level. One actually wants to prescribe
an input signal corresponding to the local pressure prescribed by the space varying meteo
input. To this end, it is possible to specify an average pressure (paverage ) — which should
correspond to your input signal on the open boundaries — which is then used to determine
local pressure gradients that need to be applied along the open boundaries to obtain an input
signal that is consistent with the local atmospheric pressure. This functionality need to be
specified in the Data Group Additional parameters, using PavBnd: Average Pressure on
Boundaries. Using this keyword one can specify an average pressure that is used on all water
level open boundaries, independent of the type of wind input. The pressure must be specified
in N/m2 .

paverage − patm
ρg

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AF

where

paverage
patm
ρ
g

(9.72)

average pressure prescribed with the keyword PavBnd,
the local atmospheric pressure, given by the meteo module (see section B.7).
density of water
acceleration due to gravity

The same correction can also be used on Riemann boundaries, and is calculated as follows:

paverage − patm
FR (t) = FR (t) ±
ρg

g
d

(9.73)

with d the local water depth, and the sign depends on the orientation of the open boundary
related to the grid.
For the transport equation, concentrations should be specified at inflow, see section 9.4.2.1,
and the concentration should be free at outflow. For salinity and heat the concentration boundary conditions influence the flow by the baroclinic pressure term. At slack water, when the
barotropic pressure gradients are small, this may lead to strange circulation cells along a long
open boundary. Therefore an additional flag (keyword) has been implemented to switch off
the baroclinic pressure term at the open boundary BarocP = #NO#. This is a global flag.
The baroclinic pressure is switched off for all open boundaries. The default value is #YES#.
For the velocity, discharge and Riemann type of boundary condition, the flow is assumed to
be perpendicular to the open boundary. Substitution of the Riemann boundary condition in
the 1D linearised continuity equation leads to the well-known radiation boundary condition.
Stelling (1984) added the time-derivative of the Riemann invariant to the water level and velocity boundary conditions, to make the boundaries less reflective for disturbances with the
eigen frequency of the model area. This reduces the spin-up time of a model from a cold
start:
Water level boundary: ζ + α

Velocity boundary: U + α

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p o
∂ n
U ± 2 gH = Fζ (t) ,
∂t

p o
∂ n
U ± 2 gH = FU (t) .
∂t

(9.74)

(9.75)

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Conceptual description

The reflection coefficient α should be chosen sufficiently large to damp the short waves introduced at the start of the simulation. The following values are advised:

s
Water level boundary: α = Td

H
, [s2 ]
g

(9.76)

Velocity boundary: α = Td [s]

(9.77)

where Td is the time it takes for a free surface wave to travel from the left boundary to the right
boundary of the model area. In ocean and sea models, the period Td is of the same order
as the period of the tidal forcing. In that case α must be set to zero, otherwise effectively the
amplitude of one of the components in the boundary condition is reduced. These values can
be derived with Fourier analysis for the 1D linear long wave equation without advection by
substituting a wave with period Td .
For the velocity and discharge type of boundary condition, the flow is assumed to be perpendicular to the open boundary. In 3D models you can prescribe:

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a uniform profile
a logarithmic profile

a so-called 3D profile

in the vertical. A 3D-profile means that the velocity at each σ -layer is specified as any of
the forcing types, i.e. as harmonic components, time-series or astronomical components; see
section 4.5.6 for details.
Remark:
A 3D-profile can only be prescribed by importing a file containing the boundary condition
at each layer. This file can be generated with the utility program Delft3D-NESTHD.
A logarithmic profile may be applied for velocity, discharge, or Riemann boundaries. The
logarithmic profile depends on the local roughness height z0 and the local water depth H . This
profile is described for a velocity boundary condition in direction perpendicular to the open
boundary. The vertical co-ordinate z is measured relative to the bed. The depth-averaged
velocity U is used to determine the friction velocity:

~u∗ =

1
κH

~
U
=
R H z+z0
ln
dz
z0
0

~
U

1
κH

(H + z0 ) ln

H+z0
z0

−H

(9.78)

The velocity of layer k , uk , is specified as:

Z zk−1
~u∗
z + z0
~uk =
ln
dz,
κ (zk−1 − zk ) zk
z0

~u∗
zk−1 + z0
zk + z0
=
(zk−1 + z0 ) ln
− 1 − (zk + z0 ) ln
−1 ,
κ (zk−1 − zk )
z0
z0
(9.79)

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with (for σ -grid):

zk = (1 + σk−1 ) H.

(9.80)

After substitution of u∗ in this equation the layer velocity uk is expressed in terms of U , H
and z0 .
The discharge is, in case of a total discharge boundary condition, at each time step distributed
over the active points of the open boundary in the following manner derived from the Chézy
equation:

Bi h1.5 Ci
qi = PN i 1.5 Q.
j=1 Bj hj Cj

(9.81)

where Bi , hi and Ci are the width, water depth and roughness of grid cell i respectively, N
is the number of boundary points, and Q is the total discharge imposed.
In case a QH-relation is used at a water level boundary the total discharge is computed from
the discharges per grid cell
K
X

N
X

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AF

N
X

j=1

ui,k ∆zi,k

k=1

Bi ūi hi

(9.82)

j=1

where Bi , ūi and hi are the width, depth averaged velocity and water depth of grid cell i, ui ,
k and ∆zi,k are the velocity and thickness of layer k at grid cell i in case of a 3D simulation,
N is the number of boundary points and K is the number of layers. The total discharge Q is
used to derive a water level from the QH-relation specified by you, which is imposed uniformly
at the boundary.
Neumann boundary conditions

Application of 2D and 3D hydrodynamic models to study the impact of engineering solutions
such as the design of nourishments, groynes, offshore breakwaters on approximately uniform
coasts is often hampered by the fact that they are considered to be difficult to set up and
difficult to calibrate. One of the main problems is the specification of suitable boundary conditions at the open boundaries. This is due to a combination of processes acting on the model
domain, a certain water level or velocity distribution will develop in cross-shore direction. For
the boundary conditions to match this distribution the solution has to be known beforehand; if
not, boundary disturbances will develop.
There are two ways to overcome this problem. The first is to try and predict the water level
setup or the current velocity along the lateral boundary by solving a 1DH or 2DV problem
along the boundary and to impose this. For simple cases this is possible but for more complex
combinations of forcing conditions it is cumbersome. A better solution suggested by Roelvink
and Walstra (2004) in the paper ‘Keeping it simple by using complex models’ is to let the
model determine the correct solution at the boundaries by imposing the alongshore water
level gradient (a so-called Neumann boundary condition) instead of a fixed water level or
velocity. In many cases the gradient can be assumed to be zero; only in tidal cases or in
cases where a storm surge travels along a coast the alongshore gradient varies in time, but
in model with a limited cross-shore extent, the alongshore gradient of the water level does not
vary much in cross-shore direction.
The alongshore water level gradient can be assumed to be zero in case of a steady wind/wave
field, or vary periodically for a tidal wave travelling along the coast. In the latter case, the alongshore gradient varies in time at the boundary. A constant periodical water level gradient for a

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Figure 9.4: Hydrodynamic model of coastal area with three open boundaries with offshore
boundary (A–B at deep water) and two cross shore boundaries (A–A’, and B–
B’)

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boundary can be applied to models with a limited cross-shore extent, under the assumption
that the alongshore gradient of the water level does not vary much in cross-shore direction.
Neumann boundaries can only be applied on cross-shore boundaries in combination with a
water level boundary at the offshore boundary, which is needed to make the solution of the
mathematical boundary value problem well-posed (see Figure 9.4).
Defining boundary conditions with Neumann boundaries

Consider the example below; describing a small coastal region with a tidal wave travelling
along the coast in eastward direction. On the cross-shore boundaries (sections A–A’, B–B’
in Figure 9.4), the water level gradient as a function of time, denoted as Neumann Boundary
∂ζ
condition will be imposed: ∂x = f (t). At the offshore boundary (A–B), the water level has to
be prescribed to make the solution fully determined. At the water level boundary we set the
reflection coefficient α to zero.
The offshore boundary is forced by a harmonic/astronomic water level according to a progressive wave given by:

ζ=

N
X

ζ̂j cos(ωj t − kj x) =

ζ̂j cos(ωj t − ϕj )

(9.83)

j=1

where: ζ̂j = amplitude [m]; ωj =

N
X

2π
Tj

frequency [rad/h]; kj =

2π
Lj

wave number [rad/m]; Let

dAB be the distance between point A and B. The phase difference (ϕj ) between points A and
2π
B is then given by kj dAB = L
dAB (to get degrees multiply it by 180
); Lj is the tidal wave
π
j
2π
length Lj = ω cj , with cj the velocity of the tidal wave. For shallow water the velocity is
j
√
independent of the frequency and is given by gH with H a characteristic water depth.
For the forcing of the two cross-shore boundaries a gradient (Neumann) type of boundary
condition is used. The forcing term f (t) is related to the offshore forcing by the relation:
N

X
X
∂ζ
π
=
kj ζ̂j sin (ωj t − kj x) =
kj ζ̂j cos ωj t − ϕj +
∂x
2
j=1
j=1

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(9.84)

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Table 9.4: Frequencies, phases and amplitude on alongshore waterlevel boundary and
corresponding frequenties, phases and amplitudes for the cross-shore Neumann boundaries

Phase [◦ ]

Amplitude
A–B : [m]
A–A0 , B –B 0 : [−]

Neumann boundaries
A–A’, B–B’

ωj (A) = ωj (B)

ωj (A) = ωj (A0 ) =
ωj (B) = ωj (B 0 )

ϕj (A) = 0◦
ϕj (B) = ϕj
ζ̂j (A) = ζ̂j (B)

ϕj (A) = ϕj (A0 ) = ±90◦
ϕj (B) = ϕj (B 0 ) = ±90◦ + ϕj

∂ζ
∂ζ
(A) = ∂x
(A0 ) = L2πj ζ̂j
∂x j
j

∂ζ
∂ζ
(B) = ∂x
(B 0 ) = L2πj ζ̂j
∂x j
j

Frequency [◦ /h]

WL–boundary
A–B

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In Table 9.4 we specify the relation between the tidal forcing at the offshore boundary (water
level type) and the forcing at the cross-shore boundaries (Neumann type) for the coastal
model of Figure 9.4.
General remarks on open boundaries
At the start of the simulation, the boundary conditions often do not match with the initial
conditions. Therefore, in Delft3D-FLOW at the open boundaries a linear interpolation is
applied between the actual field value and the boundary condition, to reduce the spin up
time of the model. The smoothing time is the last moment at which interpolation takes
place.
To define the phase difference in Delft3D-FLOW the unity degrees is used. To determine
the amplitude of the water level gradient, radians should be used.
The tidal wave length Lj may be estimated from the phase difference ∆ϕAB = L2πj dAB
between tidal stations√along the boundary, Roelvink and Walstra (2004) or be approximated using Lj = 2π
gH with H a characteristic depth along the offshore boundary.
ωj
If the tidal wave component is travelling in positive x-direction, the phase difference between the water level and Neumann boundary is π/2 (≡ +90◦ ). If the tidal wave component is travelling in negative x-direction, the phase difference is −π/2 (≡ −90◦ ).
For each tidal component, the corresponding component of water level gradient can be
determined on the basis of its frequency, phase difference between boundaries A and B
and amplitude, see Table 9.4.
The Neumann boundaries are interpreted as gradient type of boundaries for water level.
Advection terms at the offshore boundary may generate an artificial boundary layer along
the boundary. The advection terms containing normal gradients have to be switched off.
This is done by adding an additional keyword to the MDF-file:

Cstbnd =#YES#

When modelling salinity and/or heat transport, the boundary condition of these quantities
should match their initial value. Otherwise the baroclinic pressure gradient can causes
severe water level gradients, especially on deep water. These larger water level gradients
generates waves which will propagate into the domain and enlarging the spin-up time of
the model.

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9.4.1.3

Shear-stresses at closed boundaries
A closed boundary is situated at the transition between land and water. At a closed boundary,
two boundary conditions have to be prescribed. One boundary condition has to do with the
flow normal to the boundary and the other one with the shear-stress along the boundary.
The boundary condition for flow normal to the boundary is:

No flow through the boundary.
For the shear stress along the boundary one of the following conditions can be prescribed:

1 Zero tangential shear-stress (free slip).
2 Partial slip.

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For large-scale simulations, the influence of the shear-stresses along closed boundaries can
be neglected. Free slip is then applied for all closed boundaries. For simulations of smallscale flow (e.g. laboratory scale), the influence of the side walls on the flow may no longer be
neglected. This option has been implemented for closed boundaries and dry points but not for
thin dams. The reason is that the shear stress at a thin dam is dependent on the side (double
valued).
Along the side walls, the tangential shear stress is calculated based on a logarithmic law of
the wall:

τξη = τηξ = ρu2∗ .

(9.85)

The friction velocity u∗ is determined by the logarithmic-law for a rough wall, with side wall
roughness length z0n and the velocity in the first grid point near the side wall. Let ∆xs be the
grid size normal to the sidewall. Then:

u∗
∆xs
|~usidewall | =
ln 1 +
.
κ
2z0n

9.4.2
9.4.2.1

(9.86)

Transport boundary conditions

Open boundary conditions for the transport equation

The horizontal transport of dissolved substances in rivers, estuaries, and coastal seas is
dominated by advection. The horizontal diffusion in flow direction is of secondary importance.
The consequence is that the transport equation is advection dominated, has a wave character,
and from a mathematical point of view is of hyperbolic type. The equation has only one
characteristic, which is parallel to the flow. Without diffusion, an observer moving with the
flow, experiences a constant concentration. As described before, open boundaries have to
limit the computational area. At an open boundary during inflow (flood) a boundary condition
is needed. During outflow (ebb) the concentration must be free. At inflow we have to specify
the concentration which may be determined by the concentration at outflow of the former ebb
period. Because usually only the background concentration is known from measurements
or from a larger model area, a special boundary condition based on the concentration in the
interior area in combination with a return time is used, which does not completely fix the
concentration at the background value. This is the so-called Thatcher-Harleman boundary
condition (Thatcher and Harleman, 1972), which is discussed in the next section.
In Delft3D-FLOW, one of the following four vertical profiles may be specified at open boundaries:

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1 Uniform profile
The concentration value specified is applied uniformly over the vertical.
2 Linear profile
The concentration value must be specified at the surface and near the bed. The intermediate values are then determined using linear interpolation:

ck = cbottom + (1 + σk ) (csurface − cbottom )

(9.87)

or similarly for the Z -grid:

ck = cbottom +

d + zk
d+ζ

(csurface − cbottom )

(9.88)

csurface ,
cbottom ,

zk > zd ,
zk ≤ zd .

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ck =

3 Step profile
The concentration value must be specified both for the surface layer and the bed layer,
together with the initial vertical position of the discontinuity. The concentration for an
intermediate layer is determined following:
(9.89)

The zd co-ordinate specifying the position of the discontinuity is used only initially to determine the index k of the related layer. The layer index of the discontinuity is kept fixed
during the simulation. In case of σ -grid, the discontinuity is moving with the free surface,
following the position of the corresponding σ -plane.
Remark:
If the initial conditions are read from a restart file (hot start), then the position of the
jump will be determined using the water elevation read from this file. Consequently,
a mismatch between your boundary condition and the concentration distribution in
the vertical, just inside the open boundary, may occur. This mismatch can produce
oscillations in the simulation results.
4 3D profile
For a nested model Delft3D-FLOW offers the possibility to prescribe the concentration at
every σ - or Z -layer using a time-series:

ck = Fc (t) .

9.4.2.2

(9.90)

Thatcher-Harleman boundary conditions

The transport of dissolved substances such as salt, sediment, and heat is described by the
advection-diffusion equation. The horizontal transport is advection dominated and the equation is of hyperbolic type. At inflow, one boundary condition is needed and the concentration
is specified. At outflow, no boundary condition is allowed. The concentration is determined by
pure advection from the interior area:

∂C
U ∂C
+p
= 0.
∂t
Gξξ ∂ξ

(9.91)

In Delft3D-FLOW the dispersive fluxes through the open boundaries at both inflow and outflow
are zero:

D ∂C
pH
= 0.
Gξξ ∂ξ

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(9.92)

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Conceptual description

Outflow

Inflow

Outflow

Background concentration

Return time

Time

Figure 9.5: Illustration of memory effect for open boundary

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If the concentration at outflow differs from the boundary condition at inflow, there is a discontinuity in the concentration at the turn of the flow. The transition of the concentration at the
boundary from the outflow value to the inflow value may take some time. This depends on the
refreshment of the water in the boundary region. The transition time is called the return time.
The functional relationship describing the variation in concentration from the slack-water value
to the present value is arbitrary. In Delft3D-FLOW, a half-cosine variation is used. After the
return time, the boundary value remains constant until outward flow begins (Leendertse and
Gritton, 1971; Thatcher and Harleman, 1972). The mathematical formulation of this memory
effect is given as follows:

C (t) =

(
out
+
1
,
Cout + 12 (Cbnd − Cout ) cos π TretT−τ
ret
Cbnd

0 ≤ τout ≤ Tret
τout > Tret
(9.93)

where

Cout

Cbnd
τout
tout
Tret

is the computed concentration at the open boundary at the last time of outward
flow,
is the boundary concentration described by you,
is the elapsed time since the last outflow τout = t − tout
the last time of outward flow, and
is the constituent return period.

When the flow turns inward (τout = 0), the concentration is set equal to Cout . During the interval 0 ≤ τout ≤ Tret the concentration will return to the background concentration Cbnd . After
that period, the concentration will remain Cbnd . The mechanism is illustrated in Figure 9.5.
For a stratified flow the return time of the upper layer will be longer than for the bottom layer.
Delft3D-FLOW offers the opportunity to prescribe return times for the surface layer and the
bed layer. For the intermediate layers the return time is determined using linear interpolation:

TTHk = TTHbottom + (1 + σk ) (TTHsurface − TTHbottom ) ,

(9.94)

or similarly for the Z -grid:

TTHk = TTHbottom +

d + zk
d+ζ

(TTHsurface − TTHbottom )

(9.95)

with:

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TTHbottom
TTHsurface
zk , σk
d

return time bed layer.
return time surface layer.
vertical position, respectively in Z - and σ co-ordinate system.
local depth value

Therefore an additional flag (key word) has been implemented to switch off the baroclinic
pressure term at open boundaries: BarocP = #NO#. This is a global flag. The baroclinic
pressure is switched off for all open boundaries. The default value is #YES#.

9.4.2.3

Vertical boundary conditions transport equation

Remark:
When you specify a negative value for the time lag the boundary treatment for constituents, salinity and temperature will be the same as at outflow, but now for all times.
Thus, the solution for these parameters will be fully determined by the processes inside
the model area. This negative value has no physical meaning or background; it only
offers the option to fully exclude the influence of the outer world on the inner solution.

9.5

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The vertical diffusive flux through the free surface and bed is zero with exception of the heat
flux through the free surface. The mathematical formulations for the heat exchange at the free
surface are given in section 9.8:

DV ∂c
H ∂σ

σ=0

DV ∂c
H ∂σ

σ=−1

= 0,

= 0.

(9.96)

(9.97)

Turbulence

Delft3D-FLOW solves the Navier-Stokes equations for an incompressible fluid. Usually the
grid (horizontal and/or vertical) is too coarse and the time step too large to resolve the turbulent
scales of motion. The turbulent processes are “sub-grid”. The primitive variables are spaceand time-averaged quantities. Filtering the equations leads to the need for appropriate closure
assumptions.
For 3D shallow water flow the stress and diffusion tensor are an-isotropic. The horizontal eddy
viscosity coefficient νH and eddy diffusivity coefficient DH are much larger than the vertical
coefficients νV and DV , i.e. νH νV and DH DV . The horizontal coefficients are
assumed to be a superposition of three parts:
1 a part due to molecular viscosity.
2 a part due to “2D-turbulence”,
3 a part due to “3D-turbulence” see Uittenbogaard et al. (1992) and

The 2D part is associated with the contribution of horizontal motions and forcings that cannot
be resolved (“sub-grid scale turbulence”) by the horizontal grid (Reynolds averaged or eddy
resolving computations). The 3D part is referred to as the three-dimensional turbulence and
is computed following one of the turbulence closure models, described in this section. For
2D depth-averaged simulations, the horizontal eddy viscosity and eddy diffusivity coefficient
should also contain a contribution due to the vertical variation of the horizontal flow (Taylor
shear dispersion).

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back
back
The background horizontal viscosity coefficient νH
and eddy diffusivity coefficient DH
(constant or space-varying) must be specified by you via the Delft3D-FLOW GUI. Delft3DFLOW additionally has a sub-grid scale model, HLES for 2D-turbulence (see section B.8).
These coefficients can also be used to damp small-scale noise introduced by the advection
terms. They must be chosen dependent on the grid size. Furthermore the horizontal coefficients are an order of magnitude larger than the vertical coefficients determined by the
turbulence closure model specified by you.

In Delft3D-FLOW, four turbulence closure models have been implemented to determine νV
and DV :
Constant coefficient.
Algebraic Eddy viscosity closure Model (AEM).
k -L turbulence closure model.
k -ε turbulence closure model.

1
2
3
4

The turbulence closure models differ in their prescription of the turbulent kinetic energy k , the
dissipation rate of turbulent kinetic energy ε, and/or the mixing length L.

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The first turbulence closure model is the simplest closure based on a constant value which
has to be specified by you. We remark that a constant eddy viscosity will lead to parabolic
vertical velocity profiles (laminar flow). The other three turbulence closure models are based
on the so-called eddy viscosity concept of Kolmogorov (1942) and Prandtl (1945). The eddy
viscosity is related to a characteristic length scale and velocity scale. The eddy viscosity has
the following form:

√
ν3D = c0µ L k,

(9.98)

where:

c0µ

a constant determined by calibration, derived from the empirical constant cµ in
1/4

L
k

the k -ε model; c0µ = cµ , cµ = 0.09 (Rodi, 1984),
is the mixing length, and
is the turbulent kinetic energy.

The algebraic eddy viscosity model (AEM) does not involve transport equations for the turbulent quantities. This so-called zero order closure scheme is a combination of two algebraic
formulations. This model uses analytical (algebraic) formulas to determine k and L. The
turbulent kinetic energy k depends on the (friction) velocities or velocity gradients and for the
mixing length, L, the following function of the depth is taken (Bakhmetev, 1932):

L = κ (z + d)

1−

z+d
,
H

(9.99)

with κ the Von Kármán constant, κ ≈ 0.41. For a homogeneous flow this leads to a logarithmic velocity profile.
In case of vertical density gradients, the turbulent exchanges are limited by buoyancy forces
and the mixing length L of Equation (9.99) must be corrected. On the other hand high velocity gradients, increase turbulent mixing and can weaken the stratification. Stratification
stability can be described in the interaction between gravitational forces (bouyancy flux Bk ,
Equation (9.120)) and turbulent shear production (Pk , Equation (9.117)). The stratification is

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characterised by the gradient Richardson number, Ri, defined by:

Ri =
ρ

−g ∂ρ
∂z

∂u 2
+
∂z

∂v 2
∂z

(9.100)

see e.g. Richardson (1920); Taylor (1931); Miles (1987). For Ri ≥ 0 the stratification is
stable whereby for Ri < 0 the stratification is unstable. Stable stratification leads to damping
of turbulent mixing while unstable stratification leads to higher mixing. Mathematically this is
described by a so-called damping function FL (Ri) that depends on the gradient Richardson
number Ri (Simonin et al., 1989):

r
1−

z+d
FL (Ri) .
H

(9.101)

L = κ (z + d)

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These damping functions have been determined by fitting mathematical functions which fulfil
the limiting conditions to laboratory data sets. Different formulations have been suggested. In
Delft3D-FLOW the algebraic eddy viscosity model (AEM) is extended to stratified flows by the
formulation of Busch (1972):

−2.3Ri
e
,
Ri ≥ 0,
FL (Ri) =
0.25
(1 − 14Ri) , Ri < 0.

(9.102)

The third closure model for the eddy viscosity involves one transport equation for k and is
called a first order turbulence closure scheme. The mixing length L is prescribed analytically
and the same formulation, including damping functions, is used as for the AEM turbulence
model. However, to find the kinetic energy k , a transport equation is solved. This turbulence
closure model is known as the k -L model.
The fourth model is the k -ε model that is a second order turbulence closure model. In this
model both the turbulence energy k and dissipation rate of turbulent kinetic energy ε are
calculated by a transport equation. From k and ε the mixing length L and viscosity are
determined. The mixing length is now a property of the flow, and in the case of stratification
no damping functions are needed.
A brief description of each of these turbulence closure model will be given further on in this
section, for more details we refer to Uittenbogaard et al. (1992). The k -ε model has been
used in tidal simulations by Baumert and Radach (1992) and Davies and Gerritsen (1994), for
stratified flow of a river plume by Postma et al. (1999) and for the evolution of a thermocline
by Burchard and Baumert (1995).
For the combination of flow and waves, the effect of the orbital velocities on the production of
turbulence is modelled indirectly by the enhancement of the bed roughness; see section 9.7.
The shear production is determined only from the wave-averaged velocities.
The turbulence closure models do not take into account the vertical mixing induced by shearing and breaking of short and random internal gravity waves. This internal-wave-induced
mixing can be determined using an additional transport equation for Internal Wave Energy
(IWE-model) (Uittenbogaard and Baron, 1989; Uittenbogaard, 1995). The IWE model describes the energy transfer from internal waves to turbulence as well as the excitation of
internal waves by turbulence. The simplest approximation of the effect of internal waves is the
introduction of constant vertical ambient mixing coefficients of momentum ν , and/or heat and
matter D .

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For strongly stratified flows it is important to introduce suitably chosen constant ambient (background) mixing coefficients, because the mixing coefficients computed by turbulence models
with shear production only, reduce to zero. In the latter situation the vertical layers are completely de-coupled (frictionless). Disturbances are hardly damped and also the erosion of the
vertical stratification is reduced to molecular diffusion.
Based on our experience with highly stratified flows we suggest applying an ambient or background vertical eddy viscosity in the order of 10−4 m2 /s for the vertical exchange of momentum. This value corresponds with field measurements in the Rotterdam Waterway, The
Netherlands.
Eddy diffusivity

D3D =

ν3D
.
σc

The vertical eddy diffusivity is a scaled form of the eddy viscosity according to:
(9.103)

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Parameter σc is the Prandtl-Schmidt number. Its numerical value depends on the substance
C . Moreover, for zero order models (for example, the algebraic turbulence closure model),
it is affected by the stratification. It slightly widens the applicability of an algebraic model for
weakly stratified flows. In general the expression for the Prandtl-Schmidt number reads:

σc = σc0 Fσ (Ri).

(9.104)

The σc0 in this expression depends on the substance. It is a constant. Fσ (Ri) is a so-called
damping function that depends on the density stratification via the gradient Richardson’s number Ri defined in Equation (9.100), see ?.
In Delft3D-FLOW the following settings of σc0 and Fσ (Ri) are used:

In all cases, regardless the turbulence closure model, σc0 = 0.7 for the transport of
heat, salinity, and tracer concentrations. For suspended sediment concentrations in online
sediment transport computations, σc0 = 1.0.
For the transport of turbulent kinetic energy k in the k -L model and k -ε model σc0 = 1.0,
and for the transport of turbulent kinetic energy dissipation ε in the k -ε model σc0 = 1.3.
In case the algebraic turbulence closure model is applied, the damping function Fσ (Ri)
is the following Munk-Anderson formula (Munk and Anderson, 1948):


+ 3.33Ri)1.5
 (1√
, Ri ≥ 0
Fσ (Ri) =
1 + 10Ri

1,
Ri < 0.

(9.105)

The damping functions Eqs. (9.102) and (9.105) were obtained by measurements of steadystate stable stratified turbulent shear flows. In the mathematical formulation, the fluxes are
instantaneously influenced by changes in the vertical gradients of velocity and density. A
physical adjustment time of the turbulence to the variations of the vertical gradients, is not
taken into account. The fluxes are not a monotone function of the gradients. For the transport
equation of heat, for small temperature gradients the heat flux increases when the temperature gradient increases but for large temperature gradients the heat flux decreases because
the vertical eddy diffusivity is damped. For large values of the density gradients and small values of the velocity gradients, the vertical diffusion equation becomes mathematically ill-posed

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Barenblatt et al. (1993), and the computed vertical profiles may become discontinuous (stepwise). The number of “steps” is dependent on the vertical grid. For strongly stratified flows
(Ri > 1), the k -ε model is advised.
In the k -ε turbulence model no damping function is used since the influence of stratification
on the mixing length is taken into account by the buoyancy terms in the transport equations
for k and ε. Thus: Fσ (Ri) = 1 for all Ri. This is one of the main advantages of the k -ε
turbulence model. Damping functions, as used in the standard Level 2.5 turbulence closure
model of Mellor and Yamada (1974, 1982), may generate unphysical “stepwise” profiles as
observed by Deleersnijder and Luyten (1994).

The numerical scheme for the vertical advection of heat and salt (central differences) may
introduce small vertical oscillations. This computational noise may enhance the turbulent
mixing. Delft3D-FLOW has a vertical filtering technique to remove this noise and to reduce
the undesirable mixing. For more details, see chapter 10.

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In strongly-stratified flows, the turbulent eddy viscosity at the interface reduces to zero and
the vertical mixing reduces to molecular diffusion. To account for the vertical mixing induced
by shearing and breaking of short and random internal gravity waves, we suggest to apply an
ambient eddy diffusivity in the order of 10−4 to 10−5 m2 /s dependent on the Prandtl-Schmidt
number. In Delft3D-FLOW for stable stratified flows, the minimal eddy diffusivity may be based
on the Ozmidov length scale Loz , specified by you and the Brunt-Väisälä frequency of internal
waves:

DV = max D3D , 0.2L2oz

g ∂ρ
−
ρ ∂z

(9.106)

For a detailed description of the turbulence closure models of Delft3D-FLOW we refer to Rodi
(1984) and Uittenbogaard et al. (1992).
9.5.1

Algebraic turbulence model (AEM)

The Algebraic Eddy viscosity Model (AEM) in Delft3D-FLOW is a combination of two zero
order closure schemes. These models will be denoted by ALG (Algebraic closure model) and
PML (Prandtl’s Mixing Length model). Both models will be briefly described. The combination
of the two models was made to broaden the applicability of the algebraic turbulence closure.
9.5.1.1

Algebraic closure model (ALG)

In the algebraic closure model, ALG, a logarithmic velocity profile is assumed. This leads to a
linear relation between the turbulent kinetic energy at the bed and the turbulent kinetic energy
at the free surface:

1
k=√
cµ

2
ub∗

z+d
2 z +d
1−
+ u∗s
,
H
H

(9.107)

with:

cµ
u∗s
ub∗

A constant, cµ ≈ 0.09, calibrated for local-equilibrium shear layers (Rodi,
1984).
The friction velocity at the free surface, see Equation (9.67).
A modified form of the bed friction velocity u∗b .

The turbulent kinetic energy k at the bed and at the free surface is determined basing on the
shear stresses. The bed friction velocity u∗b is determined from the magnitude of the velocity

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in the first grid point above the bed, under the assumption of a logarithmic velocity profile:

~u∗b =

ln 1 +

∆zb
2z0

~ub .

(9.108)

In tidal flows, at slack water the velocities are almost zero near the bed. Higher in the water
column, the turbulence intensity may still be large. To avoid a zero eddy viscosity, velocities
higher in the water column have to be used in the determination of the bed friction velocity.
Under the assumption that the velocity profile is logarithmic in the discrete model for layer with
index k :

ln 1 +

zk +d
z0

~uk ,

(9.109)

~u∗k =

and the average value is defined as:

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AF

K
1 X
~u∗ =
~u∗k .
K k=1

(9.110)

In the linear profile for the turbulence energy, Equation (9.107),

~ub∗ = max (~u∗ , ~u∗b )

(9.111)

is used. The friction velocity at the free surface is dependent on the wind velocity at 10 m
above the free surface Eqs. (9.67) to (9.69).
In this algebraic turbulence closure model the wind stress and the bed stress affect the eddy
viscosity over the total water depth instantaneously. In deep areas, this is physically not
correct; the turbulent kinetic energy generated at the free surface and at the bed must be
transported along the water column by vertical diffusion. This will lead to phase differences
in the time-series of the turbulent energy for the different layers, see Baumert and Radach
(1992).
Given k of Equation (9.107) and L of Equation (9.101) the eddy viscosity νALG is prescribed
by Equation (9.98). The eddy viscosity is parabolic and gives in the case of wind-driven
circulation, a double logarithmic vertical velocity profile.
9.5.1.2

Prandtl’s Mixing Length model (PML)

A second algebraic expression for the eddy viscosity is obtained by assuming instantaneous
local equilibrium between production and dissipation in the k -L model. This closure scheme
is known as Prandtl’s Mixing Length model (PML). In the production term the horizontal derivatives are left out, they are small compared to the vertical derivatives, leading to:

1
k = √ L2
cµ

∂u
∂z

∂v
∂z

2 #
.

(9.112)

The mixing length L is again prescribed by Equation (9.101). Given k of Equation (9.112)
and L of Equation (9.101) the eddy viscosity νPML is prescribed by Equation (9.98). Note that
for a logarithmic velocity profile, without wind, Eqs. (9.107) and (9.112) give the same linear
distribution of k .

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For the turbulence closure scheme ALG, the turbulent kinetic energy over the whole water
column is in phase with the bed stress. For the PML model there is a phase difference in k ,
introduced by phase differences in the vertical gradient of the horizontal velocities. The phase
differences depend on the total water depth and the eddy viscosity:

T ≈

H2
,
νV

(9.113)

see e.g. Baumert and Radach (1992).
The PML-model leads to a zero eddy viscosity and eddy diffusivity at the position in the vertical where the vertical gradients of the velocity are zero (e.g. in wind-driven flows). This is
physically incorrect.

(9.114)

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ν3D = max (νALG , νPML )

For robustness, in Delft3D-FLOW the turbulence closure models PML and ALG are combined
to one algebraic model, denoted as the AEM model. The eddy viscosity is calculated following:

The eddy diffusivity is derived from the eddy viscosity, using the Prandtl-Schmidt number.
Tidal simulations using this parameterisation have been performed for the Irish Sea (Davies
and Gerritsen, 1994).
9.5.2

k -L turbulence model

A so-called first order turbulence closure scheme implemented in Delft3D-FLOW is the k -L
model. In this model the mixing length L is prescribed analytically, Equation (9.101). The
velocity scale is based on the kinetic energy of turbulent motion. The turbulent kinetic energy
k follows from a transport equation that includes an energy dissipation term, a buoyancy term
and a production term. The following two assumptions are made:

The production, buoyancy and dissipation terms are the dominating terms.
The horizontal length scales are much larger than the vertical ones (shallow water, boundary layer type of flows).

The conservation of the turbulent quantities is less important and the transport equation is
implemented in a non-conservative form. The second assumption leads to simplification of
the production term. The transport equation for k is as follows:

u ∂k
v ∂k
ω ∂k
∂k
+p
+p
+
=
∂t
Gξξ ∂ξ
Gηη ∂η d + ζ ∂σ

1
∂
∂k
+
Dk
+ Pk + Pkw + Bk − ε. (9.115)
∂σ
(d + ζ)2 ∂σ
with

Dk =

νmol ν3D
+
σmol
σk

(9.116)

In the production term Pk of turbulent kinetic energy, the horizontal gradients of the horizontal
velocity and all the gradients of the vertical velocities are neglected. The production term is

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given by:

1
Pk = ν3D
(d + ζ)2

∂u
∂σ

∂v
∂σ

2 #
.

(9.117)

For small-scale applications (e.g. simulation of laboratory flume), you can switch on a more
extended production term Pk of turbulent kinetic energy (option “partial slip”, rough side wall)
given by:



!2 
1
∂u
∂v
1 ∂u 
Pk = 2ν3D 
+
+ p
+
2
∂σ
∂σ
Gξξ ∂ξ
2 (d + ζ)

!2
!2 
1
1 ∂u
1 ∂v
1 ∂v 
p
+ 2ν3D 
+p
. (9.118)
+ p
2
Gηη ∂η
Gξξ ∂ξ
Gηη ∂η
2

2 )

(

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In this expression, ν3D is the vertical eddy viscosity, prescribed by Equation (9.98). In
Eqs. (9.117) and (9.118) it has been assumed that the gradients of the vertical velocity w
can be neglected with respect to the gradients of the horizontal velocity components u and v .
The horizontal and vertical (σ -grid) curvature of the grid has also been neglected.
The turbulent energy production due to wave action is given by Pkw ; the exact formulation is
in section 9.7.4.
Near the closed walls the normal derivative of the tangential velocity is determined with the
law of the wall:

∂u
u∗
=
.
∂y
κy

(9.119)

In stratified flows, turbulent kinetic energy is converted into potential energy. This is represented by a buoyancy flux Bk defined by:

Bk =

ν3D g ∂ρ
ρσρ H ∂σ

(9.120)

with the Prandtl-Schmidt number σρ = 0.7 for salinity and temperature and σρ = 1.0 for
suspended sediments.
In the k -L model, it is assumed that the dissipation ε depends on the mixing length L and
kinetic turbulent energy k according to:

√
k k
ε = cD
,
L

(9.121)

where cD is a constant determined by calibration, derived from the constant cµ in the k -ε
model:

cD = c3/4
µ ≈ 0.1925.

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(9.122)

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To solve the transport equation, boundary conditions must be specified. A local equilibrium of
production and dissipation of kinetic energy is assumed at the bed which leads to the following
Dirichlet boundary condition:

u2
k|σ=−1 = √∗b .
cµ

(9.123)

The friction velocity u∗b at the bed is determined from the magnitude of the velocity in the
grid point nearest to the bed, under the assumption of a logarithmic velocity profile, see Equation (9.58). The bed roughness (roughness length) may be enhanced by the presence of wind
generated short crested waves, see section 9.7.

u2
k|σ=0 = √∗s .
cµ

In case of wind forcing, a similar Dirichlet boundary condition is prescribed for the turbulent
kinetic energy k at the free surface:
(9.124)

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In the absence of wind, the turbulent kinetic energy k at the surface is set to zero.

At open boundaries, the turbulent energy k is computed using the equation for k Equation (9.107) without horizontal advection. For a logarithmic velocity profile this will approximately lead to the following linear distribution based on the shear-stress at the bed and at the
free surface:

1
z+d
2
2 z +d
k (z) = √
u
+ u∗s
.
1−
cµ ∗b
H
H
9.5.3

(9.125)

k -ε turbulence model

In the k -ε turbulence model, transport equations must be solved for both the turbulent kinetic
energy k and for the energy dissipation ε. The mixing length L is then determined from ε and
k according to:

√
k k
.
L = cD
ε

(9.126)

In the transport equations, the following two assumptions are made:

The production, buoyancy, and dissipation terms are the dominating terms.
The horizontal length scales are larger than the vertical ones (shallow water, boundary
layer type of flows).

Because of the first assumption, the conservation of the turbulent quantities is less important
and the transport equation is implemented in a non-conservation form.
The transport equations for k and ε are non-linearly coupled by means of their eddy diffusivity
Dk , Dε and the dissipation terms. The transport equations for k and ε are given by:

∂k
u ∂k
v ∂k
ω ∂k
+p
+p
+
=+
∂t
Gξξ ∂ξ
Gηη ∂η d + ζ ∂σ

1
∂
∂k
+
Dk
+ Pk + Pkw + Bk − ε, (9.127)
∂σ
(d + ζ)2 ∂σ

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Conceptual description

u ∂ε
v ∂ε
ω ∂ε
∂ε
+p
+p
+
=
∂t
Gξξ ∂ξ
Gηη ∂η d + ζ ∂σ

∂
1
∂ε
ε2
D
+
P
+
P
+
B
−
c
. (9.128)
ε
ε
εw
ε
2ε
∂σ
k
(d + ζ)2 ∂σ
with

Dk =

νmol ν3D
+
σmol
σk

and

Dε =

ν3D
σε

(9.129)

ε
Pε = c1ε Pk ,
k
ε
Bε = c1ε (1 − c3ε ) Bk ,
k

The production term Pk is defined in Eqs. (9.117) and (9.118), and the buoyancy term Bk is
defined in Equation (9.120). The production term Pε and the buoyancy flux Bε are defined
by:
(9.130)
(9.131)

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with L prescribed by Equation (9.126) and the calibration constants by (Rodi, 1984):

c1ε = 1.44,
c2ε = 1.92,

0.0
c3ε =
1.0

unstable stratification
stable stratification

(9.132)
(9.133)
(9.134)

In Delft3D-FLOW in the ε-equation for stable stratification the buoyancy flux is switched off,
so c3ε = 1.0 and for unstable stratification the buoyancy flux is switched on c3ε = 0.0.
The energy production and energy dissipation due to waves, the terms Pkw and Pεw in
Eqs. (9.127) and (9.128), are given in section 9.7.4.
The coefficients of the 3D k -ε turbulence closure model as implemented in Delft3D-FLOW are
not the same as in the depth-averaged k -ε turbulence closure model (Rodi, 1984), therefore
for depth-averaged simulations, the k -ε turbulence closure model is not available for you.
The vertical eddy viscosity ν3D is determined by:

√
k2
ν3D = c0µ L k = cµ ,
ε

(9.135)

cµ = cD c0µ .

(9.136)

with:

For the transport equation of the turbulent kinetic energy k the same Dirichlet boundary conditions are used as for the k -L model described earlier, see Equation (9.123) and (9.124).
For the transport equation of the dissipation ε, the following boundary condition is used at the
bed:

ε|σ=−1 =

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u3∗b
,
κz0

(9.137)

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and at the surface the dissipation ε is prescribed by:

ε|σ=0 =

u3∗s
.
1
κ∆zs
2

(9.138)

In case of no wind, the dissipation ε is set to zero at the free surface.
At open boundaries, the energy dissipation ε is computed using Equation (9.128) without horizontal advection. For a logarithmic velocity profile this will approximately lead to a hyperbolic
distribution which is the superposition of two hyperbola, corresponding to a double logarithmic
velocity profile, on the basis of the shear-stresses at the bed and at the free surface:

u3∗b
u3∗s
+
,
κ (z + d) κ (H − z − d)

where z denotes the vertical co-ordinate.

(9.139)

ε (z) =

9.5.4

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The k -ε turbulence model was successfully applied for the simulation of stratified flow in the
Hong Kong waters (Postma et al., 1999) and verified for the seasonal evolution of the thermocline (Burchard and Baumert, 1995).
Low Reynolds effect

In laboratory flumes or highly stratified flows e.g. by mud, the flow is nearly laminar. Then the
vertical eddy viscosity computed by the standard k-epsilon model is over-estimated because
this model lacks viscous damping terms. Therefore, in literature so-called low-Re k -ε models
are proposed. Our experience (Uittenbogaard, pers. comm.), however, is that these models
require large resolution and switch from laminar to turbulent flow conditions at too large Renumbers. Instead, we extended the k -ε turbulence model in Delft3D-FLOW by a continuous
damping function reducing its eddy viscosity, see below. In Delft3D-FLOW it is possible to
switch on this so-called Low Reynolds turbulence model by adding the keyword LRdamp in
the MDF-file. The formulation implemented is given below.
The turbulence Reynolds number is defined as

ReT =

νmol ε

ν3D
,
cµ νmol

(9.140)

If the turbulence Reynolds number is low, then the eddy viscosity and the eddy diffusivity
computed from the k-ε model are corrected by the damping function

ν3D (Relow ) = f (ReT )ν3D (k − ε; Rehigh )

(9.141)

in which

f (ReT ) = 1 − e−p

where

ReT
ν3D
=
100
100cµ νmol

(9.142)

No critical value for the Reynolds number needs to be specified, because a value of ReT =
300 (f = 0.999877) is applied. We remark that function f rapidly converges to 1 for large
values of ReT .

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Secondary flow; σ -model only
This feature is only available in the σ -model.

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9.6

Figure 9.6: Spiral motion in river bend (from Van Rijn (1990))

The flow in a river bend is basically three-dimensional. The velocity has a component in the
plane perpendicular to the river axis. This component is directed to the inner bend near the
riverbed and directed to the outer bend near the water surface, see Figure 9.6.
This so-called ’secondary flow’ (spiral motion) is of importance for the calculation of changes
of the riverbed in morphological models and the dispersion of matter. In a 3D model the
secondary flow is resolved on the vertical grid, but in 2D depth-averaged simulations the
secondary flow has to be determined indirectly using a secondary flow model. It strongly
varies over the vertical but its magnitude is small compared to the characteristic horizontal
flow velocity.
The secondary flow will be defined here as the velocity component v (σ) normal to the depthaveraged main flow. The spiral motion intensity of the secondary flow I is a measure for the
magnitude of this velocity component along the vertical:

|v (σ)| dσ.

(9.143)

−1

The vertical distribution of the secondary flow is assumed to be a universal function of the
vertical co-ordinate f (σ). The actual local velocity distribution originates from a multiplication
of this universal function with the spiral motion intensity, see Kalkwijk and Booij (1986):

ν (σ) = f (σ) I.

(9.144)

A vertical distribution for a river bend is given in Figure 9.7. The spiral motion intensity I leads
to a deviation of the direction of the bed shear stress from the direction of the depth-averaged
flow and thus affects the bedload transport direction. This effect can be taken into account in
morphological simulations.

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τbs

+s
τb

δ
τbn
+r

M
Figure 9.7: Vertical profile secondary flow (V ) in river bend and direction bed stress

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The component of the bed shear stress normal to the depth-averaged flow direction τbr reads:

~ I,
τbr = −2ρα2 (1 − α) U

(9.145)

~ is the magnitude of the depth-averaged vewhere α is defined in Equation (9.156) and U
locity. To take into account the effect of the secondary flow on the depth-averaged flow, the
depth-averaged shallow water equations have to be extended with:

An additional advection-diffusion equation to account for the generation and adaptation of
the spiral motion intensity.
Additional terms in the momentum equations to account for the horizontal effective shearstresses originating from the secondary flow.
Depth-averaged continuity equation

The depth-averaged continuity equation is given by:

p
p
∂ (d + ζ) U Gηη
∂ (d + ζ) V Gξξ
∂ζ
1
1
+p p
+p p
=Q
∂t
∂ξ
∂η
Gξξ Gηη
Gξξ Gηη
(9.146)

where U and V indicate the depth-averaged velocities on an orthogonal curvilinear grid.
Momentum equations in horizontal direction
The momentum equations in ξ - and η -direction are given by:

p
p
∂ Gξξ
∂ Gηη
∂U
U ∂U
V ∂U
UV
V2
+p
+p
+p p
−p p
+
∂t
Gξξ ∂ξ
Gηη ∂η
Gξξ Gηη ∂η
Gξξ Gηη ∂ξ
√
1
gU U 2 + V 2
− fV = − p
Pξ −
+ Fξ + Fsξ + Mξ , (9.147)
2
C2D
(d + ζ)
ρ0 Gξξ

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Conceptual description

and

p
p
∂ Gηη
∂ Gξξ
∂V
U ∂V
V ∂V
UV
U2
+p
+p
+p p
−p p
+
∂t
Gξξ ∂ξ
Gηη ∂η
Gξξ Gηη ∂ξ
Gξξ Gηη ∂η
√
1
gV U 2 + V 2
+ fU = − p
Pη −
+ Fη + Fsη + Mη . (9.148)
2
C2D
(d + ζ)
ρ0 Gηη
The fourth term in the right-hand side represents the effect of the secondary flow on the depthaveraged velocities (shear stresses by depth-averaging the non-linear acceleration terms).
Effect of secondary flow on depth-averaged momentum equations

and:

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To account for the effect of the secondary flow on the depth-averaged flow, the momentum
equations have to be extended with additional shear stresses. To close the equations these
stresses are coupled to parameters of the depth-averaged flow field. The main flow is assumed to have a logarithmic velocity profile and the secondary flow originates from a multiplication of a universal function with the spiral motion intensity, see Kalkwijk and Booij (1986).
Depth averaging of the 3D equations leads to correction terms in the depth-averaged momentum equations for the effect of spiral motion:

1
Fsξ =
d+ζ

(

1
d+ζ

(

Fsη =

)
1 ∂ [(d + ζ) Tξξ ]
1 ∂ [(d + ζ) Tξη ]
p
+p
+
∂ξ
∂η
Gξξ
Gηη
(
)
p
p
∂ Gξξ
∂ Gηη
2Tξη
2Tξξ
+ p p
+p p
, (9.149)
Gξξ Gηη ∂η
Gξξ Gηη ∂ξ

)

1 ∂ [(d + ζ) Tηξ ]
1 ∂ [(d + ζ) Tηη ]
p
+p
+
∂ξ
∂η
Gξξ
Gηη
)
(
p
p
∂ Gξξ
∂ Gηη
2Tηη
2Tηξ
+ p p
+p p
, (9.150)
Gξξ Gηη ∂η
Gξξ Gηη ∂ξ

with the shear-stresses, resulting from the secondary flow, modelled as:

Tξξ = −2βU V,

Tξη = Tηξ = β U − V
Tηη = 2βU V,

(9.151)
(9.152)
(9.153)

and:

(d + ζ)
,
Rs∗

β ∗ = βc 5α − 15.6α2 + 37.5α3 ,
βc ∈ [0, 1] , correction coefficient specified by you,
√
g
1
< ,
α=
κC2D
2
β = β∗

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(9.154)
(9.155)

(9.156)

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with Rs∗ the effective radius of curvature of a 2D streamline to be derived from the intensity
of the spiral motion and κ the Von Kármán constant. The spiral motion intensity is computed
by Equation (9.157). The limitation on α, Equation (9.156), is set to ensure that the length
scale La in Equation (9.164) is always positive. For βc = 0, the depth-averaged flow is not
influenced by the secondary flow.
Remark:
Equation (9.156) effectively means a lower limit on C2D .
The depth averaged transport equation for the spiral motion intensity
The variation of the spiral motion intensity I in space and time, is described by a depthaveraged advection-diffusion equation:

with:

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AF

(

)
p
p
∂
(d
+
ζ)
U
G
I
∂
(d
+
ζ)
V
G
I
∂ [(d + ζ) I]
1
ηη
ξξ
+p p
+
=
∂t
∂ξ
∂η
Gξξ Gηη
#
"
#)
( "
p
p
G
G
d+ζ
∂
∂
ηη ∂I
ξξ ∂I
+p p
DH p
+
DH p
+ (d + ζ) S,
∂η
Gξξ Gηη ∂ξ
Gξξ ∂ξ
Gηη ∂η

I − Ie
,
Ta
= Ibe − Ice ,
d+ζ ~
U ,
=
Rs
d+ζ
=f
,
p 2
= U 2 + V 2,

(9.157)

S=−

(9.158)

(9.159)

Ibe

Ice
~
U

(9.160)
(9.161)
(9.162)

Ta =

La
,
~
U

(9.163)

La =

(1 − 2α) (d + ζ)
,
2κ2 α

(9.164)

and Rs the radius of curvature of the stream-line defined by:

Us
∂Ur
=−
,
Rs
∂s

(9.165)

with Us and Ur the components along and perpendicular to the streamline. The effective
radius of curvature to be used for the evaluation of the coefficient β , Equation (9.155), reads:

Rs∗

~
(d + ζ) U
=

(9.166)

To guarantee stability the effective radius of curvature is bounded by the following empirical
relation:

Rs∗ ≥ 10 (d + ζ) .
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(9.167)

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Conceptual description

The above formulas account for two sources of secondary flow:

The centrifugal force in case of curved streamlines, Ibe .
The effect of the Coriolis force, Ice .
The solution of the advection-diffusion equation will take some computer time. For steady
state simulations, Delft3D-FLOW has an option to compute the spiral intensity I based on an
algebraic expression assuming local equilibrium:

I = Ibe − Ice .

(9.168)

Boundary conditions for spiral motion

Wave-current interaction

In relatively shallow areas (coastal seas) wave action becomes important because of several
processes:

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9.7

At open boundaries, during inflow the spiral motion intensity must be prescribed. The local
equilibrium value Equation (9.168) is used. For perpendicular inflow the radius of curvature
goes to infinity and the spiral intensity reduces to zero.

The vertical mixing processes are enhanced due to turbulence generated near the surface
by whitecapping and wave breaking, and near the bottom due to energy dissipation in the
bottom layer.
A net mass flux is generated which has some effect on the current profile, especially in
cross-shore direction.
In the surf zone long-shore currents and a cross-shore set-up is generated due to variations in the wave-induced momentum flux (radiation stress). In case of an irregular surf
zone, bathymetry strong circulations may be generated (rip currents).
The bed shear stress is enhanced; this affects the stirring up of sediments and increases
the bed friction.
These processes are accounted for in a wave-averaged manner. Some processes basically
act at a specific location or interface, such as the enhanced bed shear-stress or wave breaking
at the surface, while others have a (certain) distribution over the vertical, such as the energy
dissipation due to bottom friction in the wave boundary layer. A vertical distribution can, of
course, only be accounted for in a 3D computation; in a 2D computation such a process is
accounted for in a depth averaged form.
The computation of waves and wave-induced effects is the domain of wave models. Delft3DWAVE supports currently one wave model: SWAN, a third generation wave model (Ris, 1997).
SWAN computes the full (directional and frequency) spectrum on a rectilinear or curvilinear
grid with many processes formulated in detail. For details and background you are referred to
the Delft3D-WAVE User Manual (WAVE UM, 2013) and the references cited above.
For the sake of simplicity, we will describe in this section all wave-induced effects on a rectangular grid. In Delft3D-FLOW, however, these terms have been implemented in a curvilinear
co-ordinate system. For a full wave-current interaction the currents from Delft3D-FLOW are
used in Delft3D-WAVE (current refraction). The numerical grids used in the flow and wave
computation often differ. Delft3D-FLOW and SWAN can both apply a rectilinear or curvilinear
grid. To use the required grid resolution in the area of interest you can use nested grids. The
transformation of results between the nested grids and the grids used in the flow and in the
wave computations is executed automatically and is fully transparent to you. In SWAN, you

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can use the same curvilinear grid as used in Delft3D-FLOW and obtain in one computation
the required resolution in the area of interest.
The general procedure to derive the wave-induced forces is:

Average the continuity equation and the momentum equations over the wave period.
Express the residual terms that remain compared to the case without waves in terms of
the wave properties, such as the wave energy, the phase and group velocity, and wave
length or wave period.

∂ ūj
∂ ūj
∂ ζ̄
1 ∂ τ̄ij
+ ūi
+ ... + g
−
= Fj ,
∂t
∂xj
∂xj
ρ ∂xi

Obviously, there are various averaging procedures. A straightforward approach is to define the
mean motion by time averaging the equations over a wave period. The momentum equation in
x-direction, averaged over the wave motion and expressed in Cartesian co-ordinates is given
by:
(9.169)

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where for i and j the summation rule applies, i, j = {1, 2, 3}, the wave averaged quantity is
indicated by an overhead bar, ūj is the wave-mean velocity component, ζ̄ is the wave-mean
free surface elevation, τ̄ij are the components of the wave-averaged normal stress tensor,
and Fj is the wave-induced force that remains after averaging the momentum equation over
the wave period. This wave induced force can generally be written as the gradient of the
radiation-stress tensor S :

Fi = −

∂Sij
.
∂xj

(9.170)

Using wave propagation models we can express Sij in terms of the wave parameters, such
as the wave energy, the phase and group velocity, the wave length and the wave period. The
wave-induced force is computed as the gradient of the radiation stress terms.
The above given procedure can only be applied when the mean motion is uniform with depth.
In most practical cases this does not apply. Then the only way to split the mean and oscillating
motion is through the Generalised Lagrangian Mean, GLM method of Andrews and McIntyre
(1978). As shown by Andrews and McIntyre (1978), Groeneweg and Klopman (1998) and
Groeneweg (1999) the (depth averaged and 3D) flow equations written in a co-ordinate system moving with the Stokes drift are very similar to the ordinary Eulerian formulation. However,
the wave-induced driving force due to averaging over the wave motion is more accurately expressed in wave properties. The relation between the GLM velocity and the Eulerian velocity
is given by:

~uL = ~uE + ~uS ,
L

(9.171)
S

where ~
u is the GLM-velocity vector, ~u is the ordinary Eulerian-velocity vector and ~u is the
Stokes-drift vector.
The momentum equation in x-direction, averaged over the wave motion and expressed in
GLM co-ordinates is given by:

∂ ūLj
∂ ūLj
∂ ζ̄
1 ∂ τ̄ijL
+ ūLi
+ ... + g
−
= FjL ,
∂t
∂xj
∂xj
ρ ∂xi

(9.172)

where for i and j the summation rule applies, i, j = {1, 2, 3}, and the quantities have the
same meaning as in Equation (9.169), but now in GLM co-ordinates. As shown by Groeneweg

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Conceptual description

(1999) the right-hand side of Equation (9.172) contains a term related to a Stokes correction
of the shear stresses. In the current implementation this term is neglected.
So in short:

In Delft3D-FLOW, the hydrodynamic equations are written and solved in GLM-formulation,
including the wave-current interactions.

The GLM velocities are written to the communication file and are used in all (sediment)

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transport computations. Quantities moving with the flow are transported by the total, i.e.
the GLM, velocity and not the Eulerian velocity.
The Eulerian velocities are written to the Delft3D-FLOW result files to be used in comparisons of computational results with measurements.
The only difference in the computational procedure as compared to the ordinary Eulerian
formulation occurs at the boundaries. The velocity at the bottom is not the total velocity but
the Eulerian velocity; so the bed-shear-stress is corrected for the Stokes drift. At lateral
velocity boundaries, the total velocity must be prescribed; the implementation is such that
the Eulerian velocity is prescribed in the boundary conditions (by you) and the Stokes drift
is added by Delft3D-FLOW. At water level boundaries, just the wave-mean water level
must be prescribed.
In the following sections, we discuss the wave-current interaction terms and their possible
profile in the vertical. Where applicable we distinguish between the depth-averaged and the
3D formulations.
Remarks:
For brevity, we suppress the index L for GLM quantities. So, in this section a velocity
without super-script refers to the GLM velocity, unless explicitly mentioned differently.
A super-script S is used to indicate the Stokes drift.
9.7.1

Forcing by radiation stress gradients

The wave-induced force, i.e. the right-hand side of Equation (9.172), can be expressed in the
wave parameters of the wave model that is being applied. For linear current refraction the
expression can be derived analytically. To account for wave dissipation due to for instance
bottom friction, wave breaking and whitecapping and wave growth due to wind one can rely
on mild slope formulations with dissipation terms.
As shown by Dingemans et al. (1987), using the gradients of the radiation stresses in numerical models can result in spurious currents. Dingemans et al. (1987) showed that the divergence free part of the radiation stress is not capable of driving currents and can therefore
be neglected if one is primarily interested in wave-driven currents. The remaining part of the
radiation stress gradients is closely related to the wave energy dissipation, i.e. the right-hand
side of Equation (9.172) can be written as:

Fi =

Dki
,
ω

(9.173)

where D is the total energy dissipation due to waves, ki is the wave number in i-direction
and ω is the wave frequency; see Dingemans (1997) for many details and discussions on this
subject.

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2D implementation
For a depth averaged model the momentum equations in x- and y -direction, leaving out most
of the terms, can be written as:

√
∂U
gU U 2 + V 2
+ ... +
+ . . . = . . . + Fx ,
(9.174)
2
∂t
C2D
(d + ζ)
√
∂V
gV U 2 + V 2
+ ... +
+ . . . = . . . + Fy ,
(9.175)
2
∂t
C2D
(d + ζ)
where Fx and Fy are the depth averaged wave-induced forcings and given by the gradients
of the radiation stress tensor S , or following Dingemans et al. (1987) approximated by wave
kx
∂Sxx ∂Syx
−
=D ,
∂x
∂y
ω

Fy = −

∂Sxy ∂Syy
ky
−
=D .
∂x
∂y
ω

(9.176)

(9.177)

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Fx = −

energy dissipation:

The dissipation rate D (a negative quantity) is computed by the wave model and read from the
communication file. In SWAN, the dissipation rate may be computed from the bottom friction
(orbital motion), depth-induced breaking and whitecapping.
You can choose to apply the radiation stress or the dissipation rate to determine the waveinduced forces.
3D implementation

In version 5.01 (and higher) of Delft3D-FLOW the 3 different dissipation rates, calculated by
SWAN, are handled separately: dissipation due to depth-induced breaking and whitecapping
at the top layer and dissipation due to bottom friction at the bed layer. The effect of the
divergence free part of the radiation stresses is (the remaining part of the radiation stress gradients, after the wave dissipation has been subtracted) is added to the momentum equations
in Delft3D-FLOW (effect spread over the water column). This provides most adequate results,
e.g. in situations with undertow.
9.7.2

Stokes drift and mass flux

In surface waves, fluid particles describe an orbital motion. The net horizontal displacement
for a fluid particle is not zero. This wave induced drift velocity, the so-called Stokes-drift,
is always in the direction of wave propagation. A particle at the top of the orbit beneath a
wave crest moves slightly faster in the forward direction than it does in the backward direction
beneath a wave trough. The mean drift velocity is a second order quantity in the wave height.
The drift leads to additional fluxes in the wave averaged mass continuity equation.
The wave-induced mass fluxes MxS and MyS are found by integration of the components of
the Stokes drift uS and v S over the wave-averaged total water depth:

MxS

ρo uS dz =

E
kx
ω

(9.178)

ρ0 v S dz =

E
ky
ω

(9.179)

−d

MyS

=
−d

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Conceptual description

with E the wave energy defined as:

1
2
.
E = ρ0 gHrms
8

(9.180)

The mass fluxes MxS and MyS are computed by an interface program and are written to the
communication file.

