MIKE 21 Flow Model: Hydrodynamic Module

MIKE 21 Flow Model
Hydrodynamic Module
User Guide
MIKE 2017
2
PLEASE NOTE
COPYRIGHT This document refers to proprietary computer software which is pro-

tected by copyright. All rights are reserved. Copying or other repro-
duction of this manual or the related programs is prohibited without
prior written consent of DHI. For details please refer to your 'DHI
Software Licence Agreement'.
LIMITED LIABILITY The liability of DHI is limited as specified in Section III of your 'DHI
Software Licence Agreement':
'IN NO EVENT SHALL DHI OR ITS REPRESENTATIVES

(AGENTS AND SUPPLIERS) BE LIABLE FOR ANY DAMAGES
WHATSOEVER INCLUDING, WITHOUT LIMITATION, SPECIAL,
INDIRECT, INCIDENTAL OR CONSEQUENTIAL DAMAGES OR
DAMAGES FOR LOSS OF BUSINESS PROFITS OR SAVINGS,
BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMA-
TION OR OTHER PECUNIARY LOSS ARISING OUT OF THE
USE OF OR THE INABILITY TO USE THIS DHI SOFTWARE
PRODUCT, EVEN IF DHI HAS BEEN ADVISED OF THE POSSI-
BILITY OF SUCH DAMAGES. THIS LIMITATION SHALL APPLY
TO CLAIMS OF PERSONAL INJURY TO THE EXTENT PERMIT-
TED BY LAW. SOME COUNTRIES OR STATES DO NOT ALLOW
THE EXCLUSION OR LIMITATION OF LIABILITY FOR CONSE-
QUENTIAL, SPECIAL, INDIRECT, INCIDENTAL DAMAGES AND,
ACCORDINGLY, SOME PORTIONS OF THESE LIMITATIONS
MAY NOT APPLY TO YOU. BY YOUR OPENING OF THIS
SEALED PACKAGE OR INSTALLING OR USING THE SOFT-
WARE, YOU HAVE ACCEPTED THAT THE ABOVE LIMITATIONS
OR THE MAXIMUM LEGALLY APPLICABLE SUBSET OF THESE
LIMITATIONS APPLY TO YOUR PURCHASE OF THIS SOFT-
WARE.'
3
4 MIKE 21 Flow Model - © DHI
CONTENTS
5
1 About This Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.2 Assumed User Background . . . . . . . . . . . . . . . . . . . . . . . . 11
2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1.1 Application areas . . . . . . . . . . . . . . . . . . . . . . . . . 13
3 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.2 Wind Set-up in a Rectangular Lake . . . . . . . . . . . . . . . . . . . . . 15
3.2.1 Defining the model . . . . . . . . . . . . . . . . .. . . . . . . 15
3.2.2 Extracting data for plotting . . . . . . . . . . . . . .
. . . . . . . 16
3.2.3 Evaluating the results . . . . . . . . . . . . . . . .
. . . . . . . 17
3.3 Donegal Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.3.1 Purpose of the study . . . . . . . . . . . . . . . .. . . . . . . 17
3.3.2 Defining the hydrodynamic model . . . . . . . . . . . . . . . . . 18
3.3.3 Collecting data . . . . . . . . . . . . . . . . . . .
. . . . . . . 19
3.3.4 Setting up the model . . . . . . . . . . . . . . . .. . . . . . . 19
3.3.5 Calibrating and verifying the model . . . . . . . . . .
. . . . . . . 20
3.3.6 Running the production simulations . . . . . . . . .. . . . . . . 21
3.3.7 Presenting the results . . . . . . . . . . . . . . . .
. . . . . . . 21
3.3.8 List of data and specification files . . . . . . . . . .
. . . . . . . 22
3.4 Retention Basin by River . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.4.1 Purpose of the example . . . . . . . . . . . . . . .. . . . . . . 23
3.4.2 Defining the hydrodynamic model . . . . . . . . . . . . . . . . . 24
3.4.3 Presenting and evaluating the results . . . . . . . .
. . . . . . . 27
3.4.4 List of data and specification files . . . . . . . . . .
. . . . . . . 31
3.5 Turtle Bay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.1 General remarks . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5.2 About the model . . . . . . . . . . . . . . . . . . . . . . . . . 32
3.5.3 .
Data and specification files supplied with this example . . . . . . 33
3.6 Bed Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.6.2 Defining hydrodynamic model . . . . . . . . . . . . . . . . . . . 34
. . . . . . . 36
3.6.4 .
3.7 Infiltration . . . . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . 39
3.7.2 Defining hydrodynamic model . . . . . . . . . . . . . . . . . . . 39
. . . . . . . 42
3.7.4 .
4 Basic Parameters Dialog Overview . . . . . . . . . . . . . . . . . . . . . 47
4.1 Module Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
4.1.1 Inland flooding . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.1.2 HD calculations . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.2 Bathymetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.2.1 Cold start . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.2 Hot start . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.3 Coriolis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.2.4 Landslide . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.2.5 Multi-cell overland solver . . . . . . . . . . . . . . . . . . . . . 50
4.3 Simulation Period . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
4.4 Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.5 Source and Sink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.6 Mass Budget . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4.7 Flood and Dry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5 Dialog Overview . . . . . . . . . .. .. . . . . . . . . . . . . . . . . . . 55
5.1 Initial Surface Elevation . . . . .. .. . . . . . . . . . . . . . . . . . . 55
5.2 Boundary . . . . . . . . . . .. .. . . . . . . . . . . . . . . . . . . 55
5.3 Source and Sink . . . . . . . .. .. . . . . . . . . . . . . . . . . . . 57
5.3.1 Evaporation and precipitation . . . . . . . . . . . . . . . . . . . 57
5.4 Infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.4.1 Net infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . 58
5.4.2 Constant infiltration with capacity . . . . . . . . . . . . . . . . . 59
5.5 Eddy Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.6 Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5.6.1 Wave induced bed resistance parameters . . . . . . . . . . . . . 61
5.7 Fluid Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.8 Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5.9 Wave Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.10 Wind Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
5.11 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.11.1 Weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.11.2 Culverts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
5.11.3 Dikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.11.4 Composite structures . . . . . . . . . . . . . . . . . . . . . . . 72
5.11.5 Level-width relationship . . . . . . . . . . . . . . . . . . . . . 72
5.11.6 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 73
5.12 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6 Reference Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.1 Bathymetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
6.1.1 General description . . . . . . . . . . . . . . . . . . . . . . . 77
6.1.2 Selecting the model area . . . . . . . . . . . . . . . . . . . . . 77
6.1.3 Selecting the grid spacing . . . . . . . . . . . . . . . . . . . . 79
6.1.4 Selecting the reference level . . . . . . . . . . . . . . . . . . . 82
6.1.5 Specifying the bathymetry . . . . . . . . . . . . . . . . . . . . 82
6.1.6 Sign convention . . . . . . . . . . . . . . . . . . . . . . . . . 83
6.1.7 Additional area description . . . . . . . . . . . . . . . . . . . . 83
6.1.8 Landslide option . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.2 Bed Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
7
6.2.2 Specifying the bed resistance . . . . . . . . . . . . . . . . . . . 86
6.2.3 Recommended values . . . . . . . . . . . . . . . . . . . . . . 86
6.3 Blow-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.4 Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.4.1 General description . . . . . . . . . . . . . . . . . . . . . . . . 87
6.4.2 Specifying the boundary conditions . . . . . . . . . . . . . . . . 88
6.4.3 User specified boundaries . . . . . . . . . . . . . . . . . . . . . 90
6.4.4 Recommended selections and values . . . . . . . . . . . . . . . 92
6.5 Chezy Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.6 Courant Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.6.2 Recommended value . . . . . . . . . . . . . . . . . . . . . . . 95
6.7 CPU Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.7.1 Factors influencing the CPU time . . . . . . . . . . . . . . . . . 95
6.8 Current . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.9 Disk Space . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.9.1 Small files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.9.2 Large files . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.10 Eddy Viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
6.10.2 Specifying the eddy viscosity . . . . . . . . . . . . . . . . . . . 98
6.11 Evaporation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
6.12 Flooding and Drying . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
6.12.2 Specifying flooding and drying . . . . . . . . . . . . . . . . . . 100
6.12.3 Recommended values . . . . . . . . . . . . . . . . . . . . . 100
6.12.4 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . 101
6.13 Friction Factor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.14 Froude Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.15 Hot Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
6.15.2 Specifying the hot data . . . . . . . . . . . . . . . . . . . . . 102
6.16 Infiltration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
6.16.2 Net infiltration rate . . . . . . . . . . . . . . . . . . . . . . . 103
6.16.3 Infiltration and leakage . . . . . . . . . . . . . . . . . . . . . 104
6.17 Initial Surface Elevation . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.18 Inundation statistics . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.19 Manning Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.20 Mud, Debris or Oil . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
6.20.1 Recommended values . . . . . . . . . . . . . . . . . . . . . 106
6.21 Multi-cell overland Solver . . . . . . . . . . . . . . . . . . . . . . . . 109

6.21.1 Constructing the fine and the coarse bathymetries . . . . . . . . . 109
6.21.2 Evaluation of hydraulic parameters within a cell . . . . . . . . . . 110
6.22 Orientation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.23 Output Files . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
6.23.2 Specification of output files . . . . . . . . . . . . . . . . . . . . 111
6.24 Pier Resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112
6.24.2 Specifying the pier resistance . . . . . . . . . . . . . . . . . . . 113
6.25 Precipitation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.26 Simulation Type . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116
6.27 Shear Stress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.28 Smagorinsky Formulation . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.29 Soft Start . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
6.29.2 Specifying soft start . . . . . . . . . . . . . . . . . . . . . . . 118
6.30 Source and Sink . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
6.30.2 Specifying sources and sinks . . . . . . . . . . . . . . . . . . . 119
6.31 Standard vs. nested HD module . . . . . . . . . . . . . . . . . . . . . . 119
6.31.2 Nested bathymetries . . . . . . . . . . . . . . . . . . . . . . . 121
6.31.3 Nested model specifications . . . . . . . . . . . . . . . . . . . 123
6.31.4 Pre- and post-processing tools . . . . . . . . . . . . . . . . . . 125
6.32 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
6.32.1 Location of a structure . . . . . . . . . . . . . . . . . . . . . . 125
6.32.2 Weirs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.32.3 Culverts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
6.32.4 Dikes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
6.32.5 Flow directions for specific structure parameters . . . . . . . . . . 133
6.33 Time Step . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
6.33.1 Selecting the time step . . . . . . . . . . . . . . . . . . . . . . 134
6.34 Velocity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
6.35 Wave Radiation Stresses . . . . . . . . . . . . . . . . . . . . . . . . . 136
6.35.2 Specifying the wave radiation stresses. . . . . . . . . . . . . . . 136
6.36 Wind Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138
6.36.2 Specifying the wind conditions . . . . . . . . . . . . . . . . . . 138
9
6.36.3 Specifying the wind friction . . . . . . . . . . . . . . . . . . . 139
6.36.4 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . 140
6.37 List of References . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143

Purpose
1 About This Guide
1.1 Purpose
The main purpose of this User Guide is to get you started in the use of MIKE
21 Flow Model, Hydrodynamic Module (HD), for applications of hydraulic
phenomena in lakes, estuaries, bays, coastal areas and seas. It may be
applied wherever stratification can be neglected.
This User Guide is complemented by the Online Help.
1.2 Assumed User Background

Although the hydrodynamic module has been designed carefully with empha-
sis on a logical and user-friendly interface, and although the User Guide and
Online Help contains modelling procedures and a large amount of reference
material, common sense is always needed in any practical application.
In this case, “common sense” means a background in coastal hydraulics and

oceanography, which is sufficient for you to be able to check whether the
results are reasonable or not. This User Guide is not intended as a substitute
for a basic knowledge of the area in which you are working: mathematical
modelling of hydraulic phenomena.
11
About This Guide

General Description
2 Introduction
2.1 General Description

MIKE 21 Flow Model is a modelling system for 2D free-surface flows. MIKE
21 Flow Model is applicable to the simulation of hydraulic and environmental
phenomena in lakes, estuaries, bays, coastal areas and seas. It may be
applied wherever stratification can be neglected.
The hydrodynamic (HD) module is the basic module in the MIKE 21 Flow
Model. It provides the hydrodynamic basis for the computations performed in
the Environmental Hydraulics modules.
The hydrodynamic module simulates water level variations and flows in

response to a variety of forcing functions in lakes, estuaries and coastal
regions. The effects and facilities include:
 bottom shear stress

 wind shear stress
 barometric pressure gradients
 Coriolis force
 momentum dispersion
 sources and sinks
 evaporation
 flooding and drying
 wave radiation stresses
2.1.1 Application areas
MIKE 21 Flow Model, Hydrodynamic Module, can be applied to a wide range

of hydraulic and related phenomena. This includes:
 modelling of tidal hydraulics

 wind and wave generated currents
 storm surges
As mentioned previously, the MIKE 21 HD output results are also used as

input for many of the other MIKE 21 modules such as the Advection-Disper-
sion module (AD), the Sediment Transport (ST, MT), the Particle tracking
(PA) and the Environment module (MIKE ECO Lab).
As MIKE 21 HD is a very general hydraulic model, it can easily be set up to

describe specific hydraulic phenomena. Examples of such applications are:
13
Introduction
 secondary circulations, eddies and vortices

 harbour seiching
 dam-break
 tsunamis

General
3 Examples
3.1 General
One of the best ways of learning how to use a modelling system like the
MIKE 21 Flow Model is through practice. Therefore examples are included
which you can go through yourself and which you can modify, if you like, in
order to see what happens if one or other parameter is changed.
The specification files for the examples are included with the installation of
MIKE Zero. A directory is provided for each example. The directory names
are as follows (these may have been changed at your installation; please ask
your system administrator if you cannot find the directories):
 Wind set-up example:

MIKE_21\FlowModel\HD\Lake
 Donegal Bay, Water circulation example:
MIKE_21\FlowModel\HD\DonegalBay
 Retention Basin by River, Structure example:
MIKE_21\FlowModel\HD\Structure
 Turtle Bay, Nested model example:
MIKE_21\FlowModel\HD\TurtleBay
 Bed resistance example:
MIKE_21\FlowModel\HD\BedResistance
 Infiltration example:
MIKE_21\FlowModel\HD\Infiltration
 The Sound (Øresund), Denmark, From scratch to calibrated model
example:
MIKE21\FlowModel\HD\Sound
Note: The Sound example is described in a separate document, which can

be accessed via the MIKE Zero Documentation Index in the start menu:
MIKE 21 Flow Model, Hydrodynamic Module, Step-by-Step Training Guide
3.2 Wind Set-up in a Rectangular Lake
3.2.1 Defining the model
This example has been chosen as a fairly simple one, so that it is possible to
check the results analytically.
The problem is to determine the wind set-up in a lake.
15
Examples
The test conditions are:
 The lake is rectangular in shape with a length of 5 km in the east/west

direction, and a length of 2 km in the north/south direction, as shown in
Figure 3.1. The lake has a uniform depth of 10 m.
 The lake is connected to the sea by a 100 m wide channel in the middle
of the shore to the west. The sea is assumed to have a constant water
level of 0.0 m. Thus, there is one open boundary.
 A westerly wind of 35 m/s is blowing.
Figure 3.1 Wind set-up in a small lake, model layout
Additional information required by MIKE 21 is:
 The grid spacing, which on the basis of the size of the lake is selected to
be 100 meters.
 The time step, which on the basis of the grid spacing and the water depth
is selected as 20 seconds (corresponding to a Courant Number of 2).
3.2.2 Extracting data for plotting
After execution you may extract a time series of surface elevations in order to
see the effect of the wind. The time series extraction tools are located in the
MIKE Zero Toolbox.
The time series of the resulting water depth extracted in point (49, 10) is plot-
ted in Figure 3.2.

Donegal Bay
Figure 3.2 Time series of the wind set-up in a rectangular lake
3.2.3 Evaluating the results
The equations on which the calculations are based are given in the Scientific
Background Manual. Entering the parameters as you have given them above
and assuming that the model has reached a steady solution, you get a set-up
of 4.058.10-5 m/m. Thus, as the lake is 4900 m long, the total set-up at the
eastern end of the lake under steady state conditions should be 0.20 m. This
corresponds closely to the final result given in Figure 3.2.
3.3 Donegal Bay
3.3.1 Purpose of the study
From the specifications for the study we quote:
“The existing drainage system in Donegal town is a combined system

which discharges to the River Eske estuary without treatment.
To cater adequately for existing demands and to allow for future develop-
ments of the town proposals have been formulated to refurbish and
extend the drainage network. The proposals also include for the con-
struction of a comminution and pumping station and the discharge of the
effluent after comminution only through a new outfall fitted with a diffuser
and located as shown ..... [to the south west of the city].
The purpose of .... the study now required is to establish that the propos-
als for the disposal of the sewage and industrial effluents from Donegal
town are adequate in terms of protection of the environment and public
health considerations.”
17
Examples
The study was carried out by MCS International, Galway, Ireland with the
assistance of DHI. MCS International has kindly made the hydrodynamic
model, which was set up for this study, available for inclusion in this manual.
It should be noted that only part of the work, which was carried out, is
described here.
In order to do the required investigation a number of different MIKE 21 mod-

ules had to be applied. However, in this manual only the description of the
water circulation (i.e. the use of the hydrodynamic module, the MIKE 21 Flow
Model) is included.
The purpose of the water circulation study was to predict the current and
water level variations within the estuary for later calculation of the advection
and dispersion of the discharged effluents and calculation of their effects on
the water quality.
3.3.2 Defining the hydrodynamic model
The northern part of Donegal Bay including the River Eske estuary is shown
in Figure 3.3. The currents are governed by the tide, while the wind and, pos-
sibly, the outflow from the River Eske might also have an effect.
The model area was chosen based on the following considerations:
 The model is turned 50 degrees relative to true north so that the y-axis
lies parallel to the flow in the main channel running from Donegal
towards the bay. This rotation of the model also reduces the number of
grid points in the model and makes the main flow direction at the bound-
ary perpendicular to it.
 The boundary is situated not too close to the mouth of the estuary. This
ensures a uniform flow pattern at the boundary. Furthermore, the bound-
ary can not be situated in the mouth of the estuary itself, as flooding and
drying are not allowed on an open boundary.