2D implementation

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The depth-averaged Stokes drift is given by:

Remarks:
The mass flux effect is only taken into account when Delft3D-FLOW is used from within
Delft3D-MOR.
The velocities written to the communication file for use in Delft3D-MOR, Delft3D-WAVE,
and D-Water Quality are based on the total flux velocities.
The Eulerian velocities, which may be used in comparisons with measurements at a
fixed location, are written to the hydrodynamic map and history files.

MxS
,
ρ0 (d + ζ)
MyS
.
=
ρ0 (d + ζ)

US =

(9.181)

(9.182)

3D implementation

The Stokes drift is computed from the wave theory, see Dean and Dalrymple (1991, pg. 287,
eq. 10.8):

~uS (z) =

ωka2 cosh (2kz)
(cos φ, sin φ)T .
2
2 sinh (kH)

(9.183)

The wave is computed from the mass fluxes which are read from the communication file:

φ = tan−1 MxS /MyS .

9.7.3

(9.184)

Streaming

Streaming (a wave-induced current in the wave boundary layer directed in the wave propagation direction) is modelled as a time-averaged shear-stress which results from the fact that
the horizontal and vertical orbital velocities are not exactly 90◦ out of phase. It is based on
the wave bottom dissipation and is assumed to decrease linearly to zero across the wave
boundary layer (Fredsøe and Deigaard, 1992):

Df k cos φ
∂ ũw̃
−
=
∂z
ρ0 ωδ

d + ζ − z0
1−
δ

for

d + ζ − δ ≤ z 0 ≤ d + ζ (9.185)

For the definition of z 0 see Figure 9.8.
The left-hand side of Equation (9.185) is the residual term after averaging a vertical derivative
of the advection terms over the wave period. The dissipation due to bottom friction Df is

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MWL
½ H rm s

Z’

d+ ζ

δ
Figure 9.8: Vertical distribution of turbulent kinetic energy production

given by:

1
Df = √ ρ0 fw u3orb ,
2 π

(9.186)

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where uorb is the orbital velocity near the bed, given by Equation (9.204). The friction factor
fw is according to Soulsby et al. (1993b) given by:

(

fw = min 0.3, 1.39
with:

A
z0

−0.52 )

uorb
,
ω

(9.187)

(9.188)

and φ is given by Equation (9.184).

The thickness of the wave boundary layer δ is given by:

δ = H min 0.5, 20 max

9.7.4

(

ez0
ks
, 0.09
H
H

A
ks

0.82 )#

(9.189)

Wave induced turbulence

The vertical mixing processes are enhanced by the wave actions. This can best be accounted
for by adding the wave energy production and dissipation terms in the turbulence model. The
two main sources of wave energy decay that are included are wave breaking and bottom
friction due to the oscillatory wave motion in the bottom boundary layer.
In the case of breaking waves, there is a production of turbulent energy directly associated
with the energy dissipation due to breaking (Deigaard, 1986). The total depth-averaged contribution of wave breaking is given by Dw [W/m2 ], which is computed in the wave model (e.g.
SWAN). Wave energy dissipation due to bottom friction is also considered to produce turbulent kinetic energy. These processes are incorporated by introducing source terms in the
turbulent kinetic energy (for both the k -L and the k -ε turbulence model) and in the turbulent
kinetic energy dissipation equation (k -ε turbulence model).

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Conceptual description

Breaking waves
In a 3D-model the contribution due to wave breaking is linearly distributed over a half wave
height below the mean water surface, Hrms /2 . This is described by the following expression
for the turbulent kinetic energy distribution:

4Dw
Pkw (z ) =
ρw Hrms
0

2z 0
1−
Hrms

for

1
0 ≤ z 0 ≤ Hrms .
2

(9.190)

The source term Pεw in the ε-equation is coupled to Pkw according to:

ε
Pεw (z 0 ) = c1ε Pkw (z 0 ) ,
k
where c1ε is a calibration constant (c1ε = 1.44).

(9.191)

Due to the breaking of waves the boundary conditions of k and ε have to be changed. The
boundary conditions at the free surface of k and ε are given by:

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k|free surface

2Dw κ
= kwind + kwaves = kwind +
ρw cD
4Dw
= εwind + εwaves = εwind +
ρw Hrms

ε|free surface

(9.192)
(9.193)

Bottom friction

The contribution due to bottom friction is linearly distributed over the thickness of the wave
boundary layer, see Figure 9.8.

2Df
Pkw (z ) =
ρ0 δ
0

d + ζ − z0
1−
δ

for d + ζ − δ ≤ z 0 ≤ d + ζ,

(9.194)

due to wave energy decay in the bottom boundary layer. Here z 0 is the vertical co-ordinate
with its origin at the (wave averaged) water level and so z 0 is positive downward, Df represent
wave energy dissipation due to bottom friction, Df is given by Equation (9.186).
The boundary conditions at the bottom, due to the non-linear interaction of the current and
wave boundary layer is directly taken into account, by the adaptation of the bottom roughness
height, see Equation (9.212).
9.7.5

Enhancement of the bed shear-stress by waves

The boundary layers at the bed associated with the waves and the current interact non-linearly.
This has the effect of enhancing both the mean and oscillatory bed shear-stresses. In addition
the current profile is modified, because the extra turbulence generated close to the bed by the
waves appears to the current as being equivalent to an enhanced bottom roughness. The
bed shear-stress due to the combination of waves and current is enhanced beyond the value
which would result from a linear addition of the bed shear-stress due to waves, ~
τw , and the
bed shear-stress due to current ~
τc . For sediment transport modelling it is important to predict
the maximum bed shear-stress, ~
τmax , while the current velocity and the turbulent diffusion are
determined by the combined wave-current bed shear-stress ~
τm .
Various, often very complex, methods exist to describe the bottom boundary layer under combined current and wave action and the resulting virtual roughness. Soulsby et al. (1993a)

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Figure 9.9: Schematic view of non-linear interaction of wave and current bed shearstresses (from Soulsby et al. (1993b, Figure 16, p. 89))

developed a parameterisation of these methods allowing a simple implementation and comparison of various wave-current interaction models: Fredsøe (1984); Myrhaug and Slaattelid
(1990); Grant and Madsen (1979); Huynh-Thanh and Temperville (1991); Davies et al. (1988);
Bijker (1967); Christoffersen and Jonsson (1985); O’ Connor and Yoo (1988); Van Rijn et al.
(2004). All these methods have all been implemented in Delft3D-FLOW and can be applied
in 2D and 3D modelling. However, as there are minor, but specific differences in determining
certain quantities, such as determining the shear-stress at the bottom, we prefer to discuss
the 2D and 3D implementation separately.
2D implementation

Following Soulsby et al. (1993b), Figure 9.9 gives a schematic overview of the bed shearstresses for wave current interaction.
Soulsby et al. (1993b) fitted one standard formula to all of the models, each model having its
own fitting coefficients. The parameterisation of Soulsby for the time-mean bed shear-stress
is of the form:

with

|~τm | = Y (|~τc | + |~τw |) ,

(9.195)

Y = X {1 + bX p (1 − X)q } ,

(9.196)

and for the maximum bed shear-stress:

|~τmax | = Z (|~τc | + |~τw |) ,

(9.197)

Z = 1 + aX m (1 − X)n .

(9.198)

with

and:

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|~τc |
,
|~τc | + |~τw |

(9.199)

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Conceptual description

The value of the parameters a, b, p, q , m and n depends on the friction model which is
parameterised, and:

|~τc |
|~τw |
|~τm |
|~τmax |

magnitude of the bed stress due to current alone
magnitude of the bed stress for waves alone
magnitude of the mean bed stress for combined waves and current
magnitude of the maximum bed stress for combined waves and current.

Remark:
The stresses ~τm and ~τmax are assumed to have the same direction as ~τc .
Following Soulsby et al. (1993b) the expressions for the parameters χ (= a, b, p, q, m, n)
and J (= I, J ; also depending on the friction model) have the form:
J

χ = χ1 + χ2 |cos φ|

in which:

C2D
fw
φ

+ χ3 + χ4 |cos φ|

log

fw
C2D

(9.200)

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drag coefficient due to current
wave friction factor
the angle between the current direction and the direction of wave propagation.

As the radiation stress is always in the wave direction, we can derive φ from:

|cos φ| =

|U Fx + V Fy |
.
~ F~
U

(9.201)

Values of the parameters a, b, p, q and J in Equation (9.200) have been optimised by Soulsby
et al. (1993b), see Table 9.5 and Figure 9.10.
The bed shear-stress due to flow alone may be computed using various types of formulations
like Chézy, Manning or White-Colebrook, see Eqs. (9.54) to (9.56). The bed shear-stress due
to current alone can be written in the form:

~
~ U
gρ0 U

~τc =

2
C2D

(9.202)

The magnitude of the wave-averaged bed shear-stress due to waves alone is related to the
wave orbital velocity near the bottom ~
uorb and the friction coefficient fw :

1
|~τw | = ρ0 fw u2orb .
2

(9.203)

The orbital velocity is computed from the linear wave theory and is given by:

uorb =

1 √ Hrms ω
π
,
4
sinh (kH)

(9.204)

where the root-mean-square wave height Hrms and the wave period T (= 2π/ω) are read
from the communication file. The variation of the wave friction factor with relative orbital excursion at the bed under purely oscillatory flow is given by Swart (1974) (≡ Equations (11.77),

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Table 9.5: Fitting coefficients for wave/current boundary layer model

FR84
MS90
HT91
GM79
DS88
BK67
CJ85
OY88

VR04
1

-0.06
-0.01
-0.07
0.11
0.05
0.00
-0.01
-0.45

1.70
1.84
1.87
1.95
1.62
2.00
1.58
2.24

-0.29
-0.58
-0.34
-0.49
-0.38
0.00
-0.52
0.16

0.29
-0.22
-0.12
-0.28
0.25
0.00
0.09
-0.09

0.67
0.63
0.72
0.65
1.05
0.00
0.65
0.71

-0.29
-0.09
-0.33
-0.22
-0.75
0.50
-0.17
0.27

0.09
0.23
0.08
0.15
-0.08
0.00
0.18
-0.15

0.42
-0.02
0.34
0.06
0.59
0.00
0.05
0.03

0.75
0.82
0.78
0.71
0.66
0.00
0.47
1.19

-0.27
-0.30
-0.23
-0.19
-0.25
0.50
-0.03
-0.66

0.11
0.19
0.12
0.17
0.19
0.00
0.59
-0.13

-0.02
-0.21
-0.12
-0.15
-0.03
0.00
-0.50
0.12

0.80
0.67
0.82
0.67
0.82
1.00
0.64
0.77

0.29
0.65
0.27
0.73
0.22
0.32
0.47
-0.06

0.55
0.29
0.51
0.40
0.73
0.55
0.29
0.26

-0.10
-0.30
-0.10
-0.23
-0.05
0.00
-0.09
0.08

-0.14
-0.21
-0.24
-0.24
-0.35
0.00
-0.12
-0.03

-0.77
-0.60
-0.75
-0.68
-0.86
-0.63
-0.70
-1.00

0.10
0.10
0.13
0.13
0.26
0.05
0.13
0.31

0.27
0.27
0.12
0.24
0.34
0.00
0.28
0.25

0.14
-0.06
0.02
-0.07
-0.07
0.00
-0.04
-0.26

0.91
1.19
0.89
1.04
-0.89
1.14
1.65
0.38

0.25
-0.68
0.40
-0.56
2.33
0.18
-1.19
1.19

0.50
0.22
0.50
0.34
2.60
0.00
-0.42
0.25

0.45
-0.21
-0.28
-0.27
-2.50
0.00
0.49
-0.66

3.00
0.50
2.70
0.50
2.70
3.00
0.60
1.50

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FR84
MS90
HT91
GM79
DS88
BK67
CJ85
OY88

Model1

Y = 0.0 and Z = 1.0

FR84=Fredsøe (1984), MS90=Myrhaug and Slaattelid (1990),
HT91=Huynh-Thanh and Temperville (1991), GM79=Grant and Madsen (1979), DS88=Davies et al. (1988),
BK67=Bijker (1967), CJ85=Christoffersen and Jonsson (1985), OY88=O’ Connor and Yoo (1988),
VR04=Van Rijn et al. (2004)

Figure 9.10: Inter-comparison of eight models for prediction of mean and maximum bed
shear-stress due to waves and currents (from Soulsby et al. (1993b, Figure 17, p. 90))

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Conceptual description

(11.116) and (11.157)):

fw =



0.00251 exp 5.21 A −0.19 ,
ks



0.3,

A
ks

> π2 ,

A
ks

π
,
2

≤

(9.205)

with:

uorb
,
ω

(9.206)

ks is the Nikuradse roughness length-scale and ω is the wave angular frequency.

(9.207)

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|~τm | ~
S
~
~τb =
U −U ,
~
U

As the bed is in rest and the equations are formulated in GLM co-ordinates, we must correct the bed shear-stress used in the momentum equations for the Stokes drift. The total or
effective bed shear stress is given by:

~ S are given by Eqs. (9.181) and
where the components of the depth-averaged Stokes drift U
(9.182).
3D implementation

For 3D simulations the enhanced bed shear-stress is computed along the same lines, but
remark that the bed shear-stress is now a boundary condition. The magnitude of the depthaveraged velocity in Equation (9.202) is determined from the velocity near the bed, assuming
a logarithmic velocity profile.
The bed shear-stress corrected for the Stokes drift is given by:

~τb =

with:

|~τm |
~ 2D
U

~ 2D =
U

1
d+ζ

~u − ~uS ,

(9.208)

~udz.

(9.209)

−d

The Stokes drift and the angle between near bed current and the waves are given by Eqs. (9.183)
and (9.184).
Matching the velocity profile corresponding with the increased mean bed stress ~
τm for waves
and current, with a logarithmic profile for the mean flow outside the wave boundary layer:

~τm = ρ0~ũ∗ ~ũ∗

(9.210)

with ~
ũ∗ the shear-stress velocity for waves and current and following Equation (9.58):

~ũ∗
∆zb
~ub =
ln 1 +
,
κ
2z0
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(9.211)

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Figure 9.11: Overview of the heat exchange mechanisms at the surface

with ~
ub the horizontal velocity in the first layer just above the bed. The increased roughness
length for waves and current z̃0 satisfies:

z̃0 =

∆zb

.
|~
ub |
exp κ ~ũ
−1
| ∗|

(9.212)

This increased roughness length is used in the turbulence closure schemes.
9.8

Heat flux models

The heat radiation emitted by the sun reaches the earth in the form of electromagnetic waves
with wavelengths in the range of 0.15 to 4 µm. In the atmosphere the radiation undergoes
scattering, reflection and absorption by air, cloud, dust and particles. On average neither the
atmosphere nor the earth accumulates heat, which implies that the absorbed heat is emitted
back again. The wavelengths of these emitted radiations are longer (between 4 and 50 µm)
due to the lower prevailing temperature in the atmosphere and on Earth. Schematically the
radiation process, along with the heat flux mechanisms at the water surface, is shown in
Figure 9.11.
Legend for Figure 9.11:

Qsc
Qco
Qsr
Qs
Qsn
Qa
Qan
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radiation (flux) for clear sky condition in [J/m2 s]
heat loss due to convection (sensible) in [J/m2 s]
reflected solar radiation in [J/m2 s]
solar radiation (short wave radiation) in [J/m2 s]
net incident solar radiation (short wave), = Qs − Qsr
atmospheric radiation (long wave radiation) in [J/m2 s]
net incident atmospheric radiation (long wave)

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Conceptual description

Qar
Qbr
Qev

reflected atmospheric radiation in [J/m2 s]
back radiation (long wave radiation) in [J/m2 s]
heat loss due to evaporation (latent) in [J/m2 s]

In Delft3D-FLOW the heat exchange at the free surface is modelled by taking into account the
separate effects of solar (short wave) and atmospheric (long wave) radiation, and heat loss
due to back radiation, evaporation and convection. In literature there is a great variability of
empirical formulations to calculate these heat fluxes across the sea surface. Most formulations
differ in the dependency of the exchange on the meteorological parameters such as wind
speed, cloudiness and humidity. Some formulations were calibrated for coastal seas others
for lakes.
In Delft3D-FLOW five heat flux models have been implemented:

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1 Heat flux model 1
The incoming (short wave) solar radiation for a clear sky is prescribed. The net atmospheric (long wave) radiation and the heat losses due to evaporation, back radiation and
convection are computed by the model.
2 Heat flux model 2
The combined net (short wave) solar and net (long wave) atmospheric radiation is prescribed. The terms related to heat losses due to evaporation, back radiation and convection are computed by the model.
3 Excess temperature model
The heat exchange flux at the air-water interface is computed; only the background temperature is required.
4 Murakami heat flux model
The net (short wave) solar radiation is prescribed. The effective back radiation and the
heat losses due to evaporation and convection are computed by the model. The incoming
radiation is absorbed as a function of depth. The evaporative heat flux is calibrated for
Japanese waters.
5 Ocean heat flux model
The fraction of the sky covered by clouds is prescribed (in %). The effective back radiation
and the heat losses due to evaporation and convection are computed by the model. Additionally, when air and water densities and/or temperatures are such that free convection
occurs, free convection of latent and sensible heat is computed by the model. This model
formulation typically applies for large water bodies.
For the physical background of the heat exchange at the air-water interface and the definitions,
we refer to Octavio et al. (1977) for model 1 and 2, to Sweers (1976) for model 3, to Murakami
et al. (1985) for model 4 and to Gill (1982) and Lane (1989) for model 5.
With the exception of model 3 the excess temperature model, the heat fluxes through the
water surface by incoming radiation, back radiation, evaporation and convection are computed
separately. Evaporation and convection depend on the air temperature, the water temperature
near the free surface, relative humidity, and wind speed. The excess temperature model
computes the heat fluxes through the water surface in such a way that the temperature of
the surface layer relaxates to the natural background temperature specified by you. The heat
transfer coefficient mainly depends on the water temperature and the wind speed.
9.8.1

Heat balance
The total heat flux through the free surface reads:

Qtot = Qsn + Qan − Qbr − Qev − Qco ,
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(9.213)

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with:

Qsn
Qan
Qbr
Qev
Qco

net incident solar radiation (short wave)
net incident atmospheric radiation (long wave)
back radiation (long wave)
evaporative heat flux (latent heat)
convective heat flux (sensible heat).

The subscript n refers to a net contribution. Each of the heat fluxes in Equation (9.213) will
be discussed in detail.
The change in temperature in the top layer Ts (in ◦ C) is given by:

where

is the total heat flux through the air-water surface, [J/m2 s],
is the specific heat capacity of sea water (= 3930 J kg−1 K),
is the specific density of water,[kg/m3 ] and
is the thickness of the top layer, [m].

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Qtot
cp
ρw
∆zs

(9.214)

∂Ts
Qtot
=
,
∂t
ρw cp ∆zs

In Delft3D-FLOW, the heat exchange at the bed is assumed to be zero. This may lead to
over-prediction of the water temperature in shallow areas. Also the effect of precipitation on
the water temperature is not taken into account.
Remarks:
The temperature T is by default expressed in ◦ C. However, in some formulas the absolute temperature T̄ in K is used. They are related by:

T̄ = T + 273.15.

(9.215)

In Equation (9.214) the total incoming heat flux is assumed to be absorbed in the top
layer. This may result in an unrealistically high surface temperature when the top layer is
thin. This can be prevented by absorbing the incoming radiation as a function of depth.
Currently, this is only implemented in heat flux models 4 and 5.
The input parameters for the heat flux models are model dependent. For example, the
input for the solar radiation has to be specified (measured data) as incoming (shortwave) solar radiation for a clear sky (Qsc ) for heat flux model 1, as combined net solar
radiation and net atmospheric radiation (sum of Qsn and Qan ) for heat flux model 2,
as net solar radiation for heat flux model 4, or is computed by the heat flux model itself
(heat flux models 3 and 5).
When using heat flux model 5, the free convection of latent and sensible heat is also
determined. This can be switched off when needed, by setting the coefficient of free
convection cfrcon to zero.
9.8.2

Solar radiation
The short-wave radiation emitted by the sun that reaches the earth surface under a clear sky
condition can be evaluated by means of:

Direct measurements.
Applying Stefan-Boltzmann’s law for radiation from a black-body:
Q = σ T̄ 4

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(9.216)

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Conceptual description

with σ = Stefan-Boltzmann’s constant = 5.67 · 10−8 J/(m2 s K4 ) and T̄ the (absolute)
temperature in K.

Empirical formulae.
In the heat flux models 1, 2 and 4 the solar radiation has to be specified by the user. In the
excess temperature model (model 3) the solar radiation does not play an explicit role, but is
part of the background temperature. In the heat flux model 5 the solar radiation is computed
by Delft3D-FLOW and is dependent on the geographical position at the earth and the local
time.

Not all of the radiation is absorbed at the water surface. A part is transmitted to deeper water.
Short waves can penetrate over a distance of 3 to 30 meters, depending on the clarity of the
water, while the relatively longer waves are absorbed at the surface. Therefore, it is convenient
to separate the incoming solar insolation into two portions:
1 βQsn , the longer wave portion, which is absorbed at the surface and
2 (1 − β) Qsn , the remainder part, which is absorbed in deeper water.

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The absorption of heat in the water column is an exponential function of the distance H from
the water surface:

(1 − β) Qsn =

e−γz dz ⇒

(9.217)

Qsn (h) =

with:

β
γ
h
H

γe−γh
(1 − β)Qsn ,
1 − e−γH

(9.218)

part of Qsn absorbed at the water surface which is a function of the wavelength.
The default value of β in Delft3D-FLOW is 0.06.
extinction coefficient (measured) in m−1 , also related to the so-called Secchidepth γ = H 1.7
Secchi
distance to the water surface in meters.
total water depth.

Remark:
The exponential decay function, Equation (9.218) has only been implemented in the
heat flux models 4 and 5. In the other heat flux models the incoming radiation is expected to be absorbed in the top layer.
In heat flux model 5 the flux is computed dependent on the geographical position and the
local time. The incoming energy flux at the water surface depends on the angle (declination)
between the incoming radiation and the Earth’s surface. This declination depends on the
geographical position on the Earth and the local time. The Earth axis is not perpendicular
to the line connecting the Sun with Earth. This tilting (angle δ ) varies with the time of the
year and it leads to a seasonal variation of the radiation flux. At June 21, the declination is
maximal, 23.5 degrees. Of course, by the rotation of the Earth the solar radiation also varies
during the day. Near twelve o’clock local time, the sun elevation above the horizon is maximal.
For an overview of the angles used to determine the solar elevation angle γ , see Figure 9.12.
The temporal and latitude-dependent solar elevation angle γ is estimated by:

sin (γ) = sin (δ) sin

Deltares

πφ
180

− cos (δ) cos

πφ
180

cos (ω1 t)

(9.219)

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Figure 9.12: Co-ordinate system position Sun
δ : declination; θ: latitude; ωt: angular speed

with:

δ=

23.5π
cos(ω0 t − 2.95),
180

(9.220)

where ω0 is the frequency of the annual variation and ω1 the frequency of the diurnal variation;
φ is the latitude.
The incoming short-wave solar radiation through a clear sky at ground level Qsc is about 0.76
of the flux incident at the top of the atmosphere (Gill, 1982):

Qsc =

0.76S sin(γ),
0.0,

sin(γ) ≥ 0,
sin(γ) < 0.

(9.221)

The solar constant S = 1 368 J/(m2 s) or W/m2 . This is the average energy flux at the mean
radius of the Earth.
A part of the radiation that reaches the water surface is reflected. The fraction reflected or
scattered (surface albedo) is dependent on latitude and season. Cloud cover will reduce the
magnitude of the radiation flux that reaches the sea surface. The cloudiness is expressed by
a cloud cover fraction Fc , the fraction of the sky covered by clouds. The correction factor for
cloud cover is an empirical formula. The absorption of solar radiation is calculated (Gill, 1982)
as the product of the net downward flux of short wave-radiation in cloudless conditions and
factors correcting for reflection and cloud cover:

Qsn = Qs − Qsr = (1 − α) Qsc f (Fc ) ,

(9.222)

with:

Qsn
Qs
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net heat radiation (flux) from the Sun
solar radiation (short wave radiation) in [J/m2 s]

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Conceptual description

Table 9.6: Albedo coefficient and cloud function

Heat flux model

albedo (α)

f (Fc )

1
2
3
4
5

0.06
0.09
0.06

1.0 − 0.65Fc2

1.0 − 0.4Fc − 0.38Fc2

reflected solar radiation in [J/m2 s]
radiation (flux) for clear sky condition
albedo (reflection) coefficient
fraction of sky covered by clouds (user-defined input)
function of Fc

Qsr
Qsc
α
Fc
f (Fc )

9.8.3

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The cloud function f (Fc ) and the albedo coefficient α used in Delft3D-FLOW are given in
Table 9.6. For the Ocean heat flux model the net solar radiation can also be specified directly
by the user instead of letting the model determine it from the cloud coverage. Details on this
functionality can be found in section B.5.
Atmospheric radiation (long wave radiation)

Atmospheric radiation is primarily due to emission of absorbed solar radiation by water vapour,
carbon dioxide and ozone in the atmosphere. The emission spectrum of the atmosphere is
highly irregular. The amount of atmospheric radiation that reaches the earth is determined by
applying the Stefan-Boltzmann’s law that includes the emissivity coefficient of the atmosphere
ε. Taking into account the effect of reflection by the surface and reflection and absorption by
clouds, the relation for the net atmospheric radiation Qan reads (Octavio et al., 1977):

Qan = (1 − r) εσ T̄a4 g (Fc ) ,

(9.223)

where T̄a is the air temperature (in K) and the reflection coefficient r = 0.03. The emissivity
factor of the atmosphere ε may depend both on vapour pressure and air temperature. The
emissivity of the atmosphere varies between 0.7 for clear sky and low temperature and 1.0.
The presence of clouds increases the atmospheric radiation. This is expressed in the cloud
function g (Fc ).
In heat flux model 1 a simple linear formula for the net atmospheric radiation is used (Octavio
et al., 1977):

Qan = (218.0 + 6.3Ta ) g (Fc ) ,

(9.224)

with Ta the air temperature (in ◦ C). The cloud function g (Fc ) in Eqs. (9.223) and (9.224) is
given by:

g (Fc ) = 1.0 + 0.17Fc2 .

(9.225)

The linearisation of Equation (9.223) is carried out around Ta = 15 ◦ C.
Remarks:
In heat flux model 1 the atmospheric radiation is computed.

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In heat flux model 2 the atmospheric radiation is part of the (measured) net solar radiation flux specified by you.

In heat flux models 4 and 5 the atmospheric radiation is part of the total long-wave
radiation flux, the so-called effective back radiation, see section 9.8.5.

The fraction of the sky covered by clouds Fc is fixed for the whole simulation period in
the heat flux models 1 and 4. Fc is not used in heat flux models 2 and 3 and can be
prescribed as a function of time in heat flux model 5.
9.8.4

Back radiation (long wave radiation)

Qbr = (1 − r) εσ T̄s4 ,
with T̄s the (absolute) water surface temperature in K.

Water radiates as a near black body, so the heat radiated back by the water can be described
by Stefan-Boltzmann’s law of radiation, corrected by an emissivity factor ε = 0.985 of water
(Sweers, 1976; Octavio et al., 1977) and the reflection coefficient for the air-water interface
r = 0.03:
(9.226)

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For heat flux models 1 and 2 Equation (9.226) has been linearised around Ts = 15 ◦ C:

Qbr = 303 + 5.2Ts .

(9.227)

Remark:
In heat flux models 1 and 2 the back radiation from the water surface is computed
explicitly. In heat flux models 4 and 5 the back radiation is part of the total long-wave
radiation flux, the so-called effective back radiation, see section 9.8.5. In heat model 3
the back radiation is part of the heat exchange coefficient (Sweers, 1976).
9.8.5

Effective back radiation

In heat flux models 4 and 5 the total net long wave radiation flux is computed. This is called
the effective back radiation:

Qeb = Qbr − Qan .

(9.228)

The atmospheric radiation depends on the vapour pressure ea , see section 9.8.6, the air temperature Ta and the cloud cover Fc . The back radiation depends on the surface temperature
Ts .
In heat flux model 4 the effective back radiation is computed using Berliand’s formula:

√
Qeb = εσ T̄a4 (0.39 − 0.058 ea ) 1.0 − 0.65Fc2 + 4εσ T̄a3 T̄s − T̄a ,

(9.229)

with the actual vapour pressure ea given by Equation (9.235).
In heat flux model 5 the effective back radiation Qeb is computed following:

√
Qeb = εσ T̄s4 (0.39 − 0.05 ea ) 1.0 − 0.6Fc2 ,

(9.230)

with the actual vapour pressure ea given by Equation (9.237).

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Evaporative heat flux
Evaporation is an exchange process that takes place at the interface between water and air
and depends on the conditions both in the water near the surface and the air above it. The
evaporation depends on meteorological factors (wind-driven convection) and vapour pressures.
In heat flux models the evaporative heat flux Qev is defined by:

Qev = Lv E,

(9.231)

with Lv the latent heat of vaporisation in J/kg water:

Lv = 2.5 · 106 − 2.3 · 103 Ts .

(9.232)

The evaporation rate E is defined as the mass of water evaporated per unit area per unit time
[kg/(m2 s)]. It is computed differently for different heat flux models. Most heat flux models use
some form of Dalton’s law of mass transfer:

E = f (U10 ) (es − ea ) ,

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9.8.6

(9.233)

where the actual vapour pressure ea and the saturated vapour pressure es , can be given by
different relations. Heat flux models 1, 2 and 4 use vapour pressures defined as:

5 303.3
,
es = 23.38 exp 18.1 −
T̄s

5 303.3
ea = rhum 23.38 exp 18.1 −
,
T̄a

(9.234)
(9.235)

for the actual and remote vapour pressure, respectively. Heat flux model 5 uses definitions for
the vapour pressures as:

es = 10

0.7859+0.03477Ts
1.0+0.00412Ts

ea = rhum 10

0.7859+0.03477Ta
1.0+0.00412Ta

(9.236)
(9.237)

Here rhum is the relative humidity in [-].

Remarks:
The relative humidity rhum is specified as a function of time in all heat flux models but
the excess temperature model (model 3). In heat flux model 5 it can also be specified
varying in space. It should be specified in the input in percentages.
For heat flux model 5, the vapour pressures are calculated using air and water surface
temperatures in ◦ C, while for the other models the vapour pressures are computed
using temperatures in K.
The evaporation rate E computed from a heat flux model can be added as a source
term to the right hand side of the continuity equation Equation (9.3). The keyword
required is Maseva = #Y#.
By default E is computed from the heat flux model formulation selected, but E can
also be prescribed as a function of time. In the latter case this user-defined evaporation
overrules the computed evaporation both in the heat flux model and in the continuity
equation; see section B.6 on how to prescribe a time dependent evaporation.
When the computed E is negative, it is replaced by zero, assuming that it is caused by
modelling misfit and not by the actual physical process of water condensation out ot the
air into the water.

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For models 1, 2 and 3 the wind speed function f (U10 ) following Sweers (1976) is used:

f (U10 ) = (3.5 + 2.0U10 )

5.0 × 106
Sarea

0.05
,

(9.238)

where
is the exposed water surface in m2 , defined in the input and fixed for the whole
simulation.

Sarea

The coefficients calibrated by Sweers were based on the wind speed at 3 meter above the
free surface; the coefficients in Equation (9.238) are based on the wind speed 10 meter above
the water level.

f (U10 ) = cmur U10 ,

In heat flux model 4 the wind speed function following Murakami et al. (1985) is used:
(9.239)

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with cmur a constant. This was calibrated for Japanese waters (Murakami et al., 1985) to be
1.2 × 10−9 , without the influence of free convection. It corresponds to a so-called Dalton
number ce of 0.0016.
Evaporative heat flux for model 5

In heat flux model 5 the evaporation rate is computed from the difference in relative humidity,
rather than from the difference in vapour pressure. Another difference between heat flux
model 5 and the others is that, for heat flux model 5, the contribution to the evaporative heat
flux is split in a contribution by forced convection and a contribution by free convection.
The total heat flux due to evaporation then results from adding the forced convection of latent
heat in Equation (9.241) and the free convection of latent heat in Equation (9.245):

Qev = Qev,forced + Qev,free .

(9.240)

Both kinds of evaporations are discussed separately.
Forced convection of latent heat

The latent heat flux due to forced convection for heat flux model 5 reads:

Qev,forced = LV ρa f (U10 ) {qs (Ts ) − qa (Ta )} ,

(9.241)

with qs and qa the specific humidity of respectively saturated air and remote air (10 m above
water level):

0.62es
,
Patm − 0.38es
0.62ea
qa (Ta ) =
.
Patm − 0.38ea
qs (Ts ) =

(9.242)
(9.243)

The saturated and remote vapour pressures es and ea are given by Eqs. (9.236) and (9.237).
The wind function in Equation (9.241) is defined as:

f (U10 ) = ce U10 ,
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(9.244)

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Conceptual description

Without the influence of free convection, the Dalton number ce in model 5 was calibrated for
the North Sea to be ce = 0.0015.
Free convection of latent heat

Loss of heat due to evaporation occurs not only by forced convection, wind driven, but also
by free convection. Free convection is driven by buoyant forces due to density differences
(by temperature and/or water vapour content) creating unstable conditions in the atmospheric
boundary layer (ABL). Evaporation due to free convection is important in circumstances where
inverse temperature/density gradients are present and wind speeds are almost negligible so
that the amount of forced convection is small. Neglecting free convection in this situation will
lead to underestimating the heat loss. (Ryan et al., 1974) developed a correction to the wind
function, accounting for free convection. The derivation of evaporation by just free convection
is based on the analogy of heat and mass transfer.
Free convection is only included in temperature model 5 and the latent heat flux due to free
convection reads:

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Qev,free = ks LV ρa (qs − qa ) ,

(9.245)

with the average air density:

ρa0 + ρa10
,
2

ρa =

(9.246)

and with the heat transfer coefficient defined as:

if ρa10 − ρa0 ≤ 0

(
0

ks =

cf r.conv

gα2

νair ρa

o1/3
(ρa10 − ρa0 )

if ρa10 − ρa0 > 0

(9.247)

where the coefficient of free convection cf r.conv was calibrated to be 0.14, see (Ryan et al.,
1974). The viscosity of air νair is assumed to have the constant value 16.0 × 10−6 m2 /s. The
molecular diffusivity of air α m2 /s is defined as

α=

νair
,
σ

(9.248)

with σ = 0.7 (for air) the Prandtl number. In Equation (9.245), the saturated air density is
given by:

ρa0 =

100Patm −100es
Rdry

100es
Rvap

Ts + 273.15

(9.249)

the remote air density (10 m above the water level):

ρa10 =

100Patm −100ea
Rdry

100ea
Rvap

Tair + 273.15

(9.250)

where Rdry is the gas constant for dry air: 287.05 J/(kg K) and Rvap is the gas constant
for water vapour: 461.495 J/(kg K). The specific humidity of respectively saturated air and
remote air (10 m above the water level), qs and qa are given by Eqs. (9.242) and (9.243). The
saturated and remote vapour pressure es and ea are defined in Eqs. (9.236) and (9.237).
9.8.7

Convective heat flux

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Convective heat flux for model 1, 2 and 4
Assuming that the turbulent exchange of heat at the air-water interface equals the turbulent
exchange of mass, the convective heat flux can be related to the evaporative mass flux by the
Bowen ratio:

Qco = Rb Qev ,
Ts − Ta
Rb = γ
,
es − ea

(9.251)
(9.252)

with γ the so-called Bowen’s constant:

γ = 0.61 for heat flux models 1 and 2
γ = 0.66 for heat flux model 4.

Convective heat flux for model 5

The saturated and actual vapour pressures are calculated by Eqs. (9.234) and (9.235) for heat
flux models 1, 2 and 4 and by Eqs. (9.236) and (9.237) for heat flux model 5.

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In heat flux model 5 the convective heat flux is split into two parts, just as the evaporative
heat flux. The convective heat flux is divided into a contribution by forced convection and a
contribution by free convection.
The total heat flux due to convection then results from adding the forced convection of sensible
heat in Equation (9.254) and the free convection of sensible heat in Equation (9.256):

Qco = Qco,forced + Qco,free .

(9.253)

Forced convection of sensible heat

The sensible heat flux due to forced convection is computed by:

Qco,forced = ρa cp g (U10 ) (Ts − Ta ) ,

(9.254)

with cp the specific heat of air. It is considered constant and taken to be 1 004.0 J/(kg K). The
wind-speed function g (U10 ) is defined following Gill (1982):

g (U10 ) = cH U10 ,

(9.255)

with cH the so-called Stanton number. Without the influence of free convection, the Stanton
number was calibrated for the North Sea to be cH = 0.00145.
Free convection of sensible heat

The heat transfer for free convection is defined as:

Qco,free = ks ρa cp (Ts − Ta ) ,

(9.256)

with the heat transfer coefficient ks given by Equation (9.247).
9.8.8

Overview of heat flux models
Heat flux model 1
For heat flux model 1 the relations used for the computation of the heat balance, Equation (9.213), are given in Table 9.7.

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Table 9.7: Terms of the heat balance used in heat model 1

Description

According to

Qsc

short wave solar radiation for clear sky

measured

Qsn

net solar radiation

Equation (9.222)

Qan

net atmospheric radiation

Eqs. (9.224) and (9.225)

Qbr

back radiation

Equation (9.227)

Qev

heat loss due to evaporation

Eqs. (9.231) to (9.238)

Qco

heat loss due to convection

Eqs. (9.251) and (9.252)

Heat flux model 2

Quantity

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Heat flux model 2 is based on formulations given by Octavio et al. (1977). The source of
data for the combined net incoming radiation terms (Qsn + Qan ) must come from direct
measurements. The remaining terms (back radiation, evaporation, convection) are computed
similarly as for heat flux model option 1, Table 9.8.
Table 9.8: Terms of the heat balance used in heat model 2

Quantity

Description

According to

Qsn + Qan

net solar and net atmospheric radiation

measured

Qbr

back radiation

Equation (9.227)

heat loss due to evaporation

Eqs. (9.231) to (9.238)

heat loss due to convection

Eqs. (9.251) and (9.252)

Qev
Qco

Excess temperature model - heat flux model 3

The excess temperature model 3 is based on Sweers (1976), the heat exchange flux is represented by a bulk exchange formula:

Qtot = −λ (Ts − Tback ) ,

(9.257)

with

Ts
Tback

the water temperature at the free surface, [◦ C], and
the natural background temperature, [◦ C].

The heat exchange coefficient λ is a function of the surface temperature Ts and the wind
speed U10 . It is derived by linearization of the exchange fluxes for back radiation, evaporation
and convection. The following relation was derived by Sweers (1976):

λ = 4.48 + 0.049Ts + f (U10 ) 1.12 + 0.018Ts + 0.00158Ts2 .

(9.258)

For the wind function f (U10 ) Equation (9.238) is applied.

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Murakami model - heat flux model 4
The heat flux model 4 was calibrated for the Japanese waters (Murakami et al., 1985). The
following relations are used for the computation of the heat terms, Table 9.9.
Table 9.9: Terms of the heat balance used in heat model 4

Description

According to

Qsn

net solar radiation

measured

Qeb

effective back radiation

Equation (9.229)

Qev

heat loss due to evaporation

Eqs. (9.231) to (9.235)

Qco

heat loss due to convection

Eqs. (9.251) and (9.252)

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Ocean model - heat flux model 5

Quantity

The heat flux model 5 following Gill (1982) and Lane (1989) was calibrated for the North Sea
and successfully applied for great lakes. The following relations are used for the computation
of the heat terms,Table 9.10.
Table 9.10: Terms of the heat balance used in heat model 5

Quantity

Description

According to

Qsn

net solar radiation

Eqs. (9.219) and (9.222)

effective back radiation

Equation (9.230)

heat loss due to evaporation

Eqs. (9.241) to (9.240)

heat loss due to convection

Eqs. (9.254) to (9.253)

Qeb
Qev
Qco

Summary of required input data for the heat flux models

The required time dependent input data for each of the heat flux models is summarised in
Table 9.11.

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Table 9.11: Summary of time dependent input data of the heat flux models

Quantity

model 1

Qsc

model 2

Excess
temperature

Qsn
Qsn + Qan

Tback

Ocean

X(optional)

X(optional)
X

rhum

X
X

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9.9

Murakami

Tide generating forces

Numerical models of tidal motion in coastal seas generally do not account for the direct local
influence of the tide generating forces. The amount of water mass in these models is relatively
small and the effect of these forces on the flow can be neglected. For coastal areas, the
prescription of tidal forcing along open boundaries is sufficient in generating the appropriate
and accurate tidal motion.
The need to model larger seashore areas with sections of the deep ocean or large closed
basins has increased. In the numerical models of these areas the contribution of the gravitational forces on the water motion increases considerably and can no longer be neglected, see
Figure 9.13, to generate an accurate tidal motion.
The tide generating forces originate from the Newtonian gravitational forces of the terrestrial
system (Sun, Moon and Earth) on the water mass. Based on their origins the tide generated
by these forces can be distinguished into:

Equilibrium tide.

Assuming that the earth is covered entirely with water and neglecting any secondary effects (see next section), then the ocean response is called the equilibrium tide, ζ (idealised
situation).
Earth Tide.
Displacement the earth’s crust due to the elasticity of the earth.

9.9.1

Tidal potential of Equilibrium tide
The equilibrium tide is modelled by including the tide generating potential terms for equilibrium
tide in the momentum equations. The following terms are added to the right-hand side of the
momentum equations Eqs. (9.7) and (9.8), respectively:

g ∂ϕ
p
,
Gξξ ∂ξ

and

g ∂ϕ
p
.
Gηη ∂η

(9.259)

Following Schwiderski (1980), the tidal potential ϕ for equilibrium tide is decomposed into the

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Figure 9.13: Effect of tide generating force on the computed water elevation at Venice

series:

ϕ=

ϕν (λ, φ, t) ,

(9.260)

ν=0,1,2

consisting of the following major tidal species:

Long-Period species ν = 0 : ϕ0 = Ki 1.5 cos2 φ − 1 cos (ωi t + 2λ + χi ) ,
(9.261)

Diurnal species ν = 1 : ϕ1 = Ki sin (2φ) cos (ωi t + λ + χi ) ,
2

Semi-diurnal species ν = 2 : ϕ2 = Ki cos (φ) cos (ωi t + 2λ + χi ) ,
with:

λ, φ
Ki
ωi
χi
t

(9.262)
(9.263)

geographical co-ordinates
amplitude of equilibrium tide (component dependent)
frequency of equilibrium tide (component dependent)
astronomical argument of equilibrium tide (component dependent) relative to
UTC midnight
universal standard time - UTC

Table 9.12 provides an overview of frequencies ωi and constants Ki for each of the 11 tidal
constituents considered in the species Eqs. (9.261) to (9.263).
Following Schwiderski (1980), all other constituents fall below 4% of the dominating semidiurnal principal moon (M2) tide and need not be considered in global ocean tide models.
Since tidal models can be used in predictive mode (predicting the actual water elevations and
currents) the long term variations (18.6 years cycle) in the tidal components are accounted
for by including nodal corrections (see Delft3D-TIDE, User Manual; TIDE UM (2013)). In
Delft3D-FLOW the correction is carried out only once at the initialisation of the simulation.
Consequently, with regard to the accuracy of the generated tide, this imposes a restriction on
the simulation period to approximately one year.

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Table 9.12: Constants of major tidal modes

Tidal constituent

Frequency ωi (degrees/hr)

Constant Ki

28.984104237
30.000000000
28.439729554
30.082137278

0.242334
0.113033
0.046398
0.030704

Semi-diurnal Species
M2 principal lunar
S2 principal solar
N2 elliptical lunar
K2 declination lunar-solar

15.041068639
13.943035598
14.958931361
13.398660914

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K1 declination lunar-solar
O1 principal lunar
P1 principal solar
Q1 elliptical solar

Diurnal Species
0.141565
0.100514
0.046843
0.019256

Long-period Species
Mf fortnightly lunar
Mm monthly lunar
Ssa semi-annual solar

1.098033041
0.544374684
0.082137278

0.041742
0.022026
0.019446

Figure 9.14: Earth ocean tidal interaction (after Schwiderski (1980))

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For the determination of the astronomical arguments χ in Eqs. (9.261) to (9.263) a module of
Delft3D-TIDE is applied. If the computations are to be carried out in local time, then the time
difference between the local time and UTC must be specified. This difference is referred to as
the local time zone (LTZ) in the input.
9.9.2

Tidal potential of Earth tide
The equilibrium tide approach concentrates on the influence of gravitational forces on ocean
tides. It neglects the effect of these forces on terrestrial tide (i.e. it assumes that earth is a
stiff body) and/or the interaction between the two. Following Schwiderski, the following two
interaction effects should be considered:

1 Earth tide (ζ e ) and tidal loading (ζ eo = ζ e − ζ b ), are the earth tidal responses to the
equilibrium tide ϕ and oceanic tidal load ζ .
2 ϕe , ϕeo and ϕo are perturbations of the equilibrium tide ϕ in response to ζ e , ζ eo and ζ ,
respectively.

and:

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These perturbations are subsequently regrouped in the final equations according to their
causes and are approximated as follows:

ϕe − ζ e = 0.31ϕ,

(9.264)

ϕo + ζ eo − ϕeo = 0.10ζ.

(9.265)

However the improvement due to the second correction term is considerably less significant
(10% improvement in the difference between observed and simulated phases), than the inclusion of proper eddy viscosity and bottom friction coefficients for the hydrodynamics of an
ocean basin, see Schwiderski (1980). Therefore, in Delft3D-FLOW only the first correction
term has been included.
Consequently, in the momentum equations, Eqs. (9.7) and (9.8), the following net tidal potential terms are applied, yielding a 31 % reduction of the originally derived equilibrium tide
potential terms):

g ∂ϕ
,
0.69 p
Gξξ ∂ξ
9.10

and

g ∂ϕ
0.69 p
.
Gηη ∂η

(9.266)

Hydraulic structures

Obstacles in the flow may generate sudden transitions from flow contraction to flow expansion.
The grid resolution is often low compared to the gradients of the water level, the velocity and
the bathymetry. The hydrostatic pressure assumption may locally be invalid. Examples of
these obstacles in civil engineering are: gates, barriers, sluices, groynes, weirs, bridge piers
and porous plates. The obstacles generate energy losses and may change the direction of
the flow.
The forces due to obstacles in the flow which are not resolved (sub-grid) on the horizontal grid, should be parameterised. The obstacles are denoted in Delft3D-FLOW as hydraulic
structures. In the numerical model the hydraulic structures should be located at velocity points
of the staggered grid, see section 10.1. The direction of the forces: U or V should be specified at input. To model the force on the flow generated by a hydraulic structure, the flow in a

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computational layer is blocked or a quadratic energy or linear loss term is added to the momentum equation. The mathematical formulations are given in this section. For the numerical
implementation we refer to Section 10.9.
9.10.1

3D gate

In 3D simulations, constructions which partially block the horizontal flow can be modelled as
so-called “gates”. Its horizontal and vertical position can be specified. The horizontal velocities
of the computational layers at position of the gate are set to zero. This generates a vertical
structure of the horizontal flow around a hydraulic structure which is more realistic. There is
no transport of salt or sediment through the computational layers of a gate. The width of a
gate is assumed to be zero, so it has no influence on the water volume. Upstream of the
gate the flow is accelerated due to contraction and downstream the flow is decelerated due to
expansion.
Furthermore, a free slip boundary conditions has been implemented at the transition from an
open layer to a closed layer (representing a gate):

∂U
∂z

= 0,

DR
AF

νV

(9.267)

z=a

with z = a the top or the bottom of the gate.
9.10.2

Quadratic friction

The flow rate Q through a hydraulic structure can often be described by a so-called Q-H
relation. They relate the flow rate to the difference between the upstream and downstream
water levels:

p
Q = µA 2g|ζu − ζd |,

(9.268)

with µ the contraction coefficient (0 < µ ≤ 1), the wet flow-through area and and the
upstream and downstream water level, respectively. The contraction coefficient in the socalled Q-H relation is dependent on the kind of hydraulic structure. The contraction coefficient
µ can be used to determine the additional quadratic friction term in the momentum equation.

closs−u √ 2
u u + v2,
∆x
closs−v √ 2
v u + v2,
Mη = −
∆y
Mξ = −

(9.269)
(9.270)

with closs the energy loss coefficient. For the following types of hydraulic structures, a quadratic
formulation for the energy loss is implemented in Delft3D-FLOW:

barrier
bridge pier
Current Deflecting Wall (CDW)
local weir or 2D weir
porous plate
culvert

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9.10.3

Linear friction
To reduce the flow rate through a certain cross-section Delft3D-FLOW offers also the functionality of a linear friction term. This kind of hydraulic structure is denoted as a rigid sheet:

closs−u u
,
∆x
closs−v v
,
Mη = −
∆y
Mξ = −

(9.271)
(9.272)

with closs the energy loss coefficient, which should be specified by you at input.
9.11

Flow resistance: bedforms and vegetation

9.11.1

DR
AF

The terrain and vegetation excert shear stresses on the passing flow. The magnitude of
the shear stress of the bed is often characterised by means of roughness coefficient of type
Chézy, Manning or White-Colebrook as discussed in section 9.4.1. Within the main stream
flow the shear stresses are largely determined by the local conditions of the alluvial bed (bed
composition and bedform characteristics). In other areas, such the floodplains of rivers and
in the intertidal areas of estuaries, the flow resistance is determined by a combination of vegetation and an alluvial bedforms or even a non-alluvial bed. To accurately represent such
conditions in the numerical model, Delft3D-FLOW has been extended with a couple features,
this includes bedform roughness predictors and vegetation models. These types of flow resistance may be resolved in a 2D numerical model using the trachytope approach (see section 9.11.2) and in a 3D model by a combination of bed resistance formulations. First, we start
with a description of the bedform roughness height predictor.
Bedform heights

There are various types of bedforms; each type influences the hydro- and morphodynamics in its own way. Following Van Rijn (2007) we distinguish between roughness heights for
ripples, mega-ripples and dunes. Delft3D contains a module to predict dune characteristics (height/length) which may be used in determining the threshold level for dredging (see
keyword UseDunes in section A.2.23) or to compute a dune roughness height which can
be used as the bed roughness in the flow computation via trachytope formulae 105 (Equation (9.312)) or 106 (Equation (9.313)) as described in section 9.11.2. One can also determine the dune, mega-ripple, and ripple roughness heights directly according Van Rijn (2007).
Both approaches are described in the two sections below. The corresponding keywords are
described in Appendix B.16.
9.11.1.1

Dune height predictor

Four dune height predictors have been implemented: Van Rijn (1984c), Fredsøe (1982) based
on Meyer-Peter and Müller (1948) or Engelund and Hansen (1967), and a power relation. One
of these predictors can be selected using the keyword BdfH. In case of Van Rijn (1984c) the
dune height hd is computed as

hd = 0.11εH

D50
H

0.3

(1 − e−T /2 )(25 − T )

(9.273)

where ε is a calibration coefficient and T is the dimensionless bed shear parameter. Fredsøe
(1982) formulated an approach to obtain a dune height predictor for a general sediment transport formula s = f (U, H, k) depending on depth-averaged flow magnitude U , water depth
H and Nikuradse bed roughness k as

∂s
∂s
∂s
hd = εsH/ U
−H
−k
∂U
∂H
∂k
254 of 688

(9.274)

Deltares

Conceptual description

If one applies this approach to the transport formula by Meyer-Peter and Müller (1948) one
obtains

hd =

θcr
24
εH max(1 −
, 0)
63
µθ

(9.275)

where µ is the efficiency factor (C/Cg,90 )1.5 based on a grain related bed roughness of
3D90 and θcr is the critical mobility parameter based on the Shields curve or given by the
user. If one applies the formulation of Fredsøe (1982) to the transport formula by Engelund
and Hansen (1967) one obtains

1
hd = εH
5

(9.276)

The latter two formulations have been implemented in Delft3D. Finally, the power relation dune
height predictor reads

hd = aH H bH

(9.277)

DR
AF

The dune height formulations given by equations (9.273)–(9.277) are approximations for the
dune height under equilibrium conditions. Under time and spatially varying conditions, the
dune height will need time to adjust; this effect has been implemented by means of an advection relaxation equation.

∂hd
∂hd
∂hd
hd,eq − hd
+ uH
+ vH
=
∂t
∂x
∂y
TH

(9.278)

By default these effects are neglected, such that hd = hd,eq . By means of the keyword

BdfRlx one can select four options for computing the variables uH , vH and TH : (i) constant
relaxation time scale TH , (ii) constant relaxation distance LH , (iii) relaxation distance proportional to dune length Ld , and (iv) relaxation distance dependent on dune length Ld and water
depth H . In the first three advection cases, the direction of the bedform migration is assumed
to be equal to the direction of the depth averaged velocity in all cases, i.e.

u
U
v
vH = cH
U

u H = cH

(9.279)
(9.280)

where u and
√v are the x and y components of the depth averaged velocity, U the flow velocity
magnitude u2 + v 2 , and cH is the bedform celerity (magnitude) given by a power relation
derived for a generic transport formula approximation s = as U bs as

cH =

as b s U b s
aC U b C
bs s
=
=
H
H
H

(9.281)

while the relaxation time scale TH is either given, or computed from TH = LH /cH where
the relaxation distance LH is either given or proportional to the dune length LH = fLH Ld .
In the fourth advection case TH is computed again using TH = LH /cH but in that case the
relaxation distance LH is given by

"
LH = min

Deltares

Hmax
H

bLH

#
, φmax Ld

(9.282)

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and the bedform celerity is given by

"
cH = acH max

H
Hmax

bcH
, γmin

sb
H(1 − Fr2 )

(9.283)

where sb is the total bedload transport rate, Fr2 is the squared Froude number U 2 /gH and
Hmax , bLH , φmax , acH , bcH and γmin are constants that can be set. In this case the bedform
migration direction is assumed to be equal to the direction of the bedload transport vector ~
sb .
For the dune length Ld used in some of the formulations above, you can choose either one
of the following two options using keyword BdfL. If you choose to compute the dune height
according Van Rijn (1984c) then it will be computed as

Ld = 7.3H
otherwise it will be computed using the power relation

L d = aL H b L

(9.284)

(9.285)

DR
AF

Note that only the dune height is subject to the advective and relaxation behaviour formulated
in Equation (9.278); for the dune length always these equilibrium formulations are used.
Finally, you may select one of three methods for computing the bedform roughness height by
means of the keyword BdfRou; these methods are based on the formulations of Van Rijn
(1984c), Van Rijn (2007) or a power relation. This value will only be used if you use the
trachytope option for specifying bed roughness and include either one of alluvial roughness
formulae 105 and 106. In case of Van Rijn (1984c) the roughness height related to dunes is
computed as

ks,d = 1.1hd 1 − e−25hd /Ld

(9.286)

and in case of the power relation this quantity is computed as

ks,d = aR HdbR

(9.287)

The roughness height related to ripples is set in both cases equal to 3D90 . In case of Van
Rijn (2007) the roughness heights neither depend on the computed dune height nor on the
dune length; in that case the equations given in the following section are used.
9.11.1.2

Van Rijn (2007) bedform roughness height predictor

As proposed by Eq. (5a)–(5d) in Van Rijn (2007) the roughness height predictor for ripples is
given by

ks,r = αr

20Dsilt if D50 < Dsilt
∗
ks,r
otherwise

(9.288)

∗
where αr is a calibration factor, Dsilt = 32 µm and ks,r
is given by

∗
ks,r


if ψ ≤ 50
150fcs D50
= (182.5 − 0.65ψ)fcs D50 if 50 < ψ ≤ 250

20fcs D50
if ψ > 250

(9.289)

2
in which ψ is the current-wave mobility parameter defined as Uwc
/[(s − 1)gD50 ] using
2
2
2
Uwc = Uw + uc and relative density s = ρs /ρw , peak orbital velocity near bed Uw =

256 of 688

Deltares

Conceptual description

πHs /[Tr sinh(2kh)], depth-averaged current velocity uc , significant wave height Hs , wave
number k = 2π/L, wave length L derived from (L/Tp ± uc )2 = gL tanh(2πh/L)/(2π),
relative wave period Tr , peak wave period Tp , water depth H and factor fcs = (0.25Dgravel /D50 )1.5
in which Dgravel = 0.002 m. The value of ks,r is limited to values ranging from D90 to 2% of
the water depth.
Following Eq. (6a)–(6d) by Van Rijn (2007) the roughness height predictor for mega-ripples is
given by

ks,mr

0
if D50 < Dsilt
= αmr
∗
ks,mr otherwise

(9.290)

∗
is given by
where αmr is a calibration factor and ks,mr

if ψ ≤ 50

if 50 < ψ ≤ 550

(9.291)

if ψ > 550 and D50 ≥ Dsand

if ψ > 550 and Dsilt ≤ D50 < Dsand

DR
AF

∗
ks,mr


0.0002ff s ψH



(0.011 − 0.00002ψ)ff s H
=
0.02



200D50

in which ff s = (D50 /1.5Dsand ) and Dsand = 0.000062 m. The value of ks,mr is limited to
values smaller than 0.2 m.
Following Eq. (7a)–(7d) by Van Rijn (2007) the roughness height predictor for dunes is given
by

ks,d = αd

0
if D50 < Dsilt
∗
ks,d otherwise

(9.292)

∗
where αd is a calibration factor and ks,d
is given by

∗
ks,d


if ψ ≤ 100
0.0004ff s ψH
= (0.048 − 0.00008ψ)ff s H if 100 < ψ ≤ 600

0
if ψ > 600

(9.293)

Since these formulations do not depend on the equations for the dune characteristics given
in the previous section, the advection and relaxation effects represented by Equation (9.278)
cannot be included these Van Rijn (2007) formulations. Therefore, a separate relaxation
option has been implemented for all three bedform roughness heights according Van Rijn
(2007) formulations as given by

ks,r = (1 − αr )ks,r,new + αr ks,r,old

where αr = e−∆t/Tr

ks,mr = (1 − αmr )ks,mr,new + αmr ks,mr,old where αmr = e−∆t/Tmr
ks,d = (1 − αd )ks,d,new + αd ks,d,old

(9.294)

where αd = e−∆t/Td

where ∆t is the hydrodynamic time step of bed roughness updating, and Tr , Tmr and Td are
different relaxation time scales for the three bedform types. Note that if a relaxation time scale
T∗ becomes zero, the corresponding relaxation factor α∗ will be zero and the relaxation effect
disappears.
Warning:
Until Delft3D release 3.28.10, the relaxation factors α∗ are not defined as indicated
above but as max[1 − (5∆t/T∗ ), 0].

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Remarks:
In case of a simulation with multiple sediment fractions, the D50 of the grain mixture in
the surface layer is used.
Non-erodible layers and partial transport effects are not taken into account to reduce
the roughness height.
9.11.2

Trachytopes
This functionality allows you to specify the bed roughness and flow resistance on a sub-grid
level by defining and using various land use or roughness/resistance classes, further referred
to as trachytopes after the Greek word τραχύτ ης for roughness. The input parameters and
files to use the trachytopes functionality are described in section B.17.

DR
AF

√
1
Mξ = − λm,n u u2 + v 2
2
√
1
Mη = − λm,n v u2 + v 2
2

At every time step (or less frequent as requested by the user) the trachytopes are converted
into a representative bed roughness C , k or n (as described in section 9.4.1) and optional
linear flow resistance coefficient λm,n per velocity point.
(9.295)
(9.296)

To save computational time the user may choose to update the computed bed roughness and
resistance coefficients less frequently than every time step. See section B.17 for a description
of the keywords and input files associated with this feature.
The following two sections describe the various classes of trachytopes distinguished and the
way in which they are combined, respectively.
9.11.2.1

Trachytope classes

Three base classes of trachytopes are distinguished: area classes, line classes and point
classes. The area classes (type range 51–200) basically cover the whole area, therefore,
they are generally the dominant roughness factor. The line classes (type range 201–250)
may be used to represent hedges and similar flow resistance elements; it will add anisotropy
to the roughness field. The point class (type range 251–300) represents a set of point flow
resistance elements. The next six sections provide an overview of the various trachytope
formulae implemented.