Donegal Bay
Figure 3.3 The northern part of Donegal Bay and the model area for the hydrody-
namic model
A grid spacing of 150 meters was chosen as this was the maximum size,
which could be used to define the tidal channels in the estuary.
The time step was chosen to be 60 seconds, as this results in a maximum

Courant number of 5.9 in the deepest part of the model, and in Courant num-
bers of 2 to 3 in the estuary.
3.3.3 Collecting data
The digitised bathymetry was based on Admiralty Charts Nos. 2715 and
2702.
Tidal measurements, collection of wind data and measurements of flow in the

River Eske were not carried out by MCS International but were provided by
their client.
3.3.4 Setting up the model
The digitised model bathymetry is shown in Figure 3.4. Much effort was spent
in its preparation especially in the estuary where all the channels had to be
properly defined. The datum for the bathymetry is the lowest astronomical
tide (LAT), which is 2.35 m below mean sea level (MSL).
19
Examples
Figure 3.4 Model bathymetry, Donegal Bay
Simultaneous measurements of the water level close to the open boundary

and near Donegal had been made for a period of a little more than one tidal
cycle. This period was therefore selected as the calibration period. A tidal
range of 2.5 meters with a period of 12.5 hours was measured at the bound-
ary. During this period the wind was negligible.
Other measurements showed that the spring tide range is 3.5 m and the neap
tide range 1.5 m.
The discharge from the river is normally not very large. For the time of year
when the calibration data were collected, a discharge of 7.15 m3/s is normal.
3.3.5 Calibrating and verifying the model
The model was calibrated so that the simulated and measured water level
variation near Donegal showed a satisfactory agreement. The simulated
water levels are shown in Figure 3.5, while the measured ones are not availa-
ble for publication, as, unfortunately, they are included in a report, which has
not been released by MCS Internationals client.

Donegal Bay
Figure 3.5 Flow pattern during verification simulation at Donegal Bay
Most of the calibration work consisted of obtaining a correct schematisation of

the tidal channels in the estuary, while the bed resistance and the eddy vis-
cosity were not used as calibration parameters.
For the whole model a Manning number of 25 m1/3/s and a constant eddy vis-
cosity of 3 m2/s was used.
A simulation period of two tidal cycles was selected as this allowed the model
to warm up during the first cycle, while the second could then be used for
comparisons.
3.3.6 Running the production simulations
For the later advection/dispersion calculations the flow pattern during spring
tide and neap tide was needed. A conservative estimate of the river dis-
charge was used for these production simulations (3.27 m3/s corresponding
to the minimum discharge). Also a light wind (of 7.52 m/s) from south was
included.
3.3.7 Presenting the results
One good way of presenting the model bathymetry is by scanning the sea
chart used for the digitisation, running it through the Image Rectifier and plot-
ting it onto a transparent piece of paper (at the same scale as the plot of your
model bathymetry). In the report you can then include this as the page
preceding the plot of the bathymetry. This makes a comparison of the “real”
bathymetry and the model bathymetry and model results easier.
21
Examples
In addition to plots showing the verification results (as in Figure 3.5), plots of
the flow pattern should be included. Figure 3.6 shows the currents in the
model 3 hours after high tide.
Figure 3.6 Simulated water depths during the verification period at Donegal Bay
3.3.8 List of data and specification files
The following data files are supplied with MIKE 21:
Name: bathy
Description: Donegal Bay bathymetry
The following specification files were used together with the specified tasks
for running the simulations:
File: vermhd.m21
Task: m21hd (Hydrodynamic Models: Standard Hydrodynamics)
Description: Verification simulation

Retention Basin by River
File: sprmhd.m21
Description: Spring tide simulation
File: neapmhd.m21
Description: Neap tide simulation
3.4 Retention Basin by River
3.4.1 Purpose of the example
This example has been chosen to describe the flow between a river and a
retention basin during a period of flooding using structures. The example is
divided into three parts:
1. Discover the benefit of using a weir structure to simulate overflow

2. How to combine weir and culvert to simulate a flooding scenario
3. Effect of specifying a QH boundary type for downstream flow
4. Impact on flow due to dike failure
Part 1
The problem is to simulate the overflow of a river bank and subsequent filling
of a retention basin. The test conditions are:
 The river section is 210 m long and 25 m wide. The river bed level is con-
stant over the area at -4 m. The retention basin is 200 m long and 200 m
wide with a uniform bed level at -2 m. Between the river and retention
basin is a 5 m wide riverbank. The flow between the river and retention
basin may take place along a 100 long section of the river bank, where
the bathymetry level is +1 m.
 The natural flow conditions in the river correspond to an overall water
surface gradient of 0.0001, corresponding to a difference in water level
between the upstream boundary and the downstream boundary of 0.02
m, resulting in uni-directional flow.
 Initially the water level is -1 m in the river and the basin. Due to flooding
the water level upstream and downstream then increase linearly to about
+2 m during 3 hours where after the water level remains constant at the
boundaries for the next 6 hours.
Part 2
The problem is to simulate the filling and emptying of a retention basin.
23
Examples
 Using the same conditions as above the time frame is extended as the
water level in the river decrease linearly from +2 m to -2 m during a 6
hour period followed by constant water level at the boundaries for the
next 9 hours.
 The emptying of the retention basin is carried out using natural gravity
through culverts with valves that allow for flow from the retention basin to
the river but not vice versa. The culverts have a total cross-sectional area
of 0.6 m2.
Part 3
The problem is to simulate the filling and emptying of a retention basin when
knowledge of the downstream boundary water level is missing.
 The downstream boundary is defined by a QH rating curve that contains

an estimate of the relationship between the water level and discharge.
 The setup is otherwise to that of Part 2.
Part 4
The problem is to simulate the flow into a retention basin that is subject to a
dike failure occurrence. In order to compare the effect of a dike with the effect
of a weir, the filling of the basin is first simulated without dike failure.
 The riverbank subject to failure is defined by a dike structure

 The setup is otherwise that of Part 1 when simulating a weir.
3.4.2 Defining the hydrodynamic model
The main condition defining the problem is:
 A grid with 48 x 42 grid points is applied with a grid spacing of 5 m. The

grid is shown is shown in Figure 3.7.
 A time step of 5 seconds is selected for simulation 1 and 2. For simula-
tion 3 a time step of 2.5 seconds is selected.
The duration of simulation 1 is 9 hours (6480 time steps).
 The horizontal eddy viscosity type has been chosen to a flux based Sma-
gorinsky formulation and a constant Smagorinsky coefficient of 1.0 is
applied.
 The bed resistance type has been chosen to Manning number and a
constant value of 32 m1/3/s is applied.

 The water level in the river is described by a time series shown in

Figure 3.8. The initial water level in both the river and the retention basin
is -1 m.
The downstream boundary for simulation 1, 2 and 4 is defined by a water
level constantly 2 cm lower than the upstream boundary.
The downstream boundary for simulation 3 is defined by a QH rating
curve as shown in Figure 3.9.
 The length of soft start interval (warm-up period) has been chosen to 180
seconds (36 time steps).
Figure 3.7 Filling of a retention basin, model layout. DX=5m
Figure 3.8 Water level in river section during simulations
25
Examples
Figure 3.9 QH rating curve for simulation 3
Part 1
To model the filling of the retention basin two different approaches are used:
 Defining the river bank by specifying the bathymetry level to -1 m.

 Defining the river bank as a broad crested weir with crest level +1 m on a
bed level of -2 m. The weir is located along the line (31.0m, 52.5m) to
(31.0m, 152.5m). The headloss factors are defined by default values.
Part 2
To model the filling and following emptying of the retention basin the river
bank is modelled by a composite structure.
 The river bank is defined as a broad crested weir with specifications as

above.
 Three identical culverts are placed along the same line section as the
weir. The culverts are defined as closed, circular culverts with a diameter
of 0.5 m and positioned at an invert level of -1.5 m both upstream and
downstream. The headloss factors are defined by default values. The
culverts have valves that only allows for positive flow (out into the river).
Part 3
To model the filling and following emptying of the retention basin the river
bank is modelled by a composite structure similar to that described in Part 2.
Part 4
To model the failure of the riverbank next to the retention basin the riverbank
is defined by a dike structure with a space- and time varying crest level.
 The riverbank is defined by 4 (x,y) points as shown in Table 3.1.

 In the reference situation the dike is defined with a constant crest level of
1.0 m.

 The dike failure occurrence start at 01:45 and ends at 02:00. Figure 3.10
illustrates the temporal variation of the crest level during the duration of
the failure.
Table 3.1 Location of points for crest level definition
Point X-coordinate Y-coordinate
1 31 52.5
2 31 102.5
3 31 132.5
4 31 152.5
Figure 3.10 Crest level during failure occurrence.

Integers indicate location points
3.4.3 Presenting and evaluating the results
Part 1: Filling the retention basin

The filling of the basin was simulated using two approaches. Figure 3.11
shows the surface elevation in position (100m, 100m) inside the basin along
with the upstream water level in the river.
27
Examples
Figure 3.11 Water level at position (100m, 100m) inside basin.

Red stippled line: upstream water level in river for reference
Black solid line: water level using modified bathymetry for river bank
Blue dotted line: water level using weir structure for river bank
Figure 3.11 shows that modelling the river bank directly by the bathymetry
level gives a faster filling of the basin than the use of the weir structure. This
is due to the fact that the weir computation includes contraction and expan-
sion loss for the free overflow thus slowing the flow whereas the case with
modified bathymetry does not include these energy losses explicitly.
Furthermore, the model setup using the modified bathymetry is seen to give
far more disturbance in the model.
Part 2 Filling and emptying retention basin

Figure 3.12 shows the surface elevation in position (100m, 100m) inside the
basin along with the upstream water level in the river.
Figure 3.12 Water level at position (100m, 100m) inside basin

Black solid line: water level inside basin

Figure 3.12 shows that the emptying of the retention basin through the three
culverts are much slower than the time it takes to fill the basin. This is obvi-
ously because the free flow over the weir is critical and through a much larger
cross-section whereas the flow out of the basin using the culverts are sub-
critical with a much smaller cross-section.
Part 3 Using QH rating curve at downstream boundary

basing along with the upstream and downstream water level in the river.
Figure 3.13 Water level at position (100m, 100m) inside basin using QH curve.
Black solid line: Water level at position (100m, 100m) inside basin.
Figure 3.13 shows that applying the QH rating curve for boundary condition
the resulting water level becomes more fluctuating as the downstream
boundary is less restricted than experienced in Part 2.
Part 4: Impact of flow due to dike failure

basin for the stable situation along with the upstream water level in the river.
The result for a weir structure is added for comparison.
29
Examples
Figure 3.14 Resulting water level using dike with constant crest level
Black solid line: water level at position (100m, 100m) using dike.
Blue stippled line: water level using broad crested weir.
Note that applying a dike with constant crest level can result in nearly the
same discharge of water into the retention basin as when using a weir. The
theory for flow over a dike corresponds to that for a weir with Formula 1.
basin for the situation with a time-varying crest level, representing a dike fail-
ure occurrence. The result for a constant crest level dike is added for compar-
ison.
Figure 3.15 Resulting water level using during dike with time-varying crest level
Black solid line: water level at position (100m, 100m) during failure.
Green stippled line: water level for constant crest level.

Turtle Bay
3.4.4 List of data and specification files
File name: Bat0_5m.dfs2

Description: Bathymetry grid, no river bank
File name: BatB_5m.dfs2

Description: Bathymetry grid, with river bank
File name: WLBoundary.dfs0

Description: Water levels at river boundaries
File name: Sim1_Weir.m21

Description: MIKE 21 HD specification file
File name: Sim1_Bank.m21

File name: Sim2_Weir.m21

File name: Sim3_WeirQH.m21

File name: Downstream-RatingCurve.dfs0

Description: QH rating curve for downstream boundary
File name: Sim4_Dike_Constant.m21

File name: Sim4_Dike_Varying.m21

File name: CrestLevelVariation.dfs1

Description: Varying crest level for dike
3.5 Turtle Bay
3.5.1 General remarks
This example has been chosen as a fairly complex one, involving the nested
hydrodynamic and the nested advection-dispersion modules of the MIKE 21
Flow Model.
The model set-up includes:
 two-level nesting with an outer 120 m grid and an inner 40 m grid

 source specifications
31
Examples
 flooding and drying since the Turtle Bay is dominated by large tidal flats
 transfer data for HD boundaries
 conservative, decaying and heat dissipative components
 constant, time series and line series AD boundary specifications.
You may load the specification (i.e. the m21 file, see below) into the MIKE 21
Flow Model set-up editor and make your own modifications through the dia-
logs. However, to be able to run the actual model simulations requires license
to the nested hydrodynamic and/or the nested advection-dispersion modules.
In case you have a license for the nested hydrodynamic module but not for
the nested advection-dispersion module and want to run the corresponding
HD model without the AD, then you may use the sample set-up provided in
the HD-directory of the MIKE 21 Flow Model examples.
3.5.2 About the model
A few comments are given to the model set-up which aims at demonstrating
HD/AD modelling with three different components (conservative, decaying
and heat dissipative) in a rather complex area exhibiting extensive flooding
and drying.
Time step: The time step has been chosen to be 5 sec yielding a maximum
Courant number of approximately 2.1 in the fine grid area.
Bathymetry: Having generated the bathymetry files (using e.g. the Bathyme-
try Editor) it is necessary to adjust the regions surrounding the borders, see
the MIKE 21 NHD, Reference Manual. A tool to help the user doing these
adjustments is found in the Hydrodynamics part of the MIKE 21 Toolbox. The
resulting type 2 data files are supplied with this example and plotted in Figure
4.1. The origin of the 40 m fine grid is (31, 40) in coarse grid coordinates.

Turtle Bay
Figure 3.16 Nested bathymetries for the Turtle bay example
Boundary conditions: Transfer data has been obtained from a tidal simulation
by a regional model covering the above show area by use of the Transfer
Boundary tool in the Hydrodynamics part of the MIKE 21 Toolbox. The result-
ing type 1 data files are supplied with this example. The hydrodynamic model
is set-up with these data applying fluxes as primary boundary variation for the
north and east model boundaries and levels as primary boundary variation on
the south model boundary.
The AD components on the open boundaries are specified as constants on

the north boundary, as read from a type 0 data file on the south boundary,
and as read from a type 1 data file on the east boundary. These data file may
be created by use of the Time Series Editor and the Profile Series Editor,
respectively.
Eddy viscosity: The velocity based Smagorinsky formulation has been

applied with Smagorinsky coefficients of 0.5 in both areas.
Source specifications: A single constant source has been placed at grid point
(20, 20) in the fine grid.
3.5.3 Data and specification files supplied with this example
Name: m21_c1
Description: Turtle Bay bathymetry, coarse grid
33
Examples
Name: m21_f1
Description: Turtle Bay bathymetry, fine grid
Name: nbnd120lwx
Description: north model boundary
Name: ebnd120lwx
Description: east model boundary
Name: sbnd120lwx
Description: south model boundary
For the AD boundary conditions, the data files of the applied time series and
line series are:
Name: bndts
Description: AD time series boundary data
Name: bndls
Description: AD line series boundary data
The following specification files were used together with the specified tasks
for running the simulations:
File: turtle.m21
Task: m21hd (Hydrodynamic Models: Nested Standard Hydrodynamics)
Description: Simulation using nested bathymetry
3.6 Bed Resistance
This simplified example has been chosen to describe the effect the influence
of waves can have on the bed resistance and hence the flow.
Emphasis is made on the interpretation and presentation of the results.
3.6.2 Defining hydrodynamic model
The model is a channel with a L-shaped corner, initially with a constant depth
of 2 m. The computational domain is shown in Figure 3.17.

Bed Resistance
Figure 3.17 Computational domain. Grid spacing equals 50 m.

Position of output points are indicated
The problem is to evaluate the effect that the use of wave-induced bed resist-
ance can have on the flow results. For that a reference case using a constant
Manning number is also included.
 The channel is about 500 m wide, with 1 km stretch on either side of the
corner. The bottom of the channel is 2 m below datum.
 The flow goes from south to west with a current speed of approximately
0.47 m/s caused by a water level difference of 0.05 m between the two
open boundaries
 The duration of simulation is 6 hours, including 900 s for soft start. The
time step is defined as 30 s, corresponding to 720 time steps in total.
The flow is considered to be in equilibrium after 2 hours.
 SimA is the reference case where the bed resistance type has been cho-
sen to Manning number. A constant value of 75 m1/3/s over time and
domain is applied.
 For SimB and SimC the bed resistance type is chosen as Wave-induced
bed resistance, using parameterized calculation and a constant effective
grain diameter of 0.185 mm. This, combined with waves Hs = 0.21 m and
Tp=1.63, corresponds to a Manning number of 75 m1/3/s.
 In SimB the applied waves are varying in the domain but constant in
time, see Figure 3.18.
35
Examples
 In SimC the applied waves are constant in the domain but varying in
time, see Figure 3.19.
Figure 3.18 Spatial varying waves in domain for Simulation B
Figure 3.19 Temporal varying waves during Simulation C
In SimB the wave heights are constant in time, but varying in Domain, as
shown in Figure 3.18. The waves in the upper left part of the domain is signif-
icantly smaller. Even if the waves are constant in time, the soft start will cause

Bed Resistance
the bed resistance to change from initial conditions to resulting conditions, as

the generated flow also has an impact.
Figure 3.20 shows the simulated Manning number for the first and last time
step, respectively. The figures shows that while the waves clearly affects the
dynamic drag coefficient, the flow is also a dominant factor.
Figure 3.21 shows the resulting current speed in the domain for SimA and
SimB. It can be seen that the resulting current speed is slightly increased in
the upper part of the domain in SimB due to the reduced bed resistance by
the smaller waves.
Figure 3.20 Simulated drag coefficients in domain for SimB.

Left: First time step, Right: Last time step
Figure 3.21 Simulated current speed in domain at last time step

Left: SimA (Const. Manning), Right: SimB (Spatially varying waves)
In SimC the wave heights are constant in the domain, but increase in time, as
shown in Figure 3.19. The bed resistance will typically increase with increas-
ing wave height. This means that the corresponding Manning number will be
reduced, see Figure 3.22.
37
Examples
Figure 3.22 Time series of simulated Manning numbers during simulation.

Values derived from Point 1, 2 and 3 (see Figure 3.17).
Reference Manning of 75 m1/3/s is shown for comparison
Increased bed resistance will result in a reduction of the current speed.

Figure 3.23 shows a comparison of the current speed in point 2, given a con-
stant Manning or a wave-induced bed resistance where the wave heights
increase.
Figure 3.23 Time series of current speed in point 2.

Solid line correspond to reference case (SimA)
Dashed line correspond to wave-induced bed resistance (SimC)
The following files are supplied with MIKE 21:
File name: Bathy_2m.dfs2

Description: Corner grid bathymetry

Infiltration
File name: Waves_TS.dfs0

Description: Wave data varying in time
File name: Waves_Constant.dfs2

Description: Wave data varying in the domain, constant in time
File name: SimA.m21

File name: SimB.m21

File name: SimC.m21

3.7 Infiltration
This simplified example has been chosen to describe the effect infiltration
(and leakage) can have on the discharged amount of water originating from a
rainfall event on otherwise dry land.
Emphasis is made on the interpretation and presentation of the results.
3.7.2 Defining hydrodynamic model
The model area is represented by a large surface, gently sloping towards a

channel with steady flow. Initially only the channel is flooded and the remain-
ing large surface is dry. By adding precipitation during the simulation the
resulting rainfall run-off can be simulated. The computational domain is
shown in Figure 3.17.
39
Examples
Figure 3.24 Computational domain. Grid spacing equals 5 m
The problem is to evaluate the effect of infiltration, including the different infil-
tration types, can have on the results.
 The domain is about 200 m x 250 m, with a grid spacing of 5 m. An open

channel with bed level -4 m is located in the western part of the domain.
The main part of the domain is characterised by a gentle slope towards
the channel with bed levels ranging from -3 m to -2.6 m over a distance
of 200 m.
 The steady flow goes from north to south through the channel.
A constant flux of 2.0 m3/s is entering the domain through the north
boundary. The water level is kept constant at -3.01 at the southern
boundary.
 The duration of the simulation is 33 hours, including a soft-start of 1 hour.
The time step is defined as 5 s, corresponding to 23760 time steps in
total.
The flow is considered to be in equilibrium after 2 hours.
 The drying depth is set to 0.001 m and the flooding depth to 0.004 m.
 The Inland Flooding option is enabled to account for the small water
depths
 The precipitation is defined by a time series describing two events with a
constant rainfall of 100 mm/day, each lasting 3 hours. Figure 3.25 shows
the precipitation rate in time.

Infiltration
 The bed layer in the domain is considered impermeable apart from a

10000 m2 large area in the central part of the domain that has an upper
layer of porous material with a porosity of 0.2. The infiltration area is indi-
cated in Figure 3.26.
 Initially (Sim0) no infiltration occurs.
 In SimA the infiltration is described by a net infiltration rate of 10 mm/h.
 In SimB the infiltration is described by an infiltration rate of 10 mm/h, and
the thickness of the infiltration layer as 4 cm.
 In SimC the infiltration is described by an infiltration rate of 10 mm/h, and
the thickness of the infiltration layer as 40 cm, i.e. 10 times the capacity
as in SimB.
Figure 3.25 Precipitation rate during simulation
41
Examples
Figure 3.26 Infiltration area (green) within domain area
During the simulation the rainfall will accumulate in the individual grid cells
until the water depth exceeds the drying depth value at which point the water
can start to flow west towards the channel.
The water volume raining on or passing the area with porous bed material
may be subject to infiltration.
Figure 3.27 shows the water depth at point (150m,100m) in the domain. The
point is located within the porous area.
It can be seen from Figure 3.27 that without infiltration the water depth gradu-
ally builds until a level where the runoff rate equals the precipitation. For the
case with Net infiltration the infiltration rate exceed the precipitation rate why
no water accumulates in the grid cell. For the cases using Infiltration with
capacity, the water depth follows the net infiltration until the storage volume is
filled after which the depth follows the case with no infiltration.
The gradually decrease of water depth occurs when the precipitation rate
becomes 0 and the remaining water flows towards the channel. This eventu-
ally results in element becoming dry.

Infiltration
Figure 3.27 Water depth at point (150m,100m).

Note: water depths can be below drying depth due to infiltration
Figure 3.28 shows the infiltrated volume of water in the grid cell with centre
point at (150m, 100m) for SimA, SimB and SimC.
Figure 3.28 Infiltrated volume of water in grid cell at point (150m,200m)
The infiltration rate is constant when water is infiltrated to the unsaturated

zone. Once the infiltrated volume reach the capacity of the grid cell or no
water exists on the surface, infiltration stops and the volume remains con-
stant. grid cell exceed the capacity volume increase constantly (up to the
capacity volume) as long as the grid cell remains wet. Figure 3.28 shows that
the infiltration zone becomes fully saturated during the first rainfall event
when the depth of the infiltration zone is 4 cm (SimB) and fully saturated dur-
ing the second rainfall event when the capacity is 10 times larger (SimC).
43
Examples
The infiltration rate is constant as long as water exists on the surface over the
unsaturated area. However it is only possible to infiltrate the available vol-
ume. As only a part of the domain contains an unsaturated zone, water may
flow towards the unsaturated area and increase the infiltration in the nearest
grid cells. As an example of this the resulting infiltrated volume of the case of
net precipitation is shown in Figure 3.29.
Figure 3.29 Infiltrated volume at end of simulation for case of net precipitation
The following files are supplied with MIKE 21:
File name: Bathymetry.dfs2

Description: Domain grid bathymetry
File name: Rainfall.dfs0

Description: Precipitation data varying in time
File name: InfiltrationMap.dfs2

Description: Infiltration map, including capacity items
File name: InfiltrationMap_x10.dfs2

Description: Infiltration map, including (x10) capacity items
File name: Sim0.m21

File name: SimA.m21


Infiltration
File name: SimB.m21

File name: SimC.m21

45
Examples

Module Selection
4 Basic Parameters Dialog Overview

In this section, you set up the basic parameters for your MIKE 21 Flow Model
simulation. You need to specify parameters for
Module Selection
Bathymetry
Simulation Period
Boundary
Source and Sink
Mass Budget
Flood and Dry
Selections made here determine the structure of the rest of the model setup
editor, i.e. the required entries for the hydrodynamic module and possible
add-on modules. The tree-view and the number of available dialogues will
expand according to the selections made for the basic parameters.
4.1 Module Selection

The MIKE 21 Flow Model comprise a variety of modules, which can be acti-
vated through selecting the proper option on this page. You can choose
between the following modules:
 Hydrodynamic only, i.e. the HD module alone

 Hydrodynamic and Advection-Dispersion, i.e. the HD and AD modules
 Hydrodynamic and Mud Transport, i.e. the HD, AD and MT modules
 Hydrodynamic and MIKE ECO Lab, i.e. the HD, AD and MIKE ECO Lab
modules
Please note that an additional ‘AD Scheme’ selection box will appear if a dif-
ferent selection than ‘Hydrodynamic only’ is selected. In this case it is
required to select the AD-scheme to be used in solving the transport equa-
tions in the AD, MT and MIKE ECO Lab modules.
Additional check box options enable you to activate special features for your
modelling:
47
Basic Parameters Dialog Overview
1. You may choose to dedicate the hydrodynamic solution for Inland flood-
ing if you activate the 'Inland flooding' option. In this case it is not possi-
ble to select the Mud Transport module.
2. You can choose to apply an alternative hydrodynamic solution for simula-
tion of fluids with a different flow behaviour than clear-water if you acti-
vate the 'Mud, Debris or Oil' option.
Notice: Activating the Mud, Debris or Oil option will automatically introduce an
additional 'Fluid Properties' page in the Hydrodynamic Parameters section of
the Editor.
4.1.1 Inland flooding
In this case the flooding and drying is handled differently. More specifically
the approach undertaken is to suppress the momentum equation as the water
depth tends to the drying value. The suppression starts at the flooding value.
Recommended values should be so that the interval between the drying and
the flooding value should be in the order of some cm.
The hydrodynamic solver for inland flooding does not include the functionali-
ties that are usually only important at sea and in coastal regions.
Note that the influence of wave radiation and wind forcing from 2D maps are
disabled for inland flooding.
4.1.2 HD calculations
The default numerical scheme in MIKE 21 Flow Model, HD uses double pre-
cision.
4.2 Bathymetry
The MIKE 21 Flow Model requires information about the number of dynami-
cally nested grids to be applied in the simulation. The maximum number of
nested areas is 9. The first area, area number 1, is referred to as the “main
area”.
You can start a simulation in two different ways:
 as a Cold start
 as a Hot start
It is possible to include the effect of Coriolis forcing.
For modelling the hydraulic effects of a time varying bathymetry you have to
include the Landslide option.

Bathymetry
For modelling two-dimensional flow in rural and urban areas you can apply
the Multi-cell overland solver.
Additional information describing the area you are about to simulate, obtained
from the header information of the bathymetry/hot file, is:
 The geographical position of the grid origin (main area).

If you are on the southern hemisphere, you should use a negative value
for the latitude.
 The grid orientation is measured clockwise from true north to the y-axis
of your grid.
 The projection zone (e.g. UTM-32) should be specified.
 True land value is the minimum value you have specified for land points
when you prepared the bathymetry.
An example with a step-by-step description of how to use the Bathymetry Edi-

tor for creating a bathymetry data file is included with the installation. Please
find this example in your installation folder under Examples\MIKEZero\BatE-
dit. If you apply nested models, the Border Adjustment tool should be applied
to all the bathymetry data files, see the MIKE 21 Toolbox manual.
See also Additional area description (p. 83).

See also Nested bathymetries (p. 121).
4.2.1 Cold start
For a cold start the velocity field is initialized to zero. When choosing this
option you have to specify a type 2 data file for each area, containing the area
bathymetry. Except for the main area you should also specify the origin of
each nested (embedded) area. This is done in terms of the grid coordinates
referring to the (sub-) area in which it is embedded (also to be specified).
4.2.2 Hot start
The hot start facility requires a hot file for each area. must originate from a
previous simulation. The hot start files contain all necessary information to
continue a simulation. In this way simulation time can be reduced if for
instance a number of scenarios are to be compared, all based on the same
(hot start) initial conditions.
4.2.3 Coriolis
If Apply Coriolis forcing is utilized, then the Coriolis parameter f=2**sin (lati-
tude) will be evaluated and utilized for each single grid cell (j,k) in the compu-
tation (latitude variation in the domain is taken into account).
49
Note that it will take a relatively large domain for this to have a significant
impact. For inland applications Coriolis forcing is therefore almost negligible.
If Apply Coriolis forcing is not utilized, the computation will use the latitude
from the origo of the main area (area 1) in the Coriolis parameter expression,
and use this uniformly for all grid points in the computation.
4.2.4 Landslide
For modelling the hydraulic effects of a time varying bathymetry you have to
include the landslide option. When choosing this option you have to specify a
type 2 data file containing the time varying bathymetry. Please note hot files
cannot be used with this option. The landslide option can be used in nested
mode, but you have to ensure that the bathymetries satisfy the rules for nest-
ing at every time step. It is recommended to include the landslide within one
nested grid.
If the time steps in the landslide data file doesn’t cover the entire simulation,
the first time step in the file describes the bathymetry prior to the landslide
event, and the last time step in the file describes the bathymetry after the
event.
See also Landslide option (p. 84).
Note: Grid cells with land values cannot be used for landslide.
4.2.5 Multi-cell overland solver
The MIKE 21 multi-cell overland solver is designed for simulating two-dimen-

sional flow in rural and urban areas. The overall idea behind the solver is to
solve the modified equations on a coarse grid taking the variation of the
bathymetry within each grid cell into account. Results are presented on the
grid that takes the fine scale bathymetry into account. When using the multi-
cell overland solver the HD result files will also inherit the geographical infor-
mation from the fine scale bathymetry.
The MIKE 21 multi-cell overland solver has the following limitations:
 Nesting is not possible

 Only hydrodynamic simulations may be carried out
 Wave radiation stress cannot be applied
 Coriolis forces are neglected
 Wind forcing cannot be applied
 The landslide option cannot be applied

Simulation Period
Please note that even though results are presented on the fine scale, the
numerical simulations are carried out on a higher scale. The inundation is cal-
culated based on a depth varying flooded area.
To run the multi-cell overland solver the solver must be selected (see
Figure 4.1) along with the fine bathymetry file (in dfs2 format).
Note that only valid dsf2 files may be selected. If the overland solver has
been selected the Coriolis forcing will be deactivated along with the land slide
option.
Figure 4.1 The selection of the multi-cell overland solver
See also Multi-cell overland Solver (p. 109).
4.3 Simulation Period

In this dialog you must specify simulation period information:
 Time step range is the number of time steps the simulation should cover.
 The time step interval is the amount time is incremented between each
time step (equal for all areas). In case of a hot-started simulation, the
time step is taken from the hot file and cannot be changed.
 The simulation start date is the historical date and time corresponding to
time step zero. In case of a hot-started simulation, the simulation start
date is read from the hot file and cannot be changed.
 The warm-up period is a number of time steps over which the forcing
functions are gradually increased from zero to 100% of their true value.
Before you leave this dialog, the system will calculate and show the maxi-
mum Courant Number (p. 95) in the model (Max of all nested areas). The cal-
culation assumes a constant mean water level of 0.0. You should consider
reducing the time step if this Courant number exceeds (say) 8 to 10.
For your information, and as a possible check on parameter specifications,

the simulation end date (and hour) is calculated and shown in the dialog.
51
4.4 Boundary
The MIKE 21 Flow Model requires you to specify either the surface elevation
or the flux at all open boundary points.
When a bathymetry or a 'hot start' file for the main area has been specified
under 'Bathymetry' it is scanned for locating the open boundaries, i.e. they
are “program detected”.
In most cases these boundary positions can be used “as is”; but in some
cases the user might want to define the positions himself. This may be due to
borders (internal boundaries), a boundary stretching over a series of small
islands, etc.
For such “user specified” boundaries, you have to specify the number of open
boundaries as well as their locations in terms of first and last (end) points. A
maximum of 8 open boundaries is allowed.
4.5 Source and Sink

The model distinguishes between three different kinds of sources/sinks:
1. Isolated source; a point where a certain amount of water is discharged

into the model, with a certain velocity. Both the continuity and momentum
equations are affected.
2. Isolated sink; a point where water is discharged from the model. Only the
continuity equation is affected.
3. Connected source and sink pair; used for e.g. AD recirculation studies.
The amount of water removed at the sink point is reentered at the source
point, with a specified velocity.
You may select up to 1024 sources and sinks. However only 512 can be
defined by time series files.
The source and sink positions are specified by their horizontal grid coordi-
nates, in their respective model area. The model area so specified should be
the one with the finest grid resolution covering the geographical position of
the source/sink.
Do not place the sources/sinks on land, and be careful when placing

sources/sinks at locations that may occasionally dry out.
4.6 Mass Budget

The mass budget facility provides the user with a possibility to establish the
mass budget of one or more model components within a certain area of the
model domain. The specification of a mass budget comprises two steps:

Flood and Dry
Firstly the area corresponding to the mass budget has to be defined and sec-
ondly the mass budget contents and output file have to be defined. The latter
is performed in the Dialogs of the individual Modules whereas the former is
performed in the Basic Parameters Dialog.
The area corresponding to the mass budget is represented as a polygon

defined within the model domain. Note that it is possible to specify several
mass budget polygons allowing for several mass budgets. For each polygon
the associated computational area (main area/ sub-areas; only relevant for
nested models) and the number of corner points are specified. Following this,
the grid coordinates referring to the associated computational area of the cor-
ner points are given. Please note that a polygon can only contain grid points
one grid point or more inside the associated computational area; i.e. grid
points on boundaries or on borders of possible nested computational areas
can not be included. Further a polygon cannot traverse or encompass a pos-
sible nested computational area. A polygon can, on the other hand, contain
land points; the model will simply exclude the land points, when calculating
the mass budget. Please also note that the Mass Budget Dialog will not allow
the user to specify any mass budget polygons unless a Module, which sup-
ports the mass budget facility, has been selected.
4.7 Flood and Dry

If the model is located in an area with tidal flats you should probably enable
this flooding and drying facility. It incurs a certain computational overhead but
is necessary to obtain accurate results.
You can set the minimum water depth allowed in a point before it is taken out
of calculation (drying depth), and also the water depth at which the point will
be reentered into the calculation (flooding depth).
53

Initial Surface Elevation
5 Dialog Overview
5.1 Initial Surface Elevation

Having selected a cold start simulation under Bathymetry (p. 48), you must
also provide information about the initial (water) surface level. The initial sur-
face elevation for each area can be specified in two ways:
 as a constant value for the respective area, or

 to be read from a dfs2 data file (with one time step only).
Often the initial surface level can be set to a constant value to be applied over
the whole model area. This means that the simulation will start out with the
surface level raised accordingly.
You should specify values that agree with your boundary conditions, i.e. if you
start a simulation at high water with a boundary value of 0.5 m you should
also specify the initial surface elevation to 0.5 m.
For hot-starts, all initial conditions - including the surface elevations - are read
from the hot-file.
5.2 Boundary
The MIKE 21 hydrodynamic model requires you to specify either the surface
elevation or flux at all open boundary points specified on Boundary (p. 52).
The choice of variation at an open boundary can be either level or flux (the
flux is the total amount of discharge passing the open boundary). Actual val-
ues, level or flux, at each boundary can be specified in one of five different
formats:
 Constant value
 Sine series
 Time series
 Line series
 Transfer data
 Rating curve
Constant value
In the first case, you specify the constant value (constant both in space and
time) to be applied along the whole boundary.
55
Dialog Overview
Sine series
For sinusoidal variation, you must specify the reference level, range, period
and phase of the sine series.
Time series
When selecting time series boundary variation, you must specify the name of
a type 0 data file. The temporal variation given in this file is applied along the
whole boundary.
Line series
For line series, the temporal variation along the boundary is obtained from the
specified type 1 data file.
Transfer data
In the case of transfer data, boundary values are obtained from the results of
another simulation, i.e. from a transfer data file generated by the “Transfer
boundary tool”, M21trn, in the MIKE 21 Toolbox.
Rating curve
In the case of Rating curve you must specify a dfs0 time series representing
the relation between discharge and water level (specified by the relative
axis). The discharge values in the rating curve should be supplied as non-
negative values. MIKE 21 Flow Model will during the processing make sure
that the discharge in the QH relation will be effectuated as an outflow at the
boundary. The use of Rating curve is only recommended for downstream
boundaries where water flows out of the model.
Figure 5.1 Example of Rating curve
FAB type
The FAB type selects the strategy for calculating the fluxes along the open
boundary. See the manual for a description and discussion of available
options.