258 of 688

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Conceptual description

Special classes (1–50)
In addition to the three base classes two special trachytope classes have been defined: a flood
protected area and a composite trachytope class. The first class represents a sub-grid area
that is protected from flooding and thus does not contribute to the bed roughness; however,
the effect on the flow resistance should be taken into account. The second class can be used
to make derived trachytope classes that are a combination of two other trachytopes: an area
fraction α of trachytope type T1 and an area fraction β (often equal to 1 − α) of trachytope
type T2 .
FormNr

Name

Formula

Special classes (1–50)
flood protected area

area fraction shows up as fb in Eqs. (9.348)
and (9.351)

composite trachytope

fraction α of type T1 and fraction β (generally
β = 1 − α) of type T2

DR
AF

Area trachytope classes (51–200)
The class of area trachytopes is subdivided into three types: simple (51–100), alluvial (101–
150) and vegetation (151–200). Four simple area trachytopes have been implemented representing the four standard roughness types of flow module.
FormNr

Name

Formula

51
52
53
54

White-Colebrook value
Chézy value
Manning value
z0 value

k
C √
C = 6 h/n
k = 30z0

Six alluvial trachytopes have been implemented.
FormNr

Name

Formula

101
102
103
104
105
106

simplified Van Rijn
power relation
Van Rijn (1984c)
Struiksma
bedforms quadratic
bedforms linear

Equation (9.297)
Equation (9.298)
Equations (9.299) to (9.307)
Equations (9.308) to (9.311)
Equation (9.312)
Equation (9.313)

The first alluvial roughness formula is a simplified version of the Van Rijn (1984c) alluvial
roughness predictor

h
i
−0.3
k = Ah0.7 1 − e−Bh

(9.297)

it is obtained from Equation (9.299) by noting that hb ∝ h0.7 and Lb ∝ h and ignoring the
grain related roughness. The parameters A and B can be calibrated by the user. The second

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formula implemented is a straightforward general power law

C = AhB

(9.298)

where A and B are calibration coefficients. The Van Rijn (1984c) alluvial roughness predictor
reads

k = k90 + 1.1hb 1 − e−25hb /Lb

(9.299)

where the bedform height hb and length Lb are given by

hb = 0.11h

D50
h

0.3

1 − e−T /2 (25 − T )

(9.300)

Lb = 7.3h

(9.301)

where h is the local water depth and the transport stage parameter T is given by

DR
AF

u0 2∗ − u2∗,cr
T =
u2∗,cr

(9.302)

where u0 ∗ is the bed shear velocity given by
2

2
u0 ∗ = gu2 /Cg,90

where

Cg,90 = 18 10 log(12h/k90 ) and k90 = 3D90

(9.303)

(9.304)

and u∗,cr is the critical bed shear velocity according Shields given by

u2∗,cr = g∆D50 θc
given


0.24/D∗



 0.14D∗−0.64
0.04D∗−0.10
θc =

0.29


 0.013D∗
0.055
where

D∗ = D50

g∆
ν2

if D∗ ≤ 4
if 4 < D∗ ≤ 10
if 10 < D∗ ≤ 20
if 20 < D∗ ≤ 150
if 150 < D∗

(9.305)

(9.306)

1/3

(9.307)

This predictor does not contain any calibration coefficients but requires D50 and D90 data
from the morphology module. It does not include the advective and relaxation behaviour that
is available by explicitly simulating the dune height as described in Section 9.11.1 combined
with trachytope number 106.
The second alluvial roughness predictor proposed by (Struiksma, pers. comm.) allows for a
lot of adjustments, it reads

1
1
1
= (1 − ξ) 2 + ξ 2
2
C
C90
Cmin
260 of 688

(9.308)

Deltares

Conceptual description

where

C90 = A1 10 log(A2 h/D90 )

(9.309)

and

ξ=

2
− θc θg
max(0, θg − θc ) θm
θm − θc
(θm − θc )θg

(9.310)

which varies from 0 at θg ≤ θc to 1 at θg = θm where

θg =

u2
2
∆D50
C90

(9.311)

DR
AF

q
h
2
2 + k2
k = min( ks,r
s,mr + ks,d , )
2

and A1 , A2 , θc , θm , Cmin are coefficients that the user needs to specify. This formula requires
also D50 and D90 data from the morphology module. The fifth formula is based on Van Rijn
(2007) and reads
(9.312)

It uses the roughness heights of ripples kr , mega-ripples kmr and dunes kd . These roughness heights are based on Van Rijn (2007) formulae as described in section 9.11.1; these
formulae depend on D50 and D90 data which may be either specified as part of the roughness type or obtained from the morphology module. The sixth formula is similar, but uses a
linear addition

h
k = min(ks,r + ks,mr + ks,d , )
2

(9.313)

Four vegetation based area trachytopes have been implemented. Two formulae (referred to
as ‘Barneveld’) are based on the work by Klopstra et al. (1996, 1997) and two on the work by
Baptist (2005).
FormNr

Name

Formula

151
152
153
154

Barneveld 1
Barneveld 2
Baptist 1
Baptist 2

Eqs. (9.314) – (9.323), CD = 1.65
Eqs. (9.314) – (9.320), (9.324) – (9.326)
Eqs. (9.327) and (9.328)
Eqs. (9.329), (9.331) and (9.332)

The formula by Klopstra et al. (1997) reads







1 
C = 3/2
h 






√2
2A

p
2
C3
+
− C3 + uv0 +
√

√
√
( C3 ehv 2A +u2v0 −uv0 )( C3 +u2v0 +uv0 )
u
v0
√
√
ln √ h √2A 2
+
2A
( C3 e v
+uv0 +uv0 )( C3 +u2v0 −uv0 )
√

g(h−(hv −a))
h−(hv −a)
a
(h
−
(h
−
a))
ln
−
a
ln
−
(h
−
h
)
v
v
κ
z0
z0
√
ehv 2A

u2v0

(9.314)
where

Deltares

nCD
2α

(9.315)

261 of 688















Delft3D-FLOW, User Manual

C3 =

2g(h − hv )
√
√
α 2A(ehv 2A + e−hv 2A )
√

q
1+ 1+
a=

(9.316)

4E12 κ2 (h−hv )
g

(9.317)

2E12 κ2
g

and

z0 = ae−F
where

and

DR
AF

√
√
2AC3 ehv 2A
E1 = q
√
2 C3 ehv 2A + u2v0

(9.318)

q
√
κ C3 ehv 2A + u2v0
F = p
g(h − (hv − a))

(9.319)

(9.320)

Here, h is the water depth, hv is the vegetation height, and n = mD where m is the number
of stems per square metre and D is the stem diameter. For the first implementation the
parameter α in Equation (9.316) is given by

p
α = max(0.001, 0.01 hhv )

and the velocity within the vegetation is approximated by uv0

u2v0 =

√

(9.321)

i where

2g
CD n

(9.322)

and i is the water level gradient. For emerged vegetation the first implementation reads

1
CD nh
=
2
C
2g

(9.323)

The second implementation of Klopstra et al. (1996) is based on a modification by Van Velzen
et al. (2003); it is identical except for the following modifications to Eqs. (9.321) – (9.323). The
main difference between the two implementations is the inclusion of the roughness Cb of the
bed itself (without vegetation). The parameter α in Equation (9.316) is now given by

α = 0.0227h0.7
v

(9.324)

and the velocity within the vegetation is approximated by uv0

u2v0 =

262 of 688

hv
+

CD hv n
2g

1
Cb2

√

i where
(9.325)

Deltares

Conceptual description

and i is the water level gradient. For emerged vegetation the second implementation reads

1
1
CD nh
+ 2
=
2
C
2g
Cb

(9.326)

For large values of Cb the latter two equations simplify to the corresponding equations of the
first implementation. The first implementation requires vegetation height hv and density n
as input parameters (the drag coefficient CD is equal to 1.65); for second implementation
you’ll also need to specify the drag coefficient CD and the alluvial bed roughness kb (Cb in
Equation (9.326) is computed as 18 10 log(12h/kb )).

C=q

√

1
1
Cb2

CD nhv
2g

g
h
ln( )
κ
hv

The first implementation of the roughness predictor by Baptist (Baptist, 2005) reads for the
case of submerged vegetation
(9.327)

DR
AF

where n is the vegetation density (n = mD where m is the number of stems per square
metre and D is the stem diameter). The second term goes to zero at the transition from
submerged to emerged vegetation. At that transition the formula changes into the formula for
non-submerged vegetation which reads

C=q

1
Cb2

CD nh
2g

(9.328)

which is identical to the non-submerged case of the second implementation of the work by
Klopstra et al. (1996) (see Equation (9.326)).
The drawback of the three vegetation based formulations above is that they parameterize the
flow resistance by means of the bed roughness. Consequently, the presence of vegetation
will lead to a higher bed roughness and thus to a higher bed shear stress and larger sediment
transport rates in case of morphological computations. Therefore, we have included a − λ2 u2
term in the momentum equation where λ represents the flow resistance of the vegetation. For
the case of non-submerged vegetation h < hv the flow resistance and bed roughness are
strictly separated

C = Cb

and

λ = CD n

(9.329)

In the case of submerged vegetation h > hv the two terms can’t be split in an equally clean
manner. However, we can split the terms such that the bed shear stress computed using
the depth averaged velocity u and the net bed roughness C equals the bed shear stress
computed using the velocity uv within the vegetation layer and the real bed roughness Cb .

u2
u2v
=
C2
Cb2

(9.330)

With this additional requirement we can rewrite Equation (9.327) as

s
√
g
h
CD nhv Cb2
C = Cb +
ln( ) 1 +
κ
hv
2g
Deltares

(9.331)

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and

λ = CD n

hv Cb2
h C2

(9.332)

which simplify to Equation (9.329) for h = hv . Both formulae by Baptist require vegetation
height hv , density n, drag coefficient CD and alluvial bed roughness Cb as input parameters.
Linear trachytope classes (201–250)
Two formulae have been implemented for linear trachytopes such as hedges or bridge piers.
Name

Formula

201
202

hedges 1
hedges 2

Eqs. (9.333) to (9.335)
Eqs. (9.336) to (9.338)

FormNr

The first implementation reads

DR
AF

1
h Lhedge 1 − µ2
=
(9.333)
C2
2g Wcell Lcell µ2
where Lhedge is the projected length of the hedge, Wcell and Lcell are the width and length
of the grid cell. The ratio Lhedge /Wcell may be interpreted as the number of hedges that the
flow encounters per unit width. The second ratio is thus the inverse of the average distance
between these hedges within the grid cell. The last term may be loosely referred to as the
drag of the hedge, which is determined by the hedge pass factor µ given by

µ = 1 + 0.175n

h
−2
hv

(9.334)

if the hedge extends above the water level (hv > h) and is given by

µ = 1 − 0.175n

h
hv

(9.335)

if the hedge is fully submerged (h > hv ) where n is a dimensionless hedge density. The
second implementation reads

1
CD nLhedge h
=
2
C
2gLcell Wcell

(9.336)

or equivalently

2gLcell Wcell
hLhedge

CD n

(9.337)

for non-submerged conditions and

s
C=


2gLcell Wcell  hv
hLhedge
h

1
CD n

v
u
u
+ m0 t



h−hv 2
h
2 
v
− h−h
h

(9.338)

for submerged conditions. We recognize the same ratio Lcell Wcell /Lhedge that represents
the average distance between hedges. Equation (9.336) can be directly compared to similar
equations for area trachytopes (Equation (9.323)), point trachytopes (Equation (9.339)) and
bridge resistance (Equation (10.76)). Note that the formula for computing the loss coefficient
for a bridge explicitly includes the reduction in the flow area and the resulting increase in the
effective flow velocity, whereas the above mentioned trachytope formulae don’t.

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Point trachytope classes: various (251–300)
One formula for point trachytopes has been implemented. It may be used to represent groups
of individual trees or on a smaller scale plants.
FormNr

Name

Formula

251

trees

Eqn. (9.339)

The implemented formula reads

s
C=

2g
CD n min(hv , h)

(9.339)

9.11.2.2

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where n = mD with m the number of trees per unit area and D the characteristic tree
diameter, hv is the vegetation height and h is the local water depth. The formula is identical
to Equation (9.328) except for the fact that the point trachytope formula has no bed roughness
and area associated with it. The generalization of Equation (9.339) to the submerged case
(h > hv ) lacks the extra term in Equation (9.327).
Averaging and accumulation of trachytopes

Point and linear roughnesses are accumulated by summing the inverse of the squared Chézy
values Ci .

X 1
1
=
2
2
Cpnt
Cpnt,i
i
X 1
1
=
2
2
Clin
Clin,i
i

(9.340)

(9.341)

The area roughnesses are accumulated weighted by the surface area fraction fi . These
roughnesses are accumulated as White-Colebrook roughness values and as Chézy values;
for the latter values both the linear sum (“parallel”) and the sum of inverse of squared values
(“serial”) are computed. Roughness values are converted into each other as needed based
on the local water depth using Eqs. (9.54)–(9.56).

karea =

fi ki

(9.342)

Carea,p =

2
Carea,s

1
Ci2

fi Ci

(9.343)
(9.344)

For the fraction of the grid cell area for which no roughness class is specified the default
roughness is used.
The flow resistance coefficients are also accumulated proportionally to the surface area fraction fi associated with the trachytope considered. For the fraction of the grid cell area for
which no flow resistance is specified, obviously none is used.

λ=

fi λi

(9.345)

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The final effective bed roughness of the grid cell may be computed by either one of the following two methods.
Method 1
The total mean roughness is computed by summing the White-Colebrook values for the areas
and line and point resistance features.

km = karea + klin + kpnt

(9.346)

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fb = max(min(0.843, fb ), 0.014)

p
Ctotal = Cm 1.12 − 0.25fb − 0.99 fb

where klin = 12h10−Clin /18 and kpnt = 12h10−Cpnt /18 . The effect of the water free
area fraction fb is taken into account by means of the following empirical relation in which
Cm = 18 10 log(12h/km ) is the mean Chézy value corresponding to the total mean WhiteColebrook roughness value obtained from Equation (9.346).
(9.347)
(9.348)

The resulting Ctotal value is used in the computation. This method together with trachytope
classes 1, 51, 101, 151 and 201 corresponds to the NIKURADSE option of the WAQUA/TRIWAQ
flow solver.
Method 2

The total roughness is computed by first averaging over the serial and parallel averages of the
Chézy values according

Carea = αs Carea,s + (1 − αs )Carea,p

(9.349)

where αs = 0.6 by default. Subsequenty the effect of the water free area fraction fb is
taken into account by means of the following empirical relation (identical to Equation (9.348)
of method 1).

fb = max(min(0.843, fb ), 0.014)

p
Carea,corr =Carea 1.12 − 0.25fb − 0.99 fb

(9.350)
(9.351)

Finally the Chézy value representing the total bed roughness is computed by accumulating
the inverses of the squared Chézy values.

2
Ctotal

2
Carea,corr

1
1
+ 2
2
Clin
Cpnt

(9.352)

The resulting Ctotal value is used in the computation. This method together with trachytope
classes 1, 51, 52, 53, 101, 152, 202 and 251 corresponds to the ROUGHCOMBINATION
option of the WAQUA/TRIWAQ flow solver.

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(Rigid) 3D Vegetation model
In a detailed numerical model one may want to represent the vertical variations in the vegetation characteristics and study the effect of vegetation on the 3D flow and turbulence.
The interaction of submersed vegetation upon hydrodynamics and fysical processes has received increasing attention because of its influence on water quality in lakes and on morphological developments in salt marshes (Houwing et al., 2000; WL | Delft Hydraulics, 1998).
Uittenbogaard (dec. 2000) formulated theory for incorporating the effects of vegetation upon
momentum and turbulence equations and implemented this in the so called ‘(Rigid) 3D Vegetation model’, see Winterwerp and Uittenbogaard (1997), that has extensively been tested
and compared to experiments (Meijer, 1998) by Oberez (2001).

The main input parameter for this formulation is the plant geometry, see section A.2.31. The
implementation of vegetation resistance can also be applied for 2DH computations.
Theoretical background

The basic input parameters are the number of stems per unit area as function of height n(z),
and the stem width as function of height φ(z).

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9.11.3

The influence of the vegetation upon the momentum equations is given by the vertical distribution of the friction force as caused by cylindrical elements in oblique flow:

1
F (z) = ρ0 CD φ(z)n(z) |u(z)| u(z)
2

[N/m3 ]

(9.353)

with u(z) the horizontal flow velocity profile and CD the cylindrical resistance coefficient (default value 1.0).
The horizontal cross sectional plant area is given by:

Ap (z) =

π 2
φ (z)n(z)
4

(9.354)

The influence of the vegetation upon vertical mixing is reflected in an extra source term T in
the kinetic turbulent energy equation:

∂k
1
∂
=
∂t
1 − Ap ∂z

νt ∂k
(1 − Ap ) ν +
+ T + Pk − Bk − ε
σk ∂z

(9.355)

with T (z) the work spent by upon the fluid:

T (z) = F (z)u(z)

(9.356)

and an extra source term T τ −1 in the epsilon equation,

∂ε
1
∂
=
∂t
1 − Ap ∂z

νt ∂ε
(1 − Ap ) ν +
+ T τ −1 + Pε − Bε − εε
σk ∂z

(9.357)

with τ the minimum of:

τ = min(τfree , τveg )

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(9.358)

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with the dissipation time scale of free turbulence

τfree =

1 k
c2ε ε

(9.359)

and the dissipation time scale of eddies in between the plants

τveg =

1
√

r
3

c2ε cµ

L2
T

(9.360)

that have a typical size limited by the smallest distance in between the stems:

1 − Ap (z)
n(z)

(9.361)

L(z) = Cl

Cl is a coefficient reducing the geometrical length scale to the typical volume averaged turbulence length scale. Uittenbogaard presents a closure and finds that a Cl value of 0.07 is

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applicable for grid generated turbulence. For vegetation this coefficient may be tuned, values
of 0.8 are found applicable, see Uittenbogaard (dec. 2000).

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10 Numerical aspects of Delft3D-FLOW
The mathematical formulations of the 3D shallow water flow and transport model Delft3DFLOW were presented in chapter 9. To solve the partial differential equations the equations
should be transformed to the discrete space. In this chapter the space discretisation, time
integration and numerical solution methods applied in Delft3D-FLOW will be described.
The description provided here applies in most cases for both the vertical σ co-ordinate system (σ -model) and the vertical z co-ordinate system (Z -model). Numerical aspects that are
specifically valid only for the Z -model system will be described separately in chapter 12.

Staggered grid

The numerical method of Delft3D-FLOW is based on finite differences. To discretise the 3D
shallow water equations in space, the model area is covered by a curvilinear grid. It is assumed that the grid is orthogonal and well-structured, see Figure 10.1.

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10.1

Delft3D-FLOW is applied for modelling a wide range of different flow conditions: e.g. turbulent
flows in laboratory flumes, tidal flow in estuaries and seas, rapidly varying flows in rivers,
density driven flows by thermal discharges, wind driven flows in lakes and ocean dynamics.
For all these applications (with complete different length scales) Delft3D-FLOW should give a
solution. For the choice of the numerical methods, robustness had high priority.

The grid co-ordinates can be defined either in a Cartesian or in a spherical co-ordinate system.
In both cases a curvilinear grid, a file with curvilinear grid co-ordinates in the physical space,
has to be provided. Such a file may be generated by a grid generator, see the User Manual
of RGFGRID.
The numerical grid transformation is implicitly known by the mapping of the co-ordinates of
the
p grid vertices
p from the physical to the computational space. The geometrical quantities
Gξξ and Gηη introduced in the transformed equations, see Eqs. (9.3) to (9.8), have to
be discretised on the computational grid, see Figure 10.2.
The primitive variables water level and velocity (u, v , w ) describe the flow. To discretise the
3D shallow water equations, the variables are arranged in a special way on the grid, see Figure 10.2 and Figure 10.3. The pattern is called a staggered grid. This particular arrangement
of the variables is called the Arakawa C-grid. The water level points (pressure points) are
defined in the centre of a (continuity) cell. The velocity components are perpendicular to the
grid cell faces where they are situated.
Staggered grids have several advantages such as:

Boundary conditions can be implemented in a rather simple way.
It is possible to use a smaller number of discrete state variables in comparison with discretizations on non-staggered grids, to obtain the same accuracy.

Staggered grids for shallow water solvers prevent spatial oscillations in the water levels;
see e.g. Stelling (1984).

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Figure 10.1: Example of a grid in Delft3D-FLOW

Figure 10.2: Mapping of physical space to computational space

Legend:

+
→

water level (ζ ) / density (ρ) point
velocity point (u, v or w)

Figure 10.3: Grid staggering, 3D view (left) and top view (right)

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10.2

σ -grid and Z -grid
In the vertical direction, two types of grid are available:

a boundary-fitted σ co-ordinates and
a grid that is strictly horizontal also called the Z -grid.
For the σ co-ordinate grid, the number of layers over the entire horizontal computational area
is constant, irrespective of the local water depth. The distribution of the relative layer thickness
is usually non-uniform. This allows for more resolution in the zones of interest such as the
near surface area (important for e.g. wind-driven flows, heat exchange with the atmosphere)
and the near bed area (sediment transport).

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The σ -grid is commonly used in Delft3D-FLOW. However, occasionally this grid may not be
sufficient to solve problems where stratified flow can occur in combination with steep topography. The σ -grid, though boundary fitted, will generally not have enough resolution around
the pycnocline which is strictly horizontal in the physical space. High resolution around pycnocline is in this situation preferred. Therefore, recently a second vertical grid co-ordinate
system based on Cartesian co-ordinates (Z -grid) was introduced in Delft3D-FLOW for 3D
simulations of weakly forced stratified water systems.
The Z -grid has horizontal co-ordinate lines that are (nearly) parallel with density interfaces
(isopycnals) in regions with steep bottom slopes. This is important to reduce artificial mixing
of scalar properties such as salinity and temperature. The Z -grid is not boundary-fitted in the
vertical. The bottom (and free surface) is usually not a co-ordinate line and is represented as
a staircase (see previous chapter).
10.3

Definition of model boundaries

The horizontal model area is defined by specifying the so-called computational grid enclosure
(automaticly enerated by RGFGRID). The computational grid enclosure consists of one or
more closed polygons that specify the boundaries of the model area. There are two types
of boundaries: closed boundaries along “land-water” lines (coastlines, riverbanks) and open
boundaries across the flow field. The open boundaries are artificial and chosen to limit the
computational area. The polygons consist of line pieces connecting water level points on the
numerical grid, with a direction parallel to the grid lines or diagonal (45 degrees) through the
grid. The computational cells on the grid enclosure are land points (permanent dry) or open
boundary points. An island may be removed from the computational domain by specifying
a closed polygon (“land-water line”) as part of the grid enclosure. If a computational grid
enclosure is not specified, then a default rectangular computational grid is assumed. A default
enclosure is spanned by the lines connecting the water level points (1, 1), (Mmax, 1), (Mmax,
Nmax) and (1, Nmax).
Figure 10.4 shows for a horizontal model area the grid staggering, the grid enclosure and the
position of open and closed boundaries. Figure 10.5 shows the corresponding grid of control
volumes which may be generated by the grid generator RGFGRID. This example will now be
explained in detail.
The computational grid enclosure for the grid of control volumes shown in Figure 10.4 is
defined by the following polygon of line pieces:

(1,1) - (5,1)
(5,1) - (7,3)
(7,3) - (8,3)

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Closed boundary
Grid enclosure

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Water level point

Open boundary point
u-velocity point

v-velocity point

Grid cell/Computational cell/Control volume

Figure 10.4: Example of Delft3D-FLOW model area

(8,3)
(8,6)
(3,6)
(1,4)

(8,6)
(3,6)
(1,4)
(1,1)

The array dimensions Mmax=8 and Nmax=6, with Mmax-2 and Nmax-2 the number of grid
cells in ξ - and η -direction, respectively. Open boundaries are located at the line pieces
(m,n)=(1,2) to (1,3) and at (m,n)=(8,4) to (8,5). For this example, the grid lines and corresponding control volumes drawn by the grid generator RGFGRID are shown in Figure 10.5.
We remark that the dimensions of the grid in RGFGRID are Mmax-1 and Nmax-1, counting
the grid corners. Thus, in both directions the dimension of the grid in RGFGRID is one less
than the dimension specified for the model area in the MDF-file. This has to do with the staggered grid and is often a source of misunderstanding. We remark that the depth files (files
with extension ) should have entries for all Mmax by Nmax values, see <∗.dep> files
and section A.2.4. For a detailed discussion of the grid, the grid enclosure and the location of
boundary points see Appendix E.
After generating a curvilinear grid with the grid generator RGFGRID , as output file there is
also a computational grid enclosure file, which can be used by Delft3D-FLOW.
10.4

Time integration of the 3D shallow water equations
Following Stelling (1984), a robust solver for the shallow water equations has to satisfy the
following demands:

Robustness (unconditionally stable).
Accuracy (at least second order consistency).

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Figure 10.5: Example of Delft3D-FLOW grid

Suitable for both time-dependent and steady state problems.
Computationally efficient.

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An explicit time integration of the shallow water equations on a rectangular grid is subject to a
time step condition based on the Courant number for wave propagation:

CFLwave

p
= 2∆t gH

1
1
+
< 1,
2
∆x
∆y 2

(10.1)

where ∆t
is the acceleration of gravity, H is the total water depth and
pis the time step, g p
∆x =
Gξξ and ∆y =
Gηη are the smallest grid spaces in ξ - and η -direction of
the physical space. For many practical applications, this requires a time step of only a few
seconds to simulate tidal propagation. Exceeding the time step would generate instability and
from the view of robustness, this is not acceptable. Therefore, an implicit method is needed.
However, an implicit scheme can be uneconomic in computer time and storage if the inversion
of a large matrix is required. A straightforward implicit finite difference approximation is the
Crank-Nicholson method. For the linearised depth-averaged shallow water equations without
advection and bottom friction, the Crank Nicholson method in vector form reads:

with:

~ `+1 − U
~` 1
U
~ ` + 1 AU
~ `+1 = ~0,
+ AU
∆t
2
2

(10.2)

~ = (u, v, ζ)T ,
U

(10.3)

∂ 
0
−f g ∂x
∂ 
0
g ∂y
A= f
,
∂
∂
H ∂x H ∂y 0

(10.4)

H = d + ζ.

(10.5)



and:

The solution after one time step is given by

~ `+1

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−1

1
1
~ `.
= I + ∆tA
× I − ∆tA U
2
2

(10.6)

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After discretization, the spatial differential operators in both grid directions generate a system
of difference equations with a band matrix. In each row there are at least five non-zero entries,
corresponding to the grid cells surrounding the water level point. The band width is relatively
large and all grid points are implicitly coupled. Solving the equations would require a large
computational effort. In the next section a computationally efficient time integration method
will be described, which is applied for the σ -grid in Delft3D-FLOW.
ADI time integration method

Leendertse (1967); Leendertse and Gritton (1971); Leendertse et al. (1973) introduced an
Alternating Direction Implicit (ADI) method for the shallow water equations. The ADI-method
splits one time step into two stages. Each stage consists of half a time step. In both stages,
all the terms of the model equations are solved in a consistent way with at least second order
accuracy in space.
For the spatial discretization of the horizontal advection terms, three options are available in
Delft3D-FLOW. The first and second option use higher-order dissipative approximations of
the advection terms. The time integration is based on the ADI-method. The first scheme
is denoted as the WAQUA-scheme, see Stelling (1984) and Stelling and Leendertse (1992).
The second scheme is denoted as the Cyclic method; see Stelling and Leendertse (1992).
The WAQUA-scheme and the Cyclic method do not impose a time step restriction. The third
scheme can be applied for problems that include rapidly varying flows for instance in hydraulic
jumps and bores (Stelling and Duinmeijer, 2003). The scheme is denoted as the Flooding
scheme and was developed for 2D simulation with a rectilinear grid of the inundation of dry
land with obstacles such as road banks and dikes. The integration of the advection term
is explicit and the time step is restricted by the Courant number for advection. We discuss
the time integration for scheme WAQUA and method Cyclic. For the Flooding scheme, the
advection term is taken at the previous time level and moved to the right-hand side.

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10.4.1

For the water level gradient and the advection terms, the time levels are alternating; if in
one stage a term is taken implicitly in time, this term will be taken explicitly in time in the
other stage. For the complete time step, each separate term is still integrated second-order
accurate in time. The advantage of the ADI-method is that the implicitly integrated water
levels and velocities are coupled along grid lines leading to systems of equations with a small
bandwidth. Substitution of the discrete momentum equations in the continuity equation leads
to a tri-diagonal system of equations for the water levels. After computing the water levels,
back substitution of the water levels in the discrete momentum equations gives the velocities;
see Stelling (1984) for full details.
In vector form (for the 2D case) the ADI-method is given by:
Step 1:

~ `+ 21 − U
~` 1
U
~
~ `+ 21 + 1 Ay U
~ ` + BU
~ `+ 12 = d,
+ Ax U
1
2
2
∆t
2

(10.7)

Step 2:

~ `+1 − U
~ `+ 12
U
1 ~ `+ 1 1 ~ `+1
~
~ `+1 = d,
2 +
+ Ax U
Ay U
+ BU
1
2
2
∆t
2

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with:


∂
0
−f
g ∂x
∂
∂
u ∂x
+ v ∂y
0 ,
Ax =  0
∂
∂
H ∂x
0
u ∂x

(10.9)


∂
∂
u ∂x
+ v ∂y
0
0
∂ 
f
0
g ∂y
Ay = 
,
∂
∂
0
H ∂y
v ∂y

(10.10)



and:

!
,

(10.11)

λ 0 0
0 λ 0
0 0 0

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with λ the linearized bottom friction coefficient. To improve stability the bottom friction is integrated implicitly for each stage. d~ is the right-hand side containing external forcings like wind
and atmospheric pressure. The time integration of the horizontal viscosity terms is discussed
in section 10.4.4 and is dependent on the formulation.
In the first stage the time level proceeds from ` to ` + 12 and the simulation time from t = `∆t

to t = ` + 12 ∆t. In this stage first the V -momentum equation, Equation (9.8), is solved,
followed by the U -momentum equation, Equation (9.7), which is implicitly coupled with the
continuity equation, Equation (9.3), by the free surface gradient. In the second stage the time
level proceeds from ` + 21 to ` + 1. In this stage first the U -momentum equation is solved,
followed by the V -momentum equation which is implicitly coupled with the continuity equation
by the free surface gradient. In the stage, in which the barotropic pressure term (i.e. water
level gradient) is integrated implicitly, the advection terms and viscosity terms are integrated
explicitly. Similarly in the stage, in which the barotropic pressure term (i.e. water level gradient)
is integrated explicitly, the advection terms and viscosity terms are integrated implicitly.

The second stage in the ADI-method is almost similar to the first stage. The grid coefficients, direction dependent roughness coefficients and the u-velocity and v -velocity are interchanged. The only principal difference between the u- and v -momentum equations is the sign
of the Coriolis term. In Delft3D-FLOW the similarity of the difference equations is used in the
implementation. The same subroutine is used for the momentum equation in both directions,
only the sign of the Coriolis term is dependent on the computational direction.
For the 3D shallow water equations the horizontal velocity components are coupled in the
vertical direction by the vertical advection and viscosity term. An explicit time integration of
the vertical exchange terms on a σ -co-ordinate or a Z -co-ordinate grid would in shallow areas
lead to very severe time step limitations:

(∆σH)2
(∆z)2
or ∆t ≤
,
∆t ≤
2νV
2νV

(10.12)

∆σH
∆z
or ∆t ≤
,
(10.13)
ω
w
where ∆σH and ∆Z are the vertical grid size and ω is the transformed vertical velocity
∆t ≤

and w the vertical velocity. Therefore, in the vertical direction a fully implicit time integration
method is applied, which is first-order accurate in time and leads to tri-diagonal systems of
equations. The vertical coupling of the discretized momentum equations is eliminated by a
double sweep algorithm.

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10.4.2

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Figure 10.6: Numerical region of influence for one time step, “Zig-zag channel”

Accuracy of wave propagation

The standard time integration method in Delft3D-FLOW for the σ -model is the ADI-method
described in the previous section. Water levels and velocities are implicitly solved along grid
lines. The wave propagation is related to the Courant number, see Equation (10.1). It is
known, see e.g. Benqué et al. (1982) and Weare (1979), that for flow along irregular (staircase) closed boundaries, flow around islands, flow over tidal flats, and through “zig-zag”,
see Figure 10.6, channels where the grid lines do not smoothly
follow the geometry, the ADI√
method is inaccurate for Courant numbers larger than 4 2. The numerical region of influence
does not correspond to the mathematical region of influence following the theory of characteristics for hyperbolic systems of equations. The ADI-method may lead to inaccurately predicted
flow patterns, see e.g. Stelling (1984). This inaccuracy is called the ADI-effect and is introduced by the splitting of the spatial operator in two directions. A free surface wave cannot
travel through more than two bends of 90 degrees in one complete ADI time step (Stelling,
1984), see Figure 10.6.

√

The upper bound for the Courant number of 4 2 occurs in the most critical situation, namely
in case of a narrow channel (width of few grid sizes) that makes an angle of 45 degrees with
the computational grid. In practical situations the Courant number should not exceed a value
of 10. However, this is a rough estimate. You are advised to carry out sensitivity tests in order
to determine the largest time step for which the ADI-method still yields accurate results.

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10.4.3

Iterative procedure continuity equation
The non-linearity in the coupled continuity equation, Equation (9.3), and momentum equation,
Eqs. (9.7) and (9.8) requires an iterative procedure. For the U -momentum equation:

`+ 12
∂ p
≈
Gηη HU
∂ξ

`+ 12
ξ
p
Gηη HU

−

`+ 12

Gηη HU

m+ 12 ,n

m− 12 ,n

∆ξ

(10.14)

ξ [q]
ξ [q]
p
p
[q]
[q]
Gηη Hm+ 1 ,n Um+ 1 ,n −
Gηη Hm− 1 ,n Um− 1 ,n
2

≈

∆ξ

(10.15)

The iterative procedure in Delft3D-FLOW removes the non-linear term by multiplying the free
surface gradient in the discretized momentum equation by the factor:
[q−1]

Hm,n
[q]

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[q]

(10.16)

Hm,n

This factor converges to one. The iterative procedure in Delft3D-FLOW is mass conservative
after each iteration. Two iterations are enough both for accuracy and stability. The number of
iterations is set in the MDF-file by the keyword Iter.
For rapidly varying flows, the water depth at velocity points may be discontinuous. To obtain
accurate approximations of the local water depth at discontinuities slope limiters are used,
see section 10.5.1. In this way positive water depths are guaranteed. This requires local
linearization of the continuity equation. The same approach is used for the Z -model:

`+ 12
∂ p
Gηη HU
≈
∂ξ

ξ
ξ
p
p
`+ 12
`+ 12
`
`
Gηη Hm+ 1 ,n Um+ 1 ,n −
Gηη Hm− 1 ,n Um− 1 ,n
2

∆ξ

(10.17)

This linearization of the continuity equation is used in combination with the Flooding scheme
for advection and the Z -model. This approach is less stable in shallow areas.
10.4.4

Horizontal viscosity terms

In section 9.3.1 the horizontal turbulent fluxes of momentum are described. If the horizontal
viscosity terms are simplified, Eqs. (9.26) and (9.27), there results a Laplace operator along
grid lines. The u-momentum equation involves only second-order derivatives of the u-velocity.
In this case, this term is integrated fully implicitly by using operator splitting. This procedure is
unconditionally stable.
In the momentum equations, the complete Reynolds stress tensor is used, Eqs. (9.23)–(9.25),
for the following cases:

partial slip at closed boundaries,
no slip at the closed boundaries,
HLES-model for sub-grid viscosity.

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Table 10.1: Time step limitations shallow water solver Delft3D-FLOW

∆t ≤

Accuracy ADI for barotropic mode for
complex geometries
Explicit advection scheme “Flooding
scheme” and for the Z -model.
Stability baroclinic mode internal wave
propagation (Z -model only)

T
40

Cf = 2∆t gH ∆x1 2 +

1
∆y 2

√
<4 2

∆t|u|
∆x

<2
r

−ρtop ) H
1
∆t (ρbottom
g
+
ρtop
4
∆x2

1
∆x2

Stability horizontal viscosity term (HLES,
partial slip, no slip)

2∆tνH

Secondary flow (with β defined in Equation (9.155))

2∆tβ|u|
min(∆x,∆y)

1
∆y 2

Points per wave period T

≤1

DR
AF

For the complete Reynolds stress tensor the shear stress τξη in the u-momentum equation
contains derivatives of the v -velocity. The Reynolds stresses are integrated explicitly, which
leads to the following additional stability condition:

1
∆t ≤
2νH

1
1
+
2
∆x
∆y 2

−1

In case of a curvilinear grid ∆x =

(10.18)

p
p
Gξξ and ∆y = Gηη .

The stresses due to secondary flow Tξξ , Tξη in the depth averaged U -momentum equation
Equation (9.147) contain the depth averaged U - and V -velocity components. These stresses
are integrated explicitly, which leads to the following stability condition:

2∆tβ |u|
≤1
min (∆x, ∆y)

(10.19)

with β defined in Equation (9.155).
10.4.5

Overview time step limitations

In this section we give an overview of the time step limitations due to stability and accuracy
for the time integration of the shallow water equations in Delft3D-FLOW.
Let ∆x and
p
p ∆y
Gξξ and ∆y =
Gηη .
be horizontal grid sizes. In case of a curvilinear grid ∆x =
In Table 10.1 the time step limitations are given for the shallow water code Delft3D-FLOW.
Which of the limitations is most restrictive is dependent on the kind of application: length
scale, velocity scale, with or without density-coupling etc.
10.5
10.5.1

Spatial discretizations of 3D shallow water equations
Horizontal advection terms
The choice of the spatial discretization of the advective terms has great influence on the
accuracy, monotony and efficiency of the computational method. Central differences are often
second order accurate, but may give rise to non-physical spurious oscillations, the so-called

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“wiggles” (Gresho and Lee, 1981) in the solution. These wiggles arise in the vicinity of steep
gradients of the quantity to be resolved. In shallow water flow these wiggles may also be
introduced near closed boundaries and thin dams. On the other hand, first order upwinding is
unconditionally wiggle-free or monotone, thus promoting the stability of the solution process,
but introduces a truncation error, which has the form of a second-order artificial viscosity
term (Vreugdenhil, 1994). In advection-dominated flows, this artificial viscosity dominates the
physical viscosity and the computed solution is much smoother than the correct one. Higher
order upwinding is not free from numerical oscillations and introduces fourth-order artificial
viscosity. This higher order viscosity suppresses the wiggles without smoothing the solution
too much.

1
2
3
4

WAQUA-scheme
Cyclic method
Flooding-scheme
Multi directional upwind (Z -model only)

DR
AF

WAQUA-scheme

In Delft3D-FLOW the following advection schemes are implemented:

The first scheme (WAQUA) based on Stelling (1984) is an extension of the ADI-method of
Leendertse with a special approach for the horizontal advection terms. The normal advection
term u ∂u
is discretised with central differences and the cross advection term v ∂u
, based
∂ξ
∂η
on the dissipative reduced phase error scheme. It is a splitting of a third order upwind finite
difference scheme for the first derivative into two second order consistent discretizations: a
central discretization Equation (10.20) and Equation (10.21), which are successively used in
both stages of the ADI-scheme. For the cross advection term the spatial discretization is given
by:
Stage 1:

v ∂u
p
Gηη ∂η

and

m,n,k

ξη
v̄m,n,k

p
=
Gηη m,n

um,n+1,k − um,n−1,k
2∆η

(10.20)

Stage 2:

v ∂u
p
Gηη ∂η

m,n,k



ξη

v̄m,n,k
3u
−
4u
+
u
m,n,k
m,n−1,k
m,n−2,k

ξη

,
v̄m,n,k
≥0

 pG
2∆η
ηη m,n
=

ξη

v̄m,n,k
−3u
+
4u
−
u

m,n,k
m,n+1,k
m,n+2,k
ξη

, v̄m,n,k
<0

 pG
2∆η
ηη m,n

(10.21)

The advective terms for the v -momentum equation are discretized in a similar way. Spatial
oscillations in the velocities are suppressed by means of fourth-order dissipation, (Stelling,
1984; Stelling and Leendertse, 1992). The WAQUA scheme has little dissipation and is used
for the accurate prediction of water levels along the Dutch rivers.

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(a)

(b)

(c)

Cyclic-scheme

Figure 10.7: (a) Control Volume for mass for the Flooding scheme,
(b) Control Volume for momentum in horizontal and
(c) vertical direction for the Flooding scheme

DR
AF

The second method, (Cyclic), which is the default method, is based on the dissipative reduced
and the
phase error scheme Eqs. (10.20) and (10.21) for both the normal advection term u ∂u
∂ξ
(Stelling and Leendertse, 1992).
cross advection term v ∂u
∂η

For WAQUA and the Cyclic method, the advection terms are integrated implicitly in the stage
of the ADI-method in which the free surface gradient is at the old time level. In the stage
in which the free surface gradient is integrated implicitly the advection terms are at the old
time level. For stability the vertical terms are integrated implicitly in both stages. The upwind
discretization is used in the stage in which both the horizontal advection and vertical viscosity
term are integrated implicitly. The resulting linear system of equations has eleven diagonals.
The system is solved efficiently by a Red Black Jacobi iterative scheme in the horizontal
direction and a double sweep in the vertical direction. For the Cyclic method the matrix is
diagonally dominant and the iterative scheme converges well. For the WAQUA scheme, due to
the central difference scheme for the normal advection, the matrix is not diagonally dominant
for large time steps (Courant number advection more than one) and this may lead to bad
convergence behaviour.
Flooding-scheme

The third scheme, based on Stelling and Duinmeijer (2003) can be applied to rapidly varying
depth-averaged flows for instance the inundation of dry land or flow transitions due to large
gradients of the bathymetry (obstacles). The scheme can also be used in combination with
obstacles represented by only one point on coarse grids. In the Flooding scheme the bottom
is approximated by a staircase of tiles (DPUOPT=MIN), centred around the water level points,
see Figure 10.7a. In combination with the local invalidity of the hydrostatic pressure assumption, conservation properties become crucial. In flow expansions a numerical approximation is
applied that is consistent with conservation of momentum and in flow contractions a numerical
approximation is applied that is consistent with the Bernoulli equation. For sufficiently smooth
conditions, and a fine grid size, both approximations converge to the same solution. The local order of consistency depends on the solution. The approximations are second-order, but
the accuracy reduces to first order near extreme values by the use of the so-called Minmod
slope limiter (Stelling and Duinmeijer, 2003). The limiter prevents the generation of wiggles.
The conservation of momentum in the present implementation has been derived only for a
Cartesian rectangular grid and depth averaged velocities.

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We describe the discretizations for positive flow direction. For negative flow direction the
discretizations are defined accordingly. The momentum conservative approximation for the
derived for a Control Volume around a velocity point is given by
normal advection term u ∂u
∂ξ
(using q = Hu):

u ∂u
p
Gξξ ∂ξ

m+ 21 ,n

1
= p
H Gξξ

∂qu
∂q
−u
∂ξ
∂ξ

(10.22)
m+ 12 ,n

2
p
×
(Hm,n + Hm+1,n )
Gξξ m+ 1 ,n
!2
( ξ
ξ
q̄m+1,n ũm+1,n − q̄m,n ũm,n
− um+ 1 ,n
2
∆ξ

ξ
q̄m,n
=

qm+ 1 ,n + qm− 1 ,n
2

2

u

DR
AF
ũm,n

+ 12 ψ (ru ) um− 1 ,n − um− 3 ,n
2
2

=
u 1 + 1 ψ (ru ) u 1 − u 3
m+ ,n
m+ ,n
m+ ,n
2
m− 21 ,n
2

ξ
≥0
q̄m,n
ξ
<0
q̄m,n

ψ (ru ) = max(0, min(ru , 1))
um+ 1 ,n − um− 1 ,n
2
2
ru =
um− 1 ,n − um− 3 ,n
2

(10.23)

(10.24)

(10.25)
(10.26)

For negative flow direction, the limiter is defined accordingly.

Hm,n + Hm+1,n
2

q|m+ 1 ,n = u|m+ 1 ,n
2

ξ
ξ
q̄m+1,n
− q̄m,n
∆ξ

(10.27)
(10.28)

The momentum conservative approximation for the cross advection term v ∂u
is given by
∂η
(using p = Hv ):

v ∂u
p
Gηη ∂η

m+ 21 ,n

1
= p
H Gηη

∂pu
∂p
−u
∂η
∂η

(10.29)

m+ 21 ,n

p
×
(Hm,n + Hm+1,n )
Gηη m+ 1 ,n
2


ξ
ξ
 p̄m+ 1 ,n+ 1 ũm+ 1 ,n+ 1 − p̄m+ 1 ,n− 1 ũm+ 1 ,n− 1
2
2
2
2
2
2
2
2

−

∆η
 ξ

p̄m+ 1 ,n+ 1 − p̄ξm+ 1 ,n− 1 
2
2
2
2 
um+ 1 ,n 
(10.30)
2

∆η

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p̄ξm+ 1 ,n− 1 =
2

pm,n− 1 + pm+1,n− 1
2

ũm+ 1 ,n− 1
2

(10.31)



um+ 1 ,n−1 + 1 ψ (ru ) um+ 1 ,n−1 − um+ 1 ,n−2
2
2
2
2

=
1
u 1
1
1
+
ψ
(r
)
u
−
u
u
m+ ,n+1
m+ ,n+1
m+ ,n+2
2
2

p̄ξm+ 1 ,n− 1 ≥ 0
2

p̄ξm+ 1 ,n− 1 < 0
2

(10.32)

ψ (ru ) = max(0, min(ru , 1))
um+ 1 ,n − um+ 1 ,n−1
2
2
ru =
um+ 1 ,n−1 − um+ 1 ,n−2
2

(10.33)
(10.34)

p|m+ 1 ,n = v̄ ξη
2

m+ 21 ,n

Hm,n + Hm+1,n
2

For negative flow direction, the limiter is defined accordingly.
(10.35)

DR
AF

From the momentum conservative formulation a so-called energy head conservative discretization for the same Control Volume, see Figures 10.7b and 10.7c, can be derived under
steady state conditions (constant discharge q ) in 1D (along a streamline in 2D), see Equation (10.36).

q2
p
2 Gξξ

(Hm+1,n )2

−

(Hm,n )2

Energy Head Conservation

1
1
2q
p
−
λ
(10.36)
(Hm,n + Hm+1,n ) Gξξ Hm+1,n Hm,n Momentum Conservation

(

λ=

(Hm,n +Hm+1,n )2
4Hm,n Hm+1,n

q>0
q>0

∧
∧

Hm,n < Hm+1,n
Hm,n > Hm+1,n

(10.37)

The energy conservative discretization is applied for contractions in both directions. For 2D
flow the direction of the grid lines do not always coincide with streamlines and this will generate
small head losses.
Near the boundaries the higher order discretization stencils for the advection terms contain
grid points on or across the boundary. To avoid an artificial boundary layer or instabilities, the
discretizations are reduced to lower order discretizations with smaller stencils. Stelling (1984)
developed the numerical boundary treatment implemented in Delft3D-FLOW.
Multi directional upwind (Z -model only)
The fourth scheme, which is only available in the Z -model is a multi-directional upwind
scheme. It is an extension to two dimensions of the first-order upwind method. Both an explicit
and an implicit variant of the scheme is available. It is a positive and monotone scheme. For
the explicit variant there is the Courant number stability constraint. The method is described
by Bijvelds (2001).

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hk-1

uk-1

layer k-1

layer k

uk+1

layer k+1

hk+1

10.5.2

Figure 10.8: Layer numbering in σ -model

Vertical advection term

DR
AF

The horizontal velocities of adjacent vertical layers are coupled by the vertical advection and
the vertical viscosity term. The σ co-ordinate system can lead to very thin layers in shallow
areas. To prevent instabilities, a fully implicit time integration is used for the vertical exchange
terms. This results in tridiagonal systems of equations in the vertical.
In a shallow water model the horizontal length scale is much larger than the vertical length
scale. In the vertical direction the eddy viscosity term dominates the advection term. Only for
stratified flows where the turbulent exchange is reduced, advection may be dominant. For the
space discretization of the vertical advection term, a second order central difference is used:

ω ∂u
H ∂σ

ξσ
ω̄m,n,k

m,n,k

um,n,k−1 − um,n,k+1
1
h
+ hm,n,k + 12 hm,n,k+1
2 m,n,k−1

(10.38)

where hm,n,k denotes the thickness of the computational layer with index k defined by hm,n,k =
∆σk Hm,n and H the total water depth or hm,n,k = ∆zm,n,k in the Z -model.
10.5.3

Viscosity terms

The approximation of the vertical viscosity terms are based on central differences. The vertical
viscosity term in the u-equations is discretized as:

1 ∂
H 2 ∂σ

∂u
νV
∂σ

m,n,k

νV |m,n,k−1
=
hm,n,k

um,n,k−1 − um,n,k
+
1
(h
+
h
)
m,n,k−1
m,n,k
2

νV |m,n,k
um,n,k − um,nk+1
−
. (10.39)
1
hm,n,k
(hm,n,k + hm,n,k+1 )
2

The vertical eddy viscosity is computed at the layer interface, with hm,n,k = ∆σk Hm,n or
hm,n,k = ∆zm,n,k in the Z -model.
10.6

Solution method for the transport equation
A robust and accurate solver for scalar transport has to satisfy the following demands:

Mass conservation.
Monotony (positive solution).
Accuracy (at least second order consistency).
Suitable for both time-dependent and steady state problems.

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Computationally efficient.
An explicit time integration of the scalar advection-diffusion equation on a rectangular grid has
a time step limitation based on the Courant number for advection:

Cadv = max

u∆t v∆t
,
∆x ∆y

≤ 1,

(10.40)

with ∆x and ∆y the grid spaces in the physical space.
Explicit integration of the horizontal diffusion term yields an upper limit of:

1
1
+
∆x2 ∆y 2

−1
.

(10.41)

1
∆t ≤
DH

DR
AF

For the 3D transport equation the scalar concentrations are coupled in the vertical direction by
the vertical advection and diffusion term. An explicit time integration of the vertical exchange
terms on the σ -co-ordinate grid would lead to very severe time step limitations:

(∆σH)2
,
2DV
∆σH
.
∆t ≤
ω

∆t ≤

(10.42)
(10.43)

Therefore in the vertical direction a fully implicit time integration method is applied, which is
first order in time and leads to tridiagonal systems of equations. The vertical coupling of the
discretized transport equations is removed by a double sweep algorithm.
To ensure that the total mass is conserved the transport equation in Delft3D-FLOW is discretized with a mass conserving Finite Volume approach (flux form). For the spatial discretization of the horizontal advection terms, two options are available in Delft3D-FLOW. The
first (and default) option is a finite difference scheme that conserves large gradients without
generating spurious oscillations and is based on the ADI-method. This scheme is denoted as
the Cyclic method, see Stelling and Leendertse (1992). The Cyclic method of Stelling and
Leendertse is based on an implicit time integration of both advection and diffusion and does
not impose a time step restriction.
The second option is an explicit scheme that belongs to the class of monotonic schemes: the
so-called Van Leer-2 scheme (Van Leer, 1974). The Van Leer-2 scheme is slightly less accurate than the scheme of Stelling and Leendertse. It combines two numerical schemes, namely
a first order upwind scheme and the second order upwind scheme developed by Fromm. In
case of a local minimum or maximum the first order upwind scheme is applied, whereas the
upwind scheme of Fromm is used in case of a smooth numerical solution. The time integration
of the Van Leer-2 scheme is explicit and therefore a CFL condition for advection and diffusion
must be fulfilled. Owing to the explicit time integration the Van Leer-2 scheme requires per
time step less computation time than the Cyclic method of Stelling and Leendertse. However,
the Van Leer-2 scheme produces a more diffusive numerical solution, because of the fact that
a first order upwind discretization is applied in case of a local maximum or minimum. The
transport scheme for the Z -model is described by Bijvelds (2001).
The transport equation is coupled with the momentum equations by the baroclinic pressure
term, see Eqs. (9.15) and (9.16) and section 9.3.4. The temporal variations in salinity are

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slow compared to the variations in the flow and therefore the baroclinic term in the momentum equations is treated explicitly, introducing a stability condition for internal gravity waves
(baroclinic mode), see section 10.4.5. The coupling with the flow is weak and in Delft3DFLOW the transport equation is solved independently of the flow for each half time step.
For the time integration of the horizontal diffusion term along σ -planes the Crank-Nicholson
method is applied. If the spatial discretization of the horizontal diffusion term is based on
a Cartesian grid using the Finite Volume approach of Stelling and Van Kester (1994) the
integration is explicit.
Source terms are integrated explicitly. In order to avoid negative concentrations and instabilities, sink terms are integrated fully implicit.

Cyclic method
To keep the numerical diffusion as small as possible the horizontal advection terms in the
scalar transport equation are approximated by the sum of a third-order upwind scheme and a
second-order central scheme. A second order central scheme is applied for the approximation
of the vertical advection term.

DR
AF

10.6.1

For the Cyclic method the time integration follows the ADI-method for the continuity equation.
In the first stage all space derivatives with respect to ξ are taken implicitly and all derivatives
in the η -direction are taken explicitly. In the second stage the directions for explicit and implicit
integration are interchanged. If the upwind discretization is used in the stage in which both
the horizontal advection and vertical viscosity term are integrated implicitly, the resulting linear
system of equations has thirteen diagonals but the matrix is diagonally dominant. Thus, the
system can be solved effectively by a Red Black Jacobi iterative scheme in the horizontal
direction and a double sweep in the vertical direction.
For the Cyclic method the upwind discretization of the horizontal advective fluxes in ξ -direction
is described by:

p
1 ∂ huc Gηη
p
∂ξ
Gξξ

m,n,k

= p

Fm+ 1 ,n,k − Fm− 1 ,n,k

ξη

Gξξ

∆ξ

(10.44)

m,n

For the scalar flux Fm+ 1 ,n,k at the U -velocity point the interpolation is given by:
2

(

Fm+ 1 ,n,k = um+ 1 ,n,k hm+ 1 ,n,k
2

Gηη

m+ 12 ,n

10cm,n,k −5cm−1,n,k +cm−2,n,k
,
6∆ξ
10cm+1,n,k −5cm+2,n,k +cm+3,n,k
,
6∆ξ

um+ 1 ,n,k ≥ 0
2
um+ 1 ,n,k < 0
2

(10.45)
In the first stage in η -direction a central scheme is applied:

p
1 ∂ hvc Gξξ
p
∂η
Gηη

Gm,n+ 1 ,k − Gm,n− 1 ,k

m,n,k

= p
Gηη

ξη

∆η

!
, (10.46)

m,n

with the scalar flux Gm+ 1 ,n,k at the V -velocity point determined by:
2

Gm+ 1 ,n,k = vm+ 1 ,n,k hm+ 1 ,n,k
2

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p
Gξξ

m,n+ 12

cm,n,k + cm,n+1,k
.
2

(10.47)

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Near open and closed boundaries the approximations for the fluxes are reduced to lower
order.
10.6.2

Van Leer-2 scheme
For the second option in Delft3D-FLOW, namely the Van Leer-2 scheme, the interpolation
formula for the horizontal fluxes is given by:

p
Fm+ 1 ,n,k = um+ 1 ,n,k hm+ 1 ,n,k Gηη
×
2
2
2
m+ 12 ,n

cm+1,n,k −cm,n,k
cm,n,k + α (1 − CF Ladv−u ) (cm,n,k − cm−1,n,k ) cm+1,n,k
,


−cm−1,n,k


when um+ 1 ,n,k ≥ 0,
2
cm,n,k −cm+1,n,k

c
+
α
(1
+ CF Ladv−u ) (cm+1,n,k − cm+2,n,k ) cm,n,k
,
m+1,n,k

−cm+2,n,k


when um+ 1 ,n,k < 0,
2

with:

and:

∆t |u|
∆x

DR
AF

CFLadv−u =

α=


 0,

 1,

cm+1,n,k −2cm,n,k +cm−1,n,k
cm+1,n,k −cm−1,n,k
cm+1,n,k −2cm,n,k +cm−1,n,k
cm+1,n,k −cm−1,n,k

(10.48)

(10.49)

> 1, (local max. or min.),
≤ 1, (monotone).

(10.50)

In η -direction a similar discretization is applied. Eqs. (10.48) to (10.50) consist of a diffusive
first-order upwind term and a higher order anti-diffusive term.
The time integration of the Van Leer-2 scheme is explicit. The Courant number for advection
should be smaller than 1.
10.6.3

Vertical advection

In the vertical direction the fluxes are discretized with a central scheme:

1 ∂ωc
H ∂σ

m,n,k

1
=
Hm,n

Fm,n,k−1 − Fm,n,k
∆σ

(10.51)

with the flux Fm,n,k determined by:

Fm,n,k = ωm,n,k

cm,n,k + cm,n,k−1
.
2

(10.52)

The time integration in the vertical direction is fully implicit. The vertical advection leads to
a tridiagonal system in the vertical. If the flow in the vertical is advection dominated, due to
vertical stratification in combination with upwelling or downwelling near a closed boundary or
a sill, a discharge of buoyant water, the central differences in the vertical may give rise to nonphysical spurious oscillations. The solution has an unphysical maximum or minimum scalar
concentration (overshoot or undershoot).

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Forester filter

It is well-known that second or higher order advective difference methods (such as the Cyclic
method) on coarse grids may exhibit non-physical oscillations near regions of steep gradients. The difference operators do not guarantee positive solutions and consequently negative
concentrations may occur. For depth-averaged simulations the Van Leer-2 scheme is strictly
positive. In 3D, for both transport schemes, the central differences in the vertical may give
rise to non-physical spurious oscillations, so-called “wiggles” (Gresho and Lee, 1981) in the
|w|∆z
solution when the vertical grid Péclet number Pe∆z = D
≤ 2. These wiggles may arise in
V
the vicinity of steep gradients of the quantity to be resolved. In shallow water scalar transport
these wiggles may be introduced in stratified areas near closed boundaries and steep bottom
slopes. Positive solutions are not guaranteed. In case of negative concentrations an iterative
filter procedure based on local diffusion along σ -lines followed by a vertical filter is started in
order to remove the negative values. The filtering technique in this procedure is the so-called
Forester filter (Forester, 1979), a non-linear approach which removes the computational noise
without inflicting significant amplitude losses in sharply peaked solutions.
If concentration cm,n,k is negative, then the iterative, mass conservative filtering process is
described (for the sake of simplicity only in one direction, namely the ξ -direction) by:

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10.6.4

cp+1
m,n,k

cpm,n,k

cpm+1,n,k − cpm,n,k
Vm+1,n,k
min 1,
+
+
4
Vm,n,k

cpm−1,n,k − cpm,n,k
Vm−1,nk
+
min 1,
, (10.53)
4
Vm,n,k

with Vm,n,k denoting the volume of cell (m, n, k).

This filter is applied only in grid cells with a negative concentration. The superscript p denotes
the iteration number. The filter smoothes the solution and reduces the local minima (negative
concentrations). Equation (10.53), can be interpreted as an approximation of the following
advection-diffusion equation:

with:

and:

α − β ∆x ∂c α + β ∆x2 ∂ 2 c
∂c
=
+
+ (higher order terms),
∂t
4 ∆t ∂x
4 ∆t ∂x2

(10.54)

Vm+1,n,k
α = min 1,
,
Vm,n,k

(10.55)

Vm−1,n,k
β = min 1,
Vm,n,k

(10.56)

The Forester filter introduces an artificial advection and diffusion. The numerical diffusion
coefficient of the horizontal filter is:

Dnum =

α + β ∆x2
∆x2
≤
.
4 ∆t
2∆t

(10.57)

Thus the filter introduces numerical diffusion but only locally. Maximal 100 iterations are carried out. If there is still a grid cell with a negative concentration after 100 iterations, then a

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Figure 10.9: Illustration of wiggles in vertical direction

warning is generated. To further understand the influence of the Forester filter, we rewrite
Equation (10.53) as:

α
β
α+β p
cm,n,k + cpm+1,n,k + cpm−1,n,k .
= 1−
4
4
4

cp+1
m,n,k

(10.58)

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As both α ≤ 1 and β ≤ 1, all coefficients of Equation (10.58) are positive. Consequently, a
positive concentration will remain positive, i.e. it will not introduce negative concentrations irrespective the steepness of the concentration gradients. A negative concentration surrounded
by positive concentrations, usually the result of ill represented steep gradients (wiggles), will
be less negative after one iteration and is effectively removed after several iterations by adding
enough (local) diffusion to force the concentration to become positive.
In the vertical, these wiggles may lead to unrealistic vertical profiles of temperature and/or
salinity, see Figure 10.9.
Local maxima and minima in temperature or salinity in the vertical direction, generated by the
computational method may give physically unstable density profiles and can also better be
removed by a numerical filter then by turbulent vertical mixing. We should be sure that it is
a wiggle generated by the numerical method and not by physical processes like heating or
cooling through the free surface or the discharge of water somewhere in the vertical. A similar
filtering technique as in the horizontal direction is applied for points with a local maximum or
minimum in the vertical:
local maximum:

cm,n,k > max (cm,n,k+1 , cm,n,k−1 ) + ε,

and

Pe∆z =

|w| ∆z
≤2
DV

local minimum:

cm,n,k < min (cm,n,k+1 , cm,n,k−1 ) + ε, and Pe∆z =

|w| ∆z
≤2
DV

the filter is applied, with ε = 10−3 . The numerical diffusion coefficient of the vertical filter is:

Dnum =

∆z 2
.
2∆t

(10.59)

Smooth but unstable vertical density profiles of salinity and temperature in the vertical direction, can sometimes also better be vertically mixed by a numerical filter technique then by the

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turbulence model. E.g. for temperature, the algorithm is given by:

If Tm,n,k > Tm,n,k−1 + ε Then

(Tm,n,k − Tm,n,k−1 )
2∆zk
(Tm,n,k − Tm,n,k−1 )
= Tm,n,k−1 + min (∆zk , ∆zk−1 )
2∆zk−1

Tm,n,k = Tm,n,k − min (∆zk , ∆zk−1 )
Tm,n,k−1

(10.60)

Endif
−6

with ε = 10

If both the horizontal and vertical filter are switched on, then first the filter in the horizontal
direction is carried out. The maximum number of filter steps in the horizontal direction is
100. This is followed by applying the filter in the vertical direction and hereby minimising the
additional vertical mixing. The maximum number of filter steps in the vertical direction is 1000.
If the maximum number of filter steps is exceeded, a warning is written in the diagnostic file.