Source and Sink
Tilting
Tilting of a boundary is a facility that generates a setup along the open
boundary so that the slope of the surface elevation is in equilibrium with the
wind stress and Coriolis force. It should only be applied if the flux along the
boundary is negligible. You may select “linear tilting” or “non-linear tilting” and
set the tilt point. In the linear approach the bed slope is assumed to be con-
stant whereas in the non-linear approach the actual water depth is taken into
consideration. The linear approach results in a more stable solution, the non-
linear is more precise, but over a jagged bed spurious fluctuations may occur.
With respect to the tilting point, it is a good first guess to select the deepest
point along the boundary. However, trial and error in some cases is a way to
obtain the best results.
Flow direction
Default flow directions are perpendicular to the open boundary. In those situ-
ations where this can not be assumed, the possibility exists for specifying the
directions. See Boundary Conditions (p. 87).
5.3 Source and Sink

For each source
 the discharge magnitude,

 the speed and
 the outlet direction
by which the water is discharged into the ambient water must be specified
while for each sink only
 the intake magnitude
is specified since sinks do not contribute to the momentum equation, only to

the mass equation. For a connected source-sink pairs, the discharge magni-
tude at the source equals the intake magnitude at the sink. Source/sink mag-
nitudes (in m3/s) and source speed (in m/s) can either be given in a type 0 file
(time series) or as constant values. The outlet direction is the horizontal direc-
tion relative to true North and should be specified as a constant.
5.3.1 Evaporation and precipitation
On the Source and Sink (HD) dialog you also specify Evaporation and Precip-
itation rates (in mm/day). These can be given as constant values, from type 0
data files or from type 2 data files (covering the main area only).
When precipitation or evaporation data are provided in a type 0 data file, val-
ues are always considered as instantaneous values. The TS-type specified in
57
Dialog Overview
this data file for the precipitation and evaporation data should therefore be
Instantaneous.
Precipitation on dry land

The default numerical scheme in MIKE 21 Flow Model, HD handles evapora-
tion and rainfall/precipitation only at wet computational cells. To activate cal-
culations in dried cells (i.e. over the whole model domain) you need to enable
'Precipitation on dry land'.
Note that when including rainfall, the user assumes 100% runoff, which may
or may not be appropriate if significant infiltration and storage can occur in
the soil or ground material.
5.4 Infiltration
The effect of infiltration and leakage at the surface zone may be important in
cases of flooding scenarios on otherwise dry land.
You may include the effect of infiltration in two different ways:
 Net infiltration
 Constant infiltration with capacity.
5.4.1 Net infiltration
The net infiltration rate can be specified in one of three ways:
 Constant (a constant value applied over the whole area)

 Constant in time, varying in space
(a type 2 data file covering the whole area)
 Varying in time and space (a type 2 data file covering the whole area and
whole simulation period)

Infiltration
Figure 5.2 Definition of net infiltration rate
See also Net infiltration rate (p. 103).
5.4.2 Constant infiltration with capacity
For this description you first have to define the type of two parameters that
are contained in the input type 2 data file:
- The extent of the infiltration zone must be defined by Depth or Level.
- The initial water volume in the infiltration zone must be defined by Percent-
age of the Capacity (interval: 0-100 [%]) or the Water Content (interval: 0-
porosity [()]).
A type 2 data file (Constant in time, Varying in space) with 5 items must be
specified:
1. Infiltration rate
2. Porosity of infiltration zone
3. Depth OR Level value describing the extent of the infiltration zone
4. Leakage rate (specified as type infiltration)
5. Initial water volume in Percentage of capacity OR as Water Content
59
Dialog Overview
Figure 5.3 Definition of infiltration with storage and leakage
See also Infiltration and leakage (p. 104).
5.5 Eddy Viscosity

The eddy viscosity can be specified in one of four different ways:
1. Eddy terms are omitted

2. A constant value formulation with constant values specified for each area
3. To be read from a type 2 data file (one for each area) where each grid
point has its defined eddy viscosity value
4. Dynamically calculated by means of the Smagorinsky formula
Using the Smagorinsky formulation a proportionality factor for each area has
to be given.
The user may also choose between velocity or flux based eddy viscosity for-
mulations.
5.6 Resistance
The resistance type is defined as one of three types:
 Manning number
 Chezy number
 Wave induced bed resistance

Resistance
If the bottom friction is described by Manning or Chezy number, the values

can be specified in one of two ways:
 as a constant value applied over the whole area

 as a type 2 data file where each grid point has its defined friction value
Manning numbers are converted to Chezy numbers on the basis of the calcu-
lated water depth. You must specify the constant value or the file name of the
type 2 data for each area.
If the bottom friction is described by wave induced bed resistance you have to
specify the effective grain diameter, the relative density of the bed material
and some Wave induced bed resistance parameters. The effective grain
diameter can be specified in one of three ways:
 Constant (a constant value applied over the whole area)

 Constant in time, varying in space (a type 2 data file covering the main
area where each grid point has its defined grain size value)
 Varying in time, varying in space (a type 2 data file covering the main
area where each grid point has its defined grain size value, varying in
time)
In case the data is varying in space and the setup is using nested bathyme-
tries, bilinear interpolation is applied internally for all sub-areas. If the data is
varying in time the data must cover the complete simulation period.
See also Bed Resistance (p. 85).
Pier resistance can be used to model the effect of pillars or piers on the flow
field. The pier position and its geometrical layout should be defined in a type
1 data file. See Pier Resistance (p. 112) in the reference manual for a
description of such a pier file.
5.6.1 Wave induced bed resistance parameters
Using wave induced bed friction the type of calculation can be one of two:
 Parameterized
 Non-Parameterized
The applied wave height value can be restricted by the water depth. In case
this option is enabled you need to specify the maximum value of the wave
height/depth ratio. The default ratio is 0.85.
You must also specify the Update frequency by which the bed resistance from
the waves is recalculated. The default value is 1.
61
Dialog Overview
5.7 Fluid Properties

The Fluid Description page becomes visible in the Flow Model editor when
activating the 'Mud, Debris or Oil' option in the Module Selection page.
Fluid properties include the specification of values for key variables for an
alternative hydrodynamic solution targeting single-phase fluid of different flow
characteristics than clean-water. A flow resistance relationship for a flow
regime equivalent to a Bingham or Non-Newtonian flow approach is calcu-
lated under the assumption that the debris-flow material behaves like a visco-
plastic fluid. Fluids considered for this solution would typically be oil or debris
flow with high concentrated mixtures of flowing sediments and water.
Fluid property parameters to be defined include: Fluid Density, Yield stress

and Bingham fluid viscosity,
Remarks and hints

The Bingham fluid viscosity must be defined as a Dynamic viscosity.
When a Bingham formulation is activated and a resistance relation is calcu-

lated from this, the turbulent resistance (Bed resistance) defined by Manning
or Chezy values should ideally be deactivated. However, in situations where
Yield/Bingham stresses are not dominating, turbulent resistance may be cru-
cial to maintain model stability, and hence, it is important to realize that turbu-
lent resistance and the resistance relation from the Bingham solution are both
active and included as individual resistance contributions in the hydrody-
namic solution.
See also Mud, Debris or Oil (p. 106).
5.8 Waves
If you have defined the bed resistance by wave induced bed resistance you
must define the related waves to be used in your calculations. This can be
done in one of four ways:
 Constant in time and space

 Varying in time, constant in space
(values given by a type 0 data file)
 Constant in time, varying in space
 Varying in time and space
For all options you must specify the wave height, wave period and the angle
to true north. You must select to specify the wave height as the RMS wave
height or the significant wave height. You must select to specify the wave
period as the peak wave period or the mean wave period.

Wave Radiation
For the case of varying waves, you have to prepare a data file containing the
wave properties (wave heights, wave period and wave angle to true north)
before you set up the hydrodynamic simulation.
In case the data is varying in space and the setup is using nested bathyme-
tries, bilinear interpolation is applied internally for all sub-areas. If the data is
varying in time the data must cover the complete simulation period.
5.9 Wave Radiation

The second order stresses due to breaking of short period waves can be
included in the computations.
If included in the computations, a type 2 data file with the three stress compo-
nents (Sxx, Syy and Sxy) must be specified.
In order not to generate a “chock” in the computations it is recommended to

apply these stresses in combination with a soft-start (warm-up) period.
See also Wave Radiation Stresses (p. 136).
5.10 Wind Conditions

The stress generated on the water surface by wind can be included in one of
three ways:
1. as a constant value in time and space

2. as constant in space but varying in time with values given through a type
0 data file
3. varying both in time and space with values given through a type 2 data
file covering the main area (bilinear interpolation is applied internally for
all sub-areas, if present).
Note: the directions are given in degrees and measured clockwise from true
north to where the wind is coming from.
In case of time varying wind forcing, you may choose to include air pressure
corrections of the levels at the open boundaries of your model. This can be
useful if your boundary data does not take into account the air pressure varia-
tions.
The wind friction factor can be specified either as a constant or linearly inter-
polated between two values, based on the wind speed. In the latter case, if
the wind speed is below the lower limit the friction is given the value corre-
sponding to that limit, correspondingly if the wind speed is above the maxi-
mum.
63
Dialog Overview
See also Wind Conditions (p. 138).
5.11 Structures
The structures in MIKE 21 are implemented as one-dimensional structures
thus the flow across a structure is calculated as a discharge for the whole
structure. This discharge is distributed uniformly across the affected cell
faces.
Three types of Hydraulic Structures are presently available. These are:
 Weirs
 Culverts
 Dikes
Furthermore you have the option to include Composite structures by combin-

ing two or more defined structures.
You can also include a pier structure, see Resistance (p. 60).
5.11.1 Weirs
Weir data are defined in two grid tables in the present page:
Upper Input data grid and Lower Input data grid.
Figure 5.4 Setup definitions of contracted weir
Upper Input data grid

The number of weirs must be defined initially. This number defines the num-
ber of structure definition lines which will be present for defining weir input
data.

Structures
Name
The Name of weir is a user defined ID-string for each weir.
Note: Names must not be identical for different structures included in the
model simulations.
Location
'Location' and 'Projection' columns define the actual location of the weir.
Weirs are defined in the model area as a cross section specified as a list of
points (a minimum of two points required), through which the structure flow
occurs. The weir section is composed of a sequence of straight line segments
between successive points, where the geographical coordinates are defined
in the 'point selection' dialog which opens when pressing the but-
ton in the 'Location' column. You must also select the map projection (Longi-
tude/Latitude, UTM etc.) in which the specified location coordinates for the
weir are defined.
See also Location of a structure (p. 125).
Type
The weir-formula to be applied is selected from the drop down selection list in
the 'Type' column. A range of formulas are available:
 Broad crested weir formula

 Weir formula 1
 Weir formula 2 (Honma formula)
Valve
Valve regulation of the structure flow can be defined as part of the weir defini-
tion. Four different valve regulation types are available:
 None: No valve regulation applies (flow is not regulated).

 Only Positive Flow
Only flow in positive flow direction is allowed. Valve regulation does not
allow flow in negative flow direction and the flow through the structure
will be zero in this case.
 Only Negative Flow
Only flow in negative flow direction is allowed. Valve regulation does not
allow flow in positive flow direction and the flow through the structure will
be zero in this case.
 No Flow
No flow is allowed in the structure. Valve regulation closes completely
the structure.
Alpha zero
When the water level gradient across a structure is small the corresponding
gradient of the discharge with respect to the water levels is large. This in turn
65
Dialog Overview
may result in a very rapid flow response to minor changes in the water level
upstream and downstream. As a way of controlling this effect a Alpha Zero
factor has been introduced. The Alpha Zero factor defines the water level dif-
ference below which the discharge gradients are suppressed. The default
setting is 0.01 meter. If a structure shows oscillatory behaviour it is recom-
mended to increase this value slightly.
Head loss factors

The Loss Factors determines the energy (Head) loss of the flow over the
weir. These are defined in the last six columns. Each loss factor is defined by
a suffix, where '+' indicates Positive Flow direction and; suffix '-' indicates
Negative Flow direction.(e.g. 'Inflow -' means inflow loss coefficient for nega-
tive flow direction).
Three types of Loss factors are present for both positive and negative flow
direction:
 Inflow (contraction loss)

 Outflow (expansion loss)
 Free flow
Head Loss Factors are applied in structure flow calculation only for the broad
crested weir type. See also Head Loss Factors (p. 128).
Lower Input data grid

The lower input data grid contains the geometry definition for the broad
crested weir type or alternatively values of weir formula parameters if one of
the weir formulas have been selected.
For the Broad crested weir formula the geometrical shape of the active flow
area must be defined by a Level-width relationship table. The levels are
defined relative to the datum (starting from the crest or sill level and up). E.g.
for a horizontal weir positioned at invert level -10m (bed level) and extending
6 m above the bed, the weir could should be defined by L0= -4m and L1= 0m.
Datum defines an offset which is added to the level column in the level/width
table during computation.
Pressing the button in the 'Geometry' column opens a Level-Width
dialog where the geometry relation can be entered. '
For Weir formula 1 and Weir formula 2 the geometry of the structure itself
must be defined. From this the active flow area will be calculated automati-
cally in the simulation. Values for the respective weir formula parameters
must be defined in the respective columns.
See also Weirs (p. 126).

Structures
5.11.2 Culverts
Culvert data are defined in two grid tables in the present page:
Upper Input data grid and Lower Input data grid.
Figure 5.5 Setup definitions of culvert
Upper Input data grid

The number of culverts must be defined initially. This number defines the
number of structure definition lines which will be present for defining culvert
input data.
Name
The Name of culvert is a user defined ID-string for each culvert.
model simulations.
Location
'Location' and 'Projection' columns define the actual location of the culvert.
67
Dialog Overview
Culverts are defined in the model area as a cross section specified as a list of
points (a minimum of two points required) through which the structure flow
occurs. The culvert section is composed of a sequence of straight line seg-
ments between successive points, where the geographical coordinates are
defined in the 'point selection' dialog which opens when pressing the
button in the 'Location' column. You must also select the map pro-
jection (Longitude/Latitude, UTM, etc.) in which the specified location coordi-
nates for the culvert are defined.
Valve
Valve regulation of the structure flow can be defined as part of the culvert
definition. Four different valve regulation types are available:
 None: No valve regulation applies (flow is not regulated).

 Only Positive Flow
Only flow in positive flow direction is allowed. Valve regulation does not
allow flow in negative flow direction and the flow through the structure
will be zero in this case.
 Only Negative Flow´
Only flow in negative flow direction is allowed. Valve regulation does not
allow flow in positive flow direction and the flow through the structure will
be zero in this case.
 No Flow
No flow is allowed in the structure. Valve regulation closes completely
the structure.
Head loss factors

The Loss Factors determines the energy (Head) loss over the culvert. These
are defined in the last eight columns. Each loss factor is defined by a suffix,
where '+' indicates Positive Flow direction and; suffix '-' indicates Negative
Flow direction.(e.g. 'Inflow -' means inflow loss coefficient for negative flow
direction).
Four types of Loss factors are defined for both positive and negative flow
directions:
 Inflow (contraction loss)

 Outflow (expansion loss)
 Free flow
 Bends
Lower Input data grid

The lower input data grid contains the physical description of the culvert
(geometry, invert levels, length etc.).

Structures
A culvert can be defined as one of three Geometry types:
 Rectangular (requires definition of culvert Width and Height)

 Circular (requires definition of culvert (internal) Diameter)
 Irregular (Level-Width relation)
In case of an Irregular shape culvert, the geometry must be defined by a
Level-width relationship table.
Pressing the button in the 'Geometry' column opens a Level-
Width dialog where the geometry relation can be entered.
The culvert geometry defines the geometrical shape of the active flow area of
the culvert.
In the 'Section Type' column it can be defined whether a culvert structure is a

Closed or an Open section type.
In the last five columns, a number of parameters defines specific culvert char-
acteristics:
 'Upstream Invert' is the Invert level at inflow location of the culvert.

 'Downstr. Invert' is the Invert level at outflow location of the culvert.
 'Length' is the length of the culvert.
 'Manning's n' is the Manning's bed resistance number along the inside of
the culvert (for friction loss contribution).
 'No. of Culverts' is a number identifying how many culverts exist at the
specific culvert location with identical geometrical definition.
An example; Five identical shaped draining pipes are placed just next to
each other in an earth dam, and in order not to make 5 individual defini-
tions (5 lines) in the culvert page - one for each pipe - the 'No. of Cul-
verts' in this case can be defined as 5 and the simulation engine will
recognize that 5 culverts of identical shape and size are located here and
flow calculations will take this into account accordingly.
See also Culverts (p. 129).
5.11.3 Dikes
The dike data are defined in two grid tables in the present page:
Upper input data grid and Lower input data grid.
69
Dialog Overview
Figure 5.6 Example of dike defined by 6 geo-referenced points
Upper input data grid

The number of dikes must be defined initially. This number defines the num-
ber of structure definition lines which will be present for defining the dike input
data.
Name
The Name of dike is a user defined ID-string for each dike.
model simulations.
Include
It is possible to include or exclude defined dikes from the simulation.
Location
'Location' and 'Projection' columns define the actual location of the dike.
The location in the horizontal domain of a dike is given by a number of geo-

referenced points which together make up a polyline. The geographical coor-
dinates are defined in the Lower input data grid shown when pressing the
button in the 'Location' column. You must also select the map pro-
jection (Longitude/Latitude, UTM etc.) in which the specified location coordi-
nates for the dike are defined.
Discharge coefficient
For a description of the discharge coefficient see Dikes (p. 132).
Delta level
When the water level gradient across a structure is small, the corresponding
gradient of the discharge with respect to the water levels is large. This in turn

Structures
may result in a very rapid flow response to minor changes in the water level
upstream and downstream.
As a way of controlling this effect, a critical level difference has been intro-
duced. The critical water level difference defines the water level difference
below which the discharge gradients are suppressed. The default setting is
0.01 meter. If a structure shows oscillatory behaviour it is recommended to
increase this value slightly.
Crest level information

The crest level of the dike can be specified as
 Constant
 Varying in space
 Varying in space and time
When Constant is specified you have to specify the constant crest level. In
case the crest level is varying you have to specify the crest level data in the
Lower input data grid for the defined grid points.
Lower input data grid

Location
The location in the horizontal domain of a dike is given by a number of geo-
referenced points which together make up a polyline. The poly-line defines
the width of the dike perpendicular to the flow direction. A minimum of two
points is required. The polyline is composed of a sequence of line segments.
The line segments are straight lines between two successive points. The
polyline (cross section) in the numerical calculations is defined as a section of
element faces. The face is included in the section when the line between the
two element centres of the faces crosses one of the line segments.
The geo-referenced points defining the dike can be specified directly in the dialog or
imported from an ASCII file. The file format is three space separated floats
(real numbers) for the x- and y-coordinate and the crest level on separate
lines for each of the points.
Note: The faces defining the line section for the dike will be listed in the log-
file.
Crest level
The crest level of a dike can be specified as:
 Constant
 Varying in space
 Varying in space and time
71
Dialog Overview
When the crest level is specified as constant the crest level is defined by the
value specified in the Upper input data grid.
When the crest level is specified as varying in space the crest level is defined
by the values in the Lower input data grid.
When the crest level is specified as varying in space and time you have to
prepare a data file containing the crest level before you set up the simulation.
The file must be a dfs1 file, where the number of grid points corresponds to
the number of points, which is used to define the location of the dike. The
data must cover the complete simulation period. The time step of the input
data file does not, however, have to be the same as the time step of the
hydrodynamic simulation. A linear interpolation will be applied if the time
steps differ.
5.11.4 Composite structures
Composite structures can be defined by combining two or more defined

structures. A composite structure can be composed of a combination of Weirs
and/or Culverts.
An example of a composite structure could be a bridge with multiple water-

ways. Such a structure can be described by a number of culverts, each defin-
ing an individual waterway. Additionally, for a potential bridge deck
overtopping a weir can be included to describe such overflow.
A set of structures forming a composite structure are recognized by the pro-

gram from the location definitions. Locations must be completely identical for
all the structures forming the composite structure. That is, the table of coordi-
nates defining the structure locations must be exactly identical (number of
coordinates and coordinate values) for all structures defined.
5.11.5 Level-width relationship
The geometry of a structure may be defined by a level-width relation, where

the Level/Width table defines the shape of the active flow area as a set of cor-
responding levels and flow widths. Values in the levels column must be con-
tinuous, increasing values.

Structures
Figure 5.7 Definition sketch of level-width relationship

Upper: broad crested weir
Lower: Irregular culvert
5.11.6 Remarks and hints
The implementation of structures in MIKE 21 allows multiple structures at the

same location. Thus it is possible to introduce multiple culverts at the same
location or say a weir and a culvert at the same location. Each structure is
simply defined separately in the interface and the combined flow is handled
by the calculation kernel. Examples are given below.
A wide weir with a small opening

Consider a weir as illustrated in Figure 5.8.
73
Dialog Overview
Figure 5.8 Wide weir with a small opening
There are a number of possibilities when modelling this in MIKE 21:
1. One weir
2. Two weirs with width W1 and width (W2-W1), respectively
3. Three weirs with widths W1 and two with width (W2-W1)/2,
respectively
Using the first approach is only appropriate if the weir can be contained within
a single grid cell. The second approach may be used if the weir spans multi-
ple cells, keeping in mind that the flow over the highest crest (L2) is uniformly
distributed over all the affected cells. The third approach will give the best
representation of the flow. Note that the location needs to be defined for each
of the segments for case 2 and 3.
A wide weir with multiple culverts

Consider a structure as illustrated below
Figure 5.9 Wide weir with multiple culverts
The composite structure should be implemented as four separate structures:

Results
1. A weir with a constant crest level L1 and a location defined by the full
extent of the weir
2. A circular culvert
3. A rectangular culvert
4. A irregular culvert described by a level/width table
Note that the location needs to be defined for each of the four structure com-
ponents separately. The location line should correspond to the maximum
width of the structure component while still obeying the minimum requirement
with respect to intersecting a line segments connecting cell centres.
5.12 Results
Two main types of output data can be obtained from a hydrodynamic simula-
tion:
1. 'Output file', a type 0 (point series), 1 (line series) or 2 (area series) data
file, which contains results from the hydrodynamic simulation. Because
the amount of model output tends to be very large - huge - it is often not
feasible to save all output items in all computational areas and in all grid
points at all time steps. In order to reduce the file size it is possible to
specify the output file using sub-areas and sub-sets for selected items.
See also Specification of output files (p. 111)
2. 'Hot start file', a type 2 data file, which can be used to re-start computa-
tions. You have to specify the name(s) of the hot-output file(s), one for
each area. You can specify a title too, if you want.
In addition Inundation statistics can be calculated and stored as a dfs2 file.

The update frequency is given in the form of a time interval. The update fre-
quency only has an effect on how often the results are written to the file. If the
simulation runs to completion then the update frequency may be chosen
large so that disc access is reduced. To only update the inundation statistics
at the end of the simulation set the update frequency (fupdate) to the total dura-
tion of the simulation, i.e.
f update = N  t (5.1)
where N is the total number of time steps and t is the time step interval.
It is possible to add the duration in which the water depth is above a user-
specified threshold during the simulation to the inundation statistics output.
75
Dialog Overview
Note: If the dfs2 file contains ‘level and flux’ output only and has a Data type
= 1 (set automatically during output if only H, P and Q are selected), then it is
possible to use derived items from the file in other MIKE Zero components
such as Plot Composer, Result Viewer and the MIKE Zero Toolbox statistics.
Important: In case of applying nested model areas, then only items

which are calculated on fine grid points which are common to coarse grid
points will be inherited and displayed in the result file for the coarser grid. The
magnitude of the item inherited from the fine grid to the coarse grid will be the
same on both grids (no resolution related scaling!).

Bathymetry
6 Reference Manual
6.1 Bathymetry
6.1.1 General description
Describing the water depths in your model area for the hydrodynamic model
is without doubt the most important task in the modelling process. A few
hours less spent in setting up the model bathymetry might later on mean
extra days spent in the calibration process.
Giving exhaustive guidelines for how you should specify the bathymetry in
order to avoid any problems later on is, however, nearly impossible. You can
avoid many problems in the modelling process by adhering to the directions
given below, but the experience you build up through practise is valuable.
An example with a step-by-step description of how to use the Bathymetry Edi-

tor for creating a bathymetry data file is included with the installation. Please
find this example in your installation folder under Examples\MIKEZero\BatE-
dit.
6.1.2 Selecting the model area
When deciding on which area to include in your model and thus where you
should place your open boundaries you should take the following into consid-
eration:
 The MIKE 21 Flow Model is a finite difference model with constant grid
spacings in the x- and y-direction, and therefore your model area has to
be rectangular. It also means that the computational points will lie in a
square or rectangular grid.
 Your area or point of interest should lie well inside the model area, say at
least 10 grid points from the boundary but preferably more.
 You may have to include not only the area immediately surrounding the
area or point of interest but a much larger one in order to have, for exam-
ple, the wind surge computed properly.
 You should have your open boundaries in areas where the water flow is
“well behaved” and the flow direction, if possible, perpendicular to the
open boundary.
 A “well behaved” flow in this connection means that, since certain
assumptions are made in the computations at the boundaries, the flow
pattern should be smooth at the boundary and in the area inside the
boundary (that is 5 to 10 grid points inside the boundary). In other words,
the bathymetry should be smooth close to all open boundaries.
77
Reference Manual
 You will not always be able to situate all open boundaries so that the flow
runs perpendicular to the boundary line. In those cases, you will have to
specify the flow direction yourself. However, try to have the flow as close
to being perpendicular as possible.
 As you must know either the water level variation or the magnitude of the
flow at the open boundaries, you have to place the boundaries through
points or between points, where such data are known. If, for example,
you are going to do a tidal simulation, the open boundaries can be
placed such that there is a tidal station at each end of the open boundary.
 Open boundaries can meet in corners, but you have to include the corner
point in both open boundaries. You must then ensure that the boundary
conditions in the corner point are the same when seen from both open
boundaries. This requires that you have good level or flux data at the
boundary. If not, the corner should be placed on a not too small island
(see Figure 6.1).
Figure 6.1 Two open boundaries in a corner
 Avoid sudden expansions or contractions of the flow close to an open

boundary unless the current speeds are small (see Figure 6.2 and
Figure 6.3).
Figure 6.2 Sudden expansion and contraction of the flow close to an open bound-
ary

Bathymetry
Figure 6.3 Special case of sudden contraction, permitted for level boundaries
 You should especially avoid a situation like the one in Figure 6.3. How-
ever, MIKE 21 will accept it if levels (not fluxes) are prescribed at the
open boundary in order to permit flooding and drying just inside the
boundary.
 Although MIKE 21 can handle flooding and drying just inside a level
boundary, you should normally not place the open level or flux bounda-
ries too close to shallow areas which might dry out. Points at the open
boundaries should never dry out.
 If possible rotate your model so that the main flow direction inside the
model is more or less parallel to one of the coordinate axes.
 Try to place the origin of your model (which is normally the lower left cor-
ner) in a well defined set of coordinates in the surrounding coordinate
system (which will often be the UTM coordinate system or geographical
longitude and latitude). This, together with a “nice” orientation of your
model relative to north, will facilitate the transformation of model grid
coordinates into the surrounding coordinate system.
6.1.3 Selecting the grid spacing
Although the selection of the grid spacing and of the model area are closely
connected there are a number of special considerations (as listed below)
which you have to make when selecting the grid spacing. Except for the first
one and the last one they are all related to the Courant number and thus the
speed with which the information travels in the model. Please see Courant
Number (p. 95) for a description of these terms.
 First of all your grid should resolve all the variations in the bathymetry
which are important for the flow you wish to simulate.
 MIKE 21 will probably not become unstable if you have an isolated bump
or hole in your bathymetry (provided that it is not close to a boundary),
see Figure 6.4. However, a series of bumps and holes along a grid line
might lead to instabilities if the flow direction is parallel to this grid line
and the Courant number is greater than 1, see Figure 6.5.
79
Reference Manual
Figure 6.4 Unwise bathymetric resolution
Figure 6.5 Unstable bathymetric resolution for Courant numbers greater than 1
 If you cannot avoid channels which run at an angle of 45 degrees to the

grid, the grid spacing and time step should be chosen as shown in
Figure 6.6.
Figure 6.6 Flow in a channel at 45 degrees

Bathymetry
 Closely related to the condition above is the treatment of deep channels

in shallower areas. When you model an area with narrow and deep
channels (like in the example of Donegal Bay provided in the Examples)
it is quite normal that the channels are only one or a few grid points wide.
You should, however, take care when the narrow channels cross from
one grid line to the next. If the flow in the channel is of importance the
number of overlapping grid points should be greater than the local Cou-
rant number. This will ensure that the flow information is transferred
properly up the channel, see Figure 6.7.
Figure 6.7 Schematisation of a narrow channel
 You should avoid alternating land-water-land-water boundaries as shown

in Figure 6.8 if the Courant number is larger than 1.
Figure 6.8 Schematisation of land, which should be avoided
81
Reference Manual
Areas that are subject to flooding and drying should not be made completely
level but given a gentle slope towards the nearest area with deep water. This
will ensure that a series of one point ponds is not left in the otherwise dry
areas when the water withdraws.
6.1.4 Selecting the reference level
In principle you can use any reference level in the hydrodynamic computa-
tions (that is in the bathymetry), but it is recommended to use mean sea level
(MSL).
The depths on sea charts are, however, normally given relative to the lowest
astronomical tide (LAT) and the bathymetry will therefore normally be entered
(digitised) relative to this datum. You can add the difference between MSL
and LAT to all grid points in the bathymetry data file using the Grid Editor
facility for editing.
You will have to make sure that all the sea charts you are using to prepare the
bathymetry are relative to the same datum. If this is not the case, you must
choose a common datum and then convert all depths to this datum. In the
same way, all the water level recordings you will use must also be converted
to the same datum.
6.1.5 Specifying the bathymetry
Before you start a simulation you have to prepare the bathymetry in a data file
or, in other words, digitise your model area. There are several ways to do this:
 Draw the computational grid on a piece of transparent paper, put it on top

of the sea chart and write the depth for each grid node on the paper.
Then enter the depth values in a file using the data file editor for 2D
matrices provided with MIKE 21.
 If you have a digitising tablet compatible with the MIKE 21 digitising pro-
gram you can use this to create a file with (x,y) coordinates and the cor-
responding depths. This data can then be gridded using the Bathymetry
Editor facility of MIKE 21. An example with a step-by-step description of
how to use the Bathymetry Editor is included with the installation. Please
find this example in your installation folder under
Examples\MIKEZero\BatEdit.
 If you have your depth information in digital form you can create an
ASCII file (.txt) and enter this file into the standard data file format using
the Grid Editor.
In all cases please note that the depth given to a grid point represents not
only the depth right at that point, but the area surrounding the grid point, see
Figure 6.9.

Bathymetry
Figure 6.9 Depth representation in the grid
6.1.6 Sign convention
Depth values for grid points below the chosen datum are negative in the
MIKE 21 Flow Model.
6.1.7 Additional area description
In addition to the bathymetry for your model area the following area informa-
tion should also be specified:
 The initial surface elevation in the area. Because the model initialises the
fluxes or current velocities to zero, you must specify an initial surface ele-
vation that is in agreement with these conditions. In practice this means
that you should specify a value that matches the boundary conditions at
the first time step. If the model area is large and the surface levels at the
open boundaries differ substantially, you should create a data file with an
initial surface elevation at each grid point. However, in most cases you
can just use the average surface elevation at the open boundaries.
 The latitude and longitude at the lower left corner of the model should be
provided through the bathymetry data file. In dfs2 data files there is a
possibility to store information about the applied projection zone (e.g.
UTM-32), and this information is used as the default projection zone. The
user may choose to overwrite the default projection zone. If no geo-
graphical information is available through the bathymetry data file or if
the projection zone “Local coordinates” is chosen, then Coriolis forcing is
not applied.
 The orientation of your model (also provided in the bathymetry data file).
This is defined as the angle between true north and the y-axis of the
model measured clockwise. A mnemonic way of remembering this defini-
tion is by thinking of NYC, which normally means New York City, but
which for our purpose means “from North to the Y-axis Clockwise”, see
Figure 6.10.
83
Reference Manual
Figure 6.10 Definition of model orientation
 A value representing land (provided in the bathymetry data file, see

below). This means that all grid points with a depth value equal to or
greater than the value you specify will always be considered to be land
and will not be subject to possible flooding and drying.
 Whether or not the possibility of flooding and drying of land areas should
be included in your simulation. Please refer to Flooding and Drying
(p. 100) for a detailed description of this facility.
Please note: Bathymetry data files must contain a custom block called
M21_Misc which consists of 7 elements of type float:
 The first element is the orientation.