10.7

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Remark:
The vertical Forester filter does not affect sediments and other constituents. When
activated, the filter only smooths salinity and temperature.
Numerical implementation of the turbulence models

The turbulence closure models in Delft3D-FLOW are all based on the eddy viscosity concept;
see section 9.5. The eddy viscosity is always based on information of the previous half time
step. The transport equations of turbulent kinetic energy k , Equation (9.127), and dissipation
rate ε, Equation (9.128) are solved in a non-conservative form. For turbulent boundary flows
local production, dissipation, and vertical diffusion are the dominant processes. On the staggered grid, the turbulent quantities k , ε and the eddy viscosity νV are positioned at the layer
interfaces in the centre of the computational cell. This choice makes it possible to discretize
the vertical gradients in the production term and buoyancy term accurately and to implement
the vertical boundary conditions at the bed and the free surface. First order upwind differencing for the advection provides positive solutions. For more details we refer to Uittenbogaard
et al. (1992) and Van Kester (1994).
10.8

Drying and flooding

Estuaries and coastal embayments contain large, shallow, and relatively flat areas separated
and interleaved by deeper channels and creeks. When water levels are high, the entire area
is water covered but as tide falls, the shallow areas are exposed, and ultimately the flow is
confined only to the deeper channels. The dry tidal flats may occupy a substantial fraction of
the total surface area. The accurate reproduction of covering or uncovering of the tidal flats is
an important feature of numerical flow models based on the shallow water equations.
Many rivers have compound channels, consisting of a main channel which always carries
flow (the summer-bed) and one or two flood plains which only carry flow during extreme river
discharges (the winter-bed). The summer bed is surrounded by low dikes, which will overtop
when the river discharge increases. The winter-bed is surrounded by much higher dikes,
which are designed to protect the polders against extreme river discharges. The flooding of
the flood plains increases the drainage capacity of the river and reduces the local water level
gradients.
In a numerical model, the process of drying and flooding is represented by removing grid
points from the flow domain that become “dry” when the tide falls and by adding grid points

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that become “wet” when the tide rises. Drying and flooding is constrained to follow the sides
of grid cells. In this section, we specify the algorithms which have been used to determine the
moment when a grid cell (water level point) or cell boundary (velocity point) becomes dry or
wet. Drying and flooding gives a discontinuous movement of the closed boundaries and may
generate small oscillations in water levels and velocities. The oscillations introduced by the
drying and flooding algorithm are small if the grid sizes are small and the bottom has smooth
gradients.
The crucial items in a wetting and drying algorithm are:

The way in which the bottom depth is defined at a water level point.
The way in which the water level is defined at velocity points.
Criteria for setting a velocity and/or water level points wet or dry.

In the following subsections, these three items will be discussed.

10.8.1

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The standard drying and flooding algorithm in Delft3D-FLOW is efficient and accurate for
coastal regions, tidal inlets, estuaries, and rivers. In combination with the Flooding scheme for
advection in the momentum equation, the algorithm is also effective and accurate for rapidly
varying flows with large water level gradients because of the presence of hydraulic jumps or
the occurrence of bores as a result of dam breaks.
Bottom depth at water level points

Delft3D-FLOW uses a staggered grid; see Figure 10.4. At input the bottom depth can be
specified by you at the vertices of a computational cell, the so-called depth points, or in the
cell centre, the so-called water level point (DPSOPT=DP). The DPSOPT=DP-option implies
that the position of the depth points is shifted to the water level points. You should consider
this interpretation when generating the depth values with e.g. QUICKIN.
To determine the total water depth at water level points, a bottom depth in the cell centre of
the Control Volume is required. The bottom depth in a water level point dζm,n is not uniquely
defined; see Figure 10.10. The algorithm used to determine this depth value from the four
surrounding depth points depends on the choice made by you. In older versions of Delft3DFLOW, three options were available: MEAN, MAX and MIN (through the value of the parameter
DRYFLP). Recently a new flag DPSOPT has been introduced with the following extended
options: MEAN, MAX, MIN and DP. It replaces partly the function of the old input parameter
DRYFLP.
The algorithms to determine the depth in a water level point from the four surrounding depth
points are given by:

MAX-option: dζm,n = max(dm,n , dm−1,n , dm,n−1 , dm−1,n−1 )
MEAN-option: dζm,n = 0.25(dm,n + dm−1,n + dm,n−1 + dm−1,n−1 )
MIN-option: dζm,n = min(dm,n , dm−1,n , dm,n−1 , dm−1,n−1 )
DP-option: dζm,n = dm,n
With the introduction of DPSOPT the value of the keyword in the input file that is related to the
selection of additional drying and flooding procedure at a water level point, DRYFLP, is now
restricted to YES or NO. YES implies that an additional drying and flooding check is required

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Figure 10.10: Definition bottom depth on FLOW grid

based on the evaluation of the value of the total water depth. If its value drops below the user
specified threshold than all four cell interfaces are set to dry (velocities are set to zeroes).
DRYFLP=NO implies that the drying and flooding check is only to be based on the individual
test of the depth values at the cell interfaces.
For the time being, if unspecified, DPSOPT value is determined automatically from DRYFLP
by the program (default value of DPSOPT is equal to DRYFLP and subsequently DRYFLP is
then set according to its original value).
The retention volume of a dry cell is the cell area times the difference between the water
level and the bottom depth at the cell centre. For the combination of flow computations with
transport of dissolved substances, the control volume/retention volume should be positive. In
Figure 10.11 an example is shown in which the water level is below the bottom in the cell
centre (dζm,n ), determined on basis of the average depth, is below the bottom, while some of
the adjacent velocity points still have a positive flow through height.
Therefore after solving the coupled system of continuity equation and momentum equation
there is a drying check applied to the water level points, see section 10.8.3. If the total water
depth in a water level point is negative:
ζ
Hm,n
= dζm,n + ζm,n ≤ 0,

(10.61)

the continuity cell is taken out of the computation and the half time step is repeated. In case of
steep bottom slopes, the MEAN option may lead to flooding of velocity points and afterwards
drying due to a negative control volume, increasing the computational time. The use of MAX
(default) is recommended. The algorithms for flooding and drying of tidal flats have been
extensively described by Stelling et al. (1986). However, that article does not include the MAX
option. It has been found that the MAX procedure is more favourable and will produce a more
smooth solution than the options described by Stelling et al. (1986).

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d(m-1,n)

dζm,n
Hζm,n

d(m,n)

ζm,n

d(m-1,n-1)

d(m,n-1)

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Figure 10.11: Negative control volume with two positive flow-through heights, MEANoption

The initial water level at a dry cell is determined by the depth at a water level point:

ζm,n = −dζm,n .
10.8.2

(10.62)

Total water depth at velocity points

Due to the staggered grid applied in Delft3D-FLOW, the total water depth at a velocity point for
the computation of the discharge through a cell face is not uniquely defined. Usually (default
option, marginal depth DCO=-999) it is determined by the arithmetic average of the depth
specified in the vertices of the cell face (side) plus the average of the water levels computed
in the cell centres at each side of that cell face:
η

U
Hm,n
=d +ζ ,

(10.63)

For the depth values at the cell interfaces, d¯η , you can now choose from the following three
options by setting an appropriate value for the input parameter DPUOPT:
η

DPUOPT = MEAN (default option): d =
η

(dm,n +dm,n−1 )
,
2
ζ

DPUOPT = MIN(imum): d = min dζm,n , dm+1,n ,

 ζ
if Um,n > 0

 dζm,n
η
dm+1,n
DPUOPT = UPW(ind): d =

if Um,n < 0

 min dζ , dζ
if Um,n = 0
m,n m+1,n
Remark:

DPSOPT is DP and DPUOPT is MEAN should not be used together.
ξ

For the water level at the cell interfaces ζ̄ ξ as default the mean value is used: ζ =

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Figure 10.12: Drying of a tidal flat; averaging approach. The flow-through height is based
on the average water level, see Equation (10.63), the velocity point is set
dry.

Figure 10.13: Overtopping of a river bank (weir); averaging approach. The flow-through
height is based on the average water level, see Equation (10.63), the velocity point is set dry.

In the neighbourhood of steep bottom gradients, use of the average water level to compute
the total water depth at a velocity point, may lead to an inaccurate determination of the flowthrough height. The velocity point is set dry too early, see Figure 10.12 and Figure 10.13. A
large volume of water is left on the tidal flat, increasing artificially the storage capacity of the
wet area.
It is also possible to determine the water levels at the cell faces with a so-called upwind
approach. This approach was already suggested by Stelling (1984) for shallow regions. In
Delft3D-FLOW the choice between upwind and the average approach for the water level in a
U -point is controlled by flag DPUOPT. In the Z -model always upwind water levels and depth
are used in velocity points (Bijvelds, 2001). The upwind flow through height in a U -velocity
point based on an upwind water level is given by:
η

U
Hm,n
=d +ζ ,
If (DPUOPT = UPW ∨ hydraulic structure ∨ Z -model) Then
 η
Um,n > 0,
 d + ζm,n ,
η
U
Hm,n =
d + ζm+1,n ,
Um,n < 0,
 η
d + max (ζm,n , ζm+1,n ) , Um,n = 0,

Endif

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Figure 10.14: Drying of a tidal flat; upwind approach. The flow-through height is determined by flow direction, see Equation (10.64), the velocity point remains
wet.

Figure 10.15: Overtopping of a river bank; upwind approach. The flow-through height is
based on the maximum water level, see Equation (10.64), the velocity point
remains wet.

with Um,n representing the depth averaged velocity both for 2D and 3D. The computation of
V
in a V -velocity point is similar. The upwind approach is
the upwind total water depth Hm,n
physically more realistic for velocity points between cells with different bottom depth at low
water and falling tide (Figure 10.14) or for weir like situations (Figure 10.15). Upwinding the
water level in the determination of the total water depth (flow through height) enhances the
discharge because the upwind water level is generally higher than the average water level,
resulting in a larger flow area, which allows the water level gradient to drive a larger amount
of water into the neighbouring cell during the next time step. Taking the maximum of the two
surrounding water levels at a dry cell face prevents that a velocity point is artificially kept dry.
The upwind approach is physically less realistic if the flow has the opposite direction as the
water level gradient (wind driven flow).
Figure 10.15 shows the situation of a river which overtops its bank. If we take the average
water level to determine the total water depth at the crest, the velocity point remains dry. The
water level will rise too much in the main channel of the river, leading to unrealistic water levels
downstream. When the river run off increases, suddenly the flood plains are filled with water,
generating a shock wave.
The Flooding scheme, see section 10.4.4, is accurate for the approximation of the advection in rapidly varied flows due to sudden expansions or sudden contractions (Stelling and
Duinmeijer, 2003). An example of such a flow problem is the simulation of the inundation
of dry land with obstacles such as road banks and dikes. Due to a sudden contraction, the
flow speed can become critical. The accuracy in the approximation of the critical discharge
rate is dependent on the approximation (limiter) of the total water depth at a velocity point

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Figure 10.16: Special limiter for critical flow due to a sudden contraction (Flooding
scheme and increase in bottom larger than DGCUNI)

downstream.

For the Flooding scheme the bottom is assumed to be represented as a staircase (DPUOPT=MIN)
of tiles, centred around the water level points, see Figure 10.7b and Figure 10.16. The flow
through height in a U -velocity point is always based on an upwind water level, the user-defined
marginal depth DCO is set at +999.
For the Flooding scheme the accuracy in the numerical approximation of the critical discharge
rate for flow with steep bed slopes, can be increased by the use of a special approximation
(slope limiter) of the total water depth at a velocity point downstream. The limiter function
is controlled by the user-defined threshold depth for critical flow limiter DGCUNI, see Figure 10.16 and:
ζ

If (Um,n > 0 ∧ dζm,n > dm+1,n + DGCU N I) Then
U
Hm,n

2 ζ
ζ
U
H ,H
= min Hm,n , max
3 m,n m+1,n
ζ

Elseif (Um,n < 0 ∧ dζm,n + DGCU N I < dm+1,n ) Then
U
Hm,n

2 ζ
U
ζ
= min Hm,n , max Hm,n , Hm+1,n
3

Endif

(10.65)

By the introduction of the user-defined threshold DGCUNI, see Figure 10.16, the points for
this special approach, are recognised automatically during the simulation, without having to
specify all the points at input.
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U
The total water depth Hm,n
at a velocity point should at least be positive to guarantee a
realistic discharge across a cell face. If the total water level drops below half of a userspecified threshold, then the velocity point is set dry. In 3D simulations the velocities are
set to zero for all the computational layers. The computational cell is closed for the side
normal to the velocity point. If the water level rises and the total water depth is larger than
the threshold, the velocity point is set wet again. The drying threshold is given half the value
of the wetting threshold (hysteresis) to inhibit changes of state in two consecutive time steps
(“flip-flop”), due to oscillations introduced by the algorithm itself. When all four velocity points
of a computational cell surrounding a water level point are dry then this computational cell will
be set dry.

ζ
The total water depth Hm,n
at a water level point should at least be positive to guarantee a
positive control volume. If the total water level becomes negative, the four velocity points at the
cell sides are set dry. In 3D simulations the velocities are set to zero for all the computational
layers. If a negative control volume occurs, the half time step should be completely repeated
and the computational time increases. Flooding is restricted to velocity points.

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The thickness of the water layer of a dry cell (retention volume) is dependent on the threshold
d specified by you. Therefore, the threshold value d must fulfil the following condition:

δ≥

∂ζ ∆t
.
∂t 2

(10.66)

In general, the magnitude of the disturbances generated by the drying and flooding algorithm
will depend on the grid size, the bottom topography and the time step. The disturbances are
small if the grid size is small and the bottom has smooth gradients. If the bottom has steep
gradients across a large area on a tidal flat, a large area may be taken out of the flow domain
in just one half integration time step. This will produce short oscillations. You can avoid this
by smoothing the bottom gradients.
Flooding is an explicit process. The boundary of the wet area can only move one grid cell
per time step. If the time step is too large an unphysical water level gradient at the wet-dry
interface is built up, which will generate oscillations after flooding.
Attention should also be paid to the fact that depth values at points at closed boundaries are
used in the total water depth of a velocity point parallel to the boundary and for the depth at
a water level point for the MEAN-option. The depth at closed boundaries should be a bottom
value near the coastline and not a land height.
In the first stage of the ADI-method, the drying and flooding algorithm in Delft3D-FLOW consists of the following four checks:
V
1 Drying check for velocity points in y -direction (Hm,n
< 0.5δ ).
U
2 Drying check for velocity points in x-direction (Hm,n
< 0.5δ ) and flooding check for
U
velocity points in x-direction (Hm,n
> δ ). These checks are based on the water level of
the previous half time step.
U
3 Drying check for velocity points in x-direction (Hm,n
< 0.5δ ) during iterative solution for
new water level.
ζ
4 Drying check (negative volumes) for water level points (Hm,n
< 0.0).

In the second stage of the ADI-method, the directions are interchanged.
The threshold δ is specified by you at input. The total water depth at velocity points is com-

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puted according to either Equation (10.63) or Equation (10.64), corresponding to the average
and the upwind approach, respectively. Default the average approximation is used in the
σ -model and the upwind approach is always used in the Z -model.
Remark:
Near hydraulic structures: (discharge points, weirs and barriers) always upwinding
Equation (10.64) is applied, independent of the marginal depth DCO.
The total water depth in water level points depends on the way in which the bottom depth is
computed. Four options are available (see section 10.8.1).
In step four of the drying and flooding algorithm in Delft3D-FLOW, a check at each water level
point is carried out to avoid negative volumes.

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A smooth flooding behaviour is obtained if the simulation is initialised at high water, with
the initial water level at the expected maximum level. In that case the water layer (retention
volume) at dry points is initialised by the drying flooding algorithm. If a simulation is not
started at high water, the water levels at dry points are initially set at the bottom depth. The
thickness of the water layer is zero. If the computational cell is flooded, the water layer may be
very thin and cause problems in combination with online salt transport or off-line water quality
simulations. In Delft3D-FLOW the computational part is protected against “dividing by zero”
by assuming that the total water depth is at least 1 centimetre.
You may define in velocity points so-called weirs or spillways. Weirs are hydraulic structures
causing energy losses, see section 10.9. For a 2D weir the height of the crest, HKRU, is taken
into account in the drying and flooding algorithm.
The drying check for a 2D weir point at a U -point is given by:

U
Hm,n
< 21 δ ∧ max(ζm−1,n , ζm,n ) + HKRUm,n < 12 δ,

(10.67)

and flooding the flooding check:

U
Hm,n
> δ ∧ max(ζm−1,n , ζm,n ) + HKRUm,n > δ.

(10.68)

The weir acts as a thin dam for water levels lower than the crest height.
10.9

Hydraulic structures

In a Delft3D-FLOW model, so-called hydraulic structures can be defined to model the effect of
obstructions in the flow which can not be resolved on the horizontal grid (sub-grid) or where
the flow is locally non-hydrostatic. Examples of hydraulic structures in civil engineering are:
gates, sills, sluices, barriers, porous plates, bridges, groynes, weirs. A hydraulic structure
generates a loss of energy apart from the loss by bottom friction. At hydraulic structure points,
an additional force term is added to the momentum equation, to parameterise the extra loss
of energy. The term has the form of a friction term with a contraction or discharge coefficient.
In this section, the mathematical formulations and implementation of the hydraulic structures
available in Delft3D-FLOW will be described in more detail. The hydraulic structures are
divided into three basic types:

hydraulic structures with quadratic friction,
hydraulic structures with linear friction and
floating structure.

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Figure 10.17: Example of a 3D Gate (vertical cross-section)

The flow condition at hydraulic structures may be supercritical. For supercritical flow, the
downstream water level has no influence on the flow rate. The energy loss formulations
presently available in Delft3D-FLOW assume subcritical flow. Only for the hydraulic structures
of the types 2D weir and culvert also the supercritical flow rate is computed accurately.

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All hydraulic structures except for culverts are located on the interface between two computational cells. Around a hydraulic structure, there will be large horizontal gradients in the water
level, the velocity field and in the concentrations. In order to prevent unphysical oscillations in
the velocities and concentrations upstream of hydraulic structure points the user can switch
(option) the discretisation of the advective terms at such points to an upwind approximation.
For the momentum equations, the following energy preserving upwind discretization of advection is applied:

∂U
U
∂x

m,n,k

1 ∂U 2
=
2 ∂x

(

m,n,k

2
2
Um,n,k
−Um−1,n,k
,
2∆x
2
2
Um+1,n,k
−Um,n,k
,
2∆x

Um,n,k > 0,

(10.69)

Um,n,k < 0.

For the transport equation, locally a first order upwind scheme is used by default.
Culverts have been implemented as two coupled discharge locations (one inlet and one outlet) which may be located in different parts of the computational grid. Culverts with a user
defined discharge relation (type ‘u’) can be used to implement (non-local) discharge formulations representative of other kinds of structures, see section B.3.4.6.
10.9.1

3D Gate

A 3D gate is in fact a thin dam with a limited height/depth (and positioned in the vertical).
A gate may be used to model a vertical constriction of the horizontal flow such as barriers,
sluices and Current deflection walls. The vertical constriction of the flow may vary in time by
the lowering or raising of the gate.
A 3D gate is located at a velocity point and its width is assumed to be zero, so it has no
influence on the water volume in the model area. The flow at all intermediate layers of the
gate is set to zero. The layer near the top and the layer near the bottom of the gate may be
partially blocked. Upstream of the structure the flow is accelerated due to contraction and
downstream the flow is decelerated due to expansion.
For 3D gates not only the begin and end co-ordinates of its horizontal position, but also its
vertical position can be specified. This means that some of the layers can be represented as
vertical thin dams. In the σ -model the position of the 3D-gate can be:

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Figure 10.18: Computational layer partially blocked at bottom of gate

“fixed” in the computational grid (and moving with the water level in the Cartesian coordinate system),

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“fixed” in the Cartesian co-ordinate system (and moving through the σ -grid),
moving in the Cartesian co-ordinate system by lowering or raising of the gate (3D barrier).
For the latter two cases, a layer may be partially blocked near the top or the bottom of the gate,
see Figure 10.18. The wet cross section of that computational layer is reduced. The reduction
factors are computed on basis of the vertical position of the gate and the time-dependent
vertical σ -grid.
For more details on the data input requirements for the different type of 3D gates we refer to
section B.3.1.
10.9.2

Quadratic friction

The steady-state subcritical flow rate Q through a hydraulic structure is related to the difference between the upstream and downstream water levels:

p
Q = µA 2g |ζu − ζd |,

(10.70)

with µ the contraction coefficient (0 < µ ≤ 1), the wet flow-through area and and the
upstream and downstream water level, respectively. The contraction coefficient in the socalled Q-H relation is dependent on the kind of hydraulic structure. We assume that the
hydraulic structure is “sub-grid”, and that there is a local equilibrium between the force on the
flow due to the obstruction and the local water level gradient. The Q-H relation may be used
to determine the coefficient closs−U in the quadratic friction term of the momentum equation,
to model the effect of the hydraulic structure. For a Q-H relation at a U -velocity point:

~ m,n
Um,n U
ζu − ζd
Q2
g
= 2 2
= closs−U
,
∆x
2µ A ∆x
∆x

(10.71)

The resistance coefficient closs−U need to be specified by the user at input.
For the following types of hydraulic structures, a quadratic formulation for the energy loss is
implemented in Delft3D-FLOW:

barrier
bridge
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Barrier
In Delft3D-FLOW, the hydraulic structure barrier is the combination of a movable gate and a
quadratic friction term. It can be used in 2D and 3D models. In 3D models the model depth
at the barrier point should be decreased to the sill depth for appropriate modelling of salt
transport.

A barrier is located at a velocity point. For a 3D barrier, some of the layers are closed dependent on the gate height. The barrier is “sub-grid” and has no influence on the water volume in
the model area. Upstream of a barrier the flow is accelerated due to contraction and downstream the flow is decelerated due to expansion. The expansion introduces a water level jump
between the upstream and downstream water level, which is independent of the grid size. The
energy loss for a barrier is taken into account by adding an extra quadratic friction term to the
momentum equations Equation (10.71). The appropriate energy loss coefficient should be
specified for each barrier by the user, dependent on the local discharge relation, see Equation (10.71). The quadratic friction is added to the momentum equations for all layers which
are open.

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10.9.2.1

Current Deflection Wall
2D weir
local weir
porous plate
culvert

The discharge relation presently available at barrier points in Delft3D-FLOW assumes subcritical free surface flow. The depth-averaged flow-rate through a barrier is given by:

p
Q = µA 2g |ζu − ζd |,

(10.72)

with µ the barrier contraction coefficient (0 < µ ≤ 1). The contraction coefficient should
be obtained from laboratory or field measurements. The contraction coefficient is used to
determine the equivalent energy loss coefficient closs−u in Equation (9.269) or closs−v in
Equation (9.270) depending on the U/V-direction of the barrier. Based on a depth-averaged
analysis, the energy loss coefficient closs is related to the barrier contraction coefficient µ as:

closs =

1
.
2µ2

(10.73)

The user specifies either the energy loss coefficient closs directly (barrier loss type ‘a’) or the
coefficients α and β (barrier loss type ‘b’) with which the energy loss coefficient is computed
using:

closs

1
=
2

1
−p
α + βp

(10.74)

where p is the ratio of barrier opening height over total water depth at barrier (p = 0 if barrier
is fully closed, p = 1 if barrier is completely open). The value of β is typically equal to 1 − α
such that energy loss coefficient closs becomes zero for a completely open gate. Energy
losses due to barrier constrictions under fully open conditions may be schematised by means
of a pair of porous plates immediately upstream and downstream of the barrier.
For a 3D barrier, part of the energy loss is computed directly by the discretisation of the convection terms in the momentum equations and the bottom friction term. The loss coefficient
closs should be used for calibration. Between the gate and the sill we assume a uniform velocity profile. For a partial open layer k , see Figure 10.18, with reduced thickness hk the loss
coefficient is increased proportionally to the square of the layer blockage factor.

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Furthermore, free slip boundary conditions has been implemented at the transition from an
open layer to a closed layer (representing the bottom side of the gate):

∂U
∂z

(10.75)

gate
z=Zbottom

gate

with Zbottom the vertical position of the bottom of the gate.
10.9.2.2

Bridge
The flow resistance due to a jetty or a bridge is dependent on the blocking of the flow by the
piers (Farraday and Charlton, 1983). For a row of piles perpendicular to the U -direction the
energy loss coefficient closs−u perpendicular to the flow is given by (and has to be specified):

with:

Atot
Aef f

2
,

(10.76)

total cross sectional area (Atot = ζ∆y ).
effective wet cross sectional area (Atot minus the area blocked by piles: Aef f =
Atot − ζN dpile ).
the drag coefficient of a pier (pile) (1.0 for a smooth cylindrical pile).
the diameter of a pile.
the number of piles in the grid cell.

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Atot
Aef f

closs−u

N Cdrag dpile
=
2∆y

Cdrag
dpile
N

At a bridge point the quadratic friction term is added to the momentum equation for all layers
which are open. Currently, you should derive the value of the loss coefficient and specify at
input (see the structure Porous plate).
10.9.2.3

Current Deflection Wall

In Delft3D-FLOW, the hydraulic structure CDW is the combination of a fixed gate and a
quadratic friction term. It can be used in 2D and 3D models.
A CDW is located at a velocity point. In 3D some of the computational layers are closed
dependent on the gate height and the upstream water level. The CDW is “sub-grid” and
has no influence on the water volume in the model area. Upstream of a CDW the flow is
accelerated due to contraction and downstream the flow is decelerated due to expansion.
The expansion introduces a water level jump between the upstream and downstream water
level, which is independent of the grid size. The energy loss for a CDW is taken into account
by adding an extra quadratic friction term to the momentum equations Equation (10.71). The
appropriate energy loss coefficient should be specified by the user, dependent on the local
discharge relation, see Equation (10.71)) or dependent on the flow resistance that you want
to induce; see Equation (10.76). The quadratic friction is added to the momentum equations
for all layers which are open.
10.9.2.4

Weir
In Delft3D-FLOW, the hydraulic structure weir is a fixed non-movable construction generating
energy losses due to constriction of the flow. They are commonly used to model sudden
changes in depth (roads, summer dikes) and groynes in simulation models of rivers.
2D Weir
The mathematical concept was developed by Wijbenga (1990). For a 2D weir the crest height

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(HKRU) is taken into account only in the drying and flooding algorithm, to determine if a
velocity point is wet or dry, see section 10.8.3.
A 2D weir is assumed to be “sub-grid”, and the total water depth in the wet cross section to
compute the discharge is still based on the bottom without crest. So the energy loss generated
by the weir is not computed directly by the convective terms in the momentum equations. The
energy loss is parameterised and added in the momentum equation as follows:

Mξ = −

gH∆Eweir
∆x

(10.77)

The flow condition at a local weir may be sub- or supercritical. For supercritical flow the discharge at the weir is completely determined by the energy head upstream and the discharge
is limited by:

Qsuper
with

2
= ∆y Eup
3

2
gEup
3

Eup = ζup + HKRUi+ 1 ,j +
2

(10.78)

(Uup )2
(Uweir )2
= ζweir + HKRUi+ 1 ,j +
= (10.79)
2
2g
2g

The flow condition depends on the water level downstream and the discharge rate.
The flow at the weir crest is supercritical if:

2
ζdown + HKRU ≤ Eup
3

Q ≥ Qsuper

(10.80)

For supercritical flow, the difference between the energy head upstream and downstream of
the weir should be equal to the energy loss caused by the weir.

∆Eweir = Eup − Edown

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(10.81)

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with

Edown

(Udown )2
= ζdown +
2g

(10.82)

In the momentum equation, the energy loss term is used to control the discharge at the
theoretical supercritical discharge rate Equation (10.78).

Uweir =

Qweir
∆y (ζup + HKRU )

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The energy loss following Carnot is given by:

∆ECar =

with

For sub-critical flow conditions, the energy loss ∆Eweir is based on experimental data “Tabellenboek van Rijkswaterstaat” (Vermaas, 1987) ∆Etable and/or the formula of Carnot ∆ECar .
This depends on the flow velocity Uweir at the weir crest, This velocity is derived from the
discharge upstream and the crest height, assuming conservation of energy for the flow contraction.

Udown =

(Uweir − Udown )2
2g

Qweir
∆y (ζdown + HKRU + dsill )

(10.83)

(10.84)

(10.85)

If the flow velocity at the weir crest is less than 0.25 m/s the energy loss is calculated according
to ∆ECar , when the velocity is between 0.25 m/s and 0.5 m/s, a weighted average is used
between ∆ECar and ∆Etable , if the velocity is more than 0.5 m/s, ∆Etable is used.
The energy loss is assumed to be normal to the obstruction and for a U -weir it is added to the
momentum equation as follows
n+1/2

g∆E n Ui+1/2,j
∂U
+ ... = ... −
n
∂t
∆xUi+1/2,j

(10.86)

∆E n = (1 − θ) ∆E n + θ∆E n−1/2

(10.87)

where the velocity in the denominator of the first term is replaced by the critical flow velocity
over the weir in case of a perfect weir. To prevent oscillations when the flow over the weir is
just below supercritical a relaxation parameter θ has been introduced which can be set to a
value between 0 and 1 by means of the ThetaW keyword. The default value is 0 meaning
no under-relaxation used for the energy loss ∆E . See section B.3.2.4 for details on the
user-input.
Local weir
In 3D models, the model depth at a weir point should be decreased for appropriate modelling
of salt transport. The crest height of a local weir is not derived from the bottom but specified at
input. The crest height (HKRU) is taken into account only in the drying and flooding algorithm,
to determine if a velocity point is wet or dry, see section 10.8.3. The total water depth in the

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wet cross-section at a local weir point is based on the crest height. For a local weir, part
of the energy loss is computed directly by the discretisation of the convection terms in the
momentum equations and the bottom friction term. The loss coefficient closs−U should be
used for calibration.
10.9.2.5

Porous plate
For a so-called porous plate the energy loss coefficient should be specified by the user at
input.

~ m,n
Um,n U
Mξ = −closs−U

Culvert

In Delft3D-FLOW intake/outlet couplings have been implemented. A culvert is a special intake/outlet coupling in which the discharge rate depends on the flow regime. In case of a
normal intake/outlet coupling, which is called a “power station”, the discharge rate is specified
on input.

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10.9.2.6

(10.88)

∆x

Definition of a culvert

In Delft3D-FLOW four types of culverts are distinguished:
Type
‘c’
‘d’
‘e’
‘u’

Description

One-way culvert with a “simple” discharge formulation
Two-way culvert with a “more generalized” discharge formulation
One-way culvert with a “more generalized” discharge formulation
Two-way culvert/structure with user-defined discharge formulation

Culvert of type ‘c’

For a culvert of type ‘c’, which corresponds to a completely submerged culvert, the discharge
rate through the culvert (in [m3 /s]) is computed by the Delft3D-FLOW program, according to

p
Q = µA 2g max(0, ζintake − ζoutlet )

(10.89)

with µ the culvert loss coefficient (dimensionless), A the area (in m2 ) of the culvert opening
and ζintake and ζoutlet the water levels at the intake and outlet, respectively.
Culvert of type ‘d’ or ‘e’
It is known that Equation (10.89) does not perform satisfactorily in all flow conditions. In
particular, this is the case when the downstream water level is below the so-called critical
depth. Therefore, a more general formulation for the computation of the discharge through
the culvert is available. Six flow classifications are distinguished, with different discharge
relations for each type. The classification was taken from French et al. (1987), (page 368).
However, more generalized formulations were proposed by WL Borgerhout for the culvert loss
coefficient and have been encorporated.
Let us first introduce some notation:

ζu = max(0, ζintake − zculvert ) and ζd = max(0, ζoutlet − zculvert )
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in which zculvert is the vertical position of the bottom of the culvert relative to the reference
level (positive upwards). Furthermore, the critical depth is defined by

s
Hc =

Q2
gW 2

(10.91)

with W the width (in [m]) of the culvert.

To consider six flow classifications and their discharge charateristics some variables are defined. L is the length of the culvert, n the Manning’s coefficient (in [m1/3 /s]) representing
the energy loss due to the culvert and a discharge coefficient that is prescribed by the user
(c1D , c2D and c3D ), in which the superscript represents the type(s) of flow condition. Furthermore, S0 is the slope of the culvert, Sc is the so-called critical slope, u is the velocity through
the culvert and α is the so-called energy loss correction coefficient, which has to be specified
by the user as well. This coefficient represents all energy losses due to a culvert that are not
part of the other terms in the discharge relations.

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The six flow classifications and their discharge characteristics read:

Type 1 (supercritical flow with critical depth at intake; steep culvert slope)

Q = µHc W

p
2g(ζu − Hc ) with µ = c1D

(10.92)

Type 2 (supercritical flow with critical depth at outfall; mild culvert slope)

p
Q = µ(H ∗ )Hc W 2g(ζu − Hc ) with H ∗ = 0.5Hc + 0.5ζu
s

2
2gLn2
Hc
H ∗W
∗
1
∗
1 2
µ(H ) = cD / 1 +
+
α
(c
)
and
R
=
D
(R∗ )4/3
H∗
2H ∗ + W
(10.93)

Type 3 (tranquil flow):

p
Q = µ(H ∗ )ζd W 2g(ζintake − ζoutlet ) with H ∗ = 0.5ζu + 0.5ζd
s

2
2gLn2
ζd
H ∗W
2
∗
1
∗
1
µ(H ) = cD / 1 +
+
α
(c
)
and
R
=
D
(R∗ )4/3
H∗
2H ∗ + W
(10.94)

Type 4 (submerged flow)

Q = µ(H ∗ )HW

2g(ζintake − ζoutlet ) with H ∗ = H
s

2gLn2
H ∗W
∗
2
∗
2 2
+
α
(c
)
and
R
=
µ(H ) = cD / 1 +
D
(R∗ )4/3
2H ∗ + 2W

(10.95)

Type 5 (rapid flow at inlet)

Q = µ(H ∗ )HW
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2gζu with µ(H ∗ ) = c3D and H ∗ = H

(10.96)

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Type 6 (full flow free outlet)

p
2g(ζu − H) with H ∗ = H
s

2gLn2
HW
2
∗
2
µ(H ) = cD / 1 +
+ α (c2D ) and R∗ =
∗
4/3
(R )
2H + 2W

Q = µ(H ∗ )HW

(10.97)

From Eqs. (10.92) to (10.97) it can be seen that three different discharge coefficients are used,
namely

c1D : flow classification type 1, 2 and 3
c2D : flow classification types 4 and 6
c3D : flow classification type 5
In the table below the conditions are listed for these six flow regimes.
Type

Conditions

1
2
3
4
5
6

ζu

ζd

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Flow regime
supercritical flow with critical depth at
intake
supercritical flow with critical depth at
outlet
tranquil flow
submerged flow
rapid flow at inlet
full flow free outlet

other

< 1.5H

≤H

≤ Hc

So > Sc

< 1.5H

≤H

≤ Hc

So ≤ Sc

< 1.5H
>H
≥ 1.5H
≥ 1.5H

≤H
>H
≤H
≤H

> Hc

≤ Hc
≥ Hc

Remarks:
From this table it can be verified that all possible flow conditions can occur. Either,
(types 5 or 6), or (types 1, 2 or 3). If none of these flow conditions are satisfied, then
(type 4).
Flow type 1 corresponds to culverts with a steep slope, whereas flow type 2 represents a
mild culvert slope. Since the culvert implementation applied in Delft3D-FLOW is based
on strict horizontal culverts, only flow type 2 can occur and not flow type 1.
The formulations are more or less identical to the ones applied in SOBEK-RURAL of
Deltares. The differences are in the computation of the culvert loss coefficient µ.
Difference between culvert type ‘d’ and ‘e’

In the previous text it is described how the discharge through a culvert is computed. For a
one-way culvert (type ‘e’) the discharge is always from the intake location to the outlet location.
If the water level at the outlet location is higher than at the intake, then there is no flow through
the culvert. In case of a two-way culvert (type ‘d’) the location with the highest water level
(thus, either intake or outlet location) is considered as the intake location. This means that for
a two-way culvert flow through the culvert in two-directions is possible.
We note that culvert types ‘c’ and ‘e’ are comparable. Only the computation of the discharge
through the culvert differs, see Equation (10.89) versus Eqs. (10.92) to (10.97).

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Culvert of type ‘u’
The discharge Q through a culvert of type ‘u’ is determined by a subroutine that you provide
yourself. The discharge can be based on the water levels at both ends of the culvert. You can
use this routine to reproduce the formulations for culverts of types ‘c’, ‘d’ and ‘e’ and variations
thereof, or you can implement a discharge functions that is valid for some completely different
structure. This culvert type can be used to implement a variety of structures resulting in pointto-point fluxes (either uniform over the water depth or at specific heights). An example routine
is given in section B.3.8.
10.9.3

Linear friction
Rigid sheet

Mξ = −closs−U

Um,n
∆x

Floating structure

(10.98)

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10.9.4

For a so-called rigid sheet, the resistance force is assumed to be linearly dependent on the
flow. The resistance coefficient, closs−U , can be specified by the user at input.

Floating structures can be modelled. Via an external file the depth of the floating structure has
to be specified. A floating structure is simulated by assuming a local pressure that pushes the
water to a depth specified by the key word Filfls. See section B.3.6 for details of the data
input requirements.
In combination with a floating structure, an artificial compression coefficient may be specified.
Then, the time derivative in the continuity equation Equation (9.9) is multiplied by the artificial
compression coefficient α, (keyword Riglid in the input) yielding:

p
p
∂ (d + ζ) u Gηη
∂ (d + ζ) v Gξξ
1
1
∂ζ
+p p
+p p
+
α
∂t
∂ξ
∂η
Gξξ Gηη
Gξξ Gηη
∂ω
+
= H (qin − qout ) . (10.99)
∂σ

10.10

Artificial vertical mixing due to σ co-ordinates

The σ -transformation is boundary-fitted in the vertical. The bottom boundary and free surface
are represented smoothly. The water column is divided into the same number of layers independent of the water depth. In a σ -model, the vertical resolution increases automatically in
shallow areas.
For steep bottom slopes combined with vertical stratification, σ -transformed grids introduce
numerical problems for the accurate approximation of horizontal gradients both in the baroclinic pressure term and in the horizontal diffusion term. Due to truncation errors artificial
vertical mixing and artificial flow may occur, Leendertse (1990) and Stelling and Van Kester
(1994). This artificial vertical transport is sometimes called “creep”.
Let ζ be the position of the free surface, d the depth measured downward positive and H
the total water depth. If we consider the transformation from Cartesian co-ordinates to σ
co-ordinates, defined by:

x = x∗ , y = y ∗ , σ =

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,
H

(10.100)

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(a) Hydrostatic consistent grid cell

(b) Hydrostatic inconsistent grid cell

the horizontal pressure gradient reads:

Figure 10.19: Example of a hydrostatic consistent and inconsistent grid;
∂H
(a) Hδσ > σ ∂H
∂x δx, (b) Hδσ < σ ∂x δx

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∂p
∂p∗ ∂x∗ ∂p∗ ∂σ
∂p∗
1 ∂ζ
∂H ∂p∗
=
+
=
−
+σ
.
∂x
∂x∗ ∂x
∂σ ∂x
∂x∗ H ∂x
∂x ∂σ

(10.101)

In case of vertical stratification near steep bottom slopes, small pressure gradients at the
left-hand side may be the sum of relatively large terms with opposite sign at the right-hand
side. Small truncation errors in the approximation of both terms result in a relatively large
error in the pressure gradient. This artificial forcing produces artificial flow. The truncation
errors depend on the grid sizes ∆x and ∆z . Observations of this kind has led to the notion
of “hydrostatic consistency”, see also Figure 10.19. In the notation used by Haney (1991) this
consistency relation is given by:

σ ∂H
∂σ
<
.
H ∂x
∂x

(10.102)

From this equation, it can be seen that by increasing the number of σ -levels the consistency
condition will eventually be violated.
Similarly, for the horizontal diffusion term, the transformation from Cartesian co-ordinates to
σ co-ordinates leads to various cross derivatives. For example, the transformation of a simple
second order derivative leads to:

∂ 2c
∂ 2 c∗
=
+
∂x2
∂x∗2

∂σ
∂x

−

∂ 2 c∗
∂σ
∂ 2 c∗
∂ 2 σ ∂c∗
+
2
−
+
−
.
∂σ 2
∂x ∂x∗ ∂σ ∂x2
∂σ

(10.103)

For such a combination of terms it is difficult to find a numerical approximation that is stable
and positive, see Huang and Spaulding (1996). Near steep bottom slopes or near tidal flats
where the total depth becomes very small, truncations errors in the approximation of the
horizontal diffusive fluxes in σ -co-ordinates are likely to become very large, similar to the
horizontal pressure gradient.
In Delft3D-FLOW the stress tensor is redefined in the σ co-ordinate system assuming that the
horizontal length scale is much larger than the water depth (Blumberg and Mellor, 1985) and
that the flow is of boundary-layer type. The horizontal gradients are taken along σ -planes.

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Figure 10.20: Finite Volume for diffusive fluxes and pressure gradients

This approach guarantees a positive definite operator, also on the numerical grid (Beckers
et al., 1998). For a detailed description we refer to chapter 9.
If the same approach is used for the horizontal diffusion operator in the transport equation:

∂ 2 c∗
∂ 2c
≈
,
∂x2
∂x∗2

(10.104)

Horizontal diffusion will lead to vertical transport of matter through vertical stratification interfaces (pycnocline) which is unphysical. A more accurate, strict horizontal discretization is
needed.
In Delft3D-FLOW an option is available that minimises artificial vertical diffusion and artificial
flow due to truncation errors; see section 4.5.8 option Correction for sigma-co-ordinates. A
method has been implemented which gives a consistent, stable and monotonic approximation
of both the horizontal pressure gradient and the horizontal diffusion term, even when the
hydrostatic consistency condition Eq. is not fulfilled. This “anti-creep” option is based upon
a Finite Volume approach; see Figure 10.20. The horizontal diffusive fluxes and baroclinic
pressure gradients are approximated in Cartesian co-ordinates by defining rectangular finite
volumes around the σ -co-ordinate grid points. Since these boxes are not nicely connected
to each other, see Figure 10.21, an interpolation in z co-ordinates is required to compute the
fluxes at the interfaces.
Since the centres of the finite volumes on the left-hand side and right-hand side of a vertical
interval are not at the same vertical level, a z -interpolation of the scalar concentration c is
needed to compute strictly horizontal derivatives. The values obtained from this interpolation
are indicated by c∗1 and c∗2 respectively in Figure 10.21. Stelling and Van Kester (1994) apply
a non-linear filter to combine the two consistent approximations of the horizontal gradient,

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Figure 10.21: Left and right approximation of a strict horizontal gradient

s1 = (c∗2 − c1 )/∆x and s2 = (c2 − c∗1 )/∆x:
If s1 × s2 < 0 Then
∆c
∆x

Else

∆c
∆x

(10.105)

= sign (s1 ) × min (|s1 | , |s2 |)

Endif

If an interval has only grid boxes at one side, the derivative is directly set to zero. The horizontal fluxes are summed for each control volume to compute the diffusive transport. The
integration of the horizontal diffusion term is explicit with time step limitation:

1
∆t ≤
DH

1
1
+
2
∆x
∆y 2

−1

(10.106)

The derivatives are used in the integral for the baroclinic pressure force in the momentum
equation:

1
Px (x, z) =
ρ0

∂ρ (x, s)
ds.
∂x

(10.107)

Originally, this approach was implemented in Delft3D-FLOW. Slørdal (1997) stated that the
above approximation may sometimes produce errors of the same sign which leads to a systematic underestimation of the baroclinic pressure term. This underestimation can be ascribed
to the non-linear filter, which selects the minimum of the two gradients under consideration.
This limiter is fully analogous to the min-mod limiter used for the construction of monotone
advection schemes (Hirsch, 1990). Since the same approximation of the horizontal gradient
is used for the horizontal diffusion flux, it is important to ensure that the difference operator
is positive definite in order to get physically realistic solutions. The maximum and minimum
of a variable being transported by diffusion do not increase or decrease (min-max principle).

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By taking the minimum of the gradients, Stelling and Van Kester (1994) show that, the minmax principle is fulfilled. Beckers et al. (1998) show that any nine-point consistent linear discretization of the horizontal diffusion on the σ -grid does not fulfil the min-max principle. From
numerical tests Slørdal (1997) concluded that the underestimation is reduced by increasing
the vertical resolution, but is sometimes enhanced by increasing the horizontal resolution.

Let s4 be a consistent approximation of the horizontal gradient s4 = (s1 + s2 )/2. Slørdal
(1997) suggested to take s4 as approximation of the horizontal gradient. He calls his approach
the “modified Stelling and Van Kester scheme”. It is equivalent to linear interpolation at a
certain z -level before taking the gradient. It is more accurate than taking the minimum of
the absolute value of the two slopes s1 and s2 but it does not fulfil the min-max principle
for the diffusion operator. It may introduce wiggles and a small persistent artificial vertical
diffusion (except for linear vertical density distributions). Due to the related artificial mixing,
stratification may disappear entirely for long term simulations, unless the flow is dominated by
the open boundary conditions.

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By introducing an additional approximation of the horizontal gradient in the filter algorithm
defined by s3 = (c2 − c1 )/∆x, the stringent conditions of the minimum operator can be relaxed somewhat. The drawback of underestimation of the baroclinic pressure force reported
by Slørdal (1997) can be minimised without loosing that the method fulfils the min-max principle. This third gradient s3 , which is consistent for min (|s1 | , |s2 |) < s3 < max (|s1 | , |s2 |),
has point-to-point transfer properties and therefore leads to a positive scheme for sufficiently
small time steps. The following non-linear approach presently available in Delft3D-FLOW is
both consistent and assures the min-max principle:

If s1 × s2 < 0 Then
∆c
∆x

∆c
∆x

= s4

∆c
∆x

= s3

Elseif |s4 | < |s3 | Then

Elseif min (|s1 | , |s2 |) < |s3 | < max (|s1 | , |s2 |) Then

(10.108)

Else

∆c
∆x

= sign (s1 ) min (|s1 | , |s2 |)

Endif

The method requires a binary search to find the indices of neighbouring grid boxes, which is
time consuming. The increase in computation time is about 30%.
If the streamlines are strictly horizontal, transport of matter discretised on a σ co-ordinate
grid may still generate some numerical vertical diffusion by the discretisation of the advection
terms.
10.11

Smoothing parameter boundary conditions
The solution of the shallow water equations is uniquely determined by a set of initial and
boundary conditions. The boundary conditions represent the external forcing and determine
the steady state solution. The deviation between the initial condition and the steady state
solution generates a transient (mass spring system analogy).
In Delft3D-FLOW the initial conditions for the water level and velocities are obtained from:

The results of a previous run (warm start).
User-prescribed (space varying or uniform) input fields (cold start).

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1.5

0.5

-0.5

-1.5

-2

water levels
-2.5
50000

100000

150000

200000

250000

300000

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-1

350000

400000

Figure 10.22: Cold start with damping of eigen oscillations due to bottom friction

The initial values are usually inconsistent with the boundary conditions at the start time of the
simulation. This will generate a transient solution consisting of waves with eigen frequencies
of the model domain. These waves may be reflected at the boundaries and generate a standing wave system. The waves should be dissipated completely by bottom friction and viscosity
terms or leave the domain through the open boundaries, see Figure 10.22. The damping of
the transient solution determines the spin-up time of the numerical model.
To reduce the amplitude of the transient wave and the spin-up time of a model, Delft3DFLOW has an option to switch on the boundary forcing gradually by use of a smoothing period
(parameter Tsmo ). The boundary forcing is given by:

Fbsmo (t) = (1 − α)Fb (t) + αFi (t) ,
with:

Tsmo −t

α=
and:

Tsmo

t < Tsmo ,
t ≥ Tsmo ,

(10.109)

(10.110)

Fi (t)
The initial value at the boundary.
Fb (t)
The boundary condition.
Fbsmo (t) The boundary condition after smoothing.

Smoothing is possible both for a warm and a cold start. If the initial conditions are consistent
with the boundary conditions at the start time of the simulation then the smoothing time should
be set to zero.
10.12

Assumptions and restrictions
The solution of the discretized equations is just an approximation of the exact solution. The
accuracy of the solution depends not only on the numerical scheme, but also on the way in

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which the bottom topography, the geographical area, and the physical processes (turbulence,
wave-current interaction) are modelled.
The time integration method strongly influences the wave propagation when applying a large
time step. The assumption is made that, by restricting the computational time step, the free
surface waves can be propagated correctly.
The open boundaries in a numerical flow model are artificial in the sense that they are introduced to limit the computational area that is modelled. The free surface waves should pass
these boundaries completely unhindered. In the numerical model, wave reflections may occur
at the open boundaries. These reflections will be observed as spurious oscillations superimposed on the physical results. In Delft3D-FLOW, weakly reflective boundaries are available
which diminish these effects.

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The open boundary can be divided into segments (sections). The boundary conditions in
Delft3D-FLOW are specified for these segments, two values per segment are required, one for
each segment end. The boundary condition at internal points within this segment is obtained
by linearly interpolation between the end points. Therefore, if the phase variation of the tidal
forcing along an open boundary segment is non-linear then the number of open boundary
segments should be increased so that the phases at all the segments can be specified. Phase
errors may generate an artificial re-circulation flow (eddy) near the open boundary. For steadystate simulations, a similar effect may be observed near the open boundaries if the effect of
the Coriolis force on the water level gradient along the open boundary is not taken into account
in the boundary conditions.
Care must be taken when time-series of measurements are directly prescribed as forcing
functions at the open boundaries. Measurements often contain a lot of undesired noise, due
to meteorological or other effects. For tidal flow computations, calibration on processed field
data obtained from a tidal analysis or Fourier analysis, avoids this problem.

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11 Sediment transport and morphology
11.1
11.1.1

General formulations
Introduction

11.1.2

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The sediment transport and morphology module supports both bedload and suspended load
transport of non-cohesive sediments and suspended load of cohesive sediments. For schematisation we distinguish “mud” (cohesive suspended load transport), “sand” (non-cohesive bedload and suspended load transport) and “bedload” (non-cohesive bedload only or total load
transport) fractions. A model may contain a mixture of up to 99 suspended (i.e. “sand” and
“mud”) fraction and an arbitrary amount of “bedload” fractions if computer memory and simulation time allows. The only difference between “bedload” and “sand” fractions lies in the fact
that the suspended load advection-diffusion equation is not solved for the “bedload” fraction.
If the suspended load is known to be negligible (either due to sediment diameter or sediment
transport formula chosen), the “bedload” approach is more efficient. Sediment interactions
are taken into account although especially in the field of sand-mud interactions still a couple
of processes are lacking.
Suspended transport

Three-dimensional transport of suspended sediment is calculated by solving the three-dimensional
advection-diffusion (mass-balance) equation for the suspended sediment:
(`)

(`)

(`)
∂ w − ws c(`)

∂c
∂uc
∂vc
+
+
+
+
∂t
∂x
∂y
∂z

(`)
(`)
(`)
∂
∂
∂
(`) ∂c
(`) ∂c
(`) ∂c
ε
−
ε
−
εs,z
= 0, (11.1)
−
∂x s,x ∂x
∂y s,y ∂y
∂z
∂z

where:

c(`)
u, v and w
(`)
(`)
(`)
εs,x , εs,y and εs,z
(`)
ws

mass concentration of sediment fraction (`) [kg/m3 ]
flow velocity components [m/s]
eddy diffusivities of sediment fraction (`) [m2 /s]
(hindered) sediment settling velocity of sediment fraction (`) [m/s]

The local flow velocities and eddy diffusivities are based on the results of the hydrodynamic
computations. Computationally, the three-dimensional transport of sediment is computed in
exactly the same way as the transport of any other conservative constituent, such as salinity,
heat, and constituents. There are, however, a number of important differences between sediment and other constituents, for example, the exchange of sediment between the bed and
the flow, and the settling velocity of sediment under the action of gravity. These additional
processes for sediment are obviously of critical importance. Other processes such as the
effect that sediment has on the local mixture density, and hence on turbulence damping, can
also be taken into account. In addition, if a net flux of sediment from the bed to the flow, or
vice versa, occurs then the resulting change in the bathymetry should influence subsequent
hydrodynamic calculations. The formulation of several of these processes (such as, settling
velocity, sediment deposition and pickup) are sediment-type specific, this especially applies
for sand and mud. Furthermore, the interaction of sediment fractions is important for many
processes, for instance the simultaneous presence of multiple suspended sediment fractions
has implications for the calculation of the local hindered settling velocity of any one sediment
fraction as well as for the resulting mixture density.

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The following sections describe, at a conceptual level, the differences between the suspended
transport of sediments and the transport of other conservative constituents. At the same
time we discuss some of the differences in general terms and refer for the details of the
mathematical formulations to Sections 11.2 and 11.3.

11.1.3

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Remarks:
The presence of multiple sediment fractions considerably complicates the calculation
of the density of the bed and the availability of a particular class of sediment at the
bed. See the sections on sediment interaction (Sections 11.2.4 and 11.4.3) and bed
composition models (section 11.6.4).
Small negative sediment concentrations (−1 · 10−3 kg/m3 ) can be found in a computation. These negative concentrations can be suppressed by applying a horizontal
Forester filter, Sections 4.5.8 and 10.6.4. However, this can result in a substantially
larger computing time. It is suggested to accept small negative concentrations and
to apply a Forester filter only when the negative concentrations become unacceptably
large.
A vertical Forester filter applied in a sediment transport computation will not affect the
sediments. Since this filter smoothes the vertical profile and thus can have a strong
influence on the vertical mixing processes, this vertical filter has been de-activated for
sediments.
Effect of sediment on fluid density

By default Delft3D-FLOW uses the empirical relation formulated by UNESCO (1981a) to adjust the density of water in order to take into account varying temperature and salinity. For
sediment transport this relation is extended to include the density effect of sediment fractions
in the fluid mixture. This is achieved by adding (per unit volume) the mass of all sediment
fractions, and subtracting the mass of the displaced water. As a mathematical statement this
translates as:

ρmix
where:

ρw (S)
S
(`)
ρs
lsed

lsed
X

ρw (S)
(`)
S, c
= ρw (S) +
c(`) 1 − (`)
ρs
`=1

(11.2)

specific density of water with salinity concentration S [kg/m3 ]
salinity concentration [ppt]
specific density of sediment fraction (`) [kg/m3 ]
number of sediment fractions

Horizontal density gradients (now also due to differences in sediment concentrations) can
create density currents. Vertical density gradients can also have a significant effect on the
amount of vertical turbulent mixing present, as discussed below.
You can include or neglect the effect of sediment on the fluid density by setting the DENSIN
flag in the morphology input file.
Remark:
This option is included as it has been found that a secondary effect of including sediment
in the density calculations is a reduction of the flow velocity in the lower computational
layers (when compared with a standard logarithmic velocity profile) and a consequent
reduction in the computed bed shear stress. This reduction in bed shear stress is
particularly pronounced when the k -ε turbulence closure model is used, and leads to
an increase in overall flow velocity and a consequent lowering of the free surface. Our

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experience shows that this change in the free surface level (even if very slight) can lead
to calibration problems when converting an existing 2DH model to 3D if the model is
driven using water level boundary conditions. A simple method of circumventing these
problems can be achieved by setting DENSIN = .false. which has the effect of
preventing the sediment from having any effect on the density of the water/sediment
mixture.
11.1.4

Sediment settling velocity
(`)

ws(`)

ctot
1− s
Csoil

The settling velocity ws for sand and mud are strongly different in formulation; see Sections
11.2.1 and 11.3.1 for details. In high concentration mixtures, the settling velocity of a single
particle is reduced due to the presence of other particles. In order to account for this hindered
settling effect we follow Richardson and Zaki (1954) and determine the settling velocity in
a fluid-sediment mixture as a function of the sediment concentration and the non-hindered
settling fall velocity:
(`)

ws,0 .

(11.3)

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where Csoil is the reference density (input parameter), ws,0 is the ‘basic’ sediment fraction
specific settling velocity. The total mass concentration ctot
m is the sum of the mass concentrations of the sediment fractions:

ctot
m

lsed
X

c(`)
s .

(11.4)

`=1

As the fall velocity is now a function of the sediment fractions concentration, this implies that
each sediment fraction has a fall velocity which is a function of location and time.
Remark:
The process of sediment settling is computed with a first-order upwind numerical scheme.
While use of the upwind settling formulation does slightly under-predict the mass of sediment settling, the magnitude of this error has been shown to be rather small (Lesser
et al., 2000).
11.1.5

Dispersive transport

(`)

The eddy diffusivities εs,x , εs,y and εs,z depend on the flow characteristics (turbulence level,
taking into account the effect of high sediment concentrations on damping turbulent exchange
processes) and the influence of waves (due to wave induced currents and enhanced bottom
shear stresses). Delft3D-FLOW supports four so-called “turbulence closure models”:

Constant coefficient.
Algebraic eddy viscosity closure model.
k -L turbulence closure model.
k -ε turbulence closure model.

The first is a simple constant value which is specified by you. A constant eddy viscosity will
lead to parabolic vertical velocity profiles (laminar flow). The other three turbulence closure
models are based on the eddy viscosity concept of Kolmogorov (1942) and Prandtl (1945)
and offer zero, first, and second order closures for the turbulent kinetic energy (k ) and for the
mixing length (L). All three of the more advanced turbulence closure models take into account

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the effect that a vertical density gradient has on damping the amount of vertical turbulent
mixing. See section 9.5 for a full description of the available turbulence closure models.
The output of a turbulence closure model is the eddy viscosity at each layer interface; from
this the vertical sediment mixing coefficient is calculated:

ε(`)
s = βεf ,

(11.5)

where:
(`)

εs
β

vertical sediment mixing coefficient for the sediment fraction (`)
non-cohesive sediment: Van Rijn’s ‘beta’ factor or effective ‘beta’ factor.
cohesive sediment fractions and fine sand (< 150 µm): 1.0.
vertical fluid mixing coefficient calculated by the selected turbulence model.

εf

11.1.6

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Remarks:
For cohesive sediment fractions the extra turbulent mixing due to waves is not yet included in the eddy diffusivity. This is a limitation of the present implementation. See
also section 11.2.2.
For non-cohesive sediment the effect of waves is accounted for by using a modified or
effective ‘beta’ factor of Van Rijn (k -ε model) or by using a separate formula to compute
εf (algebraic or k -L) model. See also section 11.3.2.
Three-dimensional wave effects

Traditionally wave effects were only incorporated in a depth-averaged manner via a (breaking)
wave induced shear stress at the surface, a wave induced mass flux and an increased bed
shear stress. Important wave effects such as streaming in the wave boundary layer and wave
induced turbulence were not accounted for. The problem of three dimensional wave effects
has been studied by Walstra and Roelvink (2000); their main suggestions for improvement
are:
1 The wave induced mass flux is corrected with the second order Stokes drift.
2 The production of turbulent energy associated with wave breaking is incorporated by introducing an extra source term in the kinetic energy and dissipation equations of the k -ε
turbulence model.
3 The production of turbulent energy associated with dissipation in the near-bed wave boundary layer is incorporated by introducing an extra source term in the kinetic energy and
dissipation equations of the k -ε turbulence model.
4 Streaming (a wave induced current in the wave boundary layer directed in the wave propagation direction) is modelled as a time averaged shear stress.
These improvements have been implemented in Delft3D-FLOW; for full details you are referred to section 9.7. These effects are important when computing the transport of sediment
in wave and current situations; see Sections 11.2.5 and 11.3.4 for full details regarding their
effect on cohesive and non-cohesive sediments respectively.
11.1.7

Initial and boundary conditions
To solve Equation (11.1) you need to prescribe initial and boundary conditions for each suspended sediment fraction.

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11.1.7.1

Initial condition
The initial conditions for the sediment fractions are handled in exactly the same manner as
those for any other conservative constituent, i.e. you can specify:

One global initial concentration for each sediment fraction.
Space-varying initial concentrations read from a restart file generated by a previous run.
Space-varying initial concentrations read from a user-defined input file.
In these options cohesive and non-cohesive sediment fractions are treated in the same way.

Boundary conditions

For each of the model boundaries you must prescribe the boundary condition for each sediment fraction. We discuss in short the general type of conditions and refer for the details to
the sections to follow.

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11.1.7.2

In many practical applications the non-cohesive sediment concentrations adapt very rapidly to
equilibrium conditions, so in the case of a cold start where the hydrodynamic model also takes
some time to stabilise, a uniform zero concentration for the non-cohesive sediment fractions
is usually adequate.

Water surface boundary

The vertical diffusive flux through the free surface is set to zero for all conservative constituents
(except heat, which can cross this boundary). This is left unchanged for suspended sediment.

−ws(`) c(`) − ε(`)
s,z

∂c(`)
= 0,
∂z

at z = ζ

(11.6)

where z = ζ is the location of the free surface.
Bed boundary condition

The exchange of material in suspension and the bed is modelled by calculating the sediment
fluxes from the bottom computational layer to the bed, and vice versa. These fluxes are then
applied to the bottom computational layer by means of a sediment source and/or sink term in
each computational cell. The calculated fluxes are also applied to the bed in order to update
the bed level. The boundary condition at the bed is given by:

−ws(`) c(`)

−

∂c
ε(`)
s,z

(`)

∂z

= D(`) − E (`) ,

at z = zb

(11.7)

where:

D(`)
E (`)

sediment deposition rate of sediment fraction (`).
sediment erosion rate of sediment fraction (`).

The formulations of D (`) and E (`) strongly differ for cohesive and non-cohesive sediment; for
the details you are referred to Sections 11.2.3 and 11.3.4 respectively.

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Open inflow boundaries
Delft3D-FLOW requires you to specify boundary conditions for all conservative constituents at
all open inflow boundaries. When modelling in three dimensions you may choose to specify
boundary concentrations that have a uniform, linear, or step distribution over the vertical. You
may also choose to specify a “Thatcher-Harleman” return time to simulate the re-entry of
material that flowed out of the model after the flow reverses direction.