 The third element is a flag and the value -900 indicates that the data file
contains geographic information.
 The fourth element is the value representing land.
 The rest of the elements are not used in bathymetry data files.
6.1.8 Landslide option
By including the landslide option you are able to model the hydraulic effects
of a time varying bathymetry. The effect of the landslide is modelled by forc-
ing terms representing the temporal dynamic vertical deformation of the
bathymetry. The landslide may be of submarine or subaerial type. Also the
effects of a seismic seafloor deformation can be modelled using a time vary-
ing bathymetry rather than a spatial varying initial surface elevation.
The main task in preparing the input data for the model is to generate a time
varying bathymetry. Most often a number of maps (covering bathymetric and
orographic information) are digitised and interpolated on a user-defined spa-
tial grid. Subsequently the maps are copied into a time varying bathymetry.
The bathymetry may also be created by external programs and imported as
an ASCII file using the MIKE Zero Grid Series Editor.
Please note that the time step in connection with sub-aerial landslides (i.e.
cases with a moving land/water boundary) might be considerable restricted
compared to more common hydrodynamic simulations. For such kind of sim-
ulations it is necessary to use the flooding and drying facility.

Bed Resistance
The usual data file concept with a static bathymetry stored as a prefix item
does not hold when applying the landslide option. Thus, you have to be
aware that some tools used on MIKE 21 Flow Model data files cannot be
used on result data from a landslide simulation. As a work-around, the result
data files from a landslide simulation is a type 2 data file (dfs2-file) with Data
Type = 4 and containing the following 7 dynamic items:
1. Actual bathymetry
2. Water depth or surface elevation as specified by you
3. P-flux if selected otherwise a dummy item containing delete values
4. Q-flux if selected otherwise a dummy item containing delete values
5. Surface elevation
6. Dummy item containing delete values
7. Dummy item containing delete values.
6.2 Bed Resistance
You can chose between three ways of describing the bed resistance in the
MIKE 21 Flow Model: as a Chezy number, as a Manning number or by the
wave induced bed friction. In the first two cases the bed resistance used is
g u u
---------------------
2
(6.1)
C
where g is gravity, u is velocity and C is the Chezy number. Manning numbers

are converted to Chezy numbers as follows
16
C = Mh (6.2)
where M is the Manning number and h is the water depth. The units of Chezy
numbers and Manning numbers are respectively m1/2/s and m1/3/s.
Please note that the Manning number used in MIKE 21 is the reciprocal value
of the Manning number described in some textbooks.
The wave induced bed resistance value are converted to Chezy numbers as
follows
u
C = g  -------- (6.3)
 U fc
85
Reference Manual
where Ufc is the friction velocity calculated by considering the conditions in

the wave boundary layer. For a detailed description of the wave induced bed
resistance see Fredsøe (1984) and Jones et. al. (2014).
6.2.2 Specifying the bed resistance
A bed resistance number is assigned to each grid point in the model area.
You can specify this in MIKE 21 in two ways:
 as one value which is given to all grid points

 as a map similar to that for bathymetry with a resistance value for each
grid point
6.2.3 Recommended values
If the relative variation of the water depth is considerable you should specify
Manning numbers. Values in the range 20-40 m1/3/s are normally used with a
suggested value of 32 m1/3/s if no other information is available. In an estuary
with tidal channels you can use a value of 25 m1/3/s.
If you apply Chezy numbers a model calibration can normally be achieved

with values in the range 30 - 50 m1/3/s.
Because of the definition of the resistance numbers the following applies:
 Using a smaller resistance number increases the bed resistance

 Using a greater resistance number decreases the bed resistance
If the boundary conditions at one of your boundaries are inaccurate and you
therefore have stability problems (blow-ups) at this boundary, you can specify
a small band (2 to 4 grid lines) with a very high resistance. Manning numbers
in the range 5 -10 m1/3/s have been applied successfully. However, this
method should only be used if it is impossible to improve the boundary condi-
tions. Furthermore, the simulation results in the area around the small resist-
ance numbers should be used with caution.
When carrying out a tidal calibration you can use the bed resistance to
increase or decrease the tidal amplitude. The tidal phase is adjusted by
changing the water depth. When the depths have been read from a sea chart,
increasing the depth is all the more justifiable as these charts often give the
minimum depths, which are more important to shipping than the maximum
depths.
Because h1/6 is calculated for each grid point and at each time step when the
Manning formulation is selected rather than the Chezy formulation, the com-

Blow-up
putational time is increased. Please see CPU Time (p. 95) for an estimate of
the additional CPU time required.
6.3 Blow-up
Please inspect carefully the log file.
6.4 Boundary Conditions
If the description of the bathymetry is the most important task in the modelling
process then the description of the water levels and flow at the open bounda-
ries (in short called the “boundary conditions”) is the second most important
task. The better the boundary conditions the better the results and the fewer
the instability problems.
The MIKE 21 Flow Model solves the partial differential equations that govern
nearly-horizontal flow and, like all other differential equations, these need
boundary conditions. As the unknown variables are surface elevation and flux
densities in the x-direction and y-direction you must, in principle, specify two
of these three variables in all grid points along the open boundary at each
time step. However, in most applications you only know the surface elevation
and possibly the general flow direction or you know the total flow through your
boundary and its general direction. The input to the hydrodynamic module of
the MIKE 21 Flow Model has therefore been structured accordingly.
You can choose between the following two combinations of boundary input:
 Specify water levels and the direction of the flow.

The water levels can be constant or varying along the boundary line. The
variation in time can be either constant, sinusoidal or vary as specified in
a type 0 or a type 1 data file. Finally a transfer file can be used for water
level, which is obtained by use of the M21 tool Transfer Boundary.
The directions can either be specified as default, meaning perpendicular

to the boundary, or read from a type 1 data file. The data file must contain
a direction for each individual grid point along the boundary.
 Specify a flux boundary, as either discharge (constant, sinusoidal, type

0), flow flux (type 1, transfer) or Rating curve (type 0), through the bound-
ary and the flow direction.
The discharge can be constant in time, have a sinusoidal variation or
vary as specified in a type 0 data file. The distribution of the total flow in
the individual grid points along the boundary is calculated by MIKE 21
relative to the depth.
87
Reference Manual
Type 1 and transfer Boundary conditions are also possible, but in this
case the values in the cells of the input files represent the flow flux at
each cell, instead of the total discharge.
A Rating curve is a dfs0 file with axis type ‘Relative item axis’. The data
represent the variation of a discharge (as item) as a function of the water
level which is specified in the axis.
The direction should be given in the same way as for level boundaries.
6.4.2 Specifying the boundary conditions
In the boundary specification dialog you are presented with a list of the open
boundaries the model has been able to detect.
The model may detect the open boundaries by searching for lines of adjacent
water points placed along the four sides of the bathymetry. Note, the actual
locations of the open boundaries were defined when you digitised the
bathymetry.
In most cases the detected boundaries will correspond to those you have
planned. If this is not so, you should select “User specified” boundaries and
then further specify the number of open boundaries and their position in the
model, see the section “User specified” boundaries.
In the Boundary dialog under “HD parameters” you specify the type of bound-
ary data, how these vary in time and space, and finally you can enter a num-
ber of options:
First you must specify the boundary type (a “level” or a “flux” boundary) from
the combo-box selector. For a flux boundary please note that the sign on the
fluxes determine the flow direction relative to the model coordinate system:
inflow is positive on the left and bottom side, while it is negative on the top
and right side, and vice versa for outflow.
Then you specify the variation of the water levels or fluxes in time and space.
They can be given in one of the following ways:
 A constant value used at all grid points along the boundary and through-
out the whole of the simulation. This is most useful if a stationary flow
field is required.
 A sinusoidal variation during the simulation period, for example, a tidal
variation can be specified. The variation is calculated as follows:
1 N  t – Phase
Value = Reference Level + ---  Range  sin  2  ---------------------------------- (6.4)
2  Period 

Boundary Conditions
where N is the time step number and t is the time step.
The same value is used at all grid points along the boundary.
 A variation as given in a type 0 data file. The data file gives the same
value to all grid points along the boundary. If the time step in the data file
differs from the time step in the model simulation then a cubic interpola-
tion is used.
 A variation as give in a type 1 data file. The data file defines the variation
in time for each grid point along the open boundary. The data file must
have exactly as many points as there are grid points along the axis. If the
time step differs from the time step in the model simulation then a linear
interpolation is used.
This possibility allows you to introduce variations in the boundary condi-
tions along the open boundary.
 Flow conditions obtained from an encompassing model. This boundary

type, called a transfer boundary, is prepared from a previous model sim-
ulation with a model including the area of the boundary.
The transfer data file, which also is a type 1 data file, contains informa-
tion about the water levels and the flux densities in the x and y-directions.
 Discharge versus water level relationship given in a relative axis time

series file (dfs0). The data describes the resulting water level given the
computed discharge out of the model.
Note: In all cases must the reference level of the boundary data equal the ref-
erence level of the bathymetry data.
Finally you can through three options control how the boundary data should
be applied:
 What strategy to use when calculating the Flux Along the Boundary
(FAB). There are the following possibilities:
0:The flow is assumed perpendicular to the open boundary, i.e. the FAB
is zero.
1:The direction of the flow is obtained by extrapolation from the flow one
grid point inside the boundary. When the direction has been extrapo-
lated, the FAB can be calculated.
2:The direction of the flow at the boundary is explicitly given. The FAB
can then be calculated.
12:This is a combination of 1 and 2. When the flow direction is out of the

boundary, type 1 is chosen, otherwise type 2.
89
Reference Manual
Using either 2 or 12, the third option (default flow directions) can be used to
define the actual direction of the flow at the boundary.
 Should your boundary data be tilted to accommodate for a possible wind

and/or Coriolis' set-up along the boundary? A description of this facility is
given below in the section Recommended selections and values.
To activate the tilt facility, make your tilting method selection from the
combo-box, you will then be prompted for which point to tilt around.
This facility is not enabled when the boundary is a flux boundary or if the
boundary data is specified as transfer data.
 What direction does the flow have at the boundary? The default flow
direction is perpendicular to the boundary. If the flow in your model is not
perpendicular to the boundary, you should create a type 1 data file with
flow directions for each individual grid point along the boundary. The
directions should be given in degrees from true north and measured pos-
itive clockwise.
The data file with the directions should only have one time step, i.e. the
flow directions will be constant during the whole of the simulation. How-
ever, the directions are only used during inflow. During outflow the direc-
tions are extrapolated from the flow inside the model.
To activate the direction facility, select it from the combo-box and enter
the name of the data file with the directions.
This facility is not enabled when the boundary data is specified as trans-
fer data.
6.4.3 User specified boundaries
In case the open boundaries do not correspond to those you had planned,
you must specify “User specified” boundaries and then give the number of
open boundaries in the model. Further you will in the boundary definition dia-
log have to specify the location of the open boundary. That is the coordinates
of the first water point and the last water point along the boundary grid line.
It will be very unusual that you yourself have to specify the locations of the
open boundaries. It is only relevant in the following two situations:
 You have a long open boundary broken by, say, two small islands. The
menu will show you this boundary as three smaller boundaries. If the
boundary conditions are either the same for all three boundaries or it is
most conveniently to keep the boundary data for the whole boundary in
the same type 1 data file, or transfer file, you can define the three bound-
aries as one boundary.

Boundary Conditions
You will then have to specify the start point as the first water point on the
first line and the last point as the last water point on the third line. The
boundary line will then contain a few land points; but this is not an error.
 You want to have an internal open boundary in your model. An internal

boundary is a boundary that is not located on one of the model sides.
You can use an internal boundary to keep your model size small, see
Figure 6.11.
Note: If you want to include an internal boundary in your model, you must fill
the area behind the boundary with land points.
internal boundary
Figure 6.11 Example of internal boundary
Due to the computational structure of MIKE 21 there are a few restrictions to

where a boundary can be located, see Figure 6.12.
Note: All water points on the model sides must be included in an open
boundary definition.
91
Reference Manual
Figure 6.12 Restrictions on the location of an open boundary
6.4.4 Recommended selections and values
If you specify water levels for a boundary you can normally assume that there
is no spatial variation along the boundary. However, in certain situations you
may wish to specify a non-horizontal water level since a horizontal water level
may give unrealistic results. These situations are treated in the following way:
 If, for example, you are carrying out a tidal study and have a tidal station
at each end of the open boundary, a linear variation along the boundary
(or parts of it) should be specified. You do that by having a type 1 data
file with the boundary conditions. The data file can be created with Profile
Editor under MIKE Zero.

Boundary Conditions
 Another situation where a horizontal water level at the boundary is unre-

alistic is in the presence of wind and the Coriolis force. If you keep the
water level horizontal you will get a large inflow together with a large out-
flow at the same boundary, especially in a steady state situation, as the
water level should actually be tilted. The effect is illustrated in
Figure 6.13. You should therefore specify a tilt point so that MIKE 21 will
tilt the boundary to avoid this unrealistic flow pattern.
Figure 6.13 Before (upper) and after (lower) the tilting
MIKE 21 provides two alternatives for the tilting approach:
 linear tilting
 non-linear tilting.
With a selection of linear tilting MIKE 21 assumes the water level to follow a
straight line which can be rotated around the tilting point. This approach has
the advantage of smoothing the effects originating from a very jaggered sea-
bed.
The non-linear approach is more theoretically correct and provides a better

estimate in many cases where you have a gentle slope on the seabed. The
93
Reference Manual
tilting is calculated in each point along the boundary based on the steady
state Navier Stokes equations.
It is assumed that the flow is perpendicular to the boundary. However, the

correction of the flow will also work if the flow direction is nearly perpendicular
to the boundary. You should keep this in mind when selecting how the fluxes
along the boundary should be calculated: the method called type 12 together
with a perpendicular inflow is recommended.
The difficulty in using the tilt facility lies in the specification of the tilt point. A
good choice to begin with is the deepest point along the boundary. However,
you might have to find the best point through trial and error.
If you have two adjacent boundaries you should also be careful not to create
a conflicting situation in the corner.
If you specify the total flow through your boundary and select that it should be
distributed relative to the depth, it will be distributed as it would have been in
a uniform flow field with the Manning resistance law applied, i.e. is relative to
h5/3, where h is the depth. This distribution is, in most cases, the best one that
can be applied.
Accurate flow directions are more important when the flow is into the model,
while they are of less importance at the outflow. This is because any errors at
the inflow boundaries are transported into the model and may, therefore,
cause instabilities.
Introducing open boundary conditions into a finite difference model is a very

complex task as a number of different implementation solutions can be used.
The input description as given above focuses on the description as seen from
the user's practical point of view (“these data are available; how do I specify
that to the model?”), while the description as seen from the numerical point of
view is given in the Scientific Documentation.
6.5 Chezy Number

See Bed Resistance (p. 85).

Courant Number
6.6 Courant Number
The Courant number is defined as follows:
t
C R = c ------ (6.5)
x
where c is the celerity, t the time step and x the grid spacing. For a tidal
wave the celerity is
c = gh (6.6)
where g is gravity and h is the water depth.
As the information (about water levels and fluxes) in the computational grid
travels at a speed corresponding to the celerity, the Courant number actually
expresses how many grid points the information moves in one time step.
6.6.2 Recommended value
Normally you can have a maximum Courant number in your model of up to 5.

The maximum value which you can use without having stability problems
does, however, depend on your bathymetry:
 If you are modelling an estuary with tidal channels you should adhere to
the rules given under Bathymetry (p. 77). Alternatively you can use a
maximum Courant number of 1, in which case you should have no prob-
lems in resolving the flow in the channels. The CPU time requirements
might, however, become very high.
 The MIKE 21 Flow Model is designed for Courant numbers up to about
20. You should, however, only allow these very high numbers in areas
where the bathymetry is very smooth.
6.7 CPU Time
6.7.1 Factors influencing the CPU time
The CPU time required by a hydrodynamic simulation depends on the size of

your model, on the number of time steps in your simulation, on which features
you have specified for the simulation and on the general computational speed
of your computer.
95
Reference Manual
If you wish to estimate how a change in your specifications for a hydrody-

namic simulation changes the CPU time required without specifying the
model set-up and doing a verification, the following guidelines can be used:
 The CPU time varies linearly with the number of water points (or compu-
tational points) in the model.
 The CPU time also varies linearly with the number of time steps, if flood-
ing and drying is not selected. If this feature is selected the variation as a
function of the number of time steps is only approximately linear.
 The CPU time is increased by the factors listed below if the correspond-
ing features are selected. The factor is relative to a simulation where no
results are saved on disk and where none of the features are selected.
Factor.
1.10:Manning numbers applied instead of Chezy numbers.
1.15:Flooding and drying.
1.20:Smagorinsky formulation of eddy viscosity instead of constant

eddy viscosity.
1.25:Saving the results in all grids for each time step.
If you wish to calculate the CPU time required by a simulation (in real CPU
seconds, not elapsed seconds) the following formula can be used:
Number of time steps x Number of water points x Factors / BCS
where BCS (basic computational speed) is the number of water points which
your computer processes in one CPU second. “Factors” refers to the factors
listed above.
6.8 Current
See Velocity (p. 135).
6.9 Disk Space
6.9.1 Small files
The disk space required for your simulation depends mainly on the amount of
results you request to be saved. During a simulation only two or three other
files, in addition to the data files containing the results are created:

Eddy Viscosity
 The specification file (also known as the pfs file, Parameter File Stand-
ard) containing the simulation specifications. This file will be placed in
your present working directory and have a file extension of m21. It will
only take up approximately 2 Kbytes.
 The log file describing the model set-up, the statistics of the files used
and created during the simulation and a message for each time step
completed. The file extension of this file, which will also be placed in your
present working directory, is log and it will only take up to 200 Kbytes on
the disk.
 A file for the continuation of a simulation, the hot file. This file only takes
up disk space equivalent to 9 times the space taken up by the bathyme-
try file. This mean that the hot file will not take up more space than 100 -
200 Kbytes.
6.9.2 Large files
The amount of data generated by a simulation may be very large. Therefore

you should only save as much data as is needed for your further work. Never-
theless very large files will often be generated.
If you wish to calculate the disk space required for a single output data file the
following formula can be used. The result is in bytes:
N last – N first J last – J first + 1 K last – K first + 1