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All of these options are also available for sediment constituents, although they are probably
more appropriate for fine, cohesive sediment than for sand-sized particles. To assist with
modelling coarser material an additional option has been included. This option allows you to
specify that, at all open inflow boundaries, the flow should enter carrying all “sand” sediment
fractions at their “equilibrium” concentration profiles. This feature has been implemented as
a Neumann boundary condition, that is, zero concentration gradient at the boundary. By setting the sediment concentrations at the boundary equal to those just inside model domain, a
near-perfectly adapted flow will enter the domain and very little accretion or erosion should
be experienced near the model boundaries. This will generally be the desired situation if the
model boundaries are well chosen. This feature can be activated for sand and mud fraction separately by setting NeuBcSand (previously, EqmBc) and/or NeuBcMud to true in the
morphology input file.
Open outflow boundaries

No boundary condition is prescribed at outflow boundaries; effectively this means that the dispersive transport of sediment at the outflow boundary is neglected compared to the advective
transport.
11.2
11.2.1

Cohesive sediment

Cohesive sediment settling velocity

In salt water cohesive sediment tends to flocculate to form sediment “flocs”, with the degree
of flocculation depending on the salinity of the water. These flocs are much larger than the
individual sediment particles and settle at a faster rate. In order to model this salinity dependency you must supply two settling velocities and a maximum salinity. The first velocity, WS0,
is taken to be the settling velocity of the sediment fraction in fresh water (salinity = 0). The
second velocity, WSM, is the settling velocity of the fraction in water having a salinity equal to
SALMAX. The settling velocity of the sediment flocs is calculated as follows:
(`)

ws,0 =



(`)
 ws,max
2

w(`) ,
s,max

1−

cos( SπS
)
max

(`)

ws,f
2

cos( SπS
)
max

, when S ≤ Smax

(11.8)

when S > Smax

where:
(`)

ws,0
(`)
ws,max
(`)
ws,f
S
Smax

the (non-hindered) settling velocity of sediment fraction (`)
WSM, settling velocity of sediment fraction (`) at salinity concentration SALMAX
WS0, fresh water settling velocity of sediment fraction (`)
salinity
SALMAX, maximal salinity at which WSM is specified

Remarks:
Modelling turbulence induced flocculation or the break-up of sediment flocs is not yet
implemented.
The influence of flocculation is disregarded by setting WSM = WS0.

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11.2.2

Cohesive sediment dispersion
The vertical mixing coefficient for sediment is equal to the vertical fluid mixing coefficient
calculated by the selected turbulence closure model, i.e.:

ε(`)
s = εf ,

(11.9)

where:
(`)

εs
εf

Cohesive sediment erosion and deposition

For cohesive sediment fractions the fluxes between the water phase and the bed are calculated with the well-known Partheniades-Krone formulations (Partheniades, 1965):

(`)
E (`) = M (`) S τcw , τcr,e
,

(`)
(`)
(`) `
D = ws cb S τcw , τcr,d ,

∆ zb
(`)
(`)
cb = c
z=
,t ,
2

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11.2.3

vertical sediment mixing coefficient for sediment fraction (`)
vertical fluid mixing coefficient calculated by the selected turbulence closure
model

(11.10)
(11.11)
(11.12)

where:

E (`)
M(`)

(`)
S τcw , τcr,e

erosion flux [kg m−2 s−1 ]
user-defined erosion parameter EROUNI [kg m−2 s−1 ]
erosion step function:

(`)
τcw , τcr,e







D(`)
(`)
ws
(`)
cb

(`)
S τcw , τcr,d

(`)

− 1 , when τcw > τcr,e ,
when τcw ≤

(11.13)

(`)
τcr,e .

fall velocity (hindered) [m/s]

average sediment concentration in the near bottom computational
layer
deposition step function:

(`)
τcw , τcr,d







τcr,e
(`)
τcr,d

(`)
τcr,e

deposition flux [kg m−2 s−1 ]

τcw

1−

τcw

(`)
τcr,d

(`)

, when τcw < τcr,d ,
when τcw ≥

(11.14)

(`)
τcr,d .

maximum bed shear stress due to current and waves as calculated
by the wave-current interaction model selected by the user; see section 9.7 for full details
user-defined critical erosion shear stress TCEUNI [N/m2 ]
user-defined critical deposition shear stress TCDUNI [N/m2 ]

Remark:
Superscript (`) implies that this quantity applies to sediment fraction (`).

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The calculated erosion or deposition flux is applied to the near bottom computational cell by
setting the appropriate sink and source terms for that cell. Advection, particle settling, and
diffusion through the bottom of the near bottom computational cell are all set to zero to prevent
double counting these fluxes.
11.2.4

Interaction of sediment fractions

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The following notes hold only in case of multiple sediment fractions. The formulations given
in the previous section have been formulated for uniform cohesive sediment beds. However,
often the bed will be made up of a range of sediment types and sizes. In such cases the
erosion rate will be affected. If the bed stratigraphy is modelled in detail, it may be assumed
that the erosion rate is proportional to the availability of the sediment fraction considered
in the top-most layer of the bed stratigraphy. On the other hand if the bed stratigraphy is not
explicitly included in the model and only the overall characteristics of the local bed composition
is known, one must assume either that the bed composition is almost uniform (in which case
the erosion rate can again be assumed to be proportional to the bed composition) or that the
cohesive sediment fraction considered forms a layer that covers the other sediment fractions
(in this case the erosion rate of the cohesive sediment will not be reduced). The former
approach is nowadays the default approach for the online-morphology module, but the latter
behaviour may be activated by setting the OldMudFrac keyword tot true in the morphology
input file.
Remarks:
Assuming an erosion rate proportional to the availability of the sediment fraction considered may result in a significant underestimation of the erosion rate if the bed is modelled
as a single uniformly mixed layer (default setting) and the mud contents is low.
Assuming that the erosion rate is independent of the availability of the sediment fraction
considered will lead to an overestimation of the erosion rate. For instance, if the model
includes two equal cohesive sediment fractions their total transport rate will be double
that of the rate observed in an identical simulation carried out using the total amount of
the two sediment fractions in the former simulation.
11.2.5

Influence of waves on cohesive sediment transport

For cohesive sediment fractions the sediment mixing coefficient will still be set following Equation (11.9). This implies that the extra turbulent mixing due to waves will not be included in the
suspended sediment transport calculations (for these sediment fractions) except by way of
the enhancement of the bed shear stress caused by wave-current interaction, see section 9.7
for details. This is a limitation of the present implementation.
11.2.6

Inclusion of a fixed layer

If the thickness of the sediment layer becomes small then the erosion flux is reduced by a
factor fFIXFAC as defined in section 11.4.4. This reduction factor is related to the formulations implemented for non cohesive sediment transport (see Sections 11.3.5 and 11.4.4 for
suspended and bedload transport respectively).

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11.2.7

Inflow boundary conditions cohesive sediment

Although it is general good advice to locate the open boundaries sufficiently far away from
the area of interest, this is not always possible in long-term simulations. In such cases it is
desirable to impose some kind of equilibrium boundary conditions. The mud concentrations
are in general more loosely coupled to local morphology than the concentrations of coarser
non-cohesive sediment fractions; a unique “equilibrium” concentration (profile) does often not
exist due to differences in critical shear stresses for erosion and sedimentation. So, Delft3DFLOW allows for a different approach. For cohesive material you can specify that, at all open
inflow boundaries, the flow should enter carrying the same mud concentration as computed
in the interior of the model. This feature is enabled by setting NeuBcMud in the morphology
input file to true (Neumann boundary condition: concentration gradient perpendicular to open
boundary equal to zero). Although this option may sometimes be very useful, one must be
careful when applying it: the sediment concentration of the incoming flow may take on any
value that does not lead to significant deposition in the first grid cell.

11.3

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By setting NeuBcMud = false, the concentrations to be applied at the inflow boundaries
are read from the <∗.bcc> file, which has to be created with the FLOW User Interface. If the
parameter is set to true, the values specified in the <∗.bcc> file are overruled.
Non-cohesive sediment

For the transport of non-cohesive sediment, Van Rijn et al. (2000) approach is followed by
default. You can also specify a number of other transport formulations (see section 11.5)
11.3.1

Non-cohesive sediment settling velocity

The settling velocity of a non-cohesive (“sand”) sediment fraction is computed following the
method of Van Rijn (1993). The formulation used depends on the diameter of the sediment in
suspension:

(`)

ws,0


(`)2

(s(`) − 1)gDs


,
65 µm < Ds ≤ 100 µm



s
18ν



(`)3
10ν 
0.01(s(`) − 1)gDs
=
1+
− 1 , 100 µm < Ds ≤ 1000 µm

2

D
ν
s



q



(`)
1000 µm < Ds
1.1 (s(`) − 1)gDs ,
(11.15)

where:

s(`)
(`)
Ds
ν

(`)

relative density ρs /ρw of sediment fraction(`)

representative diameter of sediment fraction (`)
kinematic viscosity coefficient of water [m2 /s]

(`)

Ds is the representative diameter of the suspended sediment given by the user-defined sediment diameter SEDDIA (D50 of bed material) multiplied by the user-defined factor FACDSS
(`)
(see also remarks). This value of Ds will be overruled if IOPSUS=1 and the transport formula of Van Rijn (1993) has been selected, see section 11.5.1 for details.
Remark:
In the case of non-uniform bed material Van Rijn (1993) concluded that, on the basis of
(`)

measurements, Ds should be in the range of 60 to 100 % of D50 of the bed material.

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If the bed material is very widely graded (well sorted) consideration should be given to
using several sediment fractions to model its behaviour more accurately.
11.3.2

Non-cohesive sediment dispersion
The output of a turbulence closure model is the eddy viscosity at each layer interface; from
this the vertical sediment mixing coefficient is calculated using the following expressions:
Using the algebraic or k -L turbulence model
Without waves

(`)

ε(`)
s = βεf ,
where:
(`)

εs
β
(`)
εf

If the algebraic or k -L turbulence model is selected and waves are inactive then the vertical
mixing coefficient for sediment is computed from the vertical fluid mixing coefficient calculated by the selected turbulence closure model. For non-cohesive sediment the fluid mixing
coefficient is multiplied by Van Rijn’s ‘beta factor’ which is intended to describe the different
diffusivity of a fluid ‘particle’ and a sand grain. Expressed mathematically:

DR
AF

11.3.2.1

(11.16)

vertical sediment mixing coefficient for sediment fraction (`)
Van Rijn’s ‘beta’ factor for the sediment fraction (see Equation (11.24))
vertical fluid mixing coefficient calculated by the selected turbulence closure
model

Including waves

If waves are included in a simulation using the algebraic or k -L turbulence closure model
then the sediment mixing coefficient for non-cohesive sediment fractions is calculated entirely
separately from the turbulence closure model, using expressions given by Van Rijn (1993) for
both the current-related and wave-related vertical turbulent mixing of sediment.
The current-related mixing is calculated using the ‘parabolic-constant’ distribution recommended by Van Rijn:

ε(`)
s,c
where:
(`)

εs,c
u∗,c

κβu∗,c z(1 − z/h), when z < 0.5h,
0.25κβu∗,c h,
when z ≥ 0.5h,

(11.17)

vertical sediment mixing coefficient due to currents (for this sediment fraction)
current-related bed shear velocity

In the lower half of the water column this expression should produce similar turbulent mixing
values to those produced by the algebraic turbulence closure model. The turbulent mixing in
the upper half of the water column is generally of little importance to the transport of ‘sand’
sediment fractions as sediment concentrations in the upper half of the water column are low.
The wave-related mixing is also calculated following Van Rijn (1993). In this case Van Rijn recommends a smoothed step type distribution over the vertical, with a linear transition between
the two hinge points, see Figure 11.1.

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Figure 11.1: Sediment mixing coefficient in non-breaking waves (Source: Van Rijn
(1993))

ε(`)
s,w

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The expressions used to set this distribution are:

 (`)

εs,bed = 0.004D∗ δs(`) Ûδ ,





 (`)
(`)
(`)
ε
+
ε
−
ε
s,max
s,bed
s,bed
=



0.035γbr hHs


 ε(`)
,
s,max =
Tp

(`)

when z ≤ δs ,

(`)

z − δs

0.5h −

(`)

(`)
δs

, when δs < z < 0.5h,

(11.18)

when z ≥ 0.5h,

(`)

where δs (the thickness of the near-bed sediment mixing layer) is estimated using Van Rijn’s
formulation, given by:

δs(`) = min [0.5, max {0.1, max (5γbr δw , 10γbr ks,w )}]

(11.19)

where:

δw

thickness of the wave boundary layer:

δw = 0.072Âδ

γbr

Âδ
ks,w

!−0.25

(11.20)

empirical coefficient related to wave breaking:

γbr =

ks,w

1+
1

Hs
h

0.5
− 0.4
when
when

Hs
h
Hs
h

> 0.4
≤ 0.4

(11.21)

wave-related bed roughness (as calculated for suspended sediment transport)

We calculate the total vertical sediment mixing coefficient by following Van Rijn and taking the
sum of the squares:

ε(`)
s

q
(`)2
(`)2
= εs,c + εs,w ,

(11.22)

where εs is the vertical sediment diffusion coefficient used in the suspended sediment transport calculations for this sediment fraction.

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11.3.2.2

Using the k -ε turbulence model
In the case of the k -ε turbulence closure model the vertical sediment mixing coefficient can
be calculated directly from the vertical fluid mixing coefficient calculated by the turbulence
closure model, using the following expression:
(`)

ε(`)
s = βeff εf ,

(11.23)

where:
(`)

εs
(`)
βeff

vertical sediment mixing coefficient of sediment fraction (`)
the effective Van Rijn’s ‘beta’ factor of sediment fraction (`) As the beta factor
(`)

should only be applied to the current-related mixing this is estimated as: βeff =

c
, for non-cohesive sediment fractions
1 + β (`) − 1 τwτ+τ
c
Van Rijn’s ‘beta’ factor of the sediment fraction (`), Equation (11.24)

β (`)
τc
τw
εf

bed shear stress due to currents
bed shear stress due to waves
vertical fluid mixing coefficient calculated by the k -ε turbulence closure model

DR
AF

Van Rijn’s ’beta’ factor is calculated from (Van Rijn, 1984b):
(`)

β (`) = 1 + 2

ws
u∗,c

(11.24)

(`)

Where ws is the settling velocity of the non-cohesive sediment fraction, and u∗,c is the local
bed shear stress due to currents.
This implies that the value of β (`) is space (and time) varying, however it is constant over the
depth of the flow. In addition, due to the limited knowledge of the physical processes involved,
we follow Van Rijn (1993) and limit β (`) to the range 1 < β (`) < 1.5.
Remarks:
In a wave and current situation Van Rijn (1993) applies the β -factor to only the currentrelated turbulent mixing, whereas we apply it to the total turbulent mixing calculated by
the selected turbulence closure model. However, little is known about the dependence
of the β -factor on flow conditions; this discrepancy is expected to be of little importance
in practical situations.
The k -ε turbulence closure model has been extended by Walstra et al. (2000) to include
the three-dimensional effects of waves. However the effect of wave asymmetry on the
bedload transport is not yet included.
11.3.3

Reference concentration
For non-cohesive sediment (e.g. sand), we follow the method of Van Rijn (1993) for the combined effect of waves and currents. The reference height is given by:

∆r
, 0.01h , 0.20h ,
a = min max AKSFAC · ks ,
2

(11.25)

where:

a
AksFac

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Van Rijn’s reference height
user-defined proportionality factor (morphology input file)

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KEY
Standard computational cell
Reference cell for “sand” sediment
Concentration set equal to concentration of reference layer for
‘sand’ sediment calculations
Coarse Grid

Medium Grid

Fine Grid

kmx
kmx
Layer

kmx
kmx

BED

a
BED

Figure 11.2: Selection of the kmx layer; where a is Van Rijn’s reference height

user-defined current-related effective roughness height (see options below)
wave-induced ripple height, set to a constant value of 0.025 m
water depth

DR
AF

ks
∆r
h

Remark:
Van Rijn’s reference height a is limited to a maximum of 20% of the water depth. This
precaution is only likely to come into effect in very shallow areas.
With the keyword IOPKCW you have two options to calculate ks (and kw ):

ks and kw specified by you (constant in space).
ks derived from current-related effective roughness height as determined in the Delft3DFLOW module (spatially varying) and kw = RWAVE · ∆r .
Calculation of the reference concentration

The reference concentration ca is calculated directly by the sediment transport formula or
it is derived from the suspended sediment transport rate given by the sediment transport
formula as ca = Ss /Hu . The default transport formula (Van Rijn, 1993) includes a formula
for the reference concentration (see section 11.5.1). The reference concentration is adjusted
proportional to the relative availability of the sediment fraction in the top-layer of the bed (see
section 11.6.4 on bed composition models).
Remark:
The reference concentration and therefore the suspended load can be calibrated using
the keyword Sus in the morphology input file.

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dc
Deposition Flux = wsc Erosion Flux = εs
dz
kmx
layer

∆z
a
BED

Figure 11.3: Schematic arrangement of flux bottom boundary condition

Non-cohesive sediment erosion and deposition

The transfer of sediment between the bed and the flow is modelled using sink and source
terms acting on the near-bottom layer that is entirely above Van Rijn’s reference height. This
layer is identified as the reference layer and for brevity is referred to as the kmx-layer; see
Figure 11.2.

DR
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11.3.4

The sediment concentrations in the layer(s) that lie below the kmx layer are assumed to rapidly
adjust to the same concentration as the reference layer.
Each half time-step the source and sink terms model the quantity of sediment entering the flow
due to upward diffusion from the reference level and the quantity of sediment dropping out of
the flow due to sediment settling. A sink term is solved implicitly in the advection-diffusion
equation, whereas a source term is solved explicitly. The required sink and source terms for
the kmx layer are calculated as follows.
In order to determine the required sink and source terms for the kmx layer, the concentration
and concentration gradient at the bottom of the kmx layer need to be approximated. We
assume a standard Rouse profile between the reference level a and the centre of the kmx
layer (see Figure 11.4).

c
where:

c(`)
(`)
ca
a
h
z
A(`)

(`)

c(`)
a

a(h − z)
z(h − a)

A(`)

(11.26)

concentration of sediment fraction (`)

reference concentration of sediment fraction (`)
Van Rijn’s reference height
water depth
elevation above the bed
Rouse number

As the reference concentration and the concentration in the centre of the kmx layer ckmx are
known, the exponent A(`) can be determined.

(`)

ckmx = c(`)
a

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a(h − zkmx )
zkmx (h − a)

A(`)

⇒ A(`) =
ln

ckmx
ca

a(h−zkmx )
zkmx (h−a)

(11.27)

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H e ig h t a b o v e b e d

Approximation to concentration
gradient at bottom of kmx layer

kmx

Approximation to
concentration at
bottom of kmx layer

ckmx

Rouse profile

ca ∆z

ckmxbot
BED

Concentration

The concentration at the bottom of the kmx layer is:

a(h − zkmx(bot) )
zkmx(bot) (h − a)

A(`)

DR
AF

Figure 11.4: Approximation of concentration and concentration gradient at bottom of kmx
layer

(`)
ckmx(bot)

c(`)
a

(11.28)

We express this concentration as a function of the known concentration ckmx by introducing
a correction factor α1 :
(`) (`)

(`)

ckmx(bot) = α1 ckmx

(11.29)

The concentration gradient of the Rouse profile is given by:

∂c(`)
= A(`) c(`)
a
∂z

a(h − z)
z(h − a)

A(`) −1
·

−ah
2
z (h − a)

(11.30)

The concentration gradient at the bottom of the kmx layer is:
(`)
c0 kmx(bot)

A(`) c(`)
a

a(h − zkmx(bot) )
zkmx(bot) (h − a)

A(`) −1

−ah
2
zkmx(bot) (h − a)

!
(11.31)

We express this gradient as a function of the known concentrations ca and ckmx by introducing
another correction factor α2 :
(`)

(`)

c0 kmx(bot) = α2

(`)

ckmx − ca
∆z

!
(11.32)

Erosive flux due to upward diffusion
The upward diffusion of sediment through the bottom of the kmx layer is given by the expression:

E (`) = ε(`)
s
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∂c(`)
,
∂z

(11.33)

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(`)

where εs and

∂c(`)
∂z

are evaluated at the bottom of the kmx layer.

We approximate this expression by:
(`)

(`)
α2 ε(`)
s

E (`) ≈

(`)

ca − ckmx
∆z

!
,

(11.34)

where:
(`)

α2
(`)
εs

correction factor for sediment concentration
sediment diffusion coefficient evaluated at the bottom of the kmx cell of sediment fraction(`)

(`)

ca
(`)
ckmx
∆z

reference concentration of sediment fraction(`)

DR
AF

The erosion flux is split in a source and sink term:
(`) (`) (`)

average concentration of the kmx cell of sediment fraction(`)
difference in elevation between the centre of the kmx cell and Van Rijn’s reference height: ∆z = zkmx − a

(`)

(`) (`) (`)

α ε s ca
α εs ckmx
≈ 2
− 2
.
∆z
∆z

(11.35)

The first of these terms can be evaluated explicitly and is implemented as a sediment source
term. The second can only be evaluated implicitly and is implemented as a (positive) sink
term. Thus:
(`) (`) (`)

(`)
Sourceerosion
(`)

Sinkerosion

α ε s ca
= 2
∆z
(`) (`) (`)
α εs ckmx
= 2
∆z

(11.36)
(11.37)

Deposition flux due to sediment settling

The settling of sediment through the bottom of the kmx cell is given by the expression:
(`)

D(`) = ws(`) ckmx(bot) ,
(`)

(11.38)

(`)

where ws and ckmx(bot) are evaluated at the bottom of the kmx layer.
We set:

(`)

(`) (`)

ckmx(bot) = α1 ckmx .

(11.39)

The deposition flux is approximated by:
(`) (`)

D(`) ≈ α1 ckmx ws(`) .

(11.40)

This results in a simple deposition sink term:
(`)

(`) (`)

Sinkdeposition = α1 ckmx ws(`) .
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(11.41)

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The total source and sink terms is given by:
(`)

Source(`) = α2 c(`)
a
"

(`)
εs

∆z
!

(11.42)

(`)

Sink (`) = α2

εs
∆z

(`)

+ α1 ws(`) ckmx .

(11.43)

These source and sink terms are both guaranteed to be positive.
11.3.5

Inclusion of a fixed layer

Inflow boundary conditions non-cohesive sediment

DR
AF

11.3.6

The bedload transport is reduced if the thickness of the sediment layer becomes small (see
section 11.4.4). The same effect has been implemented as a reduction for the entrainment
and deposition terms as well as the equilibrium concentration by a factor fFIXFAC if erosion is
expected to occur.

Although it is general good advice to locate the open boundaries sufficiently far away from
the area of interest, this is not always possible in long-term simulations. In such cases it
is desirable to impose some kind of equilibrium boundary conditions. Although equilibrium
boundary conditions may be better defined for non-cohesive sediments than for cohesive
sediments, we have implemented the open boundary condition in a consistent manner. For
non-cohesive suspended material you can specify that, at all open inflow boundaries, the
flow should enter carrying the same concentration of sediment as computed in the interior
of the model. This feature is enabled by setting NeuBcSand in the morphology input file to
true (Neumann boundary condition: concentration gradient perpendicular to open boundary
equal to zero). This means that the sediment load entering through the boundaries will be
near-perfectly adapted to the local flow conditions and very little accretion or erosion should
be experienced near the model boundaries. This will generally be the desired situation if
the model boundaries are well chosen. This method gives the correct results even when the
turbulent mixing profile is clearly non-parabolic.
By setting NeuBcSand = false, the concentrations to be applied at the inflow boundaries
are read from the <∗.bcc> file, which has to be created with the FLOW User Interface. If the
parameter is set to true, the values specified in the <∗.bcc> file are overruled. This parameter
used to be called EqmBc.
11.4

Bedload sediment transport of non-cohesive sediment

Bedload (or, for the simpler transport formulae, total load) transport is calculated for all “sand”
and “bedload” sediment fractions by broadly according to the following approach: first, the
magnitude and direction of the bedload transport at the cell centres is computed using the
transport formula selected (See section 11.5), subsequently the transport rates at the cell
interfaces are determined, corrected for bed-slope effect and upwind bed composition and
sediment availability.
11.4.1

Basic formulation
For simulations including waves the magnitude and direction of the bedload transport on a
horizontal bed are calculated using the transport formula selected assuming sufficient sediment and ignoring bed composition except for e.g. hiding and exposure effects on the critical

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shear stresses. The default sediment transport formula is Van Rijn (1993) as documented in
section 11.5.1.
Some of the sediment transport formulae prescribe the bedload transport direction whereas
others predict just the magnitude of the sediment transport. In the latter case the initial transport direction will be assumed to be equal to the direction of the characteristic (near-bed) flow
direction. In the case of a depth-averaged simulation, the secondary flow/spiral flow intensity
Is optionally computed by the flow module may be taken into account; the bedload transport
direction ϕτ is given by the following formula:

tan(ϕτ ) =

v − αI Uu Is
u + αI Uv Is

(11.44)

√
g
2
αI = 2 Es 1 −
κ
κC
where:

(11.45)

gravitational acceleration
Von Kármán constant
Chézy roughness
the depth-averaged velocity
coefficient to be specified by you as Espir keyword in the morphology input
file

DR
AF

g
κ
C
U
Es

in which

The default value of Es is 0, which implies that the spiral flow effect on the bedload transport
direction is not included. The spiral flow effect is of crucial importance in a depth-averaged
simulation to get pointbar formation in river bends. This effect is only included for transport
formulae that return the bedload transport rate but not its direction, i.e. Engelund & Hansen,
Meyer-Peter & Muller, General formula, Van Rijn (1984), Ashida & Michiue and optionally the
user-defined formula.
The Van Rijn (1993) formula distinguishes the following transport components that are all
treated like bed or total load, i.e. without relaxation effects of an advection diffusion equation:

bedload due to currents, Sbc
bedload due to waves, Sbw
suspended load due to waves, Ssw .

These three transport components can be calibrated independently by using the respective
keywords Bed, BedW and SusW in the morphology input file.
11.4.2

Suspended sediment correction vector
The transport of suspended sediment is computed over the entire water column (from σ = −1
to σ = 0). However, for “sand” sediment fractions, Van Rijn regards sediment transported
below the reference height a as belonging to “bedload sediment transport” which is computed
separately as it responds almost instantaneously to changing flow conditions and feels the
effects of bed slopes. In order to prevent double counting, the suspended sediment fluxes below the reference height a are derived by means of numerical integration from the suspended
transport rates. The opposite of these fluxes are scaled with the upwind sediment availability
and subsequently imposed as corrective transport. This suspended load correction is included
in the depth-averaged suspended load written to the output files of the program.

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11.4.3

Interaction of sediment fractions
The following notes hold only in case of multiple sediment fractions. Sediment fractions may
interacted in several ways:

reference concentrations, erosion rates and sediment transport rates will be reduced pro-

No hiding and exposure correction (ξ = 1)
Egiazaroff formulation

log 19
10 log 19 + 10 log (D /D )
i
m

DR
AF

ξ=

portional to the availability of sediment fraction considered in the bed (less of the fraction
available for transport)
sediment fractions of different sizes influence each other by means of hiding and exposure:
fine sediments hide among coarse sediments and are thereby partly shielded from the
main flow while the coarser sediments are more exposed than they would be among
other sediments of the same size. This effect is taken into account by increasing the
effective critical shear stress for fine sediments while lowering it for coarse sediments.
This adjustment is carried out using a multiplicative factor ξ . The following formulations
have been implemented:

(11.46)

Ashida & Michiue formulation


Dm
if Di /Dm < 0.38889
 0.8429
Di

2
10
ξ=
. (11.47)
log 19
 10
otherwise
10
log 19 + log (Di /Dm )

Parker, Klingeman & McLean or Soehngen, Kellermann & Loy formulation

ξ=

Dm
Di

(11.48)

where α is given by the ASKLHE keyword in the morphology input file.
Wu, Wang & Jia formulation

ϕ(`) =

η (i)

(`)

1−ϕ
ϕ(`)

D(i)
D(`) − D(i)

(`) m

(11.49)

(11.50)

where m is given by the MWWJHE keyword in the morphology input file.
The hiding and exposure effect has been implemented for the following transport formulae
containing a critical shear stress: Meyer-Peter & Muller, general formula, Ashida-Michiue and
optionally the user-defined formula.
11.4.4

Inclusion of a fixed layer
Inclusion of a fixed layer implies that the quantity of sediment at the bed is finite and may, if
excessive erosion occurs, become exhausted and be unavailable to supply sediment to suspended and bedload transport modes. In case the bed is covered by bedforms, the troughs of
the bedforms will start to expose the non-erodible layer before sediment runs out completely.

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This results in a gradual reduction of the transport capacity over a certain sediment thickness
indicated by THRESH. This effect is taken into account in the bedload formulations by comparing the thickness of the sediment layer available at the bed with a user-defined threshold
value. If the quantity of sediment available is less than the threshold then the magnitude of
the calculated bedload transport vector is reduced as follows:

Sb00 = fFIXFAC Sb00 ,

(11.51)

where:

fFIXFAC
DPSED
THRESH

magnitude of the bedload transport vector (before correction for bed slope effects)
DPSED
upwind fixed layer proximity factor: fFIXFAC = THRESH
, limited to the range
0 ≤ fFIXFAC ≤ 1.
depth of sediment available at the bed
user-defined erosion threshold

Sb00

DR
AF

The equilibrium suspended load concentration in the sediment pickup term is reduced by the
same fixed layer proximity factor (in this case of course the local value and not some upwind
value is used since suspended sediment pickup has no associated horizontal direction).
In effect, because of the upwind approach used to transfer the bedload transport components
to the U and V velocity points, this method limits the sediment that can leave a computational
cell, if the quantity of the sediment at the bed is limited. One implication of the use of this
rather simple approach is that a finite (although always less than the user-defined threshold)
thickness of sediment is required at the bed if a non-zero magnitude of the bedload transport
vector is required.
Remarks:
Areas may be initially specified as containing zero bottom sediment if non-erodible areas are required. It is likely that these areas will accrete a little sediment in order to
allow an equilibrium bedload transport pattern to develop.
This effect has also been included for cohesive and non cohesive suspended sediment
as indicated in Sections 11.2.6 and 11.3.5.
11.4.5

Calculation of bedload transport at open boundaries

At open boundaries the user may either prescribe the bed level development or the bedload
transport rates. In the latter case the bedload transport rates are known from the model
input, whereas in the former case the effective bedload transport rates at the boundary could
be derived from the mass balance at the open boundary point. The bed level boundary
condition is imposed at the same location where a water level boundary condition is imposed,
that is at the grid cell just outside the model domain. A consequence of this approach is
that the bed level at the first grid cell inside the model domain will not exactly behave as
you imposed, but in general it will follow the imposed behaviour closely. In case of multiple
sediment fractions, a boundary condition for the bed composition is also needed at inflow
boundaries. See Appendices B.9.2 and B.9 for imposing various morphological boundary
conditions.
11.4.6

Bedload transport at U and V velocity points
As the control volume for bed level change calculations is centred on the water level points,
see Figure 11.5, the bedload transport vector components are actually required at the U and
V velocity points, rather than at the water level points where Sb,x and Sb,y are calculated. By
default, we use a simple “upwind” numerical scheme to set the bedload transport components

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n+1
water level point
u-velocity point
v-velocity point

depth point
control volume
bedload transport

n-1

m-1

m+1

Figure 11.5: Setting of bedload transport components at velocity points

DR
AF

at the U and V points as this ensures that the bed will remain stable. For each active velocity
point the upwind direction is determined by summing the bedload transport components at the
water level points on either side of the velocity point and taking the upwind direction relative to
the resulting net transport direction. The bedload transport component at the velocity point is
then set equal to the component computed at the water level point immediately “upwind” (see
(m,n)

Figure 11.5). In the example shown in Figure 11.5 the bedload transport component Sb,uu
(m,n)

(m,n)

(m,n+1)

is set equal to Sb,x
and the component Sb,vv is set equal to Sb,y
. It is possible
to switch from upwind to central approach by setting the UpwindBedload keyword in the
morphology input file to false; although the central approach is more accurate, it is less stable
(less damping).
11.4.7

Adjustment of bedload transport for bed-slope effects

Bedload transport is affected by bed level gradients. Two bed slope directions are distinguished: the slope in the initial direction of the transport (referred to as the longitudinal bed
slope) and the slope in the direction perpendicular to that (referred to as the transverse bed
slope). The longitudinal bed slope results in a change in the sediment transport rate as given
by:

S~ 0 b = αs S~00 ,

(11.52)

or, in vector component form:
0
00
Sb,x
= αs Sb,x
,
0
00
Sb,y = αs Sb,y ,

(11.53)
(11.54)

whereas the primary effect of the transverse bed slope is a change in transport towards the
downslope direction (this may be accomplished by either a pure rotation of the transport vector or by adding a transverse transport component). You may choose one of the following
formulations for these effects.
1 no effect of bed slope on bedload transport
2 Bagnold (1966) for longitudinal slope and Ikeda (1982, 1988) as presented by Van Rijn
(1993) for transverse slope. This is the default option for the bedload transport of all
sediment transport formulae. In this case αs is given by

αs = 1 + αbs

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cos tan−1

tan (φ)

∂z
tan (φ) +
∂s

!
∂z
∂s

−1 ,

(11.55)

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where αbs is a user-defined tuning parameter, ALFABS keyword in the morphology input file (default = 1.0). An additional bedload transport vector is subsequently calculated,
perpendicular to the main bedload transport vector. The magnitude of this vector is calculated using a formulation based on the work of Ikeda (1982, 1988) as presented by Van
Rijn (1993). Van Rijn’s equation (7.2.52) is modified to Equation (11.56) by setting the reference co-ordinates s and n aligned with and perpendicular to the local characteristic flow
direction respectively. This implies that there is no flow in the n direction: i.e. ub,n = 0:

Sb,n = |Sb0 | αbn

ub,cr ∂zb
,
|~ub | ∂n

(11.56)

where:

Sb,n
|Sb0 |

|Sb0 |

additional bedload transport vector. The direction of this vector is normal to
the unadjusted bedload transport vector, in the down slope direction
magnitude of the unadjusted bedload transport vector (adjusted for longitu-

DR
AF

0
0
.
dinal bed slope only):
=
+ Sb,y
Sb,x
αbn
user-defined coefficient, ALFABN (default = 1.5)
ub,cr
critical (threshold) near-bed fluid velocity
~ub
near-bed fluid velocity vector
∂zb
bed slope in the direction normal to the unadjusted bedload transport vector
∂n
To evaluate Equation (11.56) we substitute:

ub,cr
=
|~ub |

τb,cr
,
|~τb |

(11.57)

where:

τb,cr
~τb

critical bed shear stress
bed shear stress due to current and waves: ~
τb = µc~τb,cw + µw ~τb,w .

resulting in:

Sb,n

= |Sb0 | fnorm ,

(11.58)

where:

fnorm = αbn

τb,cr ∂zb
.
|~τb | ∂n

(11.59)

The two components of this vector are then added to the two components of the bedload
transport vector as follows:
0
0
Sb,x = Sb,x
− Sb,y
fnorm
0
0
Sb,y = Sb,y + Sb,x fnorm

(11.60)

where Sb,x and Sb,y are the components of the required bedload transport vector, calculated at the water level points
3 Koch and Flokstra (1980) as extended by Talmon et al. (1995). In this case αs is given by

αs = 1 − αbs

∂z
,
∂s

(11.61)

where αbs is a user-defined tuning parameter, ALFABS keyword in the morphology input
file (default = 1.0). The direction of the bedload is adjusted according to the following
formulation:

tan(ϕs ) =

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sin(ϕτ ) +
cos(ϕτ ) +

1 ∂zb
f (θ) ∂y
1 ∂zb
f (θ) ∂x

(11.62)

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in which ϕτ is the original direction of the sediment transport and ϕs is the final direction
and where f (θ) equals:

f (θ) =

Ash θiBsh

Di
H

Csh

Di
Dm

Dsh
,

(11.63)

where Ash , Bsh , Csh and Dsh are tuning coefficients specified by you in the morphology
input file as keywords Ashld, Bshld, Cshld and Dshld.
4 Parker and Andrews (1985). The same formulae for αs and ϕs hold as in the previous
case except for f (θ) which now equals:

θ
max

1
θ, ξθcr
10

(11.64)

cL
f (θ) =
1 + µcL

where Coulomb friction parameter cL , lift-drag ratio µ and critical shields parameter θcr
should be specified by you in the morphology input file as keywords CoulFri, FlFdRat
and ThetaCr. Note that this formula includes the hiding and exposure factor ξ .

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This completes the calculation of the bedload transport field. The transports at the U and V
velocity points are then stored for use in the computation of bed level changes, as described
in the section 11.6. In all cases the bed slope has been defined as follows.
Longitudinal bed slope

This bed slope is calculated as:

00
00
∂z(u) Sb,x
∂z(v) Sb,y
∂zb
=
+
,
∂s
∂x |Sb00 |
∂y |Sb00 |

∂zb
= 0.9 tan (φ) ,
∂s max

(11.65)
(11.66)

where:

∂zb
∂s
∂z(u)
∂x
∂z(v)
∂y

bed slope in the direction of bedload transport

bed slope in the positive x-direction evaluated at the U -point
bed slope in the positive y -direction evaluated at the V -point
internal angle of friction of bed material (assumed to be 30◦ )

Remarks:
zb is the depth down to the bed from a reference height (positive down), a downward
bed slope returns a positive value).
The bed slope is calculated at the U and V points as these are the locations at which
the bedload transport vector components will finally be applied.
Transverse bed slope
This bed slope is calculated as:
00
00
∂z(u) Sb,y
∂z(v) Sb,x
∂zb
=−
+
.
∂n
∂x |Sb00 |
∂y |Sb00 |

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(11.67)

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Table 11.1: Additional transport relations

Bedload

Waves

11.5.1, Van Rijn (1993)
11.5.2, Engelund-Hansen (1967)
11.5.3, Meyer-Peter-Muller (1948)
11.5.4, General formula
11.5.5, Bijker (1971)
11.5.6, Van Rijn (1984)
11.5.7, Soulsby/Van Rijn
11.5.8, Soulsby
11.5.9, Ashida–Michiue (1974)
11.5.10, Wilcock–Crowe (2003)
11.5.11, Gaeuman et al. (2009) laboratory calibration
11.5.12, Gaeuman et al. (2009) Trinity River calibration

Bedload + suspended
Total transport
Total transport
Total transport
Bedload + suspended
Bedload + suspended
Bedload + suspended
Bedload + suspended
Total transport
Bedload
Bedload
Bedload

Yes
No
No
No
Yes
No
Yes
Yes
No
No
No
No

Transport formulations for non-cohesive sediment

11.5

Formula

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This special feature offers a number of standard sediment transport formulations for noncohesive sediment. Table 11.1 gives a summary of the available additional formulae.
Additionally, you can implement your own sediment transport formula in a shared library
( or ) and call it from Delft3D-FLOW. See section B.9.3 for this option. Now, let
us continue with a general description of the sediment transport formulae included by default.
11.5.1

Van Rijn (1993)

Van Rijn (1993) distinguishes between sediment transport below the reference height a which
is treated as bedload transport and that above the reference height which is treated as
suspended-load. Sediment is entrained in the water column by imposing a reference concentration at the reference height.
Reference concentration
The reference concentration is calculated in accordance with Van Rijn et al. (2000) as:

c(`)
a
where:
(`)

1.5
(`)
(`)
D50 Ta
= 0.015ρ(`)

0.3
s
(`)
a D∗

(11.68)

mass concentration at reference height a

In order to evaluate this expression the following quantities must be calculated:
(`)

D∗

non-dimensional particle diameter:

D∗(`)
(`)

(`)
D50

(s(`) − 1)g
ν2

1/3
(11.69)

non-dimensional bed-shear stress:
(`)

Ta(`) =

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(`)

(µc τb,cw + µw τb,w ) − τcr
(`)

(11.70)

τcr

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(`)

µc

efficiency factor current:

µ(`)
c =
f 0 (`)
c

f 0 (`)
c
fc

(11.71)

gain related friction factor:

"
(`)
f 0c

(`)

= 0.24

12h

log

!#−2
(11.72)

(`)

3D90

total current-related friction factor:

= 0.24

log

12h
ks

−2

τb,cw = ρw u2∗

(`)

µw

(11.74)

efficiency factor waves:

µ(`)
w

τb,w

1
= max 0.063,
8

2 !
Hs
1.5 −
h

(11.75)

bed shear stress due to waves:

2
1
bδ
τb,w = ρw fw U
4

(11.73)

bed shear stress due to current in the presence of waves. Note that the bed
shear velocity u∗ is calculated in such a way that Van Rijn’s wave-current interaction factor αcw is not required.

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AF

τb,cw

fc(`)

(11.76)

total wave-related friction factor (≡ Equations (9.205), (11.116) and (11.157)):



Âδ
ks,w

fw = exp −6 + 5.2

!−0.19 


(11.77)

To avoid the need for excessive user input, the wave related roughness ks,w is related to the
estimated ripple height, using the relationship:

ks,w = RW AV E · ∆r , with ∆r = 0.025 and 0.01 m ≤ ks,w ≤ 0.1 m

(11.78)

where:

RWAVE the user-defined wave roughness adjustment factor. Recommended to be in
the range 1–3, default = 2.
(`)
τcr

critical bed shear stress:
(`)

(`)
(`)
τcr
= (ρ(`)
s − ρw )gD50 θcr
(`)

θcr

Deltares

(11.79)

(`)

threshold parameter θcr is calculated according to the classical Shields curve
as modelled by Van Rijn (1993) as a function of the non-dimensional grain size
D∗ . This avoids the need for iteration.

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(`)

Note: for clarity, in this expression the symbol D∗ has been used where D∗
would be more correct:

(`)
θcr

a
Âδ
(`)
D50
(`)
D90
h
ka

bδ
U
zu
∆r
δm
δw

1 < D∗ ≤ 4
4 < D∗ ≤ 10
10 < D∗ ≤ 20
20 < D∗ ≤ 150
150 < D∗

(11.80)

Van Rijn’s reference height
peak orbital excursion at the bed: Âδ =

Tp Ûδ
.
2π

median sediment diameter
(`)

(`)

90 % sediment passing size: D90 = 1.5D50
water depth
apparent bed roughness felt by the flow when waves are present. Calculated
by Delft3D-FLOW using the wave-current interaction formulation selected; see
section 9.7 for details: ka ≤ 10ks
user-defined current-related effective roughness height (space varying)
wave-related roughness, calculated from ripple height, see Equation (11.78)
velocity magnitude taken from a near-bed computational layer. In a current-only
situation the velocity in the bottom computational layer is used. Otherwise, if
waves are active, the velocity is taken from the layer closest to the height of the
top of the wave mixing layer δ . √
peak orbital velocity at the bed: 2 × RMS orbital velocity at bed, taken from the
wave module.
height above bed of the near-bed velocity (uz ) used in the calculation of bottom
shear stress due to current
estimated ripple height, see Equation (11.78)
thickness of wave boundary mixing layer following Van Rijn (1993): 3δw (and
δm ≥ k a )
wave boundary layer thickness:

DR
AF

ks
ks,w
uz


0.24D∗−1 ,



 0.14D∗−0.64 ,
=
0.04D∗−0.1 ,


 0.013D∗0.29 ,

0.055,

δw = 0.072Âδ

Âδ
ks,w

−0.25

We emphasise the following points regarding this implementation:

The bottom shear stress due to currents is based on a near-bed velocity taken from the
hydrodynamic calculations, rather than the depth-averaged velocity used by Van Rijn.

All sediment calculations are based on hydrodynamic calculations from the previous half
time-step. We find that this is necessary to prevent unstable oscillations developing.
The apparent roughness felt by the flow (ka ) is dependent on the hydrodynamic wave-current
interaction model applied. At this time, Van Rijn’s wave-current interaction model is not available in Delft3D-FLOW. This means that it is not possible for a user to exactly reproduce results
obtained using Van Rijn’s full formulations for waves and currents.

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Adjustment of the representative diameter of suspended sediment
(`)

The representative diameter of the suspended sediment Ds generally given by the userdefined sediment diameter SEDDIA (D50 of bed material) multiplied by the user-defined factor
FACDSS (see also remarks) can be overruled in case the Van Rijn (1993) transport formula is
selected. This achieved by setting IOPSUS=1 the representative diameter of the suspended
sediment will then be set to:

(`)

where Ta

(11.81)

is given by equation (11.70).

Ds(`)


(`)
(`)

 0.64D
50

for TA ≤ 1
(`)
(`)
(`)
D50 1 + 0.015 TA − 25
for 1 < TA ≤ 25
=

 (`)
(`)
D50
for 25 < TA

Bedload transport rate

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AF

For simulations including waves the magnitude and direction of the bedload transport on a
horizontal bed are calculated using an approximation method developed by Van Rijn et al.
(2003). The method computes the magnitude of the bedload transport as:
(`)

|Sb | = 0.006ρs ws D50 M 0.5 Me0.7

(11.82)

where:

Sb
M
Me

bedload transport [kg m-1 s-1 ]
sediment mobility number due to waves and currents [-]
excess sediment mobility number [-]

ve2f f
M=
(s − 1) gD50
(vef f − vcr )2
Me =
(s − 1) gD50
q
2
vef f = vR2 + Uon

(11.83)
(11.84)
(11.85)

in which:

vcr
vR

Uon

critical depth averaged velocity for initiation of motion (based on a parameterisation of the Shields curve) [m/s]
magnitude of an equivalent depth-averaged velocity computed from the velocity
in the bottom computational layer, assuming a logarithmic velocity profile [m/s]
near-bed peak orbital velocity [m/s] in onshore direction (in the direction on
wave propagation) based on the significant wave height

Uon (and Uof f used below) are the high frequency near-bed orbital velocities due to short
waves and are computed using a modification of the method of Isobe and Horikawa (1982).
This method is a parameterisation of fifth-order Stokes wave theory and third-order cnoidal
wave theory which can be used over a wide range of wave conditions and takes into account the non-linear effects that occur as waves propagate in shallow water (Grasmeijer and
Van Rijn, 1998).
The direction of the bedload transport vector is determined by assuming that it is composed
of two parts: part due to current (Sb,c ) which acts in the direction of the near-bed current, and

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part due to waves (Sb,w ) which acts in the direction of wave propagation. These components
are determined as follows:

Sb
Sb,c = p
1 + r2 + 2 |r| cos ϕ

(11.86)

|Sb,w | = r |Sb,c |

(11.87)

where:

(|Uon | − vcr )3
(|vR | − vcr )3

(11.88)

Sb,w = 0 if r < 0.01, Sb,c = 0 if r > 100, and ϕ = angle between current and wave

direction for which Van Rijn (2003) suggests a constant value of 90◦ .

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Also included in the “bedload” transport vector is an estimation of the suspended sediment
transport due to wave asymmetry effects. This is intended to model the effect of asymmetric
wave orbital velocities on the transport of suspended material within about 0.5 m of the bed
(the bulk of the suspended transport affected by high frequency wave oscillations).
This wave-related suspended sediment transport is again modelled using an approximation
method proposed by Van Rijn (2001):

Ss,w = fSUSW γUA LT
where:

Ss,w
fSUSW
γ
UA
LT

(11.89)

wave-related suspended transport [kg/(ms)]
user-defined tuning parameter
phase lag coefficient (= 0.2)
velocity asymmetry value [m/s] =

4 −U 4
Uon
of f

3 +U 3
Uon
of f

suspended sediment load [kg/m ] = 0.007ρs D50 Me

The three separate transport modes are imposed separately. The direction of the bedload
due to currents Sb,c is assumed to be equal to the direction of the current, whereas the two
wave related transport components Sb,w and Ss,w take on the wave propagation direction.
This results in the following transport components:

ub,u
|Sb,c |
|ub |
ub,v
=
|Sb,c |
|ub |

Sbc,u =

(11.90)

Sbc,v

(11.91)

Sbw,u = Sb,w cos φ
Sbw,v = Sb,w sin φ

(11.92)

Ssw,u = Ss,w cos φ
Ssw,v = Ss,w sin φ

(11.94)

(11.93)

(11.95)

where φ is the local angle between the direction of wave propagation and the computational
grid. The different transport components can be calibrated independently by using the Bed,
BedW and SusW keywords in the morphology input file.

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11.5.2

Engelund-Hansen (1967)
The Engelund-Hansen sediment transport relation has frequently been used in rivers and
estuaries. It reads:

0.05αq 5
S = Sb + Ss,eq = √ 3 2
gC ∆ D50

(11.96)

where:

q
∆
C
α

magnitude of flow velocity
the relative density (ρs − ρw )/ρw
Chézy friction coefficient
calibration coefficient (O(1))

The transport rate is imposed as bedload transport due to currents Sbc . The following formula specific parameters have to be specified in the input files of the Transport module (See
section B.9.3): calibration coefficient α and roughness height rk .

11.5.3

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Remarks:
The D50 grain size diameter is based on the sediment fraction considered.
A second formula specific input parameter (rk ) is required for the Engelund-Hansen
formula. This parameter, which represents the roughness height for currents alone in
[m], is only used to determine the C value when the Chézy friction in the flow has not
been defined. Generally, this parameter can thus be treated as a dummy parameter.
Meyer-Peter-Muller (1948)

The Meyer-Peter-Muller sediment transport relation is slightly more advanced than the EngelundHansen formula, as it includes a critical shear stress for transport. It reads:

S = 8αD50

p
∆gD50 (µθ − ξθcr )3/2

(11.97)

where:

α
∆
µ
θcr
ξ

calibration coefficient (O(1))
the relative density (ρs − ρw )/ρw
ripple factor or efficiency factor
critical Shields’ mobility parameter (= 0.047)
hiding and exposure factor for the sediment fraction considered

and the Shields’ mobility parameter θ given by

θ=

q 2
C

1
∆D50

(11.98)

in which q is the magnitude of the flow velocity [m/s]. The ripple factor µ reads:

µ = min

C
Cg,90

1.5

!
, 1.0

(11.99)

where Cg,90 is the Chézy coefficient related to grains, given by:
10

Cg,90 = 18 log

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12(d + ζ)
D90

(11.100)

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with D90 specified in [m]. The transport rate is imposed as bedload transport due to currents
Sbc . The following formula specific parameters have to be specified in the input files of the
Transport module (See section B.9.3): calibration coefficient α and a dummy value.
Remark:
The D50 is based on the sediment fraction considered, the D90 grain size diameters is
based on the composition of the local sediment mixture.
11.5.4

General formula

S = αD50

∆gD50 θb (µθ − ξθcr )c

The general sediment transport relation has the structure of the Meyer-Peter-Muller formula,
but all coefficients and powers can be adjusted to fit your requirements. This formula is aimed
at experienced users that want to investigate certain parameters settings. In general this
formula should not be used. It reads:
(11.101)

where ξ is the hiding and exposure factor for the sediment fraction considered and

q 2

1
∆D50

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AF

θ=

(11.102)

in which q is the magnitude of the flow velocity.

The transport rate is imposed as bedload transport due to currents Sbc . The following parameters have to be specified in the input files of the Transport module (See section B.9.3):
calibration coefficient α, powers b and c, ripple factor or efficiency factor µ, critical Shields’
mobility parameter θcr .
11.5.5

Bijker (1971)

The Bijker formula sediment transport relation is a popular formula which is often used in
coastal areas. It is robust and generally produces sediment transport of the right order of
magnitude under the combined action of currents and waves. Bedload and suspended load
are treated separately. The near-bed sediment transport (Sb ) and the suspended sediment
transport (Ss ) are given by the formulations in the first sub-section. It is possible to include
sediment transport in the wave direction due to wave asymmetry and bed slope following
the Bailard approach, see Bailard (1981), Stive (1986). Separate expressions for the wave
asymmetry and bed slope components are included:

~b = S
~b0 + S
~b,asymm + S
~s,asymm + S
~b,slope + S
~s,slope
S
~s = S
~s0
S

(11.103)
(11.104)

where Sb0 and Ss0 are the sediment transport in flow direction as computed according to the
formulations of Bijker in the first sub-section, and the asymmetry and bed slope components
for bedload and suspended transport are defined in the second sub-section. Both bedload and
suspended load terms are incorporated in the bedload transport for further processing. The
transport vectors are imposed as bedload transport vector due to currents Sbc and suspended
load transport magnitude Ss , from which the equilibrium concentration is derived, respectively.

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Basic formulation
The basic formulation of the sediment transport formula according to Bijker is given by:

q√
g (1 − φ) exp (Ar )
C

33.0h
Ss = 1.83Sb I1 ln
+ I2
rc

Sb = bD50

(11.105)
(11.106)

where

C
h
q
φ

Chézy coefficient (as specified in input of Delft3D-FLOW module)
water depth
flow velocity magnitude
porosity

and

Ar = max (−50, min (100, Ara ))

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11.5.5.1

(hw /h) − Cd
b = BD + max 0, min 1,
(BS − BD)
Cs − Cd

I1 = 0.216

I2 = 0.216

rc z∗ −1
h
z∗
1 − rhc

1−y
y

(11.107)

(11.108)

z∗

(11.109)

rc /h

ln y

1−y
y

z∗

(11.110)

rc /h

where

BS
BD
Cs
Cd
rc
and

Coefficient b for shallow water (default value 5)
Coefficient b for deep water (default value 2)
Shallow water criterion (Hs /h) (default value 0.05)
Deep water criterion (default value 0.4)
Roughness height for currents [m]

Ara =

µ=

z∗ =

Deltares

−0.27∆D50 C 2

2
Ub
2
µq 1 + 0.5 ψ q

C
10
18 log(12h/D90 )

1.5
(11.112)

w
√
κq g
C

r
1 + 0.5

ψ Uqb

(11.111)

(11.113)

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Ub =

ω=

ωhw
2 sinh (kw h)

(11.114)

2π
T

(11.115)

5.123
fw = exp −5.977 + 0.194
a0

(11.116)

(≡ Equations (9.205), (11.77) and (11.157)):

Ub
a0 = max 2,
ωrc
(

where

C
hw
kw
T
Ub
w
∆
κ

fw
2g

if wave effects are included (T > 0)

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AF

ψ=

C
0

(11.117)

(11.118)

otherwise

Chézy coefficient (as specified in input of Delft3D-FLOW module)
wave height (Hrms )
wave number
wave period computed by the waves model or specified by you as T user.
wave velocity
sediment fall velocity [m/s]
relative density (ρs − ρw )/ρw
Von Kármán constant (0.41)

The following formula specific parameters have to be specified in the input files of the Transport module (See section B.9.3): BS , BD , Cs , Cd , dummy argument, rc , w , ε and T user.
11.5.5.2

Transport in wave propagation direction (Bailard-approach)

If the Bijker formula is selected it is possible to include sediment transport in the wave direction
due to wave asymmetry following the Bailard approach, see Bailard (1981) and Stive (1986).
For a detailed description of the implementation you are referred to Nipius (1998).
Separate expressions for the wave asymmetry and bed slope components are included for
both bedload and suspended load. Both extra bedload and suspended load transport vectors
are added to the bedload transport as computed in the previous sub-section:

~b = S
~b0 + S
~b,asymm + S
~s,asymm + S
~b,slope + S
~s,slope
S

(11.119)

where the asymmetry components for respectively the bedload and suspended transport in
wave direction are written as:

Sb;asymm (t) =

ρcf εb
|u(t)|2 u(t)
(ρs − ρ) g (1 − φ) tan ϕ

(11.120)

Ss;asymm (t) =

ρcf εs
|u(t)|3 u(t)
(ρs − ρ) g (1 − φ) w

(11.121)

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from which the components in ξ and η direction are obtained by multiplying with the cosine
and sine of the wave angle θ w and the bed slope components as:

Sb;slope,ξ (t) =

∂zb
ρcf εb
1
|u(t)|3
(ρs − ρ) g (1 − φ) tan ϕ tan ϕ
∂ξ

(11.122)

Ss;slope,ξ (t) =

∂zb
ρcf εs
εs
|u(t)|5
(ρs − ρ) g (1 − φ) w w
∂ξ

(11.123)

and similar for the η direction, where:

u(t)
ρ
ρs
cf
φ
ϕ
w
εb
εs

DR
AF

near bed velocity signal [m/s]
density of water [kg/m3 ]
density of the sediment [kg/m3 ]
coefficient of the bottom shear stress [-] (constant value of 0.005)
porosity [-] (constant value of 0.4)
natural angle of repose [-] (constant value of tan ϕ = 0.63)
sediment fall velocity [m/s]
efficiency factor of bedload transport [-] (constant value of 0.10)
efficiency factor of suspended transport [-] (constant value of 0.02, but in implemented expression for suspended bed slope transport the second εs is replaced
by a user-defined calibration factor; see Equation (11.126)).

These transports are determined by generating velocity signals of the orbital velocities near
the bed by using the Rienecker and Fenton (1981) method, see also Roelvink and Stive
(1989).
The (short wave) averaged sediment transport due to wave asymmetry, Equations (11.120)
and (11.121), is determined by using the following averaging expressions of the near bed
velocity signal (calibration coefficients included):

u |u|2 = F acA ũ |ũ|2 + 3F acU ū |ũ|2

(11.124)

u |u|3 = F acA ũ |ũ|3 + 4F acU ū |ũ|3

(11.125)

in which:

ũ
ū
F acA
F acU

orbital velocity signal
averaged flow velocity (due to tide, undertow, wind, etc.)
user-defined calibration coefficient for the wave asymmetry
user-defined calibration coefficient for the averaged flow

The suspended transport relation due to the bed slope according to Equation (11.123) is
implemented as:

Ss;slope,ξ (t) =

εsl
∂zb
ρcf εs
|u(t)|5
(ρs − ρ) g (1 − φ) w w
∂ξ

(11.126)

where:

εsl

user-defined calibration coefficient EpsSL

To activate this transport option, you have to create a separate file named which
contains on three separate lines the calibration coefficients: FacA, FacU and EpsSL. The

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other parameters are read from the transport input file or are specified as general sediment
characteristics.
Note: the user-defined FacU value is currently treated as a dummy value, FacU = 0.0 will
always be used.
A validation study (Nipius, 1998) showed that the following coefficient settings yielded the best
results for the Dutch coast:

FacA = 0.4
FacU = 0.0
EpsSL = 0.11

If a relatively straight coast is considered the effect of the parameters is:

The wave asymmetry causes onshore directed sediment transport (i.e. in the wave propa-

11.5.6

DR
AF

gation direction). An increased FacA results in an increased onshore transport and hence
steepening of the cross-shore bottom profile.
The bed slope transport is in general offshore directed. By increasing EpsSL an increased flattening of the bottom profile occurs (i.e. increased offshore transports).
The ratio between these parameters determines the balance between onshore and offshore transport and hence the shape and slope of the cross-shore bottom profile. The
associated response time of the cross-shore morphology can be influenced by modifying
the values of the two parameters, but maintaining a constant ratio. Increased values result
in increased gross transports and consequently a reduced morphological response time
(and vice versa).
Van Rijn (1984)

The Van Rijn (1984a,b,c) sediment transport relation is a transport formula commonly used for
fine sediments in situations without waves. Separate expressions for bedload and suspended
load are given. The bedload transport rate is given by:


q
 0.053 ∆gD3 D−0.3 T 2.1 for T < 3.0
50 ∗
q
Sb =
 0.1 ∆gD3 D−0.3 T 1.5
for T ≥ 3.0
50 ∗

(11.127)

where T is a dimensionless bed shear parameter, written as:

T =

µc τbc − τbcr
τbcr

(11.128)

It is normalised with the critical bed shear stress according to Shields (τbcr ), the term µc τbc is
the effective shear stress. The formulas of the shear stresses are

1
τbc = ρw fcb q 2
8
0.24
fcb =
10
( log (12h/ξc ))2
10
2
18 log (12h/ξc )
µc =
Cg,90

(11.129)
(11.130)

(11.131)

where Cg,90 is the grain related Chézy coefficient
10

Cg,90 = 18 log

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12h
3D90

(11.132)

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The critical shear stress is written according to Shields:

τbcr = ρw ∆gD50 θcr

(11.133)

in which θcr is the Shields parameter which is a function of the dimensionless particle parameter D∗ :

D∗ = D50

∆g
ν2

13
(11.134)

The suspended transport formulation reads:

Ss = fcs qhCa

(11.135)

DR
AF

In which Ca is the reference concentration, q depth averaged velocity, h the water depth and
fcs is a shape factor of which only an approximate solution exists:

f0 (zc ) if zc 6= 1.2
fcs =
(11.136)
f1 (zc ) if zc = 1.2

(ξc /h)zc − (ξc /h)1.2
f0 (zc ) =
(1 − ξc /h)zc (1.2 − zc )

f1 (zc ) =

ξc /h
1 − ξc /h

(11.137)

1.2

ln (ξc /h)

(11.138)

where ξc is the reference level or roughness height (can be interpreted as the bedload layer
thickness) and zc the suspension number:

ws
+φ
zc = min 20,
βκu∗
r
fcb
u∗ = q
8
2 !
ws
β = min 1.5, 1 + 2
u∗
0.8
0.4
ws
Ca
φ = 2.5
u∗
0.65

(11.139)

(11.140)
(11.141)

(11.142)

The reference concentration is written as:

Ca = 0.015α1

D50 T 1.5
ξc D∗0.3

(11.143)

The bedload transport rate is imposed as bedload transport due to currents Sbc ,while the
computed suspended load transport rate is converted into a reference concentration equal to
fcs Ca . The following formula specific parameters have to be specified in the input files of the
Transport module (See section B.9.3): calibration coefficient α1 , dummy argument, reference
level (bedload layer thickness) or roughness height ξc [m] and settling velocity ws [m/s].

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Soulsby/Van Rijn
The sediment transport relation has been implemented based on the formulations provided in
Soulsby (1997). References in the following text refer to this book.
If the wave period Tp is smaller than 10−6 s, the wave period Tp is set to 5 s and the rootmean-square wave height is set to 1 cm. Furthermore, the wave period is limited to values
larger than 1 s. The root-mean-square wave height is limited to values smaller than 0.4 H ,
where H is the water depth.
The sediment transport is set to zero in case of velocities smaller than 10−6 m/s, water depth
larger than 200 m or smaller than 1 cm.

Urms =

√

πHrms
Tp sinh (kH)

Furthermore, D∗ is defined as (Soulsby, 1997, p.104):

The root-mean-square orbital velocity is computed as:

DR
AF

11.5.7

D∗ =

g∆
ν2

(11.144)

1/3

D50

(11.145)

Using the critical bed shear velocity according to Van Rijn (Soulsby, 1997, p.176):

Ucr =

0.1 10
0.19D50
log (4H/D90 ) if D50 ≤ 0.5 mm
0.6 10
8.5D50 log (4H/D90 ) if 0.5 mm < D50 ≤ 2 mm

(11.146)

larger values of D50 lead to an error and to the halting of the program.

The sediment transport is split into a bedload and suspended load fraction. The direction of
the bedload transport is assumed to be equal to the direction of the depth-averaged velocity
in a 2D simulation and equal to the direction of the velocity at the reference height a (see
section 11.3.3) in a 3D simulation (Soulsby, 1997, p.183):

Sbx = Acal Asb uξ
Sby = Acal Asb vξ

(11.147)
(11.148)

and the suspended transport magnitude is given by the following formula (this quantity is
lateron converted to a reference concentration to feed the advection-diffusion equation for the
suspended sediment transport as indicated in section 11.3.3):

√
Ss = Acal Ass ξ u2 + v 2

(11.149)

where

Acal
Asb

a user-defined calibration factor
bedload multiplication factor

Asb = 0.005H
Ass

1.2
(11.150)

suspended load multiplication factor

Ass = 0.012D50

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D50 /H
∆gD50

D∗−0.6
(∆gD50 )1.2

(11.151)

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a general multiplication factor

r
2.4
0.018
ξ=
U 2 − Ucr
U2 +
CD rms

(11.152)

where U is the total depth-averaged velocity and CD is the drag coefficient due
to currents, defined by:

CD =

κ
ln (H/z0 ) − 1

2
(11.153)

where z0 equals 6 mm and the Von Kármán constant κ is set to 0.4.

The bedslope correction factor is not explicitly included in this formula as it is a standard
correction factor available in the online morphology module. The method is intended for conditions in which the bed is rippled.

11.5.8

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AF

The following formula specific parameters have to be specified in the input files of the Transport module (See section B.9.3): the calibration factor Acal , the ratio of the two characteristic
grain sizes D90 /D50 and the z0 roughness height.
Soulsby

The sediment transport relation has been implemented based on the formulations provided in
Soulsby (1997). References in the following text refer to this book.
If the wave period Tp is smaller than 10−6 s, the wave period Tp is set to 5 s and the rootmean-square wave height is set to 1 cm. Furthermore, the wave period is limited to values
larger than 1 s. The root-mean-square wave height is limited to values smaller than 0.4 H ,
where H is the water depth.
The sediment transport is set to zero in case of velocities smaller than 10−6 m/s, water depth
larger than 200 m or smaller than 1 cm.
The root-mean-square orbital velocity Urms and the orbital velocity Uorb are computed as

Urms =

√

2Uorb =

√
2

πHrms
Tp sinh (kH)

(11.154)

For a flat, non-rippled bed of sand the z0 roughness length is related to the grain size as
(Soulsby, 1997, eq.25, p.48) where χ is a user-defined constant:

z0 =

D50
χ

(11.155)

The relative roughness is characterised using a∗ :

a∗ =

Uorb Tp
z0

(11.156)

which is subsequently used to determine the friction factor of the rough bed according to
Swart (1974) (≡ Equations (9.205), (11.77) and (11.116)):

fw =

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0.3
if a∗ ≤ 30π 2
−0.19
0.00251 exp (14.1a∗ ) if a∗ > 30π 2

(11.157)

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Table 11.2: Overview of the coefficients used in the various regression models (Soulsby
et al., 1993a)

1 (FR84)
2 (MS90)
3 (HT91)
4 (GM79)
5 (DS88)
6 (BK67)
7 (CJ85)
8 (OY88)

0.29
0.65
0.27
0.73
0.22
0.32
0.47
-0.06

0.55
0.29
0.51
0.40
0.73
0.55
0.29
0.26

-0.10
-0.30
-0.10
-0.23
-0.05
0.00
-0.09
0.08

-0.14
-0.21
-0.24
-0.24
-0.35
0.00
-0.12
-0.03

-0.77
-0.60
-0.75
-0.68
-0.86
-0.63
-0.70
-1.00

0.10
0.10
0.13
0.13
0.26
0.05
0.13
0.31

0.27
0.27
0.12
0.24
0.34
0.00
0.28
0.25

0.14
-0.06
0.02
-0.07
-0.07
0.00
-0.04
-0.26

Model

DR
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which corresponds to formulae 60a/b of Soulsby (p.77) using r = a∗ /(60π) where r is the
relative roughness used by Soulsby. The friction factor is used to compute the amplitude of
the bed shear-stress due to waves as:
2
τw = 0.5ρfw Uorb

(11.158)

Furthermore, the shear stress due to currents is computed as:

τc = ρCD U 2
where

CD =

κ
1 + ln (z0 /H)

(11.159)

(11.160)

as defined on Soulsby (1997, p.53–55). The interaction of the currents and waves is taken
into account using the factor Y in the following formula for mean bed shear stress during a
wave cycle under combined waves and currents (Soulsby, 1997, p.94):

τm = Y (τw + τc )

(11.161)

The formula for Y is given by:

Y = X [1 + bX p (1 − X)q ]
where:

τc
τc + τw

(11.162)

(11.163)

and b is computed using:

b = b1 + b2 |cos φ|J + b3 + b4 |cos φ|J

log (fw /CD )

(11.164)

and p and q are determined using similar equations. In this formula φ equals the angle
between the wave angle and the current angle, and the coefficients are determined by the
model index modind and tables 11.2 and 11.3 (related to Soulsby (1997, Table 9, p.91)):

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Table 11.3: Overview of the coefficients used in the various regression models, continued
(Soulsby et al., 1993a)

1 (FR84)
2 (MS90)
3 (HT91)
4 (GM79)
5 (DS88)
6 (BK67)
7 (CJ85)
8 (OY88)

0.91
1.19
0.89
1.04
-0.89
1.14
1.65
0.38

0.25
-0.68
0.40
-0.56
2.33
0.18
-1.19
1.19

0.50
0.22
0.50
0.34
2.60
0.00
-0.42
0.25

0.45
-0.21
-0.28
-0.27
-2.50
0.00
0.49
-0.66

3.0
0.50
2.7
0.50
2.7
3.0
0.60
1.50

Model

Using the shear stresses given above, the following two Shields parameters are computed:

τw
τm
and θw =
ρg∆D50
ρg∆D50

DR
AF

θm =

(11.165)

Furthermore, D∗ is defined as (Soulsby, 1997, p.104):

D∗ =

g∆
ν2

1/3

D50

(11.166)

with which a critical Shields parameter is computed (Soulsby, 1997, eq.77, p.106):

θcr =

0.30
+ 0.055 (1 − exp (−0.02D∗ ))
1 + 1.2D∗

(11.167)

The sediment transport rates are computed using the following formulations for normalised
transport in current direction and normal direction (Soulsby, 1997, eq.129, p.166/167):

Φx1 = 12 (θm − θcr )

p
θm + ε

p
Φx2 = 12 (0.95 + 0.19 cos (2φ)) θm θw + ε
Φx = max (Φx1 , Φx2 )
12 (0.19θm θw2 sin (2φ))
Φy =
(θw + ε)1.5 + 1.5 (θm + ε)1.5

(11.168)
(11.169)
(11.170)
(11.171)

where ε is a small constant (10−4 ) to prevent numerical complications. From these expression
are finally the actual bedload transport rates obtained:

3
g∆D50
(Φx u − Φy v)
p U
3
g∆D50
=
(Φx v − Φy u)
U

Sb,x =

(11.172)

Sb,y

(11.173)

The transport vector is imposed as bedload transport due to currents. The following formula
specific parameters have to be specified in the input files of the Transport module (See section B.9.3): calibration coefficient Acal , the model index for the interaction of wave and current
forces modind (integer number 1 to 8) and the D50 /z0 ratio χ (about 12).

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11.5.9

Ashida–Michiue (1974)
The transport rate is given by a generalised version of the Ashida-Michiue formulation:

p
q
θ
c
m
3
1−ξ
θ
Sbc = α ∆gD50
θ

r
1−

θc
θ

!q
(11.174)

where ξ is the hiding and exposure factor for the sediment fraction considered and:

θ=

q 2
C

1
∆D50

(11.175)

Wilcock–Crowe (2003)

The Wilcock-Crowe transport model is a fractional surface based transport model for calculating bedload transport of mixed sand and gravel sediment. The equations and their development are described in Wilcock and Crowe (2003). The bedload transport rate of each size
fraction is given by:

DR
AF

11.5.10

in which q is the magnitude of the flow velocity. The transport rate is imposed as bedload
transport due to currents Sbc . The following formula specific parameters have to be specified
in the input files of the Transport module (See section B.9.3): α, θc , m, p and q (Ashida and
Michiue recommend α=17, θc =0.05, m=1.5, p=1 and q =1).

Sbi =

Wi∗ Fi U∗3
∆g

(
0.002φ7.5
for φ < 1.35
∗
4.5

Wi =
for φ ≥ 1.35
14 1 − 0.894
φ0.5
τ
φ=
τri

b
τri
Di
=
τrm
Dm
τrm = (0.021 + 0.015 exp (−20Fs )) (ρs − ρw ) gDg
0.67

b=
Di
1 + exp 1.5 − D
g
where:

Di
Dg
Fi
Fs
Sbi
Wi∗
∆
τri
τrm

(11.176)

(11.177)
(11.178)
(11.179)
(11.180)
(11.181)

D50 of size fraction i
geometric mean grain size of whole grain size distribution
proportion of size fraction i on the bed surface
proportion of sand on the bed surface
bedload transort rate of size fraction i
dimensionless bedload transport rate of size fraction i
the relative density of the sediment (ρs − ρw ) /ρw
reference shear stress of grains of size Di
reference shear stress of grains of size Dg

Remarks:
The Wilcock-Crowe model incorporates its own hiding function so no external formulation should be applied.

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The roughness height used for the calculation of grain shear stress during the development of the Wilcock-Crowe transport model was ks = 2D65 .
This sediment transport formula does not have any input parameters that can be, or
need to be, tuned.
11.5.11

Gaeuman et al. (2009) laboratory calibration

The Gaeuman et al. sediment transport model is a modified form of the Wilcock-Crowe model
which uses the variance of grain size distribution on the phi scale (σφ2 ) rather than the fraction of sand on the bed surface (Fs ) as a measure of the bed surface condition for use in
the calculation of reference shear stress. The ’laboratory calibration’ implementation of the
Gaeuman et al. transport model is calibrated to the experimental data used in the derivation
of the Wilcock-Crowe transport model. The model, it’s derivation and calibration is described
in Gaeuman et al. (2009).
The formulae for the calculation of Sbi , Wi∗ , φ and τri are the same as for the Wilcock-Crowe
transport model (Equations (11.176), (11.177), (11.178) and (11.179)) but the calculation of
τrm and b differs.

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AF

0.015

1 + exp 10.1σφ2 − 14.14
1 − α0

b=
Di
1 + exp 1.5 − D
g
2
n
X
Di
2
σφ2 =
log
Fi
D
g
i=1

τrm =

(ρs − ρw ) gDg

θc0 +

(11.182)

(11.183)

(11.184)

where θc0 and α0 are user specified parameters (See section B.9.3). If the values θc0 =
0.021 and α0 = 0.33 are specified the original relation calibrated to the Wilcock-Crowe
laboratory data is recovered.
Remark:
The Gaeuman et al. model incorporates its own hiding function so no external formulation should be applied.
11.5.12

Gaeuman et al. (2009) Trinity River calibration

The ’Trinity River calibration’ implementation of the Gaeuman et al. transport model is calibrated to observed bedload transport rates in the Trinity River, USA and is described in Gaeuman et al. (2009). It differs from the ’laboratory calibration’ implementation in the calculation
of τrm and b.

0.022

τrm = θc0 +
1 + exp 7.1σφ2 − 11.786
1 − α0

b=
Di
1 + exp 1.9 − 3D
g

!
(ρs − ρw ) gDg

(11.185)

(11.186)

where θc0 and α0 are user specified parameters (See section B.9.3). If the values θc0 = 0.03
and α0 = 0.3 are specified the original Gaeuman et al. formulation calibrated to the Trinity
River is recovered.
Remark:

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The Gaeuman et al. model incorporates its own hiding function so no external formulation should be applied.
Morphological updating
The elevation of the bed is dynamically updated at each computational time-step. This is
one of the distinct advantages over an offline morphological computation as it means that the
hydrodynamic flow calculations are always carried out using the correct bathymetry.
At each time-step, the change in the mass of bed material that has occurred as a result of the
sediment sink and source terms and transport gradients is calculated. This change in mass is
then translated into a bed level change based on the dry bed densities of the various sediment
fractions. Both the bed levels at the cell centres and cell interfaces are updated.

Remark:
The depths stored at the depth points (which are read directly from the bathymetry
specified as input) are only updated for writing to the communication file and the result
files.
A number of additional features have been included in the morphological updating routine in
order to increase the flexibility. These are discussed below.

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11.6

Morphological “switch”

You can specify whether or not to update the calculated depths to the bed by setting the
MorUpd (or equivalently BedUpd) flag in the morphology input file. It may be useful to turn
bottom updating off if only the initial patterns of erosion and deposition are required, or an
investigation of sediment transport patterns with a constant bathymetry is required.
Remark:
The use of MorUpd or BedUpd only affects the updating of the depth values (at ζ and
velocity points); the amount of sediment available in the bed will still be updated. Use
the CmpUpd flag to switch off the updating of the bed composition. If you wish to prevent
any change in both the bottom sediments and flow depths from the initial condition then
this may also be achieved by either setting the morphological delay interval MorStt to
a value larger than the simulation period, or by setting the morphological factor MorFac
to 0. See below for a description of these two user variables.
Morphological delay

Frequently, a hydrodynamic simulation will take some time to stabilise after transitioning from
the initial conditions to the (dynamic) boundary conditions. It is likely that during this stabilisation period the patterns of erosion and accretion that take place do not accurately reflect
the true morphological development and should be ignored. This is made possible by use of
MorStt whereby you can specify a time interval (in minutes after the start time) after which
the morphological bottom updating will begin. During the MorStt time interval all other
calculations will proceed as normal (sediment will be available for suspension for example)
however the effect of the sediment fluxes on the available bottom sediments will not be taken
into account.

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Morphological time scale factor
One of the complications inherent in carrying out morphological projections on the basis of
hydrodynamic flows is that morphological developments take place on a time scale several
times longer than typical flow changes (for example, tidal flows change significantly in a period
of hours, whereas the morphology of a coastline will usually take weeks, months, or years to
change significantly). One technique for approaching this problem is to use a “morphological
time scale factor” whereby the speed of the changes in the morphology is scaled up to a rate
that it begins to have a significant impact on the hydrodynamic flows. This can be achieved
by specifying a non-unity value for the variable MorFac in the morphology input file.

Remark:
The Morphological scale factor can also be time-varying, see section B.9.8. This feature
is not yet supported by the GUI. You have to edit the <∗.mor> file manually.

DR
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The implementation of the morphological time scale factor is achieved by simply multiplying
the erosion and deposition fluxes from the bed to the flow and vice-versa by the MorFacfactor, at each computational time-step. This allows accelerated bed-level changes to be
incorporated dynamically into the hydrodynamic flow calculations.
While the maximum morphological time scale factor that can be included in a morphodynamic
model without affecting the accuracy of the model will depend on the particular situation being
modelled, and will remain a matter of judgement, tests have shown that the computations
remain stable in moderately morphologically active situations even with MorFac-factors in
excess of 1 000. We also note that setting MorFac=0 is often a convenient method of preventing both the flow depth and the quantity of sediment available at the bottom from updating,
if an investigation of a steady state solution is required.
Remarks:
Verify that the morphological factor that you use in your simulation is appropriate by
varying it (e.g. reducing it by a factor of 2) and verify that such changes do not affect
the overall simulation results.
The interpretation of the morphological factor differs for coastal and river applications.
For coastal applications with tidal motion, the morphological variations during a tidal cycle are often small and the hydrodynamics is not significantly affected by the bed level
changes. By increasing the morphological factor to for instance 10, the morphological
changes during one simulated tidal cycle are increased by this factor. From a hydrodynamical point of view this increase in morphological development rate is allowed if the
hydrodynamics is not significantly influenced. In that case the morphological development after one tidal cycle can be assumed to represent the morphological development
that would in real life only have occurred after 10 tidal cycles. In this example the number of hydrodynamic time steps required to simulate a certain period is reduced by a
factor of 10 compared to a full 1:1 simulation. This leads to a significant reduction in
simulation time. However, one should note that by following this approach the order
of events is changed, possible conflicts may arise in combination with limited sediment
availability and bed stratigraphy simulations. In river applications there is no such periodicity as a tidal cycle. For such applications, the morphological factor should be
interpreted as a speed-up factor for morphological development without changing the
order of events. Effectively, it means that the morphological development is simulated
using a, for instance 10 times, larger time step than the hydrodynamics, or phrased
more correctly the hydrodynamics is simulated at a 10 times faster rate. This means
that in case of time-varying boundary conditions (e.g. river hydrograph) the time-scale
of these forcings should be sped up: a 20 day flood peak will be compressed in 2 days.
However, one should take care that by speeding up the hydrodynamic forcings one

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n+1

water level point
n

u-velocity point
v-velocity point
depth point
control volume

n-1

m+1

m-1

Figure 11.6: Morphological control volume and bedload transport components

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does not substantially change the nature of the overall hydrodynamic and morphological development: a quasi-steady flood period should not become a short, dynamic flash
flood. For river applications, changing the morphological factor must be associated with
changing all external time-varying forcings. For coastal applications only the overall
simulation time should be adjusted. Note that the combination of a river-like flood peak
and a tidal motion will cause problems when interpreting morphological factor not equal
to 1.
The effect of the morphological factor is different for bed and suspended load. At each
time step bedload is picked-up from the bed and deposited on the bed: only the transports are increased by the morphological factor used for the time step considered. However, in case of suspended load there is a time-delay between the time of erosion and
the time of deposition. The erosion and deposition fluxes are increased by the morphological factor, but the suspended concentrations are not (since that would influence the
density effects). It is possible to vary the morphological factor during a simulation to
speed up relatively quiet periods more than relatively active periods. Such changes in
the morphological factor will not influence the mass balance of a bed or total load simulation since pickup and deposition are combined into one time step. However, in case
of suspended load the entrainment and deposition may occur at time-steps governed
by different morphological factors. In such cases the entrainment flux that generated a
certain suspended sediment concentration will differ from the deposition flux that was
caused by the settling of the same suspended sediment. A change in morphological
factor during a period of non-zero suspended sediment concentrations, will thus lead to
a mass-balance error in the order of the suspended sediment volume times the change
in morphological factor. The error may kept to a minimum by appropriately choosing the
transition times.
11.6.1

Bathymetry updating including bedload transport
The change in the quantity of bottom sediments caused by the bedload transport is calculated
using the expression:
(m,n)
∆SED

∆tfMORFAC
=
A(m,n)

(m−1,n)

(m,n)

Sb,uu ∆y (m−1,n) − Sb,uu ∆y (m,n) +
(m,n−1)
(m,n)
Sb,vv
∆x(m,n−1) − Sb,vv ∆x(m,n)

!
,

(11.187)

where:
(m,n)

∆SED

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change in quantity of bottom sediment at location (m, n) [kg/m2 ]

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∆t
fMORFAC
A(m,n)
(m,n)
Sb,uu
∆x(m,n)
∆y (m,n)

computational time-step [s]
user-defined morphological acceleration factor, MORFAC
area of computational cell at location (m, n) [m2 ]
computed bedload sediment transport vector in u direction, held at
the u point of the computational cell at location (m, n) [kg/(m s)]
cell width in the x direction, held at the V point of cell (m, n) [m]
cell width in the y direction, held at the U point of cell (m, n) [m]

11.6.2

Erosion of (temporarily) dry points

This calculation is repeated for all ‘sand’ and ‘bedload’ sediment fractions, if more than one is
present, and the resulting change in the bottom sediment mass is added to the change due
to the suspended sediment sources and sinks and included in the bed composition and bed
level updating scheme.

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In the case of erosion near a dry beach or bank, the standard scheme will not allow erosion
of the adjacent cells, even when a steep scour hole would develop right next to the beach.
Therefore a scheme has been implemented that allows the (partial) redistribution of an erosion
flux from a wet cell to the adjacent dry cells. The distribution is governed by a user-defined
factor ThetSD, which determines the fraction of the erosion to assign (evenly) to the adjacent
cells. If ThetSD equals zero the standard scheme is used, i.e. all erosion occurs at the wet
cell. If ThetSD equals 1 all erosion that would occur in the wet cell is assigned to the adjacent
dry cells. The ‘wet’ and ‘dry’ cells in the paragraph above are defined as cells at which the
water depths are, respectively, above and below the threshold depth SedThr for computing
sediment transport.
A modification to this method may be activated by specifying a parameter HMaxTH larger
than the threshold depth SedThr for computing sediment transport. In this case, the factor
ThetSD is used as upper limit for the fraction of the erosion to be transferred to adjacent dry
cells. The actual factor to be transferred is equal to Thet , which is computed as:

Thet = (h1 − SedThr )/(HMaxTH − SedThr ) × ThetSD
where Thet = min(Thet, ThetSD) (11.188)

Here, h1 is the local water depth. The purpose of this formulation is to allow erosion of parts
that are inactive in terms of transport but still wet, while limiting the erosion of the dry beach.
If erosion of the dry beach is desired, this option is not recommended, so HMaxTH should be
set less than SedThr.
Remark:
The overall erosion flux is redistributed to the adjacent cells. Depending on the availability of individual sediment fractions at the central ‘wet’ cell and the surrounding ‘dry’
cells, the erosion from the adjacent cells will replenish the eroded cell with different
sediment fractions than those that were eroded.
11.6.3

Dredging and dumping
If the bed levels are updated, you may also include some dredging and dumping activities at
the end of each half time step. This feature can also be used for sand mining (only dredging,
no associated dumping within the model domain) and sediment nourishment (only dumping,
no associated dredging within the model domain). Dredging and dumping is performed at this
stage in the following order:

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For each dredge area: if the bed level exceeds a threshold level (or the water depth drops
below a certain level) then the bed level is lowered based on the dredging option and the
corresponding volume of sediment is removed. If the dredging capacity is less than the
volume to be dredged, the sequence of dredging (e.g. top first or uniform) determines
which grid cells are dredging at the current point in time.
The volume of dredged material is summed over all cells in a dredge area and distributed
over the dump areas, using the link percentages or the link order (up to the dump capacity).
In simulations with multiple sediment fractions the sediment composition is tracked.
For each dump area: the bed level is raised and the bed composition is adjusted based on
the volume and characteristics of material to be dumped. The sediment may be distributed
equally or non-uniformly (e.g. deepest points first) over the grid cells in the dump area.

Remark:
Dredging and dumping may also performed during initialization, before the first timestep.

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Warning:
Dredging large amounts of material may harm the stability of the calculation.

The dredging and dumping feature allows you to specify dredging and dumping areas as
x,y polygons. Within each dredging polygon the bed levels are lowered to a user-defined
depth; by default grid cells are considered to lie within a polygon if their centre lies within
the polygon. It is possible to distribute the dredged material over multiple dumping locations.
You may also decide to not dump the sediment back into the model (feature referred to as
sand mining); this can be implemented by defining a dump polygon outside the grid, or by not
specifying any dump polygon at all. This option cannot be combined with the option to dredge
only as much as dump capacity is available. For sediment nourishment one should use a
[nourishment] block specifying the amount (and, if applicable, the composition) of the
nourished sediment. The dredging and dumping activities should be specified in a <∗.dad>
file; for a description of this attribute file see section A.2.23. The file should contain a
keyword Fildad referring to the file used. The <∗.dad> file refers to the file containing the
polygons.
11.6.4

Bed composition models and sediment availability

The morphology module currently implements two bed composition models:

A uniformly mixed bed (one sediment layer). There is no bookkeeping of the order in which
sediments are deposited and all sediments are available for erosion.

A layered bed stratigraphy (multiple sediment layers). A user-defined number of bed composition bookkeeping layers may be included to keep track of sediment deposits. When
sediments are deposited, they are initially added to the top-most layer. After mixing in
the top layer, sediments are pushed towards the bookkeeping layers beneath it. The
bookkeeping layers are filled up to a user-defined maximum thickness, if this threshold is
exceeded a new layer is created. If the creation of a new layer would exceed the maximum number of layers specified by you, layers at the bottom of the stratigraphy stack will
be merged. Only sediments in the top-most layer are available for erosion. After erosion,
the top-most layer is replenished from below.
The default bed composition model is the uniformly mixed one. Currently only the default bed
composition model is supported by the user interface. See section B.9.2 on how to select the
other bed composition model.

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At input you must specify the amount of sediment available at the bed as the total (dry) mass
of all sediment fractions in [kg/m2 ]. This may be a constant value for the entire model or,
alternatively, a space-varying initial sediment file (values to be specified at cell centres). The
initial bed composition is assumed to be uniformly mixed.1 The thickness of the total sediment
layer is calculated from the sediment mass by dividing by the user-defined dry bed density
CDryB. Currently, CDryB is constant in time and space for each individual sediment fraction.
The top of these sediment deposits will coincide with the initial bed level. Below the bottom
of these deposits the model assumes a non-erodible bed (sometimes referred to as a fixed
layer).

Cohesive sediment fractions

When the model almost runs out of sediment at a particular location, the sediment flux terms
will be reduced. The reduction starts when the available sediment thickness drops below a
user-defined threshold Thresh. The flux terms affected are slightly different for cohesive and
non-cohesive sediments, as described below.

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In the case of cohesive sediment, the erosive sediment source term is reduced proportionally to the ratio of available sediment thickness over Thresh. The deposition term is never
reduced.
Non-cohesive sediment fractions

In the case of non-cohesive sediments all bedload transport rates out of a grid cell are reduced
by the upwind ratio of available sediment thickness over Thresh. The source and sink terms
of the advection-diffusion equation are not reduced unless the erosive sediment source term
is predicted to be larger than the deposition (sink) term, in that case both terms are reduced by
the ratio of available sediment thickness over Thresh as shown by the following equations:

Sourcetotal = Sourcetotal ∗ fr ,
Sinktotal = Sinktotal ∗ fr ,

(11.189)
(11.190)

where fr is a reduction factor determined by:

fr = min

∆sed

Thresh

,1 ,

(11.191)

where ∆sed is the thickness of sediment at the bed.

The likelihood of erosive conditions occurring is assessed by calculating the total sediment
source and sink terms using the concentration from the previous time-step to evaluate the
implicit sink term. If the sink term is greater than the source term, then deposition is expected,
and fr is set to 1.0 so that deposition close to the fixed layer is not hindered.
11.7

Specific implementation aspects
Negative water depth check
In rare situations (with high morphological acceleration factors) it is possible that, in one timestep, the bed accretes more than the water depth. If this occurs the water depth will become
negative (water surface level is below the bed level). This situation is checked for and, if it
1
The uniformly mixed bed can be used as input for both bed composition models. If you have more detailed
information on the bed stratigraphy, you may use the bed stratigraphy model and specify an initial layering of the
bed composition by means of the IniComp keyword (see section B.9.2) and associated initial bed composition
file (see section B.9.9). In that case the bed composition given in the <∗.sed> file will overruled, you have to
specify dummy values though.

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occurs, the water surface level for the cell is set equal to the new bed level. The cell will then
be set dry.

Threshold depth for sediment calculations introduced
If the water depth in a cell is less than SedThr, specified in the morphology input file, then
the sediment source and sink terms for the suspended sediment fractions (‘sand’ and ‘mud’)
will be set to zero (such that neither erosion nor resuspension will occur there). Note that
the advection diffusion equation may bring suspended sediment into such cells but it will not
interact with the bed; the only way for this sediment to leave the water column is by an increase
in water depth (such that interaction is allowed) or by advective/diffusive transport out of the
shallow cell. Furthermore, the bedload transport into (and out of) these cells for ‘sand’ and
‘bedload’ sediment fractions will be set to zero (bed load transport for ‘mud’ fractions is zero
always). This restriction has been included in order to prevent numerical problems during the
computation of the reference concentration, e.g. to prevent sudden bursts of sediment from
occurring when computational cells are flooded.

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Remark:
In areas with very shallow water depths and sediment sources and sinks, you must
ensure that the user-defined threshold depth for drying and flooding, see section 4.5.8,
is not set too large.
Calculation of bed shear in wave and current situations altered

The calculation of the bed shear velocity u∗ has been simplified in situations with waves and
currents. The bed shear is always calculated using the velocities computed in the bottom
computational layer, rather than using the computational layer closest to the top of the sediment mixing layer. The reference velocity in the bottom computational layer is adjusted to the
top of the sediment mixing layer using the apparent bed roughness ka before being used to
compute the bed shear velocity using the physical bed roughness ks .
Depth at grid cell faces (velocity points)

During a morphological simulation the depth stored at the U and V velocity points must be
updated to reflect the bed level changes calculated in the water level points. This used to be
performed by setting the new depth for the velocity point by copying the new depth held at the
water level point, using a simple upwind numerical scheme. As this may introduce instabilities in the flow computation, especially near drying and flooding and in tidal simulations, this
method has been replaced by setting the depth at U and V points equal to the minimum of
the adjacent depths in water level points. This change significantly improves the smoothness
of flooding dry cells.
Remarks:
The setting of depths at velocity points as the minimum of the adjacent water level
points only comes into effect if sediment is present and the user-defined flag MORUPD
is .true. (i.e. bathymetrical changes are expected to occur at some point during the
simulation period). If this condition is not met then the depths at the velocity points do
not need to be updated during the course of the simulation.
The program still requires the depth at velocity points to be set to MOR for morphological
simulations. This anticipated that this restriction is lifted in a coming release.
Since the MOR and MIN procedures for computing the depth at cell interfaces are equivalent, we advise you to use the MIN procedure during the calibration of a hydronamic
model that will later on be converted into a morphological model.

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Validation
To test and validate the formulations and implementation of the 3D sediment transport feature
many simulations have been executed. These are reported in Lesser et al. (2000); Lesser
(2003); Ruessink and Roelvink (2000); Lesser et al. (2004); Roelvink (2003).

Remarks:
Small negative sediment concentrations (−1 · 10−3 kg/m3 ) can be found in a computation. These negative concentrations can be suppressed by applying a horizontal
Forester filter, Sections 4.5.8 and 10.6.4. However, this can result in a substantially
larger computing time. It is suggested to accept small negative concentrations and
to apply a Forester filter only when the negative concentrations become unacceptably
large.
A vertical Forester filter applied in a sediment transport computation will not affect the
sediments. Since it smoothes the vertical profile and thus can have a strong influence
on the vertical mixing processes, the vertical Forester filter is always de-activated for
sediment.

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11.8

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12 Fixed layers in Z -model
Background
In coastal seas, estuaries and lakes, stratified flow occurs in combination with steep topography. 3D numerical modelling of the hydrodynamics and water quality in these areas requires
accurate treatment of the vertical exchange processes. The existence of vertical stratification
influences the turbulent exchange of heat, salinity and passive contaminants. The accuracy of
the discretisation of the vertical exchange processes is determined by the vertical grid system.
The vertical grid should:

resolve the boundary layer near the bottom to allow an accurate evaluation of the bed
stress

be fine around pycnocline
avoid large truncation errors in the approximation of strict horizontal gradients.
The commonly used σ co-ordinate system does not meet all the requirements. The σ coordinate system is boundary fitted but will not always have enough resolution around the pycnocline. The grid co-ordinate lines intersect the density interfaces. The σ co-ordinate gives significant errors in the approximation of strictly horizontal density gradients (Leendertse, 1990;
Stelling and Van Kester, 1994) in areas with steep bottom topography. Therefore, in 2003 a
second vertical grid co-ordinate system based on Cartesian co-ordinates (Z -grid) was introduced in Delft3D-FLOW for 3D simulations of weakly forced stratified water systems, referred
as Z -model in this manual.

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12.1

The Cartesian Z co-ordinate system has horizontal co-ordinate lines, which are (nearly) parallel with density interfaces (isopycnals) in regions with steep bottom slopes. This is important
to reduce artificial mixing of scalar properties such as salinity and temperature. The Z -model
is not boundary-fitted in the vertical. The bottom (and free surface) is usually not a co-ordinate
line and is represented as a staircase (zig-zag boundary). The number of grid cells in the vertical varies for each horizontal grid point. In the Z co-ordinate system, the vertical index of the
free surface cell is “kmax” and the vertical index of the bottom layer is “kmin”. These indices
are dependent on the horizontal index. The vertical layer index in the Z -model decreases
from top to bottom. In the σ -model of Delft3D-FLOW the vertical index of the free surface
cell is always “1” and the vertical index of the bottom layer is “kmax”, which is independent
of the horizontal index. In other words, the vertical index increases from top to bottom. The
difference between the numbering in both grid systems has a historical background.
The staircase representation of the bottom, see Figure 12.1 leads to inaccuracies in the approximation of the bed stress and the horizontal advection near the bed (Bijvelds, 2001). A
transport flux along the bed is split into a horizontal and vertical part, which leads to numerical
cross-wind diffusion in the transport equation for matter. The inaccuracies related to the staircase boundary representation of the bed in the Z -model are reduced by simple adjustments
of the determination of the bed shear stress and the advection near solid vertical walls.
Grid spacing in the σ co-ordinate model is constructed by lines of constant σ . In a finitedifference model, due to the σ -transformation, the number of control volumes in the vertical
direction is constant over the entire computational domain. The relative layer thickness ∆σ
does not depend on the horizontal co-ordinates x and y . This makes it impossible to locally
refine the grid around pycnocline in regions with steep bed topography. Moreover, the σ transformation gives rise to, not always required, high grid resolution in shallow areas (tidal
flats) and possibly insufficient grid resolution in deeper parts (holes) of the computational
domain. At tidal flats at low tide, the mapping may even become singular. The numerical
scheme may become non-convergent in these areas due to hydrostatic inconsistency (Haney,

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∆zk

Figure 12.1: Irregular representation of bottom boundary layer in the Z -model

1991).

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The vertical grid system of a Z co-ordinate model is based on horizontal surfaces with constant z co-ordinate value intersecting the water column; see Figure 12.1. The concept of
layers used here should not be confused with layers of constant density in stratified flows.
The layer thickness here is defined as the distance between two consecutive grid surfaces
and is independent of space and time for an intermediate layer. The layer thickness of the
top layer ∆zkmax is defined as the distance between the free surface and the first horizontal
surface. The layer thickness may vary in space and time. The free surface moves through the
vertical grid (Casulli and Cheng, 1992). The vertical index k of the top layer of neighbouring
horizontal grid cells may vary. In that case, fluxes may be defined at cell faces that do not
necessarily have a “wet” neighbouring grid cell. The thickness of the bottom layer is the distance between the bottom z = −d(x, y) and the first horizontal surface above the bed. The
layer thickness of the top and bottom cells can be very small, even approaching zero as the
top cell becomes dry.
Let z = zk be strict horizontal surfaces, where k is an integer indicating the layer index. In
the present model, the vertical grid spacing ∆zk is defined by:

∆zk (x, y, t) = min [ζ(x, y, t), zk ] − max [−d(x, y), zk−1 ]

(12.1)

Taking into account variable grid sizes near the bed and allowing the free surface to move
through the vertical grid introduces a lot of book keeping and makes the free surface boundary
elaborate to treat in the numerical method. The grid points that are “wet” are determined every
half time step. A computational cell is set “wet” when ever ∆zi,j,k > 0. Since the grid spacing
near the bed and free surface may vary as a function of space and time, velocity points on
the staggered grid of two adjacent grid cells may be situated at different vertical positions.
Formally, this leads to additional terms in the discretized equations but these terms are not
taken into account. The variation of the free surface and bed topography is smooth in most
areas, which justifies the neglect of the cross terms involved.
The 3D shallow-water models in Delft3D-FLOW using σ co-ordinates and z co-ordinates respectively, are based on almost the same numerical methods.
The 3D shallow-water equations are discretized on a staggered grid (Arakawa C-grid). The
shallow-water equations (SWE) are solved by an ADI-type of factorization for the barotropic
pressure (Stelling, 1984). Both the horizontal components of the velocity vector, u and v ,
are computed once in a full time step ∆t. The vertical grid space may vanish due to drying and flooding of shallow areas. The vertical viscosity terms are integrated fully implicitly
in order to avoid an excessive small time step imposed by the relatively small vertical grid

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Figure 12.2: Vertical computational grid Z -model (left) and σ -model (right)

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spaces. The vertical advection terms can be integrated using either an implicit scheme (central differences), or an explicit upwind (finite volume scheme), depending on the application.
The explicit scheme introduced a time step criterium for stability. The horizontal viscosity
terms are integrated explicitly. For the integration of the horizontal advection terms, different
schemes are available:
Explicit Multi-Directional Upwind scheme (MOMSOL = MDUE, default option)
Implicit Multi-Directional Upwind scheme (MOMSOL = MDUI)
Implicit (first-order) Upwind scheme (MOMSOL = IUPW )
Explicit Flooding scheme (MOMSOL = FLOOD)
Explicit Upwind Finite-Volume scheme (MOMSOL = FINVOL)

The characteristics of these different schemes are explained in section 12.5.1.
For the explicit integration schemes (or when flooding of dry cells is involved), the time step is
restricted by the Courant-Friedrichs-Lewy condition for horizontal advection.
For the computation of the vertical eddy viscosity and eddy diffusivity several methods are
available, just as for the σ -model. The standard k -ε turbulence closure model (Rodi, 1984) is
commonly recommended. It uses two partial differential equations to compute the transport
of turbulent kinetic energy and energy dissipation rate. The production term only depends
on the vertical gradients of the horizontal velocity. The presence of stratification is taken into
account by the buoyancy flux.
A finite volume approach is used for the discretisation of the scalar transport equation, which
ensures mass conservation. To circumvent time step restrictions imposed by the small vertical grid size in drying areas, implicit time integration is used for the vertical derivatives in the
transport equation. In horizontal and vertical direction, diffusion is discretized using central
differences. For horizontal derivatives, either explicit or implicit approximations can be used,
depending on the application. The horizontal advective terms can be computed by either the
Van Leer-2 TVD scheme or the Implicit Upwind scheme (first order accurate) and vertical advection is computed using an implicit central difference method to avoid time step limitations.
Apart from the free surface, the vertical grid spacing is not a function of time.
An overview of all available schemes for horizontal and vertical advection and diffusion for
both the momentum equation and the transport equation in the Z -layer model is given in
Table 12.1. For comparison also the options available in the σ -model have been included.

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Table 12.1: Available advection and diffusion schemes in the Z -layer model (for comparison also the options available in the σ -model have been included).

Method

Process

Options

Remarks

Time integration

ADI

section 10.4

Hor. advection
(momentum)

- CYCLIC
- WAQUA
- FLOOD

section 10.5.1

Vert. advection
(momentum)

Central implicit

section 10.5.2

Hor. advection
and diffusion
(transport)

- Cyclic
- Van Leer-2

12.2
12.2.1

section 10.6

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Z -model

σ -model

Time integration

ADI

section 12.2

Hor. advection
(momentum)

- MDUE
- MDUI
- IUPW
- FLOOD
- FINVOL

section 12.5.1

Vert. advection
(momentum)

- Central implicit
- Upwind explicit
(finite volume)

section 12.5.2

Hor. advection
(transport)

- Van Leer-2
- IUPW

section 12.6

Hor. diffusion
(transport)

- Central explicit
- Central implicit

section 12.6

Time integration of the 3D shallow water equations
ADI time integration method

The 3D shallow-water equations are discretized on a staggered grid (Arakawa C-grid). The
shallow-water equations (SWE) are solved by an ADI-type of factorization for the barotropic
pressure (Stelling, 1984). Both the horizontal components of the velocity vector, u and v , are
computed once in a full time step ∆t. The vertical advection and viscosity term are integrated
fully implicitly in order to avoid an excessive small time step imposed by the relatively small
vertical grid spaces near the bottom and the free surface. The vertical grid space may vanish
due to drying and flooding of the top layer. The horizontal advection and viscosity terms are
integrated explicitly. The time step is restricted by the Courant-Friedrichs-Lewy condition for
horizontal advection.
In vector form (for the 2D case), the ADI-method is given by:

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Step 1:

~` 1
~ `+ 21 − U
U
~
~ `+ 21 + 1 Ay U
~ ` + BU
~ `+ 12 = d,
+ Ax U
1
2
2
∆t
2

(12.2)

Step 2:

~ `+1 − U
~ `+ 12
1 ~ `+ 1 1 ~ `+1
U
~
~ `+1 = d,
2 +
+ Ax U
Ay U
+ BU
1
2
2
∆t
2

(12.3)


∂
0
−f g ∂x
0
0 ,
Ax =  0
∂
∂
H ∂x 0 u ∂x

(12.4)

with:


0
0
0
∂
,
0
g ∂y
Ay =  f
∂
∂
0 H ∂y v ∂y

and:

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

λ 0 0
0 λ 0
0 0 0

(12.5)

(12.6)

with λ the linearised bottom friction coefficient.

To improve stability the bottom friction is integrated implicitly for each stage. d~ is the right-hand
side containing the horizontal advection terms, external forcing like wind and atmospheric
pressure. The time integration of the horizontal viscosity terms is discussed in section 10.5.1
and is dependent on the formulation.
In the first stage, the time level proceeds from ` to `+ 12 and the simulation time from t = `∆t

to t = ` + 21 ∆t. In this stage the U -momentum equation is solved, which is implicitly
coupled with the continuity equation, Equation (9.3), by the free surface gradient. In the
second stage, the time level proceeds from ` + 12 to ` + 1. The V -momentum equation is
solved, which is implicitly coupled with the continuity equation by the free surface gradient.

For the 3D shallow water equations, the horizontal velocity components are coupled in the
vertical direction by the vertical advection and viscosity term. In the vertical direction a fully
implicit time integration method is applied, which is first-order accurate in time and leads to tridiagonal systems of equations. The vertical coupling of the discretised momentum equations
is eliminated by a double sweep algorithm.

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12.2.2

Linearisation of the continuity equation
The non-linear terms in the coupled continuity equation and momentum equations, given by
Eqs. (9.3), (9.7) and (9.8), are removed by linearisation of the fluxes in time. For the terms
containing U velocity in the continuity equation, the linearisation leads to1 :

`+ 12
∂ p
∂ p
` `+ 21
≈
Gηη HU
≈
Gηη H U
∂ξ
∂ξ
p

` `+ 12
` `+ 12
Gηη H U
−
Gηη H U
m+ 12 ,n
m− 12 ,n
≈
∆ξ
(12.7)
Bed stress term

12.3

DR
AF

The bed stress term is computed using the logarithmic boundary layer relation expressed by
Equation (9.58). In this expression the grid distance of the first grid point above the bed, ∆zb
is used to determine the bed stress. When the distribution of the layer thickness at the bottom
shows large variation then large errors in the water level gradient may be introduced. This
is caused by local maxima of the turbulent energy level computed by the turbulence closure
model that affects the vertical viscosity term and vertical velocity.
In the Z -model this situation is more likely to occur than in the σ -model because the grid
distance of the first grid point above the bed, ∆zb can vary strongly in the x-, y -space and its
value can locally be quite small; see Figure 12.1. This will result in a bed stress term that is
inaccurate and discontinuous.
To reduce this effect, the bed stress term is computed using the velocity at one grid point
above the bed (unless the number of active layers equals one):

u∗ =

ubottom+1 κ

ln 1 +

∆zbottom+1
+∆zbottom
2
z0

(12.8)

An additional option is added to Delft3D-FLOW to improve the accuracy and smoothness of
the computed bottom shear stress significantly. This option involves the local remapping of
the near-bed layering to an equidistant layering, as described in Platzek et al. (2012), see
section B.26.
12.4

Horizontal viscosity terms

The horizontal viscosity term is simplified (see Eqs. (9.26) and (9.27)). The simplification
yields a Laplace operator along grid lines. The u-momentum equation involves only secondorder derivatives of the u-velocity.
In the momentum equations, the complete Reynolds stress tensor, given by Eqs. (9.23) to
(9.25), is used in the following cases:

partial slip at closed boundaries,
no slip at the closed boundaries,
HLES-model for sub-grid viscosity.
1

This linearisation of the continuity equation is also used in the σ -model in combination with the Flooding
scheme for advection

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Table 12.2: Time step limitations shallow water solver Delft3D-FLOW

Points per wave period T
Accuracy ADI for barotropic
mode for complex geometries

∆t ≤

T
40

Cf = 2∆t gH ∆x1 2 +

Stability baroclinic mode
Explicit algorithm flooding

∆t|u|
∆x

√
<4 2

∆t2νH ∆x1 2 +

1
∆y 2

Stability horizontal viscosity
term

∆t|u|
∆x

<2
r

gH
1
∆t ∆ρ
+
ρ 4
∆x2

Explicit advection scheme

1
∆y 2

DR
AF

For the complete Reynolds stress tensor, the shear stress τξη in the u-momentum equation
contains derivatives of the v -velocity. The horizontal viscosity term is integrated explicitly,
which leads to the following additional stability condition:

1
∆t ≤
2νH

1
1
+
2
∆x
∆y 2

−1

In case of a curvilinear grid ∆x =
12.4.1

Gξξ and ∆y =

(12.9)

p
Gηη .

Overview time step limitations

In Table 12.2 an overview of the time step limitations due to stability and accuracy for the
time integration limitations are given for the shallow water code Delft3D-FLOW. Which of the
limitations is most restrictive is dependent on the kind of application: length scale, velocity
scale, with or without density-coupling, etc.
below ∆x and ∆y are horizontal
p In the relationsp
grid sizes. For a curvilinear grid ∆x =
Gξξ and ∆y = Gηη .
12.5
12.5.1

Spatial discretisations of 3D shallow water equations
Horizontal advection terms

The horizontal advective terms in the Z -model can be approximated by a number of different
schemes:

Explicit Multi-Directional Upwind scheme (MOMSOL = MDUE, default option)
Implicit Multi-Directional Upwind scheme (MOMSOL = MDUI)
Implicit (first-order) Upwind scheme (MOMSOL = IUPW )
Explicit Flooding scheme (MOMSOL = FLOOD)
Explicit Upwind Finite-Volume scheme (MOMSOL = FINVOL)

The Multi-Directional Upwind MDUE (explicit) and MDUI (Implicit) discretisations approximate
the advection terms along streamlines (Van Eijkeren et al., 1993). Although this method is
formally of first order accuracy, it was found to be much less diffusive than the standard first
order upwind method (Bijvelds, 1997). The discretisation stencil is dependent on the direction
of the flow; see Figure 12.3. The discretisation for flow with a positive U and V -component is

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given by the following two equations.


um,n,k
um,n−1,k −um−1,n−1,k
ξη

√
v̄m,n,k
> um,n,k > 0

∆ξ
( Gηη )m,n

=
,
u
um,n,k −um−1,n,k
ξη

u
>
v̄
>
0
 √Gm,n,k
m,n,k
m,n,k
∆ξ
( ηη )m,n

DR
AF

u ∂u
p
Gξξ ∂ξ

and:

Figure 12.3: discretisation along streamlines. Grid points in difference stencil dependent
on flow direction

v ∂u
p
Gηη ∂η

m,n,k

(12.10)



ξη
v̄m,n,k
um,n,k −um,n−1,k

ξη

√
v̄m,n,k
> um,n,k > 0

∆η
G
( ηη )m,n

=
,
ξη
v̄m,n,k
um−1,n,k −um−1,n−1,k
ξη


u
>
v̄
>
0
m,n,k
 (√Gηη )
m,n,k
∆η
m,n
(12.11)

The implicit first order upwind IUPW method can be employed when stability is most important
and accuracy is of less interest. This method provides most damping or numerical diffusion
of the available options.
The flooding solver FLOOD is the same as for the σ -model (see section 10.5.1. It switches between conservation of momentum and conservation of energy based on local flow expansions
and contractions due to bottom gradients.
The finite-volume FINVOL scheme is momentum-conservative and can also be applied in
flooding simulations where conservation of momentum is required.
The FLOOD and FINVOL scheme are both fully explicit and thus require the time step to fullfil
the Courant-Friedrichs-Lewy stability condition.
Near the boundaries, the discretisation stencils for the advection terms may contain grid points
on or across the boundary. To avoid an artificial boundary layer or instabilities, the discretisations are reduced to smaller stencils.

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12.5.2

Vertical advection term
The horizontal velocities of adjacent vertical layers are coupled by the vertical advection and
the vertical viscosity term. The Z -model can have a very thin layer near the bottom or near
the free surface. To prevent instabilities, we recommend the use of the fully implicit time
integration for the vertical exchange terms (default). This results in tridiagonal systems of
equations in the vertical.
In a shallow water model the horizontal length scale is much larger than the vertical length
scale. In the vertical direction the eddy viscosity term dominates the advection term, except
in stratified flows where the turbulent exchange is reduced and advection may be dominant.
For the space discretisation of the vertical advection term, a second order central difference
is used:

ξz
w̄m,n,k

m,n,k

um,n,k+1 − um,n,k−1
,
1
h
+ hm,n,k + 21 hm,n,k+1
2 m,n,k−1

∂u
w
∂z

(12.12)

where hm,n,k denotes the thickness of layer with index k defined by hm,n,k = zk − zk−1 .

12.5.3

DR
AF

An explicit, momentum-conservative, upwind finite volume scheme is also available if momentum conservation is considered to be more crucial than stability for a certain application. At
present, this scheme for vertical advection can only be used in combination with the finite
volume FINVOL scheme for horizontal advection. The vertical advection scheme is automatically switched to this explicit upwind approach when the horizontal advection scheme is set
to MOMSOL = FINVOL. The user should note that this scheme is fully explicit and thus requires the time step to fullfil the Courant-Friedrichs-Lewy stability condition, also for vertical
advection, i.e. depending on the vertical grid spacing ∆z and the vertical velocity w .
Viscosity terms

The approximation of the viscosity terms are based on central differences. The vertical viscosity term is discretised as:

∂
∂z

∂u
νV
∂z

m,n,k

νV |m,n,k+1
=
hm,n,k

um,n,k+1 − um,n,k
+
1
(hm,n,k+1 + hm,n,k )
2

νV |m,n,k
um,n,k − um,n,k−1
. (12.13)
−
1
hm,n,k
(hm,n,k + hm,n,k−1 )
2

The vertical eddy viscosity is computed at the layer interface.

We note that near the bottom, the grid layering may be highly non-uniform due to the fact
that the bottom introduces thin layers. In such situations, the approximation given in Equation (12.13), is very inaccurate due to the linear approximations of the (often) near-logarithmic
velocity profiles near the bottom, see e.g. Platzek et al. (2012). To avoid these problems, a
near-bed, layer-remapping approach was implemented as proposed by Platzek et al. (2012).
This option can be switched on using an additional keyword, described in section B.26.
12.6

Solution method for the transport equation
A robust and accurate solver for scalar transport has to satisfy the following demands:

mass conservation by consistency with the discrete continuity equation,
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monotonicity (positive solution),
accuracy,
suitable for both time-dependent and steady state problems and
computationally efficient.

To ensure that the total mass is conserved, the transport equation is discretised with a mass
conserving Finite Volume approach (flux form). The transport equation formulated in a conservative form in Cartesian co-ordinates is given by:

∂ (∆zm,n,k c)
1
+
{∂x (uc∆y∆zm,n,k ) + ∂y (vc∆x∆zm,n,k )}
∂t
∆x∆y
+ (wc)m,n,k − (wc)m,n,k−1 =

1
∂c
∂c
+
∂x DH ∆y∆zm,n,k
+ ∂y DH ∆x∆zm,n,k
+
∆x∆y
∂x
∂y

∂c
∂c
+ DV
− DV
− λd ∆zm,n,k c + S, (12.14)
∂z m,n,k
∂z m,n,k−1

DR
AF

with λd representing the first order decay process and S the source and sink terms per unit
area. ∆x and ∆y are the grid spaces in the physical space. The index of the computational
layer k increases in the positive Z -direction. kmin and kmax are the indices of the bottom
and top cells respectively. The range of vertical index varies over the horizontal grid. The
vertical grid spacing of the top layer ∆zkmax changes in time as the free surface moves.
There is no scalar flux through the free surface and the bottom.
Two methods have been implemented in the Delft3D-FLOW transport solver in Z -model to
approximate the horizontal advective fluxes. The default option is the so-called Van Leer-2
scheme (Van Leer, 1974), which guarantees monotonicity of the solution. The time integration
of the Van Leer-2 scheme is explicit and therefore the CFL condition for advection gives a
stability condition:

Cadv = max

u∆t v∆t
,
∆x ∆y

≤ 1,

(12.15)

The second available method is an implicit first-order upwind scheme IUPW, which does not
have the CFL stability condition, but which is less accrate than the Van Leer-2 scheme.
The horizontal diffusive terms are discretized conform the choice made for the horizontal
advective terms, i.e. when the Van Leer-2 scheme is chosen, the diffusive terms are approximated explicitly, whereas when the IUPW scheme is chosen, they are modelled implicitly. In
the case the explicit integration of the horizontal diffusive fluxes is used (i.e. for the Van Leer-2
scheme) an upper limit for the time step is given by:

1
∆t ≤
2DH

1
1
+
2
∆x
∆y 2

−1
.

(12.16)

The scalar concentrations are coupled in the vertical direction by the vertical advection and
diffusion term. The vertical transport is computed at the layer interfaces which are situated
entirely under the free surface layer both at the old and the new time level. An explicit time
integration of the vertical exchange terms near the bottom and free surface would lead to very

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zk-1

t+∆t/2

(m,kmax)
(m,kmax)

(m,kmax)

(m,k)

DR
AF

( m ,k m a x (m -1 ) )

Figure 12.4: Aggregation of Control volumes in the vertical due to variation position free
surface

(m ,k m a x (m ))

Figure 12.5: Horizontal fluxes between neighbouring cells with variation in position free
surface

severe time step limitations:

(∆z)2
,
2DV
∆z
∆t ≤
.
w
∆t ≤

(12.17)
(12.18)

Therefore in the vertical direction a fully implicit time integration method is applied, which is
first order in time and leads to tri-diagonal systems of equations. The vertical coupling of the
discretised transport equations is removed by a double sweep algorithm.
To combine the horizontal and vertical transport, we introduce an approach based on a fractional step method. The water column is divided into two parts; see Figure 12.4. In this case,
the free surface at the old time level t and the new time level t + 21 ∆t are in a different computational layer. The 3D part of the water column consists of the cells (finite volumes) which are
situated entirely under the free surface layer at both time levels. The remaining “wet” cells are
aggregated to one Control Volume and the horizontal fluxes are summed, see Figure 12.5.
The concentrations at the new time level, t + 12 ∆t are computed. If the index of free surface
the cell has increased, the concentration at the new time level is assumed to be constant over
all the computational layers in the free surface cell.

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Source terms are integrated explicitly. In order to avoid negative concentrations and instabilities, sink terms are integrated fully implicitly.
12.6.1

Horizontal advection
Two methods have been implemented in the Delft3D-FLOW transport solver to approximate
the horizontal advective fluxes. The default option is the so-called Van Leer-2 scheme (Van
Leer, 1974), the second option is an implicit first-order upwind scheme IUPW.

12.6.1.1

Van Leer-2 scheme

The Van Leer-2 scheme (Van Leer, 1974) is used for the approximation of the horizontal
transport terms. It combines two numerical schemes, namely a first order upwind scheme
and the second order upwind scheme developed by Fromm. In case of a local minimum or
maximum the first order upwind scheme is applied, whereas the upwind scheme of Fromm is
used in case of a smooth numerical solution.
The interpolation formula for the horizontal fluxes is given by:

with:

DR
AF

Fm,n,k


cm+1,n,k −cm,n,k
cm,n,k + α (1 − CFLadv −u ) (cm,n,k − cm−1,n,k ) cm+1,n,k
,

−cm−1,n,k


when um,n,k ≥ 0,
= um,n,k hm,n,k ∆y
c
−cm+2,n,k

c
+ α (1 + CFLadv −u ) (cm,n,k − cm−1,n,k ) m+1,n,k
,

cm,n,k −cm+2,n,k
 m+1,n,k
when um,n,k < 0,

CFLadv −u =
and:

α=


 0,
 1,

∆t |u|
∆x

cmm+1,n,k −2cm,n,k +cm−1,n,k
cm+1,n,k −cm−1,n,k
cm+1,n,k −2cm,n,k +cm−1,n,k
cm+1,n,k −cm−1,n,k

(12.19)

(12.20)

> 1, (local max. or min.),

≤ 1, (monotone).

(12.21)

In y -direction, a similar discretisation is applied. The time integration of the Van Leer-2
scheme is explicit. The Courant number for advection should be smaller than 1.
12.6.1.2

Implicit upwind scheme

The interpolation formula for the horizontal fluxes in x-direction is given by:

`+1
Fm,n,k
= u`m,n,k h`m,n,k ∆y

 `+1
c
,


 m,n,k

when u`m,n,k ≥ 0,

c`+1
,


 m+1,n,k

(12.22)

when u`m,n,k < 0,

It is a first order upwind scheme. Note that we now added the time level superscript ` to
indicate the implicit treatment of the concentrations c in the fluxes. In y -direction the fluxes
are discretized similarly.

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12.6.2

Vertical advection
In the vertical direction, the fluxes are discretised with a central scheme:

cm,n,k + cm,n,k+1
= wm,n,k
2

cm,n,k + cm,n,k−1
−wm,n,k−1
.
2

(wc)m,n,k − (wc)m,n,k−1

(12.23)

Forester filter

In 3D, the central differences in the vertical may give rise to non-physical spurious oscillations,
so-called “wiggles” (Gresho and Lee, 1981) in the solution. These wiggles arise in the vicinity
of steep gradients of the quantity to be resolved. The wiggles in the concentration may be
introduced in stratified areas near closed boundaries and steep bottom slopes. Positive solutions are not guaranteed, because there the vertical transport is large. In case of negative
concentrations, an iterative filter procedure based on local diffusion along Z -lines followed by
a vertical filter is started in order to remove the negative values. These filters can be switched
on by the user (see section 4.5.8). The filtering technique in this procedure is the so-called
Forester filter (Forester, 1979), a non-linear approach which removes the computational noise
without inflicting significant amplitude losses in sharply peaked solutions.

DR
AF

12.6.3

The time integration in the vertical direction is fully implicit. The vertical advection leads to
a tri-diagonal system in the vertical. If the flow in the vertical is advection dominated due to
vertical stratification in combination with up welling or down welling near a closed boundary, a
sill or a discharge of buoyant water, the central differences in the vertical may give rise to nonphysical spurious oscillations. The scalar concentration then computed has an unphysical
maximum or minimum (overshoot or undershoot).

If concentration cm,n,k is negative, then the iterative filtering process in the x-direction is given
by:

cp+1
m,n,k

cpm,n,k

cpm+1,n,k − 2cpm,n,k + cpm−1,n,k
,
+
4

(12.24)

This filter is applied only in grid cells where a negative concentration occurs.
The superscript p denotes the iteration number. The filter smooths the solution and reduces
the local minima (negative concentrations). Consequently, a positive concentration will remain
positive, i.e. it will not introduce negative concentrations irrespective the steepness of the concentration gradients. A negative concentration surrounded by positive concentrations, usually
the result of ill-represented steep gradients (wiggles), will be less negative after one iteration
and is effectively removed after several iterations by adding enough (local) diffusion to force
the concentration to become positive. Maximally 100 iterations are carried out. If there is still
a grid cell with a negative concentration after 100 iterations, then a warning is generated.
Local maxima and minima in temperature or salinity in the vertical direction, generated by the
computational method may give physically unstable density profiles and can also better be
removed by a numerical filter then by turbulent vertical mixing. A similar filtering technique
as in the horizontal direction is applied for points with a local maximum or minimum in the
vertical:
local maximum: cm,n,k > max (cm,n,k+1 , cm,n,k−1 ) + ε,

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local minimum: cm,n,k < min (cm,n,k+1 , cm,n,k−1 ) + ε,
the filter is applied, with ε = 10−3 . The numerical diffusion coefficient of the vertical filter is:

Dnum =

∆z 2
.
2∆t

(12.25)

Smooth but unstable vertical density profiles of salinity and temperature in the vertical direction, can sometimes also better be vertically mixed by a numerical filter then by the turbulence
model. For salinity, the algorithm is given by:

If sm,n,k > sm,n,k−1 + ε Then

sm,n,k−1

DR
AF

Endif

(sm,n,k − sm,n,k−1 )
2∆zk
(sm,n,k − sm,n,k−1 )
= sm,n,k−1 + min (∆zk , ∆zk−1 )
2∆zk−1

sm,n,k = sm,n,k − min (∆zk , ∆zk−1 )

(12.26)

with ε = 10−3 .