4  3   -----------------------------
- + 1  ------------------------------------
-  --------------------------------------- + 1052 (6.7)
 N frequency  J frequency K frequency
where N denotes time steps, J denotes points in the x-direction and K points
in the y-direction.
Please note that MIKE 21 does not check whether or not you have enough
free disk space for your requested output files.
6.10 Eddy Viscosity
The effective shear stresses in the momentum equations contain momentum

fluxes due to turbulence, vertical integration and subgrid scale fluctuations.
The terms are included using an eddy viscosity formulation to provide damp-
ing of short-wave length oscillations and to represent subgrid scale effects
(see e.g. Madsen et al., 1988; Wang, 1990).
97
Reference Manual
The formulation of the eddy viscosity in the equations has been implemented
in two ways:
 Flux based formulation
  P    P 
E +  E  (x- momentum)
x  x  y  y 
where P is the flux in the x-direction and E is the eddy viscosity coeffi-
cient.
 Velocity based formulation
  u    u 
 hE +  h  E 
x  x  y  y 
where u is the velocity in the x-direction and h the water depth.
Strictly speaking the first formulation is only correct at a constant depth and
should be applied with great care in order to avoid falsification of the flow pat-
tern.
The velocity based formulation, which is more correct, is unfortunately also

more difficult to implement in the numerical algorithm. This is because the
system uses the fluxes as the unknown parameters and not the velocities.
Therefore the velocity-based formulation is implemented by using the veloci-
ties from the previous time step. This can, however, lead to stability problems
when the eddy viscosity coefficient E becomes large. The coefficient must ful-
fil the criterion:
E  t 1
-------------  --- (6.8)
x
2 2
6.10.2 Specifying the eddy viscosity
The eddy viscosity coefficient E can be specified in three different ways:
 As a constant value for the entire computational domain

 From a type 2 data file giving the value at each grid point

Evaporation
 A time-varying function of the local gradients in the velocity field. This for-
mulation is based on the so-called Smagorinsky concept, which yields:
U 2 1 U V V
E = C s2  2  ------- + ---  ------
- + ------ +  ------ (6.9)
 x  2  y x   y 
where U,V are depth-averaged velocity components in the x- and y-direction,

 is the grid spacing and CS is a constant to be chosen in the interval of 0.25
to 1.0.
The Smagorinsky facility is combined with the following formulation of the

shear stresses, i.e.
  U    1  U V 
 hE +  hE  +  
x  x  y  2  y x 
which is in agreement with Rodi (1980) and Wang (1990). For more details on
this formulation, the reader is referred to Smagorinsky (1963), Lilly (1967),
Leonard (1974), Aupoix (1984), and Horiuti (1987).
If you choose the Smagorinsky formulation you must specify the Smagorin-
sky factor CS.
In the same way as for the bed resistance you can use the eddy coefficients
to damp out numerical instability (see Bed Resistance (p. 85)). You should
only use this as a last resort to your stability problem: the schematisation of
the bathymetry and the boundary conditions are the primary causes for a
blow-up.
When you use the Smagorinsky formulation of the turbulence the CPU time
for a simulation is increased. Please see CPU Time (p. 95) for an estimate of
the additional time required.
When using the model for inland flooding always use the flux-based
approach for stability reasons. A typical viscosity coefficient can be set to
2
E = 0,02  x  t (6.10)
6.11 Evaporation
In applications where the evaporation is important, you can include evapora-
tion in your simulation.
99
Reference Manual
This is done either as a constant value or as a time series (type 0 data file),
which then is applied to the entire model area, or as a time series of maps
(type 2 data file) in which case each grid point is assigned its own value. The
evaporation rate is specified in mm/day.
 You can include evaporation in your simulation in three different ways.

 If your simulation does not include any density variations you can include
evaporation by specifying the evaporation rate in the Source and Sink
dialog.
 You can also use the precipitation facility to include evaporation in your
simulation. This is simply done by selecting the “included as net-precipi-
tation” option and specifying a negative precipitation. See the Precipita-
tion (p. 116) description for more details.
 If your simulation on the other hand include density variations (or more
precisely, temperature variations) you should select “AD feed-back on
HD” option and the heat exchange option on the AD dialogs (see AD
Feed Back on HD (p. 21) and Heat Exchange (p. 32)). This implies that
the evaporation rate can be calculated as a function of the latent heat
flux.
6.12 Flooding and Drying
A very valuable facility in MIKE 21 is its capability to include and exclude

computational areas dynamically during the simulation or, in other words,
compute the flow in an area which sometimes dries out and sometimes is
flooded (e.g. tidal flats).
You should use this facility whenever points in your model might be flooded or
dried out.
6.12.2 Specifying flooding and drying
You enable the possibility of flooding and drying of areas in the Flood and Dry
dialog. You will then be asked at what depth the computational points should
be taken out and reentered into the computations.
Coastal flooding
The Drying Depth can normally be specified in the range 0.1 - 0.2 m and the
Flooding Depth in the range 0.2 - 0.4 m. A difference between the two
depths of 0.1 m is recommended. If the water level variations occur very rap-

Friction Factor
idly (compared to the time step) you can increase the difference to 0.2 m or
even more.
Inland flooding
In certain situations MIKE 21 may yield negative water depths. This can occur
for instance in areas with steep gradients in the bathymetry (or topography)
or by a relatively large time step in the model. To minimize the potential for
mass falsification you should generally use smaller flood and dry levels for
inland flooding. Appropriate values in inland flooding could be Drying depth
in the range 0.001 - 0.02 m and Flooding depth in the range 0.002 - 0.05 m,
where Flooding depth > Drying depth.
Note: The drying and flooding depth must be larger than 0.0001 m and
0.0002 m, respectively.
The CPU time increases when you request that checks be made for flooding
and drying. For an estimate please see CPU Time (p. 95).
In order to avoid drying and flooding following rapidly after each other (which
will lead to instabilities in the computations) a point is not dried out if the water
depths at the four grid points immediately below, above, to the right and to the
left all are larger than the flooding depth. However, if the depth at the point in
question is nearly zero, it is always dried out.
A point is flooded if the water level at one of the four grid points immediately
below, above, to the right or to the left is more than the value you have speci-
fied as the minimum flooding depth.
If you have instabilities in your model, you might be able to avoid them by first
of all checking for flooding and drying after each time step. If the problems
persist, you can increase the drying and flooding depths and, in particular, the
difference between the two.
Continuity is preserved during the flooding and drying process as the water
depths at the points which are dried out are saved and then reused when the
point becomes flooded again. However, in cases of excessive flooding and
drying, e.g. during rainfall on otherwise dry land, the model may resort to
numerical water level correction in order to stabilize the model. This may give
reason to inconsistency in the water balance. For more details, and how to
reduce inconsistency, please see the section on Flooding and Drying in the
MIKE 21 HD Scientific Background.
6.13 Friction Factor

See Wind Conditions (p. 138).
101
Reference Manual
6.14 Froude Number

The Froude number, F, which may be selected as output in the HD module is
based on the equation
F = V   gh  (6.11)
where V is current speed, g is gravity and h is the water depth.
6.15 Hot Data
You can start your simulation either from scratch (a “cold start”) or on the
basis of a previous simulation (a “hot start”). In the latter case you need to
save information about the simulation you wish to continue. These data are
called “hot data”.
The hot data consist of the following model information:
 Model dimensions and grid spacings, time step and time at end of simu-
lation, information on flooding and drying, the latitude of the model and
its orientation (relative to true north), and the value above which a point
is always considered to be land
 Bathymetry
 Initial surface elevation (i.e. the surface elevation at the last time step in
the previous simulation)
 Fluxes in the x-direction at the last time step
 Fluxes in the y-direction at the last time step
 Fluxes in the x-direction a full time step before the last one
 Fluxes in the y-direction a full time step before the last one
 Water depth in dried out points (if you had chosen the flooding and dry-
ing facility).
Thus, if you use a hot start, you need not (and cannot) specify the data listed
above.
6.15.2 Specifying the hot data
You specify that you wish to be able to continue the simulation you are about
to execute by selecting 2Generate Hot Start” in the Results dialog, and then
writing the name of the hot data file.

Infiltration
You specify that you wish to do a simulation as a continuation of a previous

one by selecting “Hot Start” in the Bathymetry dialog, and then writing name
of the hot data file created earlier.
6.16 Infiltration
Infiltration describes the flow of water from the free surface zone to the infil-
tration zone below the ground level.
This effect may be a relevant factor in flood modelling where even a small
precipitation can invoke flow on a dry surface. The effect of infiltration is
included by subtracting the net infiltration volume from the volume of water in
the individual grid cell. This is similar to a sink effect in the spatial domain
however the effect will not affect the overall flow. The resulting water depth
can be expressed by
H (j,k) = H (j,k) – V infiltration (j,k)   x  y  (6.12)
where Vinfiltration is the net infiltrated volume in the grid cell.
6.16.2 Net infiltration rate
The most direct way of including infiltration is to specify the net infiltration
rate.
Figure 6.14 Definition of net infiltration rate
103
Reference Manual
Note: The specified infiltration rates will always be fully effectuated as long as
there is enough water available in the cell. It is possible that the infiltration
flow completely drains the free surface zone from water and thus creates a
dried-out point in the two-dimensional horizontal flow calculations.
6.16.3 Infiltration and leakage
It is possible to calculate the net infiltration rate by a simplified model that

describes the infiltration from the free surface zone to the unsaturated zone
and the leakage from the unsaturated zone to the saturated zone. This way
the model can e.g. account for a decreased storage capacity due to previous
rainfall events.
The model assumes the following:
 The unsaturated zone is modelled as an infiltration zone with constant

porosity over the full depth of the zone.
 The infiltrated volume between the free surface zone and the infiltration
zone is based on a constant flow rate,
i.e. Vinfiltration = Qi×t where Qi is the prescribed infiltration rate.
 The leaked volume between the saturated and unsaturated zone is also
based on a constant flow rate,
i.e. Vleakage = Ql×t where Qlis the prescribed leakage rate.
Figure 6.15 Definition of infiltration with storage and leakage

Initial Surface Elevation
Note: The infiltration flow cannot exceed the amount of water available in the
free surface water zone nor the difference between the water capacity of the
infiltration zone and the actual amount of water stored there. It is possible that
the infiltration flow completely drains the free surface zone from water and
thus creates a dried-out point in the two-dimensional horizontal flow calcula-
tions.
6.17 Initial Surface Elevation

See Additional area description (p. 83).
6.18 Inundation statistics

Inundation statistics can be calculated and stored as a dfs2 file. Seven quan-
tities are calculated and stored as separate items in the output file:
1. maximum water depth, Hmax (j,k)

2. time at maximum water depth, T@Hmax (j,k)
3. maximum flux magnitude, Fmax (j,k)
4. time at maximum flux magnitude, T@Fmax (j,k)
5. maximum current speed, Vmax (j,k)
6. current direction at maximum current speed, Dir@Vmax (i,j)
7. time at maximum current speed, T@Vmax (j,k)
8. duration above threshold (Optional)
These are all initialized as delete values and subsequently updated according
to the specified update frequency (wet points only).
Water depths are grid cell centred values. All items in the inundation statistics
are evaluated at the cell centre, making them directly identifiable with the val-
ues from the HD output files.
Please note that the 8 characters “Aaa.dfs2”, are added to the user specified
file name automatically. Here “Aaa” is an area number identification where
the uppercase “A” is fixed and “aa” is replaced by the respective area number
(e.g. “A01” for the main area, area number 1, and “A02” for area number 2,
etc).
6.19 Manning Number

See Bed Resistance (p. 85).
105
Reference Manual
6.20 Mud, Debris or Oil

The 'Mud, Debris or Oil' feature enable an alternative hydrodynamic solution
in which a fluid dependent flow resistance is added to the standard flow
momentum equations.
Naef et al (2006) defines a number of formulations for calculating flow resist-

ance relations and the flow resistance term; 0/. The current implementation
include a 'Full Bingham' relation, which in addition allows for applying simpler
resistance formulations which excludes the Bingham viscosity term (e.g. the
'Turbulent and Yield' relation as defined in Naef et al (2006)).
The full Bingham flow resistance relation determine the flow resistance term
(0/gh) from the following third order equation (see Naef et al, 2006):
 B q 2
2 03 – 3   y + 2 ---------
-  0 +  y3 = 0 (6.13)
 h 
2
where q is the flux (discharge per unit width), h is the fluid depth, y is the
yield stress and B is the Bingham fluid viscosity.
The third order equation is solved numerically during the simulation to give 0
as function of the yield stress (y), Bingham viscosity (B), water depth (h) and
flux (q).
Note, that it is possible to activate e.g. the Turbulent and Yield resistance for-
mulation by simply setting the Bingham Viscosity parameter, B, equal to
zero.
The rheological properties of non-Newtonian fluid are driven by the complex

interaction of a fluid's chemical and material composition. Key composition
properties include the particle size distribution (e.g. percent fines), solids con-
centration, water content, chemical composition, and mineralogy such as the
presence of clay minerals.
The Bingham rheological model is well suited for homogenous fluid mixtures
with high concentrations of fine particles (e.g. mudflows, hyper-concentra-
tions of fine sand, silt, and clay-size sediment) and other material types such
as oils.

Mud, Debris or Oil
The key parameters for the Mud/Debris/Oil model are the following (default
unit shown in brackets):
Fluid density: Density of the fluid mixture [kg/m3]
Yield Stress: Shear stress threshold that needs to be exceeded for the
fluid to flow [Pa]
Dynamic viscosity: Dynamic viscosity of the Bingham fluid mixture [PS s]
Fluid density
The fluid density can be determined from either measurements of the fluid to
be modelled or calculated using the solids concentrations of the fluid mixture.
Yield Stress
Ideally, the yield stress (i.e. yield strength) of the fluid to be modelled can be
determined from rheograms developed from viscometric measurements in a
laboratory. A rheogram relates the shear rate of the fluid to the applied shear
stress. A commercially available concentric cylindrical viscometer is ideally
suited for this type of analysis because it is capable of developing the rheo-
gram for a wide shear rate range. However laboratory derived rheological
analyses may not always be possible or practical.
Yield stress can also be determined empirically from both case studies involv-
ing similar fluid compositions and empirical relationships. For hyper-concen-
trations composed of fine sediment, yield stress is often formulated as a
function of material type (e.g. clay mineralogy) and sediment concentration.
Julien (2010) provides the following recommended empirical relationships for
yield stress as a function of sediment concentration for a variety of material
types using this exponential form:
b  Cv
 y = a  10 (6.14)
where yis the yield stress [Pa], a and b are coefficients (see Table 6.1) and
Cv is the volumetric sediment concentration.
Table 6.1 Coefficients for yield stress empirical relationships from Julien (2010)
Material a b
Bentonite (montmorillonite) 0.002 100
Sensitive clays 0.3 10
Kaolinite 0.05 9
Typical soils 0.005 7.5
107
Reference Manual
Oils are a special application where the yield stress is typically set to zero and
the dynamic viscosity dictates the laminar flow nature represented by the
Bingham rheological model. For zero yield stress the Bingham fluid model is
valid for laminar depth-integrated flow.
Note that the typical exponential relationship between yield stress and sedi-
ment concentration indicates that at some point small changes in concentra-
tions can dramatically change yield stress. This is an important dynamic
sensitivity to consider when evaluating Bingham fluids.
Dynamic viscosity
Once the fluid is in motion, the dynamic viscosity (i.e. plastic viscosity) repre-
sents how the fluid flows under applied shear stresses. Similar to yield stress,
the dynamic viscosity can be determined from rheograms developed from
viscometric measurements in a laboratory. However laboratory derived rheo-
logical analyses may not always be possible or practical.
Dynamic viscosity can also be determined empirically from both case studies
involving similar fluid compositions and empirical relationships. Julien (2010)
provides the following recommended empirical relationships for yield stress
as a function of sediment concentration for a variety of material types using
this exponential form:
c  Cv
 m = 0,001  10 (6.15)
where m is the dynamic viscosity [Pa s], c is a coefficient (see Table 6.2) and
Cv is the volumetric sediment concentration.
Table 6.2 Coefficients for dynamic viscosity empirical relationships from Julien
(2010)
Material c
Bentonite (montmorillonite) 100
Sensitive clays 10
Kaolinite 9
Typical soils 7.5
For modelling viscous, low-strength fluids such as oils, the dynamic viscosity
is the key parameter for the Bingham model as the yield stress is often set to
zero. The dynamic viscosity for such materials is best determined from rheo-
grams developed from viscometric measurements in a laboratory, e.g. com-
mercially available concentric cylindrical viscometer. Available literature (e.g.
product descriptions) and case studies for commercially derived materials are
other appropriate sources for choosing the value for the dynamic viscosity
parameter.