If both the horizontal and vertical filters are switched on, then first the filter in the horizontal
direction is carried out. It is followed by the filter in the vertical direction, thereby minimising
the additional vertical mixing.
Remark:
The vertical Forester filter does not affect other constituents. When activated it only
smooths salinity and temperature.
12.7

Baroclinic pressure term

The transport equation is coupled with the momentum equations by the baroclinic pressure
term; see Eqs. (9.15) and (9.16) and section 9.3.4. The baroclinic pressure term reads:

1
Px (x, z) =
ρ0

∂ρ (x, z)
dz.
∂x

(12.27)

In the Z -model, the horizontal derivatives of the density can be discretised straightforwardly
on the computational grid:

Px |m,n,k

g
=
ρ0

(

)
kmax
X
1
ρm+1,n,k − ρm,n,k
ρm+1,n,j − ρm,n,j
∆zm,n,k
+
∆zm,n,j
2
∆x
∆x
j=k+1
(12.28)

The temporal variations in salinity and temperature are slow compared to the variations in
the flow and therefore the baroclinic term in the momentum equations is treated explicitly,
introducing a stability condition for internal gravity waves (baroclinic mode), see Table 12.2.
The coupling with the flow is weak and in Delft3D-FLOW, the transport equation is solved
independently of the flow for each half time step.

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12.8

Numerical implementation of the turbulence models

12.9

Drying and flooding

The turbulence closure models in Delft3D-FLOW are all based on the eddy viscosity concept;
see section 9.5. The eddy viscosity is always based on information of the previous half time
step. The transport equations of turbulent kinetic energy k , Equation (9.127), and dissipation
rate ε, Equation (9.128) are solved in a non-conservative form. For turbulent boundary flows
local production, dissipation, and vertical diffusion are the dominant processes. On the staggered grid, the turbulent quantities k , ε and the eddy viscosity νV are positioned at the layer
interfaces in the centre of the computational cell. This choice makes it possible to discretise
the vertical gradients in the production term and buoyancy term accurately and to implement
the vertical boundary conditions at the bed and the free surface. First order upwind differencing for the advection provides positive solutions. For more details we refer to Uittenbogaard
et al. (1992) and Bijvelds (2001).

DR
AF

Just as in the σ -model, in the Z -model shallow parts of estuaries and coastal seas are subject
to drying and flooding during the tidal cycle. The drying and flooding procedure in the Z -model
is almost identical to the procedure applied in the σ -model. Due to different representation of
the bottom depth (see following section) the procedure is somewhat simplified.
Furthermore, a technical difference is introduced due to the nature of the grid definition in
the vertical. In a σ -model, when a point is set to dry, then all the layers are deactivated
simultaneously. In a Z -model however, the free surface can move freely through the vertical
grid, resulting in the fact that . The top layer can vanish due to ’wetting and drying’ in the
vertical.
The crucial issues in a wetting and drying algorithm are:

The way in which the bottom depth is defined at a water level point.
The way in which the water level is defined at velocity points.
The way in which the total water depth is defined.
Criteria for setting a velocity and/or water level point wet or dry.

These items will be discussed below.
12.9.1

Bottom depth at water level points

The main difference between the σ -model and the Z -model is the representation of the bottom
in the model. In the Z -model it is represented as a staircase around the depth in the water
level points; see Figure 12.1. However, due to grid staggering, the bottom depth in a water
level point dζm,n is not uniquely defined; see Figure 12.6.
The manner in which this depth value can be determined from the four surrounding depth
points may be influenced by the user. In both the σ - and the Z -model, four options are available: MEAN, MAX, DP, and MIN. The option is specified through the value of the parameter
DPSOPT. For the definition and a detailed discussion on this topic we refer you to Chapter 10.

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Figure 12.6: Definition bottom depth on Delft3D-FLOW grid

Drying and flooding switch

DR
AF

The drying and flooding switch, DRYFLP, works exactly the same as in the σ -model; see
section 10.8.3. To activate the additional drying and flooding procedure at a water level point,
based on the evaluation of the value of the total water depth, the value of DRYFLP must be
set to YES. DRYFLP = NO implies that the drying and flooding check is only to be based on
the individual test of the depth values at the cell interfaces.
If the total water depth in a water level point is negative:
ζ
= dζm,n + ζm,n ≤ 0,
Hm,n

(12.29)

the horizontal cell is taken out of the computation and the half time step is repeated. The initial
water level at a dry cell is determined by the depth at a water level point:

ζm,n = −dζm,n .

(12.30)

The surface layer thickness

The vertical grid size near the free surface depends on the spatial location and on time. Once
the new free surface location has been computed, the following equation is used to determine
the vertical grid size:

∆zk (x, y, t) = min [ζ(x, y, t), zk ] − max [−d(x, y), zk−1 ] ,

(12.31)

except for the situation where the water level exceeds the maximum grid layer interface Ztop.
In that case the vertical grid size of the top layer is increased to include the free surface:

∆zk (x, y, t) = ζ(x, y, t) − max [−d(x, y), zk−1 ] .
12.9.2

(12.32)

Bottom depth at velocity points

Due to the staggered grid applied in Delft3D-FLOW, see Figure 12.6, the bottom and total
water depth at velocity points are not uniquely defined. For the Z -model the bottom is represented as a staircase (DPUOPT=MIN) of tiles, centred around the water level points, see
Figure 12.7. The bottom depth at a velocity point is thus the minimum depth of the two surrounding bottom depths in the ζ -points:
η

DPUOPT = MIN : d = min

dζm,n , dζm+1,n

(12.33)

In contrast to the σ -model, this value for DPUOPT is fixed. So any other value will not be
accepted by the program.

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ζ m,n

z = zk max( m,n )

ζ m+1,n
U

z = zk +1

H m,n

U
m,n

H m+1,n

dpmζ +1,n

z = zk
z = zk −1

dpmζ ,n
Figure 12.7: The flow-through height is determined by the flow direction. The bottom is
represented as a staircase around the depth in water level points.

Upwinding of the water level in defining the total water depth

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12.9.3

The total water depth in a U -velocity point is computed using the upwind water level:
U
Hm,n

 η
Um,n > 0,
 d + ζm,n ,
η
=
d + ζm+1,n ,
Um,n < 0,
 η
d + max (ζm,n , ζm+1,n ) , Um,n = 0,

(12.34)

Drying and flooding criteria
As described in section 10.4 an Alternating Direction Implicit (ADI) time integration method is
used in Delft3D-FLOW. This method consists of two stages (half-time steps). At both stages
the same drying and flooding algorithm is applied. Therefore, we will only describe the drying
and flooding algorithm for the first half time step. If a new water level is computed, both the
horizontal geometry (wet versus dry) and the vertical geometry (number of vertical layers) are
updated.
U
The total water depth Hm,n
at a velocity point should at least be positive to guarantee a
realistic discharge across a cell face. If the total water level drops below half of a user-specified
threshold, then the velocity point is set dry. In 3D simulations, the velocity of a computational

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layer is set to zero if the vertical grid space ∆zkU vanishes. The computational cell is closed
for the side normal to that velocity point. If the water level rises and the total water depth is
larger than the threshold, the velocity point is set wet again. The drying threshold is given half
the value of the wetting threshold (hysteresis) to inhibit changes of state in two consecutive
time steps (“flip-flop”), due to oscillations introduced by the algorithm itself. If the vertical grid
space ∆zkU is larger than a threshold ∆zmin the computational layer is taken into account.
The initial velocity of the layer is the same as the velocity of the top layer of the previous half
time level.

SlpLim=#Y#,

In Delft3D-FLOW it is also possible to initiate the bottom friction term in velocity points that
have just become active in case of flooding. This makes sure that the flow through such a
cell interface, directly experiences some bottom friction, which would not be the case if the
cell face would be initialised with zero velocity. This algorithm is automatically switched on
when using the bottom depth option DPSOPT=DP. Otherwise, it can be switched on using the
additional parameter (see Appendix B):

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(a slope limiter), which also makes sure that the flow along steep bottom slopes occurs with a
limited water level gradient (see section B.27).
ζ
at a water level point should at least be positive to guarantee
In 2D, the total water depth Hm,n
a positive control volume. If the total water depth becomes negative, the four velocity points
ζ
at the cell sides are set dry. In 3D simulations, the vertical grid space ∆zk should be positive.

The thickness of the water layer of a dry cell (retention volume) is dependent on the threshold
d specified by you. Therefore, the threshold value d must fulfil the following condition:

δ≥

∂ζ ∆t
.
∂t 2

(12.35)

In general, the magnitude of the disturbances generated by the drying and flooding algorithm
will depend on the grid size, the bottom topography and the time step. The disturbances are
small if the grid size is small and the bottom has smooth gradients. If the bottom has steep
gradients across a large area on a tidal flat, a large area may be taken out of the flow domain
in just one half integration time step. This will produce short oscillations. You can avoid this
by smoothing the bottom gradients. Flooding is an explicit process. The boundary of the wet
area can only move one grid cell per time step. If the time step is too large an unphysical
water level gradient at the wet-dry interface is built up, which will generate a shock wave after
flooding.
In the first stage of the ADI-method the drying and flooding algorithm in Delft3D-FLOW consists of the following checks:
U
U
1 Drying check for velocity points in x-direction (Hm,n
< 0.5δ and ∆zm,n,k
< zmin ) and
U
U
flooding check for velocity points in x-direction (Hm,n
> δ and ∆zm,n,k
> zmin ). These
checks are based on the water level of the previous half time step.
U
2 Drying check for velocity points in x-direction (Hm,n
< 0.5δ ) during iterative solution for
new water level.
ζ
3 Drying check (negative volumes) for water level points (Hm,n
< 0.0).

In the second stage of the ADI-method, the directions are interchanged.

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The threshold δ is specified at input. The total water depth at velocity points is computed by
the upwind approach.
When a computational cell is dry, the thickness of the water layer is below the drying threshold.
If the computational cell is flooded, the water layer may be very thin and may cause problems
in combination with online salt transport or off-line water quality simulations. In Delft3D-FLOW
the computational part is protected against “dividing by zero” by assuming that the total water
depth is at least 10% of the drying and flooding threshold Dryflc, which is also the minimum
layer thickness ∆zmin .
You may define in velocity points so-called weirs or spillways. Weirs are hydraulic structures
causing energy losses, see section 10.9. For a 2D weir the height of the crest, HKRU, is taken
into account in the drying and flooding algorithm.

The drying check for a 2D weir point at a U -point is given by:

1
1
U
Hm,n
< δ or max(ζm−1,n , ζm,n ) + HKRUm,n < δ,
2
2

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and the flooding check:

U
Hm,n
> δ or max(ζm−1,n , ζm,n ) + HKRUm,n > δ.

(12.36)

(12.37)

The weir acts as a thin dam for water levels lower than the crest height.
12.10

Cut-cell and 45 degrees closed boundaries
This feature applies for the Z -model only.

12.10.1

Introduction

A staircase closed boundary is sometimes unavoidable when schematising the land-water
interface, even in curvilinear co-ordinates. To avoid inaccuracies introduced by the staircase
closed boundaries in the Z -model, two methods for removal of such inaccuracies are implemented in Delft3D-FLOW. One is derived from the so-called Cut Cell method, for general
curved closed boundaries which do not coincide with a gridline. The second one is derived
for 45 degrees boundaries (1 to 1).
12.10.2

Cut Cells

The Cut Cell approach involves truncating the Control Volumes at the boundary surface to
create new cells which conform to the shape of the boundary, see Figure 12.8 (left). In the
grid generator corner points are shifted, Figure 12.8 (right) to remove the staircase. This
approach is called a “Cut Cell” method; see Kirkpatrick et al. (2003).
We discuss the approximation of the fluxes through the boundary cells and the pressure
gradients. It is necessary to relocate the velocity nodes associated with the cut boundary
cells. The velocity nodes are placed at the centre of the cut face of the Control Volume. It
allows the mass conservation to be discretised in the same manner as for a standard cell. The
only difference is that the horizontal area (volume) is recalculated for the truncated cells. In 3D
the horizontal area is the same for all layers. The pressure (water level) points are left in the
original position, even though this may mean that they are physically outside the boundaries
of the associated Control Volume. In the present implementation, the advection terms and the
wall shear stresses are not corrected for the cut cells.

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Figure 12.8: left: Cut Cell (definition) and right: defined by shifting (exaggerated) the
corner point to boundary.

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Figure 12.9: Flow along staircase boundary.

The spatial approximation of the advection terms was not adapted. Only for Cut Cells the
curvature term was removed because the grid cells are no longer orthogonal.
On the staggered grid you need averaging to determine the V -velocity in a U -velocity point.
For Cut cells we changed the averaging procedure, to reduce the effect of the zero velocities
at the closed boundaries on the bottom stress. In the averaging procedure only velocity points
which are not at closed boundaries are taken into account. This reduces the artificial boundary
layer along closed “staircase” boundaries.
12.10.3

45 degrees closed boundary

For a staircase boundary of 45 degrees (1-1), a special approach is implemented for the
advection terms. The velocities are reflected in the boundary line, taking into account the
aspect ratio of the grid cells.

Vi,j = −

∆y
Ui,j
∆x

(12.38)

The advection terms for these 45 degree boundary cells are discretised with an explicit first
order upwind scheme using the velocities at the boundaries.

Figure 12.10: Reflection of velocities

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Figure 12.11: Example of a 3D Gate (vertical cross-section)

Figure 12.12: Computational layer partially blocked at the bottom of the 3D gate

12.11

Hydraulic structures

Also in the Z -model, the so-called hydraulic structures can be defined to model the effect of
obstructions in the flow that cannot be resolved on the horizontal grid (sub-grid) or where the
flow is locally non-hydrostatic. Examples of hydraulic structures in civil engineering are gates,
sills, sluices, barriers, porous plates, bridges, groynes, weirs. A hydraulic structure generates
a loss of energy apart from the loss by bottom friction. At these points an additional force term
is added to the momentum equation, to parameterise the extra loss of energy. The term has
the form of a friction term with a contraction or discharge coefficient.
In section 10.9, the mathematical formulations and implementation of the hydraulic structures
available in Delft3D-FLOW has been described thoroughly. In this section only the parts that
deviate will be discussed.
12.11.1

3D Gate

A 3D gate is in fact a thin dam with a limited height/depth (and position in the vertical). It is
located at a velocity point and its width is assumed to be zero, so it has no influence on the
water volume in the model area. The flow at all intermediate layers of the gate is set to zero.
The layer near the top and the layer near the bottom of the gate may be partially blocked.
Upstream of the structure the flow is accelerated due to contraction and downstream the flow
is decelerated due to expansion.
A 3D gate may be used to model a vertical constriction of the horizontal flow such as near
barriers, sluices and Current deflection walls. The vertical constriction of the flow may vary
in time by the lowering or raising of the gate. The implementation of the 3D gate has been
described in section 10.9.1. In this section, the figures showing the 3D gate as defined in the
Z -model will be shown.

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For more details on the data input requirements for the different type of 3D gates, we refer to
Appendix B.3.1.
12.11.2

Quadratic friction
The only hydraulic structure where quadratic friction is applied that is not available within the
Z -model is the so-called 2D Weir. The remaining structure may be defined in the Z -model in
a similar manner as the σ -model; see Eqs. (10.70) to (10.76).

12.11.3

Linear friction

12.11.4

Floating structure

The resistance force that is assumed to be linearly dependent on the flow is applied for the
rigid sheet. Rigid sheet in the Z -model is treated in a similar manner as in the σ -model; see
Equation (10.98).

12.12

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Floating structures can also be modelled in the Z -model. It is treated in a similar manner as
in the σ -model; see Equation (10.99).
Assumptions and restrictions

The solution of the discretised equations is just an approximation of the exact solution. The
accuracy of the solution depends not only on the numerical scheme, but also on the way in
which the bottom topography, the geographical area, and the physical processes (turbulence,
wave-current interaction) are modelled.
The time integration method strongly influences the wave propagation when applying a large
time step. The assumption is made that, by restricting the computational time step, the free
surface waves can be propagated correctly.
The open boundaries in a numerical flow model are artificial in the sense that they are introduced to limit the computational area that is modelled. The free surface waves should pass
these boundaries completely unhindered. In the numerical model, wave reflections may occur
at the open boundaries. These reflections will be observed as spurious oscillations superimposed on the physical results. In Delft3D-FLOW weakly-reflective boundaries are available
which diminish these effects.
The open boundary can be divided into segments (sections). The boundary conditions in
Delft3D-FLOW are specified for these segments, two values per segment are required, one for
each segment end. The boundary condition at internal points within this segment is obtained
by linearly interpolation between the end points. Therefore, if the phase variation of the tidal
forcing along an open boundary segment is non-linear then the number of open boundary
segments should be increased so that the phases at all the segments can be specified. Phase
errors may generate an artificial re-circulation flow (eddy) near the open boundary. For steadystate simulations, a similar effect may be observed near the open boundaries if the effect of
the Coriolis force on the water level gradient along the open boundary is not taken into account
in the boundary conditions.
Care must be taken when time-series of measurements are directly prescribed as forcing
functions at the open boundaries. Measurements often contain a lot of undesired noise, due
to meteorological or other effects. For tidal flow computations, calibration on processed field
data obtained from a tidal analysis or Fourier analysis, avoids this problem.

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The following functionalities can not be used in combination with the Z -model:

Parallel calculation
Roller model
Real Time Control
Morphology
Secondary flow
Internal waves
Fluid mud
Gauss Seidel solver
Q2E 2D turbulence model

Heat model other than option 5
Evaporation model
Tide generating forces
Q-H boundary
Drogues
Spherical coordinates
HLES
Structures
Domain decomposition
Wall friction

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The following functionalities are not fully tested in combination with the Z -model:

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Lesser, 2003. Not yet known.

Leer, B. van, 1974. “Towards the ultimate conservative difference scheme II. Monotonicity and
conservation combined in a second order scheme.” Journal of Computational Physics 32:
101–136.

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Glossary of terms

bottom roughness
coefficient

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AF

boundary section

boundary conditions
calibration

coupling program

cross-section

current

cyclic tide

default
GPP

Geometric domain for the models.
Amplitude and phase of the tidal constituents which represent the
tide. See also Delft3D-TIDE.
The measurement of depths of the model area. Represented in
Delft3D-FLOW by a matrix of depth values; each value is defined
in the right upper corner of the corresponding grid cell. Prepared
as an attribute file for Delft3D-FLOW or entered in the MDF-file as a
uniform value for the whole grid. Default: 0.0. Unit: meter.
Measure of the resistance of the flow to the bottom. Physical parameter for Delft3D-FLOW. Defined in the middle of grid sides. Prepared
as an input file for Delft3D-FLOW (containing non-uniform values in
U and V direction) or entered in the MDF-file as a uniform value;
Presentation: table or single value. Given according to: Manning,
Chézy [m1/2 /s], White Colebrook.
Boundaries are separation lines between the model area and the
outside world. Boundaries can be divided in open boundaries, located in open water, and closed boundaries representing the landwater interface. A boundary section is a part of a boundary on which
boundary conditions are prescribed.
Boundary conditions describe the influence of the outside world on
the inside of the model area.
Tuning of model parameters such that the simulation results match
an observed data set within a prescribed accuracy interval.
Program which performs some operations on Delft3D-FLOW output
files in order to create input files for D-Water Quality or D-Waq PART.
With the coupling program, aggregation in time and/or space is possible. Delft3D-FLOW itself can now also perform these actions (See
B.18).
A line defined along a fixed ξ - or η -co-ordinate, where the sum of
computed fluxes, flux rates, fluxes of matter (if exist) and transport
rates of matter (if exists) are stored sequentially in time at a prescribed interval.
In case of 2D computation: Speed and direction of the hydrodynamic
depth-averaged flow. In case of 3D computation: Speed and direction of the hydrodynamic flow in a layer.
Tidal condition in which the tide repeats itself (e.g. cyclic semi-diurnal
tide which repeats itself after it’s period of approximately 24 hours
and 50 minutes).
Initial value for a parameter, to be used in the FLOW Input Processor
at simulation start time if no MDF-file has been opened.
Program for the visualisation and animation of results of Delft3D
modules.
Program for the generation and manipulation of grid related data,
such as bathymetry, or initial conditions.
A second program for the visualisation and animation of results of
Delft3D modules.
Program for the generation of orthogonal curvilinear grids.
Program for the analysis of observed and simulated tide, used during
calibration.
Simulation program for tidal and wind driven flow, including the effect
of density differences due to a non-uniform heat and salt concentration distribution. Previously known as TRISULA.

area
astronomical tidal
constituent
bathymetry

QUICKIN
Delft3D-QUICKPLOT
RGFGRID
Delft3D-TRIANA
Delft3D-FLOW

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discharge rate
domain
drogues
dry area/dry point

drying and flooding

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AF

flow rate
flow velocity

Hydrodynamic speed, averaged over the depth.
Presentation of the bathymetry by iso-lines of depth values.
Location where water and possibly constituents dissolved in the water are released into or subtracted from the model area.
The amount of water and possibly constituents dissolved in the water
released into or subtracted from the model area per unit of time.
Range of values a parameter can have for meaningful results. A
domain is represented by its lower and upper limit.
Floating objects moving with the flow.
Part of the model area that is not flooded. Represented by a collection of cells in the grid (dry points) which are either temporarily or
permanently dry.
A process in which points or sub-areas of the model area are becoming dry or wet depending on the local water depth.
Volume of fluid passing a cross-section per unit of time.
Speed and direction of a water particle. In the staggered grid the
speed is computed at the water level point using only the velocity
components with the same grid co-ordinates as the water level point,
i.e. the velocity components are not averaged over the velocity points
on both sides of the water level point before being used.
Direction in which the flow of a water particle is moving. North = 0◦ ;
East = 90◦ ; South = 180◦ and West = 270◦ . The convention is:

depth averaged speed
depth contours
discharge

flow direction

flow direction β = 90◦ − α
with:

α
β

history file

mathematical angle
angle according Nautical convention
Structured set of virtual points covering the model area in the horizontal direction on which the simulation results are obtained. In
Delft3D-FLOW two types of horizontal grid co-ordinate systems can
be applied: a Cartesian or a spherical co-ordinate system. In both
systems the grid is curvilinear and orthogonal.
Structured set of virtual points covering the model area in the vertical
direction on which the simulation results are obtained. In Delft3DFLOW two types of vertical grids can be distinguished: a σ -grid and
a Z -grid.
Amplitudes and phases that constitute a time dependent signal, such
as a tide. Generally these components are obtained as a result of
Fourier analysis. Fourier components are often prescribed as model
forcing when a cyclic tidal movement is required.
Time of the tide with maximum water level.
Pressure exerted by a fluid due to its weight. When the vertical motion of fluid is small compared to the motion in the horizontal direction
we may still apply this principle in the computation.
File that contains the results of a simulation in monitoring stations as

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grid (horizontal)

grid (vertical)

harmonic components

high water
hydrostatic pressure

Glossary of terms

hydrodynamic
conditions
integrity check
logarithmic
speed/velocity profile
lon/lat
map file

DR
AF

model area

Verification of input and output data on both its domain and its internal consistency.
An expression for the velocity distribution over the depth. The velocity is assumed to be a logarithmic function of the water depth and
depends on the depth averaged speed.
Longitudinal and latitudinal co-ordinates in degrees, minutes and
seconds.
File that contains the results of a simulation in all grid points at specific instances of time.
A part of the physical space (the world) that is (schematically) represented in the simulation. The model area is connected to the outer
world through closed and open boundaries. The forcing of the outer
world on the model area is described by boundary conditions and
external forces such as wind.
Virtual point in the model area, where computational results, such as
the current, the water level and/or the concentration of constituents
are monitored as a function of time. Also called observation point.
Change of bathymetry due to sedimentation and erosion. Computed
with the module 3DMOR feature of FLOW.
Tide with a small tidal range.
Pressure exerted by the fluid due to its (relatively large) vertical motion. The vertical motion, that may be in the order of magnitude of
(or greater than) the horizontal motion, may be induced by buoyancy
or by obstacles or a hydraulic jump.
Monitoring point for current, water level and/or temperature and salinity. Observation points are defined at the centre of grid cells. Delft3DFLOW writes the results of the simulation in this point to a history file.
File that contains a sub-set of the results in ASCII format that can be
listed on a printer.
Start of a simulation using the results of a previous run as initial
conditions.
File with the simulation results at the last time step of a previous
simulation, to be used as initial conditions in a restart run.
Amount of water flowing from the river into the model area.
Equivalent to ‘bottom roughness’. Recommended term is bottom
roughness.
Constituent of (sea) water. Salinity causes a density induced flow
additional to the hydrodynamic flow.
Set of conditions which determine the hydrodynamic simulation completely. A scenario is defined (stored) in an MDF-file and its attribute
files.
Time period between simulation start and stop time, expressed as
real time or in the number of time steps.
Time required by the model to adjust itself to match the prescribed
boundary and initial conditions. Also known as initial period, tran-

horizontal velocity

a function of time.
In case of 2D computation: Speed and direction of the hydrodynamic
depth-averaged flow. In case of 3D computation: Speed and direction of the hydrodynamic flow in a layer.
Remark:
the velocity in a layer is in a σ -layer and is not in a horizontal
plane.
Set of data which determines the input for Delft3D-FLOW.

monitoring station

morphological
dynamics
neap tide
non-hydrostatic
pressure

observation station

print file
restart

restart file

river outflow/run-off
roughness
salinity
scenario

simulation time
spin-up time

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steady state
temperature

test run
thin dam

threshold
tidal constants

TIDE

DR
AF

tidal cycle

time frame

time history
time-series

time step
vector field
verification
viscosity

water level
wind velocity

Z -grid

spring tide
staggered grid

sient time or warming-up time.
Tide with a large tidal range.
Grid in which the water level, velocity components and depth points
are defined at different locations.
Equilibrium situation; all time variations are absent.
Thermodynamic condition of the material concerned. In Delft3DFLOW the temperature is treated as a constituent. Temperature
causes a density induced flow additional to the hydrodynamic flow.
Simulation run to check the hydrodynamic behaviour of the model as
described by the scenario.
A virtual dam along the side of a grid cell across which no flow exchange is possible. Thin dams are defined in the middle of the grid
sides.
Water depth above which a dry grid cell is becoming wet.
Amplitude and phase of the tidal constituents which represent the
tide. See also Delft3D-TIDE.
Time period of the dominant tidal component; about 12 hours and 25
minutes for a semi-diurnal tide and about 24 hours and 50 minutes
for a diurnal tide.
Program for the analysis of observed or simulated water levels or
flows in terms of astronomical tidal components, in order to calculate
a geometric series to represent the tide.
Start and stop time of the simulation and the forcing of all (sub)processes in the simulation, including writing the results to file.
Sequence of numbers giving the value of one or more parameters in
an observation point at sequential moments.
Sequence of numbers giving the value of one or more parameters
used in the model input, or of the simulation results in an observation
point at sequential moments.
Time interval at which the results of the simulation are computed.
Flow data in all grid cells expressed as arrows at a certain instance
in time. The arrow represents the speed and direction of the flow.
Evaluation of the quality of simulated results by comparison with observed data. Also called validation.
Measure of the resistance of the fluid to the flow.
Defined as a uniform value in the MDF-file or as non-uniform values
in every grid point in an attribute file.
Elevation of the free water surface above some reference level.
Magnitude and direction of wind; usually defined relative to true North,
positive angle measured clock wise.
Vertical grid in a 3D model that is strictly horizontal. Index k = 1
in the Z-grid refers to the bottom layer and index k = kmax to the
surface layer.
A 3D model that has been defined with a vertical grid that is strictly
horizontal.
Vertical grid in a 3D model that follows the depth profile, i.e. the socalled σ -plane. Index k = 1 in the σ -grid refers to the surface layer
and index k = kmax to the bottom layer.
A 3D model that has been defined with a vertical grid using σ -planes.

Z -model
σ -grid
σ -model

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A.1
A.1.1

MDF-file
Introduction
File contents
Filetype
File format
Filename
Generated

The Master Definition FLOW file (MDF-file) is the input file for the
hydrodynamic simulation program.
ASCII
Free formatted

FLOW-GUI or manually offline

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The Master Definition FLOW file (MDF-file) is the input file for the hydrodynamic simulation
program. It contains all the necessary data required for defining a model and running the
simulation program. In the MDF-file you can define attribute files in which relevant data (for
some parameters) are stored. This is especially useful when parameters contain a large
number of data (e.g. time-dependent or space varying data). The user-definable attribute files
are listed and described in section A.2.
The MDF-file has the following general characteristics:

Each line contains a maximum of 300 characters.
Each (set of) input parameter(s) is preceded by a Keyword.
A Keyword is at most 6 characters long (a combination of numerical and alpha-numerical
characters, but starting with an alpha-numeric character), followed by an equal sign “=”.
The MDF-file is an intermediate file between the FLOW-GUI and the hydrodynamic simulation
program. As it is an ASCII-file, it can be transported to an arbitrary hardware platform. Consequently, the hydrodynamic simulation program and the FLOW-GUI do not necessarily have
to reside on the same hardware platform.
Generally, you need not to bother about the internal layout or content of the MDF-file. It is,
however, sometimes useful to be able to inspect the file and/or make small changes manually.
Therefore the MDF-file is an ordinary ASCII-file which you can inspect and change with your
favourite ASCII-editor.
The MDF-file is self contained, i.e. it contains all the necessary information about the model
concerned. It can therefore be used as model archive by printing the file.
A.1.2

Example

In this section an example MDF-file is listed and described. The same area is used as in
Chapter 5, but the scenario applies to a 3D computation. The left column contains the keyword
and its value(s); the central column contains the dimension (if useful) and the right column
contains a short description.
Record description:
Keyword and value

Format

Description

Ident = #Delft3D-FLOW .03.02 3.39.12#

C*28

Identification string FLOW-GUI
Comment line (not used)

Commnt=
Runtxt= #Demonstration model Delft3D #

C*20

Up to ten lines of free text to
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Keyword and value

Format

Description

#Friesian Tidal Inlet model #

clarify the purpose of the simulation

#3 layers #

and to indicate specific parameter selections.
C*256

Name of the grid file <∗.grd>

Fmtcco= #FR#

C*2

Format of grid file

Anglat= 5.5000000e+001

Latitude of model centre

Grdang= 0.0000000e+000

Angle between true North and y-axis

Filgrd= #fti_02.enc#

C*256

Grid enclosure file <∗.enc>

Fmtgrd= #FR#

C*2

Format of grid enclosure file

MNKmax= 15 22 3

Number of grid points 3D simulation

Thick = 50.0000

Layer thickness from top to bottom

35.0000

in percentage of total water depth

15.0000

Fildep= #fti_ch02.dep#

C*256

File with depth values <∗.dep>

Fmtdep= #FR#

C*2

Format of depth file

Fildry= #tut_fti_1.dry#

C*256

File with indices of dry points <∗.dry>

Fmtdry= #FR#

C*2

Format of dry points file

Filtd = #tut_fti_1.thd#

C*256

File with indices of thin dams <∗.thd>

Fmttd = #FR#

C*2

Format of thin dam file

Itdate= #1990-08-05#

C*10

Reference date for all time functions

Tunit = #M#

C*1

Time unit of time dependent data

Tstart= 0.000000

Start time after Itdate in Tunits

Tstop = 1.5000000e+003

Stop time after Itdate in Tunits

Dt = 5.00000

Time step in Tunits

Tzone = 0

Local time zone

Sub1 = #S W #

C*4

Flags to activate the processes in two

Sub2 = #PC #

C*3

groups of four and three characters

Namc1 = #Conservative Spill #

C*20

Name of first constituents

Wnsvwp= #N#

C*1

Flag for space varying wind and pressure

Filwnd= #tut_fti_1.wnd#

C*256

File with wind data <∗.wnd>

Fmtwnd= #FR#

C*2

Format of wind data file

Wndint= #Y#

C*1

Wind data interpolation flag

Zeta0 = 1.90000

Initial condition water level

U0 = [.]

Initial condition x-velocity

Initial condition y-velocity

S0 = 3.0000000e+001

Initial condition salinity, one value for each layer

C01 = 1.0000000e+000

Initial concentration constituent 1

Filbnd= #tut_fti_1.bnd#

C*256

File with boundary locations <∗.bnd>

Fmtbnd= #FR#

C*2

Format of boundary file

FilbcH= #tut_fti_1.bch#

C*256

File with harmonic flow boundary conditions <∗.bch>

FmtbcH= #FR#

C*2

Format of harmonic conditions file

FilbcC= #tut_fti_1.bcc#

C*256

File with transport boundary conditions <∗.bcc>

FmtbcC= #FR#

C*2

Format of transport conditions file

Rettis= 1.0000000e+002
1.0000000e+002

Thatcher-Harleman return time at surface
(for x open boundaries)

Rettib= 1.0000000e+002
1.0000000e+002

Thatcher-Harleman return time at bed level
(for x open boundaries)

Filcco= #fti_02.grd#

Commnt=

V0 = [.]

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Keyword and value

Format

Description

Ag = 9.81300

Gravitational acceleration

Rhow = 1030.00

Density of water at background temperature and salinity

Commnt=

Reflection coefficient

Alph0 = [.]
1R

Background water temperature

Salw = 3.1000000e+001

Background salinity

Rouwav= # #

C*4

Bottom stress formulation due to wave action

Wstres= 0.00250000 0.000000 0.00250000
100.000 0.00250000 0.000000

Wind stress and wind speed coefficients

Rhoa = 1.00000

Air density

Betac = 0.500000

Parameter spiral motion

Equili= #N#

C*1

Flag for computation spiral motion

Tkemod= #Algebraic #

C*12

Type of turbulence closure model

Ktemp = 0

Selection flag for heat model

Fclou = 0.000000

Percentage sky cloudiness

Sarea = 0.000000

Surface area in heat model

Ivapop = 0

Vapour pressure user specified. Only for heat model 4.

Temint= #Y#

C*1

Interpolation flag for temperature data

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Tempw = 15.0000

Commnt=

Roumet= #C#

C*1

Type of bottom friction formulation

Ccofu = 45.0000

Uniform bottom roughness in u-dir.

Ccofv = 45.0000

Uniform bottom roughness in v-dir.

Xlo = 0.000000

Ozmidov length scale

Htur2d= #N#

C*2

Flag for HLES sub-grid model

Vicouv= 2.00000

Uniform horizontal eddy viscosity

Dicouv= 10.0000

Uniform horizontal eddy diffusivity

Vicoww= 1.00000e-006

Uniform vertical eddy viscosity

Dicoww= 1.00000e-006

Uniform vertical eddy diffusivity

Irov = 0

Flag to activate partial slip conditions

Z0v = [.]

Roughness length vertical side walls

Iter = 2

Number of iterations in cont.eq.

Dryflp= #YES#

C*3

Flag for extra drying and flooding

Dpsopt= #MAX#

C*3

Option for check at water level points

Dpuopt= #MEAN#

C*4

Option for check at velocity points

Dryflc= 0.0500000

Threshold depth drying and flooding

Dco = -999.999

Marginal depth in shallow area’s

Tlfsmo= 0.000000

Time interval to smooth the hydrodynamic boundary conditions

ThetQH= 0.0000000e+000

Relaxation parameter for QH relation (0 = no relaxation)

ThetQT= 0.0000000e+000

Relaxation parameter for total discharge boundary (0 = no relaxation)

Forfuv= #Y#

C*1

Flag horizontal Forester filter

Forfww= #Y#

C*1

Flag vertical Forester filter

Sigcor= #N#

C*1

Flag to activate anti-creep

Trasol= #Cyclic-method#

C*13

Numerical method for advective terms

Momsol= #Cyclic#

C*6

Numerical method for momentum terms

Filsrc= #tut_fti_1.src#

C*256

File with discharge locations <∗.src>

Fmtsrc= #FR#

C*2

Format of discharge locations file

Fildis= #tut_fti_1.dis#

C*256

File with discharge data <∗.dis>

Fmtdis= #FR#

C*2

Format of discharge data file

Commnt=

Commnt= no.

observation points:

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Keyword and value

Format

Description

Filsta= #tut_fti_1.obs#

C*256

File with observation points <∗.obs>

Fmtsta= #FR#

C*2

Format of observation points file

Filpar= #tut_fti_1.par#

C*256

File with drogues <∗.par>

Fmtpar= #FR#

C*2

Format of drogues file

Filcrs= #tut_fti_1.crs#

C*256

File with cross-sections <∗.crs>

Fmtcrs= #FR#

C*2

Format of cross-sections file

C*256

File with vegetation description <*.pla>

PMhydr= #YYYYYY#

C*6

Flags print map output hydrodynamic quantities

PMproc= #YYYYYYYYYY#

C*10

Flags print map output constituents and turbulence

PMderv= #YYY#

C*3

Flags print map output derived quantities

PHhydr= #YYYYYY#

C*6

Flags print time history hydrodynamic quantities

PHproc= #YYYYYYYYYY#

C*10

Flags print time history constituents and turbulence

PHderv= #YYY#

C*3

Flags print time history derived quantities

PHflux= #YYYY#

C*4

Print flags time history fluxes through cross-sections

SMhydr= #YYYYY#

C*5

Flags store map output hydrodynamic quantities

SMproc= #YYYYYYYYYY#

C*10

Flags store map output constituents and turbulence

SMderv= #YYYYY#

C*6

Flags store map output derived quantities

SHhydr= #YYYY#

C*4

Flags store time history output hydrodynamic quantities

SHproc= #YYYYYYYYYY#

C*10

Flags store time history output constituents and turbulence

SHderv= #YYYYY#

C*5

Flags store time history output derived quantities

SHflux= #YYYY#

C*4

Flags store time history output fluxes through cross-sections

Filfou= # #

C*256

File with quantities to be Fourier analysed <∗.fou>

Online= #YES#

C*3

Flag for online visualisation

Prmap = [.]

Time instances to print map output

Prhis = 750.000 0.000000 60.0000

Time information to print history output

Flmap = 2190.00 120.000 2940.00

Time information to store map output

Flhis = 0.000000 5.00000 2940.00

Time information to store history output

Flpp = 2190.00 10.0000 2940.00

Time information to write to the communication file

Flrst = -999.999

Time interval to write restart file

C*1

Flag for activating barocline pressure term at open boundaries. Default = #Y#

Commnt=
Eps = [.]
Commnt=
Commnt= no.

cross sections:

Filpla= #name.pla#

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Commnt=

Commnt= attribute file Fourier analysis

Commnt=

BarocP = #Y#

A.1.3

Physical parameters
For Tide Generating forces and Thatcher-Harleman return times there is an extra explanation
on the use of the keywords in the following sections

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A.1.3.1

Tide Generating Forces
For tide generating forces you can specify the tidal components that are taken into account.
The layout of Tidfor is defined as follows:
Tidfor = #M2 S2 N2 K2#
#K1 O1 P1 Q1#
#Mf Mm Ssa #

A.1.3.2

Thatcher-Harleman Conditions

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Rettis = 1.0000000e+002
0.0000000e+000
5.0000000e+001
Rettib = 1.0000000e+002
0.0000000e+000
5.0000000e+001

The Thatcher-Harleman conditions are by default specified by a return time (in minutes) for
the surface and the bed level for each open boundary. Example with 3 open boundaries:

It is also possible to specify return times for individual constituents, using the following keywords:

RetsS
RetbS
RetsT
RetbT
Rets01
Retb01

Return time for Salinity at surface
Return time for Salinity at bed level
Return time for Temperature at surface
Return time for Temperature at bed level
Return time for Constituent number 1 at surface
Return time for Constituent number 1 at bed level

Idem for constituents with other numbers.
Remarks:

Rettis and Rettib can be combined with the additional keywords to specify return
times for all constituents, with varying values for specific constituents. Here is an example specifying a return time of 100 minutes for all constituents, except for temperature,
having a return time of 200 minutes:
Rettis = 1.0000000e+002
1.0000000e+002
Rettib = 1.0000000e+002
1.0000000e+002
RetsT = 2.0000000e+002
2.0000000e+002
RetbT = 2.0000000e+002
2.0000000e+002

Rettis and Rettib are supported by FLOW-GUI; the constituent specific variants
are not; you have to add them with a text editor to the mdf-file.
A.1.4

Output options
The MDF-file contains a number of keywords for selecting output options to print (ascii) files
and binary map-, his-, dro-, and com-files.
The keywords related to 2D/3D ascii output are PMhydr, PMproc, PMderv to select which
quantities to write and Prmap to indicate the time steps at which to write these fields. The

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keywords related to history station and cross-section ascii output are PHhydr, PHproc,
PHderv, PHflux to select the quantities and Prhis to select the output times. The ascii
output options are generally not used except for debugging purposes.
The keywords related to 2D/3D binary map-file output are SMhydr, SMproc, SMderv to
select the quantities and Flmap to select the output times. The keywords related to history
station and cross-section binary output are SHhydr, SHproc, SHderv, SHflux to select
the quantities again and Flhis to select the times. The format used for the binary map-,
his-, dro-files is by default NEFIS; this can be switched to NetCDF by means of the keyword
FlNcdf. The keyword Flpp specifies the output times for the com-file; the quantities written
to the com-file and the file format of the com-file cannot be changed.

The values to be specified for the PM*, PH*, SM* and SH* keywords are strings of Y and N
characters representing flags for output of different quantities. These quantities differ slightly
for storing results to file and for printing, so the flags for each option are described in the tables
below. Finally Table A.6 lists a couple of options for additional output to map- and his-files and
the tri-diag file which can be switched on in the Additional parameters section of the user
interface.

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Table A.2: Print flags for map-data

Keyword and value

Number/Description

PMhydr = #YYYYYY#

1
2–5
6

Water level
U and V-velocities, magnitude and direction
ω -velocities relative to σ -plane and wvelocities

PMproc =
#YYYYYYYYYY#

1
2
3–7
8
9 and 10

Concentration salinity
Temperature
Concentration constituents
Intensity spiral motion
Turbulent energy and dissipation

PMderv=#YYY#

1 and 2

Vertical eddy viscosity and vertical eddy diffusivity. Richardson number if either or both
are selected
Density

Table A.3: Print flags for history-data

Keyword and value

Number/Description

PHhydr = #YYYYYY#

1
2–5
6

Water level
U- and V-velocities, magnitude and direction
ω -velocities relative to σ -plane and wvelocities

PHproc =
#YYYYYYYYYY#

1
2
3–7
8
9 and 10

Concentration salinity
Temperature
Concentration constituents
Intensity spiral motion
Turbulent energy and dissipation

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Table A.3: Print flags for history-data

Keyword and value

PHderv=#YYY#

PHflux = #YYYY#

Number/Description
1 and 2

Vertical eddy viscosity and vertical eddy diffusivity. Richardson number if either or both
are selected
Density

1
2
3
4

Total flux through cross-setions
Momentary flux through cross-sections
Advective transport through cross-sections
Dispersive transport through cross-sections

Keyword and value

Table A.4: Storage flags for map-data

Number/Description
1
2 and 3
4 and 5

Water level
U- and V-velocities
ω -velocities relative to σ -plane and wvelocities

SMproc =
#YYYYYYYYYY#

1
2
3–7
8
9 and 10

Concentration salinity
Temperature
Concentration constituents
Intensity spiral motion
Turbulent energy and dissipation

SMderv=#YYYYYY#

1 and 2
3 and 4

U- and V- bed stress components
Vertical eddy viscosity and vertical eddy diffusivity. Richardson number if either or both
are selected
Density
Filtered U- and V-velocities of HLES model
and horizontal eddy viscosity

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SMhydr = #YYYYY#

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6

Table A.5: Storage flags for history-data

Keyword and value

Number/Description

SHhydr = #YYYY#

1
2 and 3
4

water level
U- and V-velocities
W-velocities

SHproc =
#YYYYYYYYYY#

1
2
3–7
8
9
10

Concentration salinity
Temperature
Concentration constituents
Intensity spiral motion
Turbulent kinetic energy
Turbulent dissipation

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Table A.5: Storage flags for history-data

Number/Description
1 and 2
3 and 4

SHderv=#YYYYY#

5
1

SHflux=#YYYY#

2
3
4
1)

U- and V- bed stress components
Vertical eddy viscosity and vertical eddy diffusivity. Richardson number if either or both
are selected
Density
Flux in U- and V-direction in ζ -point Total
flux through cross-sections1)
Momentary flux through cross-sections1)
Advective flux through cross-sections1)
Dispersive flux through cross-sections1)

if cross-sections are defined.

Keyword and value

Item

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The layout of the time information to store results, such as Prhis and Flmap, is defined as:
Description

First real number

Start time in Tunit after the computation start time

Second real number

Time interval in Tunit

Third real number

Stop time in Tunit after the computation start time

Table A.6: Optional output flags under Additional parameters

Keyword

Value

Description

Default

AddTim

#Y# or #N#

Flag for additional performance timing output to
file.

#N#

AdvFlx

#Y# or #N#

Flag for output of instaneous horizontal fluxes
of the advection diffusion equation per substance.
Note: anticreep and Forester filter fluxes are
not included in these fluxes.

#N#

AirOut

#Y# or #N#

Write meteo input to map- and his-file. This
can be used to check the meteorological model
forcing. The following quantities will be written
to the map-file: wind velocity vector, pressure,
cloud coverage (if space varying), air humidity (if space varying), air temperature (if space
varying), precipitation rate (if space varying),
and evaporation rate (if computed). The following quantities will be written for the station locations to the his-file: wind velocity vector, pressure, precipitation rate, and evaporation rate.

#N#

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Table A.6 – continued from previous page
Value

Description

Default

CflMsg

#Y# or #N#

Write warnings for too high advective Courant
numbers during whole simulation (instead of a
maximum of 100 warnings).

#N#

Chezy

#Y# or #N#

Write roughness as Chézy values to map-file.

#N#

CumAFl

#Y# or #N#

Flag for output of cumulative horizontal fluxes
of the advection diffusion equation per substance.
Note 1: anticreep and Forester filter fluxes are
not included in these fluxes.
Note 2: AdvFlx will be automatically switched
on if CumAFl is activated.

#N#

Filbal

#filename#

Triggers mass balance output for the polygons
on the history-file: volume, area, average concentration and average bed level data as well
as total water, constituent and sediment flux
data. The polygon file should match the file
format described in section A.2.25. The values
will be accumulated over grid cells for which the
centre point is located within the polygon. If
the centre point is located in multiple polygons,
the grid cell will be assigned to the first polygon
only.

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Keyword

FlNcdf

#string#

The value string lists the binary file types that
should use NetCDF instead of NEFIS (or ascii
in case of the Fourier file) as file format. The
program will check whether the following substrings occur in the value string: map, his,
dro, and fou for map-, history-, drogue-, and
Fourier-files respectively.

HisBar

#Y# or #N#

Flag for output of barrier height data to history
file

#N#

HisDis

#Y# or #N#

Flag for output of flow rate data of discharges
and culverts to history file

#N# (#Y#
in case of
culverts)

HdtOut

#Y# or #N#

Flag for output at every half time step to investigate fluctuations in the results due to the two
steps of the ADI solution. Both time steps will
be labelled with the same (end of full time step)
time.

#N#

HeaOut

#Y# or #N#

Flag for output of heat fluxes determined by
temperature models.

#N#

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Table A.6 – continued from previous page
Value

Description

Default

KfMnMx

#Y# or #N#

Flag for output of kfumin, kfumax, kfvmin, kfvmax, kfsmin, and kfsmax arrays to the map-file.
These administrative arrays indicate which layers of a Z-model are active at velocity (U, V)
and water level points.

#N#

LayOut

#Y# or #N#

Flag for output of vertical coordinates of layer
interfaces to the map-file.

#N#

MapWav

#Y# or #N#

Write wave data to map-file. This can be used
to check that the wave parameters have been
passed correctly to the flow computation.

#N#

MergeMap

#Y# or #N#

Flag for merging the results of a parallel simulation when writing the map and Fourier files. If
MergeMap equals #Y# the simulation will create one map file and one Fourier file for the
whole domain (if output of these files is requested). If MergeMap equals #N# the simulation will create one map file and one Fourier
file per partition (if output of these files is requested). Please note that a split (non-merged)
map-file cannot be used for restarting.

#Y#

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Keyword

MomTrm

#Y# or #N#

Flag for output of momentum terms to the mapfile (see details in Section A.1.4.1).

#N#

PrecOut

4 or 8

Precision of the data written to the output (history, map, drogue, Fourier) files: single (4) or
double (8) precision. If the simulation runs in
single precision, then PrecOut can only be
set to 4.

Rough

#Y# or #N#

Write roughness in input unit (as specified
Roumet keyword) to map-file. This is particularly useful when using the water depth dependent roughness formulations offered by trachytopes.

#N#

SgrThr

10−3 to 103

Threshold value in [m] for reporting water level
change messages to file.

25 m

SHlay

136

Specification of the layers for which the output parameters are written to history-file. By
default all layers are written. This specification may be useful when output reduction is
needed. Postprocessing (e.g. with Delft3DQUICKPLOT) may be unable/awkward when
necessary information is missing, (e.g. depth
averaged velocity, vertical profiles).

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Table A.6 – continued from previous page
Description

Default

SMlay

2578

Specification of the layers for which the output parameters are written to map-file. By
default all layers are written. This specification may be useful when output reduction is
needed. Postprocessing (e.g. with Delft3DQUICKPLOT) may be unable/awkward when
necessary information is missing, (e.g. depth
averaged velocity, vertical profiles).

SMVelo

#glm# or
#euler#

Flag for velocity output to his- and map-files.

#euler#

UgrThr

10−3 to 103

Threshold value in [m/s] for reporting velocity component change messages to
file.

5 m/s

Vortic

#Y# or #N#

Flag for output of vorticity and enstrophy.

#N#

Value

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A.1.4.1

Keyword

Momentum terms output

The momentum Eqs. (9.7) and (9.8) in section 9.3.1 can be combined to the following vectorized form in which everything except for the partial velocity derivatives in time has been
moved to the right hand side:



∂u

√

− √u

∂u
∂ξ

−√

∂ Gξξ
uv
√
∂η
Gξξ Gηη





− √v

∂u
∂η

+√

∂

2
v√

√



Gηη
∂ξ


Gξξ
Gηη
Gξξ Gηη


√ 
√ 
=
+
∂ Gξξ
G
∂
2
ηη
v
∂v
uv
u
∂v
u
− √ ∂η − √ √
− √ ∂ξ + √ √
| {z }
∂ξ
∂η
Gξξ
Gηη
Gξξ Gηη
Gξξ Gηη
A
|
{z
} |
{z
}
B
C


1
ω ∂u

√
−
P
ξ
− d+ζ ∂σ
ρ0 Gξξ
fv
F


+ Fξ
+
1
ω ∂v + −f u +
√
−
Pη
−
η
{z ∂σ } | {z } | ρ0 {zGηη } | {z }
| d+ζ
E
G
D
F
" 1 ∂
#
∂u
νV ∂σ
(d+ζ)2 ∂σ
+ Mξ (A.1)
+
∂v
1
∂
Mη
ν
V ∂σ
(d+ζ)2 ∂σ
|
{z
} | {z }
∂t
∂v
∂t

When the keyword MomTrm is activated, then most of the marked terms will be written to the
map-file. This feature is available as of DelftD-FLOW version 6.01.01 for sigma-layer models
only. The variables are added as elements to the map-series group. The field contains the
terms valid for the last whole time step (i.e. averaged over the two half time steps of the ADI
solver) for regular output, and terms valid for each half time step in case of half time step
output (HdtOut active). The element names for the M- and N-components respectively, as
well as a textual description of the meaning of the terms is given in the list below.
A elements MOM_DUDT and MOM_DVDT: acceleration (in GLM coordinates)

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A.2.1

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B elements MOM_UDUDX and MOM_VDVDY: acceleration due to streamwise momentum
transport
C elements MOM_VDUDY and MOM_UDVDX: acceleration due to lateral momentum transport
D vertical advection of momentum (not yet included in output file)
E elements MOM_UCORIOLIS and MOM_VCORIOLIS: acceleration due to Coriolis force
F the pressure term is split into acceleration due to barotropic pressure gradients as given
by the first term in Eqs. (9.15) and (9.16) including the atmospheric pressure gradient (elements MOM_UPRESSURE and MOM_VPRESSURE) and the baroclinic pressure gradient (elements MOM_UDENSITY and MOM_VDENSITY) as given by the second term in
the aforementioned equations
G elements MOM_UVISCO and MOM_VVISCO: acceleration due to viscosity as given by
Eqs. (9.26) and (9.27)
H vertical diffusion of momentum (not yetincluded in the output file)
I all other terms are further subdivided into flow resistance for instance due to vegetation (elements MOM_URESISTANCE and MOM_VRESISTANCE), tide generating forces
(elements MOM_UTIDEGEN and MOM_VTIDEGEN), wind force in top layer (elements
MOM_UWINDFORCE and MOM_VWINDFORCE), bed shear in bottom layer (elements
MOM_UBEDSHEAR and MOM_VBEDSHEAR), and waves forces (elements MOM_UWAVES
and MOM_VWAVES).
Attribute files
Introduction

In the following sections we describe the attribute files used in the input file (MDF-file) of
Delft3D-FLOW. Most of these files contain the quantities that describe one specific item, such
as the location of open boundaries, or time dependent data of fluxes discharged in the model
area by discharge stations.
Most of the attribute files can be generated by the FLOW-GUI after defining an input scenario.
Some files can almost only be generated by utility programs such as the curvilinear grid generated by RGFGRID. Still, we describe both type of files as it might be useful to know how
the input data is structured to be able to generate (large) files, such as astronomic boundary
conditions, or time-series for wind speed and direction by client specific tools.
For each file we give the following information:

File contents.
Filetype (free formatted, fix formatted or unformatted).
Filename and extension.
Generated by (i.e. how to generate the file).
Restrictions on the file contents.
Example(s).

Remarks:
The access mode of all attribute files is sequential.
In the examples the file content is printed in font Courier and comment (not included in
the file) between curly brackets font, unless explicitly stated differently.

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Orthogonal curvilinear grid
The orthogonal curvilinear grid file can be specified in the FLOW-GUI in Data group Domain
- Grid parameters.
File contents
Filetype
File format
Filename
Generated

The co-ordinates of the orthogonal curvilinear grid at the depth points.
ASCII
Free formatted

RGFGRID

Record description:
Record description

Record

Preceding description records, starting with an asterisk (∗), will be
ignored.
1

Record with Co-ordinate System = Cartesian or value

Spherical
2

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A.2.2

Record with

Missing Value = -9.99999000000000024E+02.
If this record is not given 0.0 will be assumed as missing value.

3
4

The number of grid points in m- and n-direction (2 integers).
Three real values (not used).

5 to K+5

A label and record number, the x-component of the world coordinates of all points in m-direction, starting with row 1 to row
nmax, with as many continuation records as required by mmax
and the number of co-ordinates per record. The label and record
number are suppressed on the continuation lines. This set of records
is repeated for each row until n = nmax.

K+5 to 2K+4

A similar set of records for the y -component of the world coordinates.

K is the number of records to specify for all grid points a set of x- and y -co-ordinates.
Restrictions:
The grid must be orthogonal.
Input items in a record are separated by one or more blanks.
Example:
*
* Deltares, Delft3D-RGFGRID Version 4.16.01.4531, Sep 30 2008, 23:32:27
* File creation date: 2008-10-01, 23:19:22
*
Coordinate System = Cartesian
9
7
0 0 0
Eta=
1
0.00000000000000000E+00
1.00000000000000000E+02
2.000000...
5.00000000000000000E+02
6.00000000000000000E+02
7.000000...

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Eta=

A.2.3

0.00000000000000000E+00
5.00000000000000000E+02
0.00000000000000000E+00
5.00000000000000000E+02
0.00000000000000000E+00
5.00000000000000000E+02
0.00000000000000000E+00
5.00000000000000000E+02
0.00000000000000000E+00
5.00000000000000000E+02
0.00000000000000000E+00
5.00000000000000000E+02
1.00000000000000000E+02
1.00000000000000000E+02
2.00000000000000000E+02
2.00000000000000000E+02
3.00000000000000000E+02
3.00000000000000000E+02
4.00000000000000000E+02
4.00000000000000000E+02
5.00000000000000000E+02
5.00000000000000000E+02
6.00000000000000000E+02
6.00000000000000000E+02
7.00000000000000000E+02
7.00000000000000000E+02

1.00000000000000000E+02
6.00000000000000000E+02
1.00000000000000000E+02
6.00000000000000000E+02
1.00000000000000000E+02
6.00000000000000000E+02
1.00000000000000000E+02
6.00000000000000000E+02
1.00000000000000000E+02
6.00000000000000000E+02
1.00000000000000000E+02
6.00000000000000000E+02
1.00000000000000000E+02
1.00000000000000000E+02
2.00000000000000000E+02
2.00000000000000000E+02
3.00000000000000000E+02
3.00000000000000000E+02
4.00000000000000000E+02
4.00000000000000000E+02
5.00000000000000000E+02
5.00000000000000000E+02
6.00000000000000000E+02
6.00000000000000000E+02
7.00000000000000000E+02
7.00000000000000000E+02

2.000000...
7.000000...
2.000000...
7.000000...
2.000000...
7.000000...
2.000000...
7.000000...
2.000000...
7.000000...
2.000000...
7.000000...
1.000000...
1.000000...
2.000000...
2.000000...
3.000000...
3.000000...
4.000000...
4.000000...
5.000000...
5.000000...
6.000000...
6.000000...
7.000000...
7.000000...

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Eta=

Computational grid enclosure

The computational grid enclosure file need to be specified in the FLOW-GUI in Data Group
Domain - Grid parameters, the file itself is generated by RGFGRID, see RGFGRID UM (2016).
File contents

Filetype
File format
Filename
Generated

The indices of the external computational grid enclosure(s) and optionally one or more internal computational grid enclosures that outlines the active computational points in a Delft3D-FLOW computation. The file is strongly related to the curvilinear grid file.
ASCII
Free formatted

RGFGRID

Record description:
Record

Record description

All

One pair of M and N indices representing the grid co-ordinates
where a line segment of the computational grid enclosure (polygon)
changes direction.

Restrictions:
A polygon must be closed. The first point of the polygon is repeated as last point.
A line segment may not intersect or touch any other line segment.
The angle formed by consecutive line segments (measured counter clock-wise) can
have a value of: 45, 90, 135, 225, 270 or 315 degrees, but not 0, 180 and 360 degrees.
In a row or column there should be at least two active computational grid cells.
Input items in a record are separated by one or more blanks.
Example:

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N- direction

+ - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + -

+ - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + -

6
5

+ - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + -

+ - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + -

2
1

+ - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + - + 1

17 18

M- direction

Legend:

+
|
−

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Full thick line

water level point
v-velocity point
u-velocity point
grid enclosure and (for the external polygon only) location of water level open boundaries.
location for velocity or discharge open boundaries.

Full thin line

Figure A.1: Example of computational grid enclosures

Model area with (one) external and one internal polygon, see Figure A.1.
1
6
8
9
9
16
19
19
17
4
1
1
13
14
14
13
13

A.2.4

1
1
3
3
1
1
4
6
8
8
5
1
4
4
5
5
4

begin external polygon

end external polygon
begin internal polygon

end internal polygon

Bathymetry
The bathymetry file can be specified in the FLOW-GUI in Data Group Domain - Bathymetry.
File contents
Filetype
File format
Filename
Generated

Deltares

The bathymetry in the model area, represented by depth values (in
metres) for all grid points.
ASCII
Free formatted or unformatted

FLOW-GUI (only for uniform depth values).
Offline with QUICKIN and data from digitised charts or GIS-database.

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Record description:
Filetype

Record description

Free formatted

Depth values per row, starting at N = 1 to N = Nmax, separated
by one or more blanks. The number of continuation lines is determined by the number of grid points per row (Mmax) and the maximum record size of 132.

Unformatted

Mmax depth values per row for N = 1 to N = Nmax.

Restrictions:
The file contains one M and N line more than the grid dimension.
The maximum record length in the free formatted file is 132.
Depth values from the file will not be checked against their domain.
The input items are separated by one or more blanks (free formatted file only).
The default missing value is: −999.0

DR
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Example:

File containing 16 ∗ 8 data values for a model area with 15 ∗ 7 grid points (free formatted file).
1.0
2.0
3.0
4.0
-5.0
-5.0
-5.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
-5.0 -999.0
3.0
4.0
5.0
6.0
7.0
-6.0
-6.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0 -999.0
5.0
6.0
7.0
8.0
9.0
10.0
-7.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0 -999.0
7.0
8.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
-7.0
19.0 -999.0
9.0
10.0
11.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
19.0
18.0
17.0 -999.0
-7.0
12.0
13.0
14.0
15.0
16.0
17.0
18.0
19.0
20.0
19.0
18.0
17.0
16.0
15.0 -999.0
-8.0
-8.0
15.0
16.0
17.0
18.0
19.0
20.0
19.0
18.0
17.0
16.0
15.0
14.0
13.0 -999.0
-999.0 -999.0 -999.0 -999.0 -999.0 -999.0 -999.0 -999.0 -999.0 -999.0 -999.0
-999.0 -999.0 -999.0 -999.0 -999.0

A.2.5

Thin dams

The thin dams file can be specified in the FLOW-GUI in Data Group Domain - Thin dams.
File contents
Filetype
File format
Filename
Generated

Location and type of thin dams.
ASCII
Free formatted

QUICKIN or FLOW-GUI

Record description:
Record

Record description

each record

The grid indices of the begin and end point of a line of thin dams (4
integers). A character indicating the type of thin dams (U or V).

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Figure A.2: Example of thin dams in a model area

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Restrictions:
The angle of the line segment and the horizontal numerical grid axis may be an integer
multiple of 45 degrees.
Thin dams can not be defined along the model boundaries (which by default lie along
the lines M = 1, N = 1, M = Mmax or N = Nmax). Therefore, the indices of thin dams
must lie between M = 2 and Mmax-1 and N = 2 and Nmax-1 respectively.
Input items are separated by one or more blanks.
The direction of the dam is perpendicular to the velocity direction over which the dams
are superimposed!
Example:

Three (sets of) thin dams in model area of 19 ∗ 8 grid points, see Figure A.2.
6
7
12

A.2.6

2
4
3

6
10
12

4 V
7 U
7 U

Dry points

The dry points file can be specified in the FLOW-GUI in Data Group Domain - Dry points.
File contents
Filetype
File format
Filename
Generated

Index location of (permanently) dry points.
ASCII
Free formatted

QUICKIN or FLOW-GUI

Record description:
Record

Record description

each record

The grid indices of the begin and end point of a dry section (4
integers).

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Figure A.3: Dry points in model area

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Restrictions:
The angle of a line of dry points and the horizontal numerical grid axis can be an integer
multiple of 45 degrees.
Dry points may not be defined along the model boundaries (which by default lie along
the lines M = 1, N = 1, M = Mmax or N = Nmax). Therefore, the indices of these points
must lie between M = 2 and Mmax-1 and N = 2 and Nmax-1, respectively.
The input items are separated by one or more blanks.
The most lower-left dry point has indices (2, 2).
Example:

Five sets of dry points in a model area of 19 ∗ 8 grid points, see Figure A.3.
5
8
13
13
14

A.2.7

3
4
3
4
6

5
10
14
14
14

6
6
3
4
6

Time-series uniform wind

Time-series for wind speed and direction for a uniform wind can be specified in the FLOW-GUI
in Data Group Physical parameters - Wind.
File contents

Filetype
File format
Filename
Generated

Time-series for wind speed and direction for a uniform wind. The
wind direction is defined according to the nautical convention, i.e.
relative to north and positive in clock-wise direction, see Figure A.4.
ASCII or binary
Free formatted or unformatted

FLOW-GUI, WAVE-GUI, or manually offline

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Figure A.4: Definition sketch of wind direction according to Nautical convention

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Record description:
Record

Record description

each record

The time in minutes after the Reference date 00:00:00 hr (1 real). The
wind speed in m/s and the wind direction relative to north, positive clock
wise (2 reals).

Restrictions:
Times must be an integer multiple of the simulation time step.
The contents of the file will not be checked on its domain.
The input items are separated by one or more blanks.
Example:

Time-series for uniform wind field, starting as a north wind, turning to south-west and back to
north, see Figure A.4. The wind direction in Figure A.4 is about +60 degrees.
0.
10.
30.
150.
600.
610.
900.

A.2.8

0.0
1.2
3.7
4.2
5.7
4.0
0.0

0.
315.
270.
225.
225.
235.
0.

Space varying wind and pressure
In this section the different options are described for specifying space varying meteo data
(wind, atmospheric pressure, etc.) as input for your simulation. The descriptions in this section
are applicable to meteo input files of a certain version. More details on the compatibility
of the meteo input files and the conversion from one version to another can be found in
Appendix B.7.

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Defined on the computational grid
Time-series for space varying wind velocity components (east-west and south-north) and atmospheric pressure can be specified in the FLOW-GUI in Data Group Physical parameters Wind.

Filetype
File format
Filename
Generated

Time-series for space varying wind velocity components (east-west
and south-north) and atmospheric pressure, defined on the computational grid. The file consists of a header, followed by datablocks
containing the wind and pressure fields at times specified using a
standardised time definition above each datablock. The header specifies the type of file and the input it contains using a number of keywords. The keywords are case insensitive and the order of the keywords is not fixed.
ASCII or binary.
Free formatted or unformatted, keyword based.

Some offline program.

File contents

Header description:

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A.2.8.1

Keywords

Value

Description

FileVersion

1.03

version of file format

Filetype

meteo_on_computational_grid

meteo input on computational grid

NODATA_value

free

value used for input that is
to be neglected

n_quantity

number of quantities specified in the file

quantity1

x_wind

wind in x-direction

quantity2

y_wind

wind in y -direction

quantity3

air_pressure

air pressure

unit1

m s-1

unit
of
quantity1,
meters/second

m s-1

unit
of
quantity2,
meter/second

Pa or
mbar

unit of quantity3, Pa or
millibar

unit2

unit3

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Time definition and data block description
Keywords

Value

Description

Time

fixed format described below

time definition string

The time definition string has a fixed format, used to completely determine the time at which
a dataset is valid. The time definition string has the following format:

TIME minutes/hours since YYYY-MM-DD HH:MM:SS TIME ZONE, e.g.

360 minutes since 2008-07-28 10:55:00 +01:00

DR
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The format of the string is completely fixed. No extra spaces or tabs can be added between
the different parts of the definition. The time definition is followed by the datablock of input
values corresponding to the specified time. The data block consists of three subsequent
blocks containing the velocity component in M-direction, the velocity component in N-direction
and the atmospheric pressure, respectively. All three quantities are given for Nmax by Mmax
points, where the first value in the dataset corresponds to cell (1, 1) on the grid. Every next
line in the dataset then corresponds to a row on the grid. The time definition and the data
block — for all three quantities — are repeated for each time instance of the time-series.
File version and conversion

The current description holds for FileVersion 1.03. The table below shows the latest
modifications in the file format (and version number).
FileVersion

Modifications

1.03

No changes for this meteo input type, but for the meteo types meteo_on_equidistant_grid and meteo_on_curvilinear_grid

1.02

No changes for this meteo input type, but for the meteo type meteo_on_spider_web_grid

1.01

Changed keyword MeteoType to FileType

Changed fixed value of input type (Keyword Filetype) from Svwp to
meteo_on_computational_grid (meteo_on_flow_grid is also allowed)

Restrictions:
Keywords are followed by an equal sign ’=’ and the value of the keyword.
When a keyword has value free the value of this keyword is free to choose by the user.
When only one value is given for a keyword, this keyword has a fixed value and when 2
or more options are shown, the user can choose between those values.
Times must be specified exactly according to the time definition. See the examples
shown in this section.
The contents of the file will not be checked on its domain.
The wind components are specified at the cell centres (water level points) of the computational grid.
Input items in a data block are separated by one or more blanks (free formatted file
only).

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Figure A.5: Definition wind components for space varying wind

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Remarks:
The time definition in the meteorological file contains the number of minutes or hours
since a reference data and time in a certain time zone. The reference time and time
zone may differ from those of the simulation. The computational engine will search
in the meteo file for the simulation time and interpolate between neighbouring times if
necessary. Possible differences in time zone will be accounted for by shifting the meteo
input data with the difference. The reference times within the time definition string may
vary in a meteo file, i.e. it is possible to attach new input with a different reference time,
behind the last data block.
Comments can be added after #’s.
Example

Model area of 25 ∗ 33 grid points (Mmax = 25; Nmax = 33). The input data is printed in
Courier, comments are printed behind #’s.
Time = 0.0 minutes since 2008-09-20 10:30:00 +01:00
{33 records with 25 values each}
{33 records with 25 values each}
{33 records with 25 values each}
Time = 340.0 minutes since 2008-09-20 10:30:00 +01:00
{33 records with 25 values each}
{33 records with 25 values each}
{33 records with 25 values each}
Time = 600.0 minutes since 2008-09-20 10:30:00 +01:00
{33 records with 25 values each}
{33 records with 25 values each}
{33 records with 25 values each}
Time = 1240.0 minutes since 2008-09-20 10:30:00 +01:00
{33 records with 25 values each}
{33 records with 25 values each}
{33 records with 25 values each}

# Time definition
# Wind component west to east
# Wind component south to north
# Atmospheric pressure
# Time definition
# Wind component west to east
# Wind component south to north
# Atmospheric pressure
# Time definition
# Wind component west to east
# Wind component south to north
# Atmospheric pressure
# Time definition
# Wind component west to east
# Wind component south to north
# Atmospheric pressure

Remarks:
To obtain the wind direction according to the nautical convention, the wind direction is
reversed.
The wind is specified in terms of its components along the west-east (x_wind) and
south-north (y_wind) co-ordinate system, see Figure A.5. These definitions differ
from the nautical convention (used for uniform wind), which is specified relative to true

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North, see Figure A.4.

PavBnd= 101300.0

Defined on an equidistant grid

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A.2.8.2

Remark:
On open boundaries, an input signal is prescribed that is consistent with some average
pressure. Usually the signal corresponds to Mean Sea Level. One actually wants to
prescribe an input signal corresponding to the local pressure prescribed by the space
varying meteo input. To this end, it is possible to specify an average pressure - which
should correspond to your input signal on the open boundaries - which is then used to
determine local pressure gradients that need to be applied along the open boundaries
to obtain an input signal that is consistent with the local atmospheric pressure. This
functionality used to be specified in the wind file but it should now be specified in the
Master Definition File in the Data Group Additional parameters, using PavBnd: Average Pressure on Boundaries. Using this keyword one can specify an average pressure
that is used on all open boundaries, independent of the type of wind input. The pressure
must be specified in N/m2 . An example:

Time-series for space varying wind velocity components (east-west and south-north) and atmospheric pressure on an equidistant grid (other than the computational grid) can be specified
in the FLOW-GUI in Data Group Additional parameters.
File contents

Filetype
File format
Filename

Generated

Time-series of a space varying wind and atmospheric pressure defined on an equidistant rectilinear or spherical grid (other than the
computational grid).
ASCII.
Free formatted, keyword based.
for atmospheric pressure in [Pa] or [millibar],
for the wind speed component in east-west-direction
in [m/s],
for the wind speed component in north-south direction in [m/s].
Some offline program.

Remark:
Space varying wind and pressure on an equidistant grid is implemented as a special
feature. You must specify some additional keywords and values in Data Group Additional parameters or in the MDF-file; see section B.7.1 for details.
A.2.8.3

Defined on a curvilinear grid

Time-series for space varying wind velocity components (east-west and south-north) and atmospheric pressure on a separate curvilinear grid (other than the computational grid) can be
specified in the FLOW-GUI in Data Group Additional parameters.
File contents

Filetype
File format
Filename

Deltares

Time-series of a space varying wind and atmospheric pressure defined on a curvilinear (Cartesian or spherical) grid (other than the
computational grid).
ASCII.
Free formatted, keyword based.
for atmospheric pressure in [Pa] or [millibar],
for the wind speed component in east-west-direction
in [m/s],

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for the wind speed component in north-south direction in [m/s],
for the curvilinear grid on which the wind and pressure
are specified.
Some offline program.

Generated

Remark:
Space varying wind and pressure on a curvilinear grid is implemented as a special feature. You must specify some additional keywords and values in Data Group Additional
parameters or in the MDF-file; see section B.7.2 for details.
A.2.8.4

Defined on a Spiderweb grid

Time-series for space varying wind velocity components (east-west and south-north) and atmospheric pressure on a Spiderweb grid can be specified in the FLOW-GUI in Data Group
Additional parameters.
Time-series of a space varying wind and atmospheric pressure defined on a Spiderweb grid. The grid can be rectilinear or spherical.
This type of wind input is used to describe (rotating) cyclone winds.
ASCII.
Free formatted, keyword based.
containing the wind speed in [m/s], wind (from) direction in [degree] and atmospheric pressure in [Pa] or [millibar].
Some offline program.

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File contents

Filetype
File format
Filename
Generated

Remark:
Space varying wind and pressure on a Spiderweb grid is implemented as a special feature. You must specify some additional keywords and values in Data Group Additional
parameters or in the MDF-file; see section B.7.3 for details.
A.2.9

Initial conditions
File contents

Initial conditions for the hydrodynamics, the transported constituents
(if any) and the secondary flow intensity (if any) at all points (Data
Group Initial conditions).
Free formatted or unformatted.

Offline by some external program.

File format
Filename
Generated

Initial conditions for separate quantities can be generated with the program QUICKIN.
Record description:
Record

Record description

each record

A record contains a row of Mmax values (Mmax reals).

The file contains a matrix of dimensions (Mmax∗Nmax) for each quantity and if relevant for
each layer for which an initial condition is required.
The matrices are given in the following order:
1 Water elevation (one matrix).

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2
3
4
5
6
7

U-velocities (Kmax matrices).
V-velocities (Kmax matrices).
Salinity, only if selected as an active process (Kmax matrices).
Temperature, only if selected as an active process (Kmax matrices).
Constituent number 1, 2, 3 to the last constituent chosen, only if selected (Kmax matrices).
Secondary flow (for 2D simulations only), only if selected as an active process (one matrix).

In total there will be (Cmax+2)∗Kmax + 1 matrices of Mmax∗Nmax where:
number of grid points in M (U or ξ ) direction.
number of grid points in N (V or η ) direction.
number of layers.
number of constituents (including temperature, salinity, secondary flow).

Mmax
Nmax
Kmax
Cmax

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Restrictions:
The maximum record length in the free formatted file is 132
The contents of the file will not be checked on its domain.
Input items in a record are separated by one or more blanks (free formatted file only).
Example 1:

A model of 1 layer, Mmax = 25 and Nmax = 33, with two constituents, TEST1 and TEST2,
and secondary flow.
The input data is printed in Courier; comment (not in the file) is printed between brackets.
{33
{33
{33
{33
{33
{33

records
records
records
records
records
records

with
with
with
with
with
with

25
25
25
25
25
25

values
values
values
values
values
values

each}
each}
each}
each}
each}
each}

{Water elevation}
{U-velocity component}
{V-velocity component}
{Concentrations constituent TEST1}
{Concentrations constituent TEST2}
{Secondary flow intensity}

Example 2:

A model with 2 layers, Mmax = 25 and Nmax = 33, with salinity, temperature and one constituent, denoted by TEST.
The input data is printed in Courier; comment (not in the file) is printed between brackets.
{33
{33
{33
{33
{33
{33
{33
{33
{33
{33
{33

records
records
records
records
records
records
records
records
records
records
records

with
with
with
with
with
with
with
with
with
with
with

25
25
25
25
25
25
25
25
25
25
25

values
values
values
values
values
values
values
values
values
values
values

each}
each}
each}
each}
each}
each}
each}
each}
each}
each}
each}

{Water elevation}
{U-velocity component in layer 1}
{U-velocity component in layer 2}
{V-velocity component in layer 1}
{V-velocity component in layer 2}
{Salinity in layer 1}
{Salinity in layer 2}
{Temperature in layer 1}
{Temperature in layer 2}
{Concentrations constituent TEST in layer 1}
{Concentrations constituent TEST in layer 2}

Remarks:
A record for the free formatted file is to be interpreted as a logical record. The length
of a physical record is limited to 132, so a logical record consists of as many physical
records as required by Mmax and the number of values per (physical) record.

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The velocity components are the computational U and V components, not the east and
north components.
Open boundaries
The open boundaries file(s) can be specified in the FLOW-GUI in Data Group Boundaries.
File contents
Filetype
File format
Filename
Generated

The location and description of open boundaries.
ASCII
Fix formatted for text variables; free formatted for real and integer
values.

FLOW-GUI

Record description:
Record

Record description

each record

Name of the open boundary section (20 characters).
Type of boundary (1 character).

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A.2.10

Z
C
N
Q
T
R

water level
current
Neumann
discharge per grid cell
total discharge for boundary section
Riemann

Type of data (1 character).
A
H
Q
T

astronomic
harmonic
QH tables (only for water level boundaries)
time-series

Grid indices of the begin and end point of the boundary section (4
integers).
Reflection coefficient (1 real), not for Neumann or Riemann.
Vertical profile (three strings); only for 3D simulations and velocity
type boundaries (C, Q, T and R).
Uniform
Logarithmic
3D profile
Two labels (each 12 characters, no blanks in the label name) referencing to the blocks in the amplitude and phase file <∗.bca>; only
if the type of data is A.

Restrictions:
Maximum record length in the free formatted file is 132.
The boundary section name must start at position one in a record.
The value of the reflection coefficient will not be checked on its domain.
All input items in a record must be separated by one or more blanks.

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Astronomic and harmonic forced boundaries must be specified before QH-relation forced
boundaries, which in turn should be specified before time-series forced boundaries.

Astronomic and harmonic forced boundaries cannot be combined.
Example:
Two boundary sections with data type A(stronomic) and one with type T(ime series).
Paradise Bay 1
Paradise Bay 2
Sea Entrance

Q A
C A
Z T

1
16
4

1
3
8

1
16
14

5 0.0 Uniform
6 0.0 Logarithmic
8 0.0

Paradise_1A
Paradise_2A

Paradisee_lB
Paradisee_2B

Astronomic flow boundary conditions
File contents
Boundary conditions for open boundary sections of type Astronomic
(Data Group Boundaries - Flow conditions) in terms of amplitudes
and phases for the astronomic components.
Filetype
ASCII
File format
Fix formatted for text variables, free formatted for real and integer
values.
Filename

Generated
FLOW-GUI or offline by program Delft3D-TRIANA.

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A.2.11

Remarks:
A label may not contain blanks between non-blank characters.
For the labels 12 characters are read. Be sure the second label starts at least 13
positions after the start of the first.

Record description:
Record

Record description

Label for end point A of open boundary section (12 characters, no
blanks)

2 to 2+NCOM-1

For each component its name (8 characters), amplitude and phases (2
reals).

2+NCOM

Label for end point B of open boundary section (12 characters, no
blanks).

2+NCOM+1 to
2+2∗NCOM

For each component its name (8 characters), amplitude and phases (2
reals).

where:
NCOM

number of tidal components.

These records are repeated for each open boundary section.
Restrictions:
The labels for the end points of an open boundary section are defined in the
file.
The name of the label may not contain blanks between non-blnak characters.

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All component names are written in upper case.
The label and component name must start in position one.
The number of components and the components used may differ between boundary
sections.

At both ends of a section the same set of components must be defined. Between
sections these sets may differ.
Example:
A model with 3 open boundary sections (with astronomical boundary conditions).

A.2.12

{section name, end point A}
{mean value}
{component name, amplitude and phase}

{section name, end point B}
{mean value}
{component name, amplitude and phase}

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East_bound_A
A0 0.02 0.0
M2 1.87 314.3
S2 0.32 276.4
O1 0.21 14.3
East_bound_B
A0 0.03 0.0
M2 1.89 264.7
S2 0.29 220.9
O1 0.19 38.3
West_bound_A
A0 0.06 0.0
M2 1.71 122.5
S2 0.18 46.4
West_bound_B
A0 0.06 0.0
M2 1.69 110.3
S2 0.19 22.4
Sea_bound_A
A0 0.07 0.0
M2 1.67 300.9
S2 0.32 76.2
K1 0.05 33.1
Sea_bound_B
A0 0.07 0.0
M2 1.69 324.1
S2 0.29 110.1
K1 0.09 6.1

The input data is printed in Courier; comment (not in the file) is printed between brackets.

{section name, end point A}
{mean value}
{component name, amplitude and phase}
{section name, end point B}
{mean value}
{component name, amplitude and phase}
{section name, end point A}
{mean value}
{component name, amplitude and phase}

{section name, end point B}
{mean value}
{component name, amplitude and phase}

Astronomic correction factors
File contents
The file contains corrections to the astronomical components of the
open boundary sections with data type astronomic. These corrections may be applied during calibration. This file avoids a large processing effort of your tidal data. Just specify the appropriate boundary section and the component(s) that you wish to alter and how
much it needs be changed (Data Group Boundaries - Flow conditions). The amplitude factor is a multiplicative factor and the phase
factor is an additive factor.
Filetype
ASCII
File format
Fix formatted for text variables, free formatted for real and integer
values.
Filename

Generated
FLOW-GUI

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Record description:
Record description

Label for begin point (12 characters).

2 to 1+NCOMR

Component name (8 characters), amplitude and phase correction factors (2 reals).

2+NCOMR

Label for end point (12 characters).

3+NCOMR to
2+2∗NCOMR

Component name (8 characters), amplitude and phase correction factors (2 reals).

Record

where:
NCOMR

the number of tidal components that requires corrections.

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The records (1 to 2+2∗NCOMR) may be repeated for the number of open boundary sections.
Restrictions:
The name of the label may not contain blanks between non-blnak characters.
Label names for the begin and end points are defined in the file.
All component names are written in upper case.
The label and component name must start in record position one.
The number of components and the components used may differ per boundary section.
The astronomical component A0 cannot be corrected.
Example:

Model for which two open boundary sections, with astronomical boundary conditions, need
corrections.
The input data is printed in Courier; comment (not in the file) is printed between brackets.
East_bound_A
M2 0.90 10.0
S2 0.95 -7.5
East_bound_B
M2 0.90 10.0
S2 0.95 -7.5
Sea_bound_A
M2 0.95 7.0
S2 0.90 -3.0
Q1 1.10 15.0
K1 1.10 10.0
Sea_bound_B
M2 0.95 7.0
S2 0.90 -3.0
Q1 1.10 15.0
K1 1.10 10.0

{section name, end point A}
{component name, amplitude and phase}
{section name, end point B}
{component name, amplitude and phase}
{section name, end point A}
{component name, amplitude and phase}

{section name, end point B}
{component name, amplitude and phase}

Remark:
In the example the correction factors are the same for both end points; but this is not
mandatory.

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Harmonic flow boundary conditions
File contents
The frequencies, amplitudes and phases for all open boundary sections with data type equal to H(armonic) (Data Group Boundaries Flow conditions).
Filetype
ASCII
File format
Free formatted
Filename

Generated
FLOW-GUI or manually offline
Record description:
Record description

Frequencies (including 0.0 for the the mean value) (reals).

Blank

3 to NTOH+2

Amplitudes at the begin of each boundary section for all frequencies
(reals).

Record

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A.2.13

NTOH+3
2∗NTOH+2

2∗NTOH+3

Amplitudes at the end of each boundary section for all frequencies
(reals).
Blank

2∗NTOH+4
3∗NTOH+3

Phases at the begin of each boundary section for all frequencies (blanks
for mean value) (reals).

3∗NTOH+4
4∗NTOH+3

Phases at the end of each boundary section for all frequencies (blanks
for mean value) (reals).

where:
NTOH

number of open boundary sections driven with harmonic frequencies.

Restrictions:
Maximum record length is 132.
The input items will not be checked on their domain.
Input items in a record are separated by one or more blanks.

Remark:
The phase values at intermediate points are interpolated from the values specified at the
begin and end of the opening section. You should take care for a good representation
of phases at transition points (e.g. an interpolation between 356 and 13 degrees).
Example:
Model area with 3 open boundary sections (NTOH = 3) with H data type and two harmonic
frequencies including the mean value (which has frequency 0.0).
The input data is printed in Courier; comment (not in the file) is printed between brackets.

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0.0

30.0000

-1.6
-1.5
1.6
-1.7
-1.7
1.8

2.1
2.3
2.2
2.2
2.1
2.2
120.5
79.6
245.8
125.6
88.9
283.7

QH-relation flow boundary conditions
File contents
QH relations at water level boundaries for boundary sections with the
data type Q (Data Group Boundaries - Flow conditions).
File format
Fix format for header information; free format for time series data.
Filename

Generated
FLOW-GUI or manually offline

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A.2.14

{KC = 2, including zero frequency for the mean value}
{blank record}
{amplitudes at end A, section 1}
{amplitudes at end A, section 2}
{amplitudes at end A, section 3}
{amplitudes at end B, section 1}
{amplitudes at end B, section 2}
{amplitudes at end B, section 3}
{blank record}
{phase at end A, 1-st component, section 1}
{phase at end A, 1-st component, section 2}
{phase at end A, 1-st component, section 3}
{phase at end B, 1-st component, section 1}
{phase at end B, 1-st component, section 2}
{phase at end B, 1-st component, section 3}

Record description:

For each water level boundary segment with data type Q a data block must be prescribed
consisting of:

Header records containing a number of compulsory and optional keywords accompanied
by their values.

A set of records containing the discharge/water level data.
Each record contains a discharge in [m3 /s] and a water level in [m].
Restrictions:
Maximum record length is 5000.
Position, format of the keywords and the format of keyword-values in the header are
fixed (see example).
All keywords have a length of 20 characters.
Header in each block must be ended with the (compulsory) keyword: ‘records in table’
accompanied by the number of data records to follow.
Positive discharges indicate flow in positive M/N direction. If the model flows in negative
M/N direction negative discharges must be specified.
Discharges must be specified in increasing order. That is, Q = 100.0 should be
specified before Q = 200.0. For negative discharges Q = −200.0 must be specified
before Q = −100.0.
QH boundaries should only be specified as outflow boundaries.
The sequence of blocks must be consistent with the sequence of water level boundary
sections with data type Q.
Example:
Model with open boundary sections with data type Q. Flow in negative M or N direction.

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table-name
contents
location1
xy-function
interpolation2
parameter
parameter
records in table
-2000.0000
-1500.0000
-1000.0000
-500.0000
-300.0000

a20,1x,a40
a20,1x,a20
a20,1x,a20
a20,1x,free
a20,1x,a20,1x,a20,free
a20,1x,a20,1x,a20,free
a20,1x,i6

Time-series flow boundary conditions
File contents
Time-series for flow boundary conditions of all open boundary sections with data type T (Data Group Boundaries - Flow conditions).
Filetype
ASCII
File format
Fix format for header information; free format for time-series data.
Filename

Generated
FLOW-GUI, program Delft3D-NESTHD or manually offline

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A.2.15

Boundary Section : 2
uniform
open boundary number 2
’equidistant’
linear
’total discharge (t) ’ unit ’[m**3/s]’
’water elevation (z) ’ unit ’[m]’
5
2.1455
1.7711
1.3516
0.8514
0.6057

Record description:

For each open boundary segment with boundary data of type T (time-series) the data is given
in two related blocks:
1 A header block containing a number of compulsory and optional keywords accompanied
by their values.
2 A data block containing the time dependent data.
Description header block:
1
2

sequence must follow sequential order of open boundaries in pre-processor
Optional Keywords and values

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Text

Format

Value

Format

table-name

a20, 1x

’Boundary Section: ##’

contents

a20,1x

’Logarithmic ’
’Uniform ’
’3d-profile ’

location

a20, 1x

’name boundary section’ (see
file)

time-function

a20, 1x

’non-equidistant’

reference-time

a20, 1x

yyyymmdd (must be equal to itdate)

time-unit

a20, 1x

’minutes’

interpolation

a20, 1x

’linear’

8 to 8+NPAR+1

parameter

a20, 1x

’parameter name and location’,
’layer and location’, units ’[ccc]’

a,
’units’,
a

10+NPAR

records-in-table

a20, 1x

number of records in the data
block

integer

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Record

Remark:
NPAR is the number of parameters for which a time varying boundary condition is being
specified.
Description data block:
Record

Record description

each record

Time in minutes after the Reference Date and NPAR∗{2 of Kmax} values
representing the parameter for which a time varying boundary condition
is being specified (all reals). The number of values to be specified for
each end point of a boundary section depends on the type of profile in
the vertical:
2 real values for either a uniform or logarithmic profile
Kmax∗2 real values for 3D-profile where the end points for each layer
are prescribed.

Restrictions:
Maximum record length is 5000.
Position, format of the keywords and the format of keyword-values in the header are
fixed (see example).
All keywords have a length of 20 characters.
Header in each block must be ended with the (compulsory) keyword: ‘records in table’
accompanied by the number of data records to follow.
Times must be multiples of the integration time step; the times specified will be checked
on their domain.
The sequence of blocks must be consistent with the sequence of open boundary sec-

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tions with data type T(ime).
All open boundaries that have ‘3D-profile’ must precede other open boundaries.
Example 1:
Model with 2 open boundary sections with time-series as boundary conditions.

The first boundary section concerns a discharge boundary for which the boundary condition
is given at two time breakpoints, i.e. at 0.0 and 8 000.0 minutes after the Reference Date. The
vertical profile is logarithmic, the interpolation method linear, the time-series is assumed to be
non-equidistant and the time is given in minutes. The second boundary section concerns a
current boundary for which the boundary condition is given at two time breakpoints, i.e. at 0.0
and 8 000.0 minutes after the Reference Date. The vertical profile is uniform, the interpolation
method linear, the time series is assumed to be non-equidistant and the time is given in
minutes.

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table-name
’Boundary Section : 1’
contents
’logarithmic
’
location
’East Boundary
’
time-function
’non-equidistant
’
reference-time
19941001
time-unit
’minutes’
interpolation
’linear’
parameter
’time
’
unit ’ ’
parameter
’flux/discharge (q) end A’ unit ’ ’
parameter
’flux/discharge (q) end B’ unit ’ ’
records in table
2
0.0000
50000.0
100000.
8000.0000
75000.0
133000.
table-name
’Boundary Section : 2’
contents
’uniform
’
location
’West boundary
’
time-function
’non-equidistant
’
reference-time
19941001
time-unit
’minutes’
interpolation
’linear’
parameter
’time
’ unit ’[min]’
parameter
’current
(c) end A’ unit ’[m/s]’
parameter
’current
(c) end B’ unit ’[m/s]’
records in table
2
0.0000
1.50000
1.60000
8000.0000
1.75000
1.80000

Example 2:

The second example concerns an open sea boundary consisting of three sections, one section is velocity controlled, one section is Riemann controlled and one section is water level
controlled. The computation is depth averaged. See section A.2.17 for the corresponding
bcc-file.
table-name
contents
location
time-function
reference-time
time-unit
interpolation
parameter
parameter
parameter

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’Boundary Section : 1’
’Uniform
’
’west-vel-1
’
’non-equidistant’
19960718
’minutes’
’linear’
’time
’
unit ’[min]’
’current
(c) end A’ unit ’[m/s]’
’current
(c) end B’ unit ’[m/s]’

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’Boundary Section : 2’
’Uniform
’
’west-vel-2
’
’non-equidistant’
19960718
’minutes’
’linear’
’time
’
unit ’[min]’
’riemann
(r) end A’ unit ’[m/s]’
’riemann
(r) end B’ unit ’[m/s]’
185

’Boundary Section : 3’
’Uniform
’
’west-wl
’
’non-equidistant’
19960718
’minutes’
’linear’
’time
’
’water elevation (z) end A’
’water elevation (z) end B’
185

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records-in-table
840.0 0.000 0.000
855.0 0.120 0.116
...................
...................
3555.0 -0.651 -0.845
3570.0 -0.589 -0.783
table-name
contents
location
time-function
reference-time
time-unit
interpolation
parameter
parameter
parameter
records-in-table
840.0 0.000 0.000
855.0 0.113 0.104
...................
3555.0 -0.815 -0.341
3570.0 -0.756 -0.301
table-name
contents
location
time-function
reference-time
time-unit
interpolation
parameter
parameter
parameter
records-in-table
840.0 1.899 1.858
855.0 1.848 1.808
...................
3585.0 2.197 2.192
3600.0 2.186 2.183

unit ’[min]’
unit ’[m]’
unit ’[m]’

Example 3:

The third example concerns the same open boundary of the second example, but now for a
3D computation with 5 layers in the vertical. See section A.2.17 for the bcc-file.
table-name
contents
location
time-function
reference-time
time-unit
interpolation
parameter
parameter
parameter
parameter
parameter
parameter
parameter
parameter
parameter
parameter
parameter
records-in-table

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’3d-profile
’
’west-vel-1
’
’non-equidistant’
19960718
’minutes’
’linear’
’time
’current
(c) end A
’current
(c) end A
’current
(c) end A
’current
(c) end A
’current
(c) end A
’current
(c) end B
’current
(c) end B
’current
(c) end B
’current
(c) end B
’current
(c) end B
185

layer:
layer:
layer:
layer:
layer:
layer:
layer:
layer:
layer:
layer:

’

’
1’
2’
3’
4’
5’
1’
2’
3’
4’
5’

unit
unit
unit
unit
unit
unit
unit
unit
unit
unit
unit

’[min]’
’[m/s]’
’[m/s]’
’[m/s]’
’[m/s]’
’[m/s]’
’[m/s]’
’[m/s]’
’[m/s]’
’[m/s]’
’[m/s]’

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A.2.16

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840.0 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
855.0 .124 .118 .109 .109 .106 .126 .119 .115 .112 .107
.................................................................
3585.0 -.583 -.641 -.736 -.788 -.776 -.444 -.529 -.651 -.766 -.841
3600.0 -.499 -.549 -.636 -.691 -.682 -.374 -.447 -.557 -.668 -.741
table-name
’Nested flow BC west-vel-2
’
contents
’3d-profile
’
location
’west-vel-2
’
time-function
’non-equidistant’
reference-time
19960718
time-unit
’minutes’
interpolation
’linear’
parameter
’time
’ unit ’[min]’
parameter
’current
(c) end A layer:
1’ unit ’[m/s]’
parameter
’current
(c) end A layer:
2’ unit ’[m/s]’
parameter
’current
(c) end A layer:
3’ unit ’[m/s]’
parameter
’current
(c) end A layer:
4’ unit ’[m/s]’
parameter
’current
(c) end A layer:
5’ unit ’[m/s]’
parameter
’current
(c) end B layer:
1’ unit ’[m/s]’
parameter
’current
(c) end B layer:
2’ unit ’[m/s]’
parameter
’current
(c) end B layer:
3’ unit ’[m/s]’
parameter
’current
(c) end B layer:
4’ unit ’[m/s]’
parameter
’current
(c) end B layer:
5’ unit ’[m/s]’
records-in-table
185
840.0 .000 .000 .000 .000 .000 .000 .000 .000 .000 .000
855.0 .119 .113 .109 .106 .103 .104 .104 .101 .999 .102
.................................................................
3585.0 -.403 -.491 -.612 -.728 -.804 -.450 -.454 -.454 -.422 -.365
3600.0 -.339 -.415 -.524 -.634 -.705 -.409 -.407 -.390 -.349 -.286
table-name
’Nested flow BC west-wl
’
contents
’uniform
’
location
’west-wl
’
time-function
’non-equidistant’
reference-time
19960718
time-unit
’minutes’
interpolation
’linear’
parameter
’time
’ unit ’[min]’
parameter
’water elevation (z) end A
’ unit ’[m]’
parameter
’Water elevation (z) end B
’ unit ’[m]’
records-in-table
185
840.0 1.899 1.856
855.0 1.883 1.857
...................
3585.0 2.186 2.181
3600.0 2.185 2.177

Time-series correction of flow boundary conditions
File contents
Time-series corrections for flow boundary conditions of all open boundary sections with data type T (Data Group Boundaries - Flow conditions in GUI).
Filetype
ASCII
File format
Fix format for header information; free format for time-series data.
Same format as .bct file described above.
Filename

MDF file example line Filbc0 = # name.bc0 #
Generated
program Delft3D-NESTHD or manually offline

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Files of Delft3D-FLOW

Record description:
For each open boundary segment with boundary data of type T (time-series) the data is given
in two related blocks:
1 A header block containing a number of compulsory and optional keywords accompanied
by their values.
2 A data block containing the time dependent data.
Description header block:
Text

Format

Value

Format

table-name

a20, 1x

’Boundary Section: ##’

contents

a20,1x

’Logarithmic ’
’Uniform ’
’3d-profile ’

location

a20, 1x

’name boundary section’ (see
file)

time-function

a20, 1x

’non-equidistant’

reference-time

a20, 1x

yyyymmdd (must be equal to itdate)

time-unit

a20, 1x

’minutes’

interpolation

a20, 1x

’linear’

8 to 8+NPAR+1

parameter

a20, 1x

’parameter name and location’,
’layer and location’, units ’[ccc]’

a,
’units’,
a

10+NPAR

records-in-table

a20, 1x

number of records in the data
block

integer

5
6
7

DR
AF

Record

Remark:
NPAR is the number of parameters for which a time varying boundary condition is being
specified.
Description data block:
Record

Record description

each record

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Example 1:

Restrictions:
Maximum record length is 5000.
Position, format of the keywords and the format of keyword-values in the header are
fixed (see example).
All keywords have a length of 20 characters. The keywords are case-sensitive.
Header in each block must be ended with the (compulsory) keyword: ‘records in table’
accompanied by the number of data records to follow.
Times must be multiples of the integration time step; the times specified will be checked
on their domain.
The sequence of blocks must be consistent with the sequence of open boundary sections with data type T(ime).
All open boundaries that have ‘3D-profile’ must precede other open boundaries.

One of the open boundary sections with time-varying boundary correction in additional to the
boundary condition.

DR
AF

A water level correction at the east boundary for which the boundary condition is given at two
time breakpoints, i.e. at 40.0 and 50.0 minutes after the Reference Date. The vertical profile is
logarithmic, the interpolation method linear, the time-series is assumed to be non-equidistant
and the time is given in minutes.
table-name
’Boundary Section : 1’
contents
’logarithmic
’
location
’East Boundary
’
time-function
’non-equidistant
’
reference-time
19941001
time-unit
’minutes’
interpolation
’linear’
parameter
’time
’
unit ’ ’
parameter
’water elevation (z) end A’ unit ’[m]’
parameter
’water elevation (z) end B’ unit ’[m]’
records in table
2
4.0000000e+001 -9.0207780e-005 1.0587220e-004
5.0000000e+001 -1.9945080e-004 7.0667030e-005
...

A.2.17

Time-series transport boundary conditions
File contents
Time-series for transport boundary conditions of all open boundary
sections (Data Group Boundaries - Transport conditions).
Filetype
ASCII
File format
Fix format for header information; free format for time-series data
Filename

Generated
FLOW-GUI, program Delft3D-NESTHD or manually offline

440 of 688

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Files of Delft3D-FLOW

Record description:
For each open boundary segment the data is given in two related blocks:
1 A header block containing a number of compulsory and optional keywords accompanied
by their values.
2 A data block containing the time dependent data.
Description header block:
Text

Format

Value

Format

table-name

a20, 1x

’Boundary Section : ##’

contents

a20,1x

’Logarithmic ’
’Uniform ’
’Step ’
’3d-profile ’

location

a20, 1x

’name boundary section’ (see
file

time-function

a20, 1x

’non-equidistant’

reference-time

a20, 1x

yyyymmdd (must be equal to itdate)

time-unit

a20, 1x

’minutes’

interpolation

a20, 1x

’linear’

8 to 8+NPAR+1

parameter

a20, 1x

’parameter name and location’,
’layer and location’,
units ’[ccc]’

a,
’units’,
a

10+NPAR

records in table

a20, 1x

number of records in the data
block

integer

5
6
7

DR
AF

Record

Remark:
NPAR is the number of parameters for which a time-varying boundary condition is being
specified.
Description data block:

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Record description

each record

Time in minutes after the Reference Date and NPAR values representing the parameter for which a time varying boundary condition is being
specified (all reals). The number of values to be specified for each end
point of a boundary section depends on the type of profile in the vertical:
uniform: 2 real values for each parameter specified
linear: 4 real values for each parameter specifying the parameter in the
surface and in the bottom layer for both section end points.
step: 5 real values; 4 reals for each parameter specifying the parameter
in the surface and in the bottom layer for both section end points and
the location of the discontinuity/jump in the vertical in metres below the
surface
3D-profile: Kmax∗2 real values for each layer in both end points of the
boundary section being prescribed.

Record

DR
AF

Restrictions:
Maximum record length is 5000.
Position, format of the keywords and the format of keyword-values in the header are
fixed (format in example).
All keywords have a length of 20 characters.
Header in each block must be ended with the (compulsory) keyword: ‘records in table’
accompanied by the number of data records to follow.
Times must be multiples of the integration time step; the times specified will be checked
on their domain.
Not all values of other parameters from the file will be checked on their domain.
The sequence of blocks must be consistent with the sequence of open boundary sections and the sequence of constituents.
All open boundaries that have ‘3D-profile’ must precede other open boundaries.
Example 1:

Model area with two open boundary sections. A 3D simulation (KMAX >1) has been specified; the profiles in the vertical are prescribed as functions. Salinity and one constituent are
included in the simulation. The boundary condition is specified as follows:

For a boundary section called West BOUNDARY, the salinity has a ‘Step’ profile with
the discontinuity occurring at 2.5 metres below the surface and a constituent called ’test
constituent’ has a Uniform profile in the vertical. The boundary conditions are given for
two time breakpoints, i.e. at 0.0 and 8000.0 minutes after the Reference Date 00:00:00 hr.
For a boundary section called East BOUNDARY, the salinity has a linear profile in the
vertical and a constituent called ’test constituent’ has a Uniform profile in the vertical. The
boundary conditions are given for two time breakpoints, i.e. at 0.0 and 8000.0 minutes
after midnight on the Reference Date.
table-name
contents
location
time-function
reference-time
time-unit
parameter
parameter
parameter
parameter

442 of 688

’T-series BC for process run: 123’
’step’
’West BOUNDARY’
’non-equidistant’
19941001
’minutes’
’time
’
’salinity
end A surface’
’salinity
end A bed
’
’salinity
end B surface’

unit
unit
unit
unit

’[min]’
’[ppt]’
’[ppt]’
’[ppt]’

Deltares

Files of Delft3D-FLOW

DR
AF

parameter
’salinity
end B bed
’ unit ’[ppt]’
parameter
’discontinuity
’ unit ’[m]’
records in table
2
0.0000
33.0000
35.000
34.0000
36.0000
2.5000
8000.0000
32.7000
34.000
35.0000
36.2000
2.5000
table-name
’T-series BC for flow run: 123’
contents
’uniform’
location
’West BOUNDARY’
time-function
’non-equidistant’
reference-time
19941001
time-unit
’minutes’
interpolation
’linear’
parameter
’time
’ unit ’[min]’
parameter
’test constituent
end A
’ unit ’[-]’
parameter
’test constituent
end B
’ unit ’[-]’
records in table
2
0.0000
1.50000
1.60000
8000.0000
1.75000
1.80000
table-name
’T-series BC for process run: 123’
contents
’linear’
location
’East BOUNDARY’
time-function
’non-equidistant’
reference-time
19941001
time-unit
’minutes’
interpolation
’linear’
parameter
’time
’ unit ’[min]’
parameter
’salinity
end A surface’ unit ’[ppt]’
parameter
’salinity
end A bed
’ unit ’[ppt]’
parameter
’salinity
end B surface’ unit ’[ppt]’
parameter
’salinity
end B bed
’ unit ’[ppt]’
records in table
2
0.0000
33.0000
35.000
34.0000
36.0000
8000.0000
32.7000
34.000
35.0000
36.2000
table-name
’T-series BC for flow run: 123’
contents
’uniform’
location
’East BOUNDARY’
time-function
’non-equidistant’
reference-time
19941001
time-unit
’minutes’
interpolation
’linear’
parameter
’time
’ unit ’[min]’
parameter
’test constituent
end A
’ unit ’[-]’
parameter
’test constituent
end B
’ unit ’[-]’
records in table
2
0.0000
1.50000
1.60000
8000.0000
1.75000
1.80000

Example 2:

The second example concerns an open sea boundary consisting of three sections for which
the salinity concentrations are prescribed. The computation is depth averaged; see section A.2.15 for the corresponding bct-file.
table-name
contents
location
time-function
reference-time
time-unit
interpolation
parameter
parameter
parameter
records-in-table

Deltares

’Boundary Section : 1’
’Uniform
’
’west-vel-1
’
’non-equidistant’
19960718
’minutes’
’linear’
’time
’
’Salinity
end A uniform’
’Salinity
end B uniform’
185

unit ’[min]’
unit ’[ppt]’
unit ’[ppt]’

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unit ’[min]’
unit ’[ppt]’
unit ’[ppt]’

’Boundary Section : 2’
’Uniform
’
’west-vel-2
’
’non-equidistant’
19960718
’minutes’
’linear’
’time
’
’Salinity
end A uniform’
’Salinity
end B uniform’
185

DR
AF

840.0 20.9 23.2
855.0 20.9 23.2
870.0 20.9 23.0
885.0 20.9 22.8
900.0 20.9 22.5
..................
3555.0 20.2 21.2
3570.0 20.5 21.2
3585.0 20.7 21.3
3600.0 20.9 21.4
table-name
contents
location
time-function
reference-time
time-unit
interpolation
parameter
parameter
parameter
records-in-table
840.0 23.2 21.9
855.0 23.1 21.9
870.0 23.0 21.8
885.0 22.8 21.6
900.0 22.5 21.4
..................
3555.0 21.1 17.8
3570.0 21.1 17.8
3585.0 21.2 17.8
3600.0 21.3 17.9
table-name
contents
location
time-function
reference-time
time-unit
interpolation
parameter
parameter
parameter
records-in-table
840.0 20.6 22.2
855.0 20.6 22.1
870.0 20.5 21.8
885.0 20.4 21.4
900.0 20.3 20.8
..................
3555.0 16.7 12.4
3570.0 16.7 13.0
3585.0 16.7 13.5
3600.0 16.8 13.9

’Boundary Section : 3’
’Uniform
’
’west-vel-3
’
’non-equidistant’
19960718
’minutes’
’linear’
’time
’
’Salinity
end A uniform’
’Salinity
end B uniform’
185

unit ’[min]’
unit ’[ppt]’
unit ’[ppt]’

Example 3:
The third example concerns the same open boundary of the second example, i.e. consisting
of three sections for which the salinity concentrations are prescribed. The computation is a
3D computation with 5 layers in the vertical; see section A.2.15 for the corresponding bct-file.
table-name
contents
location
time-function
reference-time

444 of 688

’Nested transport bc salinity west-vel-1
’
’3d-profile’ # at ends A&B of open boundary segment
’west-vel-1
’
’non-equidistant’
19960718

Deltares

Files of Delft3D-FLOW

A.2.18

DR
AF

time-unit
’minutes’
interpolation
’linear’
parameter
’time
’ unit ’[min]’
parameter
’salinity
end A layer:
1’ unit ’[ppt]’
parameter
’salinity
end A layer:
2’ unit ’[ppt]’
parameter
’salinity
end A layer:
3’ unit ’[ppt]’
parameter
’salinity
end A layer:
4’ unit ’[ppt]’
parameter
’salinity
end A layer:
5’ unit ’[ppt]’
parameter
’salinity
end B layer:
1’ unit ’[ppt]’
parameter
’salinity
end B layer:
2’ unit ’[ppt]’
parameter
’salinity
end B layer:
3’ unit ’[ppt]’
parameter
’salinity
end B layer:
4’ unit ’[ppt]’
parameter
’salinity
end B layer:
5’ unit ’[ppt]’
records-in-table
185
840.0 15.6 16.5 19.3 19.3 20.3 17.1 18.4 21.1 23.0 24.1
855.0 15.6 16.7 19.4 19.5 20.6 16.9 17.9 20.6 22.6 23.8
.................................................................
3585.0 11.7 13.1 15.2 16.7 17.8 10.7 13.1 18.1 19.3 20.6
3600.0 11.8 13.1 15.2 16.7 17.6 11.1 13.1 18.0 19.1 20.4
table-name
’Nested transport bc salinity west-vel-2
’
contents
’3d-profile’ # at ends A&B of open boundary segment
location
’west-vel-2
’
time-function
’non-equidistant’
reference-time
19960718
time-unit
’minutes’
interpolation
’linear’
parameter
’time
’ unit ’[min]’
parameter
’salinity
end A layer:
1’ unit ’[ppt]’
parameter
’salinity
end A layer:
2’ unit ’[ppt]’
parameter
’salinity
end A layer:
3’ unit ’[ppt]’
parameter
’salinity
end A layer:
4’ unit ’[ppt]’
parameter
’salinity
end A layer:
5’ unit ’[ppt]’
parameter
’salinity
end B layer:
1’ unit ’[ppt]’
parameter
’salinity
end B layer:
2’ unit ’[ppt]’
parameter
’salinity
end B layer:
3’ unit ’[ppt]’
parameter
’salinity
end B layer:
4’ unit ’[ppt]’
parameter
’salinity
end B layer:
5’ unit ’[ppt]’
records-in-table
185
840.0 17.3 18.4 20.6 22.9 24.2 16.5 16.5 17.9 20.2 23.3
855.0 17.2 18.0 20.2 22.6 23.9 16.4 16.5 17.8 20.0 23.1
.................................................................
.................................................................
3585.0 10.7 13.1 18.3 19.5 20.8 11.2 12.3 15.0 17.4 19.2
3600.0 11.1 13.2 18.2 19.4 20.7 11.9 12.8 15.4 17.8 19.5

Time-series for the heat model parameters
File contents
Time dependent data for heat model (Data Group Physical parameters - Heat flux model).
Filetype
ASCII
File format
Free formatted
Filename

Generated
FLOW-GUI, or manually offline

Deltares

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Record description:
The record description depends on the heat flux model selected.
Option 1: Absolute temperature model, total incoming solar radiation
Record

Record description

each record

Time after midnight on the Reference Date [minutes].
Relative humidity [percentage].
Air temperature [◦ C].
Incoming solar radiation for a cloudless sky [J/m2 s] [4 reals].

Option 2: Absolute temperature model, net solar radiation
Record description

each record

Time after midnight on the Reference Date [minutes].
Relative humidity [percentage].
Air temperature [◦ C].
Net (sum of short and long wave radiation, reflection accounted for) solar
radiation [J/m2 s], [4 reals].

DR
AF

Record

Option 3: Excess temperature model
Record

Record description

each record

Time after midnight on the Reference Date [minutes].
Background temperature [◦ C], [2 reals].

Option 4A: Murakami heat flux model

In this option the vapour pressure will be computed (IVAPOP = 0).
Record

Record description

each record

Time after midnight on the Reference Date [minutes].
Relative humidity [percentage].
Air temperature [◦ C].
Net (short wave) solar radiation [J/m2 s], [4 reals].

Option 4B: Murakami heat flux model
In this option the vapour pressure is user-defined (IVAPOP = 1).

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Files of Delft3D-FLOW

Record

Record description

each record

Time after midnight on the Reference Date [minutes].
Relative humidity [percentage].
Air temperature [◦ C].
Net (short wave) solar radiation [J/m2 s].
Vapour pressure [mbar], [5 reals].

Option 5A: Ocean model
In this option the solar radiation will be computed from the cloud coverage (SolRad = #N#)
Record description

each record

Time after midnight on the Reference Date [minutes].
Relative humidity [percentage].
Air temperature [◦ C].
Fraction cloud coverage [percentage], [4 reals].

DR
AF

Record

Option 5B: Ocean model

In this option the solar radiation is specified directly, additional to the cloud coverage (SolRad
= #Y#)
Record

Record description

each record

Time after midnight on the Reference Date [minutes].
Relative humidity [percentage].
Air temperature [◦ C].
Fraction cloud coverage [percentage]
Net (short wave) solar radiation [J/m2 s], [5 reals].

Remark:
The parameter IVAPOP is specified in the MDF-file.

Restrictions:
Times must be multiples of the integration time step.
Relative humidity must be a percentage (0–100).
The other parameters will not be checked against their domain.
Input items in a record must be separated by one or more blanks.
Only for the Ocean model: Using SolRad as described for option 5B, one can specify
the measured net solar radiation directly as a time series. The specified solar radiation
is then only reduced using the Albedo coefficient.
Example 1:
Heat flux model option 3 is selected.
0.
10.
20.

Deltares

0.
15.
17.

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Delft3D-FLOW, User Manual

30.
150.
600.
610.
900.

17.
16.
16.
15.
0.

Example 2:
Heat flux model option 2 is selected.
40.
45.
47.
47.
46.
46.
45.
40.

18.
21.
24.
22.
25.
23.
18.
17.

0.
50.
200.
200.
250.
200.
50.
0.

0.
10.
20.
30.
150.
600.
610.
900.

DR
AF

Example 3:

Heat flux model option 4B is selected. You have to add IVAPOP = 1 in the Data Group
Additional parameters.
0.
10.
20.
30.
150.
600.
610.
900.

A.2.19

40.0
45.0
47.0
47.0
46.0
46.0
45.0
40.0

18.0
21.0
24.0
22.0
25.0
23.0
18.0
17.0

0.
50.
200.
200.
250.
200.
50.
0.

8.3412
11.2994
14.1575
12.5449
14.7110
13.0460
9.3838
7.8337

Bottom roughness coefficients
File contents
Bottom roughness coefficients in U- and V-direction for all grid points
(Data Group Physical parameters - Roughness).
Filetype
ASCII
File format
Free formatted or unformatted
Filename

Generated
Free formatted: FLOW-GUI (only for uniform depth values), QUICKIN
or manually offline.
Unformatted: by some external program.
Record description:

Two blocks with data are needed: one for U- and one for V-direction.
Filetype

Record description

Free formatted

The bottom roughness is given per row, starting at N = 1 to N = Nmax,
separated by one or more blanks. The number of continuation lines
is determined by the number of grid points per row (Mmax) and the
maximum record size of 132.

Unformatted

Mmax bottom roughness values per row for N = 1 to N = Nmax.

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Files of Delft3D-FLOW

Restrictions:
The maximum record length in the free formatted file is 132.
The value of these parameters will not be checked against their domain.
Input items in a record must be separated by one or more blanks (free formatted file
only).
Example:
Bottom roughness coefficients (Chézy formulation) for a model containing 11∗7 points.
The records are filled with (maximal) 8 reals.

A.2.20

65.0
65.0
65.0
65.0
60.0
60.0
60.0
60.0
55.0
55.0
55.0
55.0
55.0
55.0
60.0
60.0
60.0
60.0
65.0
65.0
65.0
65.0
65.0
65.0
65.0
65.0
65.0
65.0

65.0 65.0 65.0 65.0 65.0
65.0 65.0 65.0 65.0 65.0
60.0 60.0 60.0 60.0 60.0

{start U-roughness coefficient}

DR
AF

65.0
65.0
65.0
65.0
60.0
60.0
60.0
60.0
55.0
55.0
55.0
55.0
55.0
55.0
60.0
60.0
60.0
60.0
65.0
65.0
65.0
65.0
65.0
65.0
65.0
65.0
65.0
65.0

The input data is printed in Courier; comment (not in the file) is printed between brackets.

60.0 60.0 60.0 60.0 60.0
55.0 55.0 55.0 55.0 55.0
55.0 55.0 55.0 55.0 55.0
55.0 55.0 55.0 55.0 55.0
60.0 60.0 60.0 60.0 60.0

{start V-roughness coefficient)

60.0 60.0 60.0 60.0 60.0
65.0 65.0 65.0 65.0 65.0
65.0 65.0 65.0 65.0 65.0
65.0 65.0 65.0 65.0 65.0
65.0 65.0 65.0 65.0 65.0
65.0 65.0 65.0 65.0 65.0

Horizontal eddy viscosity and diffusivity
File contents
Horizontal eddy viscosity and eddy diffusivity for all grid points (Data
Group Physical parameters - Viscosity ).
Filetype
ASCII or binary
File format
Free formatted or unformatted
Filename

Generated
Free formatted: FLOW-GUI, QUICKIN or manually offline.
Unformatted: by some external program.
Remark:

Horizontal eddy diffusivity is only needed in case of salinity, temperature or constituents.

Deltares

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Record description:
Record description

Free formatted

The eddy viscosity is given per row, starting at N = 1 to N = Nmax,
separated by one or more blanks. The number of continuation lines
is determined by the number of grid points per row (Mmax) and the
maximum record size of 132.
The eddy diffusivity is given per row in a similar fashion as the eddy
viscosity is given.

Unformatted

Mmax eddy viscosity values per row for N = 1 to N = Nmax.
First the eddy viscosity is given followed by the eddy diffusivity.

Filetype

DR
AF

Restrictions:
The maximum record length in the free formatted file is 132.
The value of the input parameters will not be checked against their domain.
Items in a record must be separated by one or more blanks (free formatted file only).
Example:

Eddy viscosity and eddy diffusivity for a model with (one layer and) m=8, n=12 grid points. A
constituent is included in the model.
The input data is printed in Courier; comment (not in the file) is printed between brackets.
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
1.0 1.0 1.0 1.0 1.0
10.0 10.0 10.0 10.0
10.0 10.0 10.0 10.0
10.0 10.0 10.0 10.0
10.0 10.0 10.0 10.0
10.0 10.0 25.0 25.0
10.0 10.0 10.0 10.0
10.0 10.0 25.0 25.0
10.0 10.0 10.0 10.0
10.0 10.0 25.0 25.0
10.0 10.0 10.0 10.0
10.0 10.0 10.0 10.0
10.0 10.0 10.0 10.0

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1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0
1.0 1.0 1.0
10.0 10.0 10.0
10.0 10.0 10.0
10.0 10.0 10.0
10.0 10.0 10.0
25.0 10.0 10.0
10.0 10.0 10.0
25.0 10.0 10.0
10.0 10.0 10.0
25.0 10.0 10.0
10.0 10.0 10.0
10.0 10.0 10.0
10.0 10.0 10.0

{start eddy viscosity}

10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0
10.0

{start eddy diffusivity}

Deltares

Files of Delft3D-FLOW

Discharge locations
File contents

Description (name, grid indices and interpolation method for discharge rate) for discharge stations (Data Group Operations - Discharges).
ASCII
Fix formatted for text variables, free formatted for real and integer
values.

FLOW-GUI or manually offline

Filetype
File format
Filename
Generated
Record description:

Record description

each record

Name of discharge (20 characters),
Type of interpolation (1 character):

Record

y
linear,
n
block,
Grid indices of discharge location (3 integers),
Character to indicate the type of discharge:

DR
AF

A.2.21

blank | n
normal discharge,
b
bubble screen, see section B.22,
c | d | e| u
culvert, see section 10.9.2.6,
m
discharge with momentum,
p
power station,
w
walking discharge,
Grid indices of power station outlet (3 integers).

Restrictions:
One record per discharge
Maximum record length is 132.
The discharge name is read as string of length 20 and must start in position one.
If K = 0, the discharge will be distributed over the vertical proportional to the relative
layer thickness.
A discharge must be located inside the computational grid enclosure.
Items in a record must be separated by one or more blanks.
Example:

The application requires 5 discharges. The first two discharges are ‘normal’ discharges, the
first discharge is only in layer 5, the second discharge is distributed over the vertical. The third
discharge is a walking discharge; the release point moves with drying and flooding. The last
two discharges are so-called power stations. The intake of the first power station is distributed
over the vertical and its outlet is in layer 1, while the second power station has its intake in
layer 5 and its outlet distributed over the vertical.
Discharge
Discharge
Discharge
Discharge
Discharge

Deltares

Station
Station
Station
Station
Station

A
B
C
D
E

Y 10
Y 15
Y 114
N 115
Y 88

11
5
88
93
119

5
0
3
0
5

w
p
p

110
80

90
115

1
0

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Flow rate and concentrations at discharges
File contents
Discharge rate and concentrations as a function of time for each
discharge location (Data Group Operations - Discharges).
Filetype
ASCII
File format
Fix formatted for text variables, free formatted for real and integer
values.
Filename

Generated
FLOW-GUI, or manually offline
Record description:
For each discharge the data is given in two related blocks:

1 A header block containing a number of compulsory and optional keywords with their values.
2 A data block containing the time dependent data.
Description header block:

DR
AF

A.2.22

Record

Text

Value

table-name

’T-series for discharges run: runid’

contents

regular, momentum, walking, power

location

name of the discharge

time-function

equidistant or non-equidistant

reference-time

yyyymmdd

time-unit

minutes

interpolation

linear or block

8 to 8+NPAR+1

parameter

name of parameter, ’unit’, units of parameter

10+NPAR

records in table

the number of records in the data block

2
3
4
5
6
7

where:

NPAR is the number of parameters for which a time discharge is being specified.
Description data block:
Record

Record description

each record

Time in minutes after 00:00:00 on the Reference Date (1 real),
NPAR values representing the parameters for which a time varying discharge is being specified (all reals).

Restrictions:

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Deltares

Files of Delft3D-FLOW

The parameters must be given in the following mandatory sequence: discharge flux,
salinity, temperature, constituents, velocity and direction relative to the ξ -axis (positive

Example:

counter-clock wise). Only those constituents are specified in the time dependent data
that are specified in the header.
The maximum record length in the file is 132.
The format of keywords and keyword-values in the header are fixed.
All keywords have a length of 20 characters.
Header records must start in position one.
Header in each block must be ended with the (compulsory) keyword: ‘records in table’
accompanied by its appropriate value.
Times must be a multiple of the integration time step; times will be checked.
Not all other parameters will be checked against their domain.
The order of the blocks must be consistent with the sequence of discharge locations as
specified in the FLOW-GUI.
Input items in the data records must be separated by one or more blanks.

DR
AF

The number of discharges is 3. Each discharge releases salinity and one constituent in addition to the water released.
table-name
contents
location
time-function
reference-time
time-unit
interpolation
parameter
parameter
parameter
parameter
parameter
records in table
0.0 90.0
1440.0 90.0
table-name
contents
location
time-function
reference-time
time-unit
interpolation
parameter
parameter
parameter
records in table
0.0 65.0
1440.0 65.0
table-name
contents
location
time-function
reference-time
time-unit
interpolation
parameter
parameter
parameter
records in table
0.0
40.0

Deltares

’T-series for discharges run: 1’
’momentum’
’Ara River’
’non-equidistant’
19941001
’minutes’
’linear’
’flux/discharge rate ’ unit ’[m**3/s]’
’salinity
’ unit ’[ppt]’
’test
’ unit ’[kg/m**3]’
’flow magnitude [m/s]’ unit ’[m/s]’
’flow direction [deg]’ unit ’[deg]’
2
5.0
0.0 45.0 18.0
0.0
0.0 50.0 20.0
’T-series for discharges run: 123’
’regular’
’Sumida River’
’non-equidistant’
19941001
’minutes’
’linear’
’flux/discharge rate ’ unit ’[m**3/s]’
’salinity
’ unit ’[ppt]’
’test
’ unit ’