Multi-cell overland Solver
6.21 Multi-cell overland Solver

The MIKE 21 multi-cell overland solver is designed for simulating two-dimen-
sional flow in rural and urban areas. The overall idea behind the solver is to
solve the modified equations on a coarse grid taking the variation of the
bathymetry within each grid cell into account. Results are presented on the
grid that takes the fine scale bathymetry into account.
6.21.1 Constructing the fine and the coarse bathymetries
To apply the multi-cell overland solver two bathymetries must be constructed
 A bathymetry with a coarse resolution which defines the calculation grid

and the location of boundary conditions
 A fine resolution bathymetry which is used for result presentation and
evaluation of hydraulic parameters within a coarse grid cell
The two bathymetry must obey a number of rules
1. The extent of the bathymetries must be identical.
2. The number of grid cells in the J and the K direction for the fine grid must
be dividable by the number of cells in the J and K direction respectively
in the coarse grid i.e. the number fine grid cells within a coarse grid cell
must be integer.
The first of these points may at first glance easy to satisfy simply by ensuring
that the two bathymetries have the same origo and the same length in the X
and the Y direction. A word of caution is in order here. The origo of a dfs2 file
which has a true projection such as a UTM type associated with it refers to
the centre of the cell (j,k)=(0,0). The situation is illustrated in Figure 6.16.
Figure 6.16 The location of the origo of the coarse and fine grid when a true projec-
tion is applied.
109
Reference Manual
The Origo of the fine grid should be placed according to
 1 – N J fine   1 – N K fine 
O  x y  = O  X Y  +  ------------------------------ x ------------------------------- y (6.16)
 2 2 
where the capitalized X and Y refer to the origo of the coarse grid and NJ,fine
and NK,fine refer to the number of fine grid cells within a coarse grid cell in the
J and K direction respectively.
As a rule of thumb the difference in grid size should be not be higher than a
factor 4 to 5.
Along the boundaries the topography from the coarse grid is used i.e. the
bathymetry in the fine grid is modified to be equal to the coarse grid at bound-
aries. To ensure stability is recommended to smooth out the bathymetry of
the fine grid close to boundaries to avoid sudden changes in the water depth.
True land points are defined by the coarse grid and any land points will be
transferred to the fine bathymetry at run time.
Note: All values in the fine bathymetry must be lower than the specified land
value in the coarse bathymetry.
6.21.2 Evaluation of hydraulic parameters within a cell
The methodology adapted for the multi-cell overland solver requires an evalu-
ation of the hydraulic parameters such as the flooded area within a grid cell.
The flooded area within a grid cell is illustrated in Figure 6.17.
Figure 6.17 The flooded area is a function of the surface level within a grid cell.
The calculation of the flooded area, hydraulic radius, flow area within a cell
etc. may be a time consuming process. For this reason MIKE 21 evaluates
these parameters at a number of levels within each cell in a preprocessing
initialisation phase. The calculated parameters are stored in three dimen-

Orientation
sional arrays (in memory) which are subsequently used at each time step in
the simulation.
By default MIKE 21 calculates the parameters at 100 equidistant levels

between the highest and the lowest point within each cell. The number of lev-
els may be adjusted through the adding an optional parameter in the hydro-
dynamic section of the input file. The parameter is termed
Number_Levels_Overland.
Note that the higher this value is, the greater the amount of memory is
reserved for processed data. On the other hand if the value is too small the
variation of the topography within a grid cell will not be sufficiently resolved.
The number should reflect the variability within one coarse grid cell.
6.22 Orientation
See Additional area description (p. 83).
6.23 Output Files
Computers are not yet so powerful that a simulation can be run each time a
plot of, for example, the current field is needed. Therefore it is necessary to
store the basic results from the simulations. On the other hand, the amount of
output produced by a single simulation is often so large that it is necessary to
limit the amount of output saved. You therefore have the option of saving up
to 18 output files.
6.23.2 Specification of output files
In the Results dialog you first specify how many output files you wish to pro-
duce from the simulation (maximum is 18). You can then specify the contents
of each data file:
 Specify the output files type: 0 (point series), 1 (line series) or 2 (area
series).
 Specify the number of the computational area to be included in the out-
put file.
111
Reference Manual
 Specify the spatial and temporal sub-set of the data. This is best done
using the pop-up dialogs, which is activated with the buttons in the col-
umn after the 'Time' column. Grid line series (type 1 data files) is speci-
fied by choosing identical 'First Point' and 'Last Point' in either 'J
direction' or 'K direction'. For points series (type 0 data files) you can
choose the number of points in each file.
 Specify the data file (name) and title of the output file.
 Finally select the desired output items.
Note: The selection of the first item (Water level) or first three items (Water
level, P flux and Q flux) correspond to the standard 'level' (Data type = -1) or
'level and flux' output files (Data type = 1), respectively. When storing your
own selection of items (e.g. Velocity or Shear Stress in the two directions) the
data type is set to 0.
If the dfs2 file is created as a standard “level and flux” file then other MIKE
Zero components such as Plot Composer, Result Viewer and the MIKE Zero
Toolbox statistics can display and process other variables - surface elevation
and velocities - derived from these items.
One way of following the progression of your simulation is by following the

number of time steps written in your log file (or one of them). In most post-
processing tasks you start by specifying the data name and after having done
so, you are presented with the description of the data. This description
includes the number of time steps already written and thus finished.
6.24 Pier Resistance
The impact of bridge piers on the flow conditions can be included in the
hydrodynamic calculations by activating the pier resistance option.
The MIKE 21 solution method involves the use of a finite difference grid with
a selected grid mesh size. A typical choice of say 100-1000 metres implies
that bridge piers with a typical horizontal dimension of say 5-10 metres are
not directly resolvable in the computational grid. Therefore, the presence of
piers must be modelled by a subgrid scaling technique.
The resistance to the flow due to the piers is modelled by calculating the cur-
rent induced drag force on each individual pier and equate this force with a
shear stress contribution compatible with the MIKE 21 momentum formula-
tion.

Pier Resistance
Thus
 p  x  y = n  F (6.17)
where
p:equivalent shear stress
F:drag force on one pier (the sign of F is such that p acts against
the current direction)
n:number of piers allocated to one grid point (density of piers)
x, y: grid spacing
The resulting shear stress at the bottom is then implemented as the sum of p
and the bottom shear stress, o.
The drag force is determined from
1 2
F = --- C D B e H e  v (6.18)
2
where
CD:drag coefficient
:density of water
Be:effective width of pier
He:height of pier exposed to current
v:current speed
6.24.2 Specifying the pier resistance
If the resistance effect on the flow from bridge piers has to be included in the
simulation, the position and geometrical layout of the piers must be specified.
This various information must be grouped together in a pier data file. A pier
data file is a type 1 data file where the number of time steps in fact is the num-
ber of piers, i.e. the time axis in the data file is not a true time axis. In the
same way, the spatial axis is not a true spatial axis, but merely a collection of
data describing the pier.
The pier data file has the layout depicted in Figure 6.18.
113
Reference Manual
Figure 6.18 Layout of pier data file
The data file is created with the Profile Editor tool. In the following the param-
eters of the file are described:
 The x- and y-coordinates must be specified as map projection coordi-

nates, e.g. UTM-33 coordinates.
Note: The map projection is defined by the Geographical Information in the

data file (in Release 2007 and previous the projection system was defined by
the item description, e.g. PROJ=UTM-33).
 The type 1 data file must have Data Type=800.

 The angle is measured from projection north to the alignment, positive
clockwise and in degrees. Note that projection north is not the same as
geographical north.
 The number of sections means the number of pier segments, i.e. the
number of parts with different geometrical layout.
 The streamline factor is a factor that is multiplied on the total drag force
to take into account the increased flow velocity due to the blocking of
piers. A typical value is 1.02.
 The following five parameters describe the geometrical layout of one pier
section. These five parameters have to be repeated at each section of
the pier. The pier section type can be one of:
0:circular
1:rectangular
2:elliptical
See Figure 6.19 and Figure 6.20 below for a definition sketch.
For a circular pier section please note: Both width and length should be equal
to the diameter of the pier section and the parameter “Radius of rounded cor-
ners” is not used but should be assigned a value e.g. 0 or 1.

Pier Resistance
Figure 6.19 Pier definition sketch
Figure 6.20 Definition sketch. Effective height
115
Reference Manual
6.25 Precipitation
In applications where the rainfall is important for the flow, you can include pre-
cipitation in your simulation. This is done either as a constant value or as a
time series (type 0 data file), which then is applied to the entire model area, or
as a time series of maps (type 2 data file) in which case each grid point is
assigned its own value. The precipitation rate is specified in mm/day. You can
use the Time Series Editor or the Grid Editor tool to create your precipita-
tion data.
You can also use the precipitation facility to include evaporation in your simu-
lation. This is simply done by selecting the “included as net-precipitation”
option and specifying a negative precipitation.
The precipitation rate is specified in the Source and Sink (p. 57) dialog.
Please note that, in simulations with temperature variations the evaporation

may be calculated as part of the latent heat flux if the heat exchange option is
selected (see Heat Exchange (p. 32)). Thus you should be careful not to
specify evaporation from both options.
If you have selected the Heat Exchange (p. 32) option and you choose to
include precipitation as net-precipitation, then evaporation obtained through
the latent heat flux is not considered.
6.26 Simulation Type
There are two ways of starting your simulation:
 From scratch, also called a “cold start”, which means that you have to
specify the model bathymetry as well as all other model parameters.
 As the continuation of a previous simulation, also called a “hot start”, in
which case you must prepare “hot data” when doing the previous simula-
tion. This is done by requesting that a file containing “hot data” be pre-
pared in the Results dialog.
When your simulation is a continuation of a previous one, the bathymetry

together with the additional area description from the previous simulation, is
reused and cannot be changed. The rest of the model parameters you spec-
ify as for a “cold start”.

Shear Stress
In most applications all simulations will be “cold started”. However, if you

have very long simulations or your computer system often stops (planned or
unplanned) it is wise to use the “hot start” facility.
6.27 Shear Stress

The shear stress which may be selected as output in the HD module is based
on the equation
1 2
 = --- fV (6.19)
2
The relation between the friction factor f and the Chezy number C is
2g-
f = ----- (6.20)
2
C
Resulting in
g 2
 = -----2- V (6.21)
C
Or expressed using Manning’s M
g
- V 2
 = ----------------- (6.22)
2 1 3
M h
The stress is a vector and may be output both as components in the x- and y-
direction and by the absolute size.
6.28 Smagorinsky Formulation

See Eddy Viscosity (p. 97).
6.29 Soft Start
In order to avoid numerical shocks in the simulation it can often be a good

idea to introduce the hydrographic forcing parameters in a gentle way. This is
achieved by the “warm up” parameters.
117
Reference Manual
6.29.2 Specifying soft start
The soft start parameter gives the number of time steps to be used in build-
ing-up the forcing parameters from zero to their specified value.
The following parameters are affected by the soft start:
 boundary conditions, except for type 1 and transfer data

 wind, except for 2 dimensional wind maps
 radiation stresses.
Note that level boundary conditions are not increased from a zero value but
from the value indicated by the initial surface elevation.
It is very important to have a long soft start period when including radiation
stresses in the simulation, see Wave Radiation Stresses (p. 136).
6.30 Source and Sink
The effects of rivers, intakes and outlets from power stations etc. can be
included in a simulation. These sources and sinks are included in the hydro-
dynamic equations in the following way:
 If your source or sink has a magnitude of Q m3/s, then the additional term
on the right hand side of the continuity equation is
Q / x  y 
 If, for sources, you specify a speed of V m/s in direction , then the addi-
tional term on the right hand side of the momentum equations are
Q  V  sin   -  NYC  (x- direction)
Q  V  cos   -  NYC  (y- direction)

where NYC is the orientation of the model (see Orientation (p. 111)).

Standard vs. nested HD module
6.30.2 Specifying sources and sinks
In your model you can have up to a total of 256 sources and sinks. The
sources and sinks are then numbered in succession and you specify (or edit)
each of them by giving the corresponding number.
For a source you specify:
 The source location is specified as a constant in time and space.

 The source direction of the flow is specified as a constant in time and
space.
 The source discharge and flow speed can be specified as a constant in
time and space or as a time series. The discharge is given in m3/s and
the flow speed in m/s.
For the above specifications, the only requirement is that the source data be
specified for the complete simulation period.
For a sink you specify:
 The location (in grid coordinates). The location is a constant in time and
space.
 Either a constant intake (in m3/s) or the name of a data file as described
for a source but with only one item, the intake discharge.
You should if possible avoid placing sources and sinks in points that are sub-
jected to flooding and drying. If you have a source or sink in such a point, it
will be inactivated when the point is dry during a sweep. But a separate mass
budget is performed at all dried source/sink points such that the mass out-
let/intake at a source/sink is correct. That is, for sources at dried points the
mass outlet is accounted for until the particular point eventually floods (i.e.
water depth increases the flooding depth) and thus enters the computations
in the usual way. For sinks at dried points the sink intake is subtracted from
the particular point until the water depths becomes very small (MIKE 21 can-
not handle artificially generated non-positive water depths).
6.31 Standard vs. nested HD module
The purpose of this section is to enable the user to use the Nested HydroDy-
namic module of MIKE 21 Flow Module, the MIKE 21 NHD. As most features
in MIKE 21 NHD are identical to the features in the standard Hydrodynamic
Module, the MIKE 21 HD, this manual only describes the nested facilities.
119
Reference Manual
The nested hydrodynamic module, MIKE 21 NHD, solves the hydrodynamic

equations simultaneously in a user-defined number of dynamically nested
grids.
The advantage of applying the nested grid facility compared to the standard
approach of using only one grid is mainly the reduced CPU requirements.
Typical applications of the hydrodynamic module have a limited physical area
of main interest, which covers only a smaller part of the total modelling area.
To obtain a satisfactory spatial resolution of the model within this area of inter-
est, the standard hydrodynamic module can be used. But this will often result
in a very large number of computational grid points, many of which are often
wasted in areas of only limited interest for the application, and accordingly
this approach will require much computer time and memory. Applying the
nested module, the spatial resolution can be optimised to save computer
time. See Figure 6.21 for an example.
Figure 6.21 Example of a nested model set-up applied in an investigation of the

Øresund Link, Denmark-Sweden. The nested model contains four
model areas: an outer area (the main area) with a resolution of 900 m,
two intermediate areas of 300 m resolution, and an inner area with a
resolution of 100 m
The possibility of applying multiple grids of different spatial resolution is also

available within the standard MIKE 21 HD, where e.g. a coarse grid regional
model is first run and the results are stored and subsequently used to force a
fine grid model. (See Boundary Conditions (p. 87)). In this case the grids are
not coupled dynamically. This means that there is no feedback from the fine
resolution grid to the enclosing coarser grid with respect to phenomena being
resolved only with the fine resolution (narrow channels and constructions). In

the MIKE 21 NHD the grids are dynamically coupled and interact accordingly.
The two-way nesting secures a dynamically exchange of mass and momen-
tum between the modelling grids of different resolution.
6.31.2 Nested bathymetries
The standard hydrodynamic module, MIKE 21 HD, can only be applied with
one bathymetry with a certain spatial resolution. The nested version, MIKE 21
NHD, can work with up to nine bathymetries (model areas) of different resolu-
tions. The bathymetries can be nested into each other with a progressive
increase in resolution and/or with more than one model area at each level of
equal spatial resolution, cf. Figure 6.22 and Figure 6.23.
Figure 6.22 Sketch showing possible nesting of bathymetries
As with the standard hydrodynamic module, specification of the bathymetric

information is very important. There are a number of rules to obey when pre-
paring nested bathymetries to obtain compatibility between a subarea (fine
grid) and its enclosing area (coarse grid):
 The ratio between the horizontal spatial resolution at one level to the next
level must be 3, i.e.
xCOARSExFINE
The factor of 3, which is fixed, has been found appropriate for a wide
range of applications.
 Model areas at the same level must not overlap. The distance between
model areas at the same level should be at least three times
xCOARSE
121
Reference Manual
 Corners of sub-areas must be placed in grid points (integer values) of

the respective enclosing grid. This means that, in each horizontal direc-
tion, every third grid point of the fine grid is common to a grid point in the
coarse grid, a so-called common grid point. I.e. the relation between
the number of coarse grid points, NCOARSE, and the number of fine grid
points, NFINE, for a given subarea must be
NFINE = 3*NCOARSE+1
in each main direction.
 Open boundaries are only allowed in the coarsest grid, referred to as

the main area.
 Model sub-areas must be placed at least three grid points within the
boundary of the enclosing area if the closest boundary point is a water
point. If the boundary point is a land point, a distance of one grid point is
sufficient.
 The water depths in common grid points along borders between areas
must be equal in the coarse grid and in the fine grid. The water depths in
the two border grid points of the fine grid between two common grid
points must have values which are linearly interpolated from the water
depths of the two surrounding common grid points. That is, the border
bathymetry should be fully resolved in the coarse grid.
 To avoid instabilities, it has been chosen to demand that the water
depths across borders should be equal within a band of xCOARSE on
each side of the border. This means that the water depth in the coarse
grid must be equal in three points orthogonal to the border (one point at
the border and one point on each side). In the fine grid, the water depth
in the first four grid points orthogonal to the border should be equal. If the
border is land, this rule does not need to be satisfied.
Note: No flooding or drying must occur in the common grids along bor-
ders between areas.
 Moving along a border from a water point towards a land point (if any),
the last water point before reaching land should be common in the
coarse grid and the fine grid. This is an important rule, which might not
seem quite obvious, cf. Figure 6.23, but keep in mind that at the border
the topography should be fully resolved on the coarse grid scale.

Figure 6.23 Principle of water depths and land-water boundary along a border line
 Finally, all interior common points should have equal water depth in
the coarse grid and in the fine grid. As the nested model does not per-
form any coarse grid calculations in the area covered by the fine grid, this
rule is only included in order to ease pre- and post-processing. Fine grid
solutions of any model quantity are always copied to the coarse grid.
Please be very careful when choosing the extents of sub-areas. Many hours
of annoyance during an application could be avoided, if some time is spent
choosing the sub-domain structure. Borders and the positions of these should
be treated with equally care as the open boundaries of your model.
A pre-processing tool for border adjustment of nested bathymetries should

be applied prior to the MIKE 21 NHD module, see also Pre- and post-pro-
cessing tools (p. 125).
6.31.3 Nested model specifications
Most model specifications in MIKE 21 NHD are identical to those in MIKE 21

HD. The major difference is that in the nested model you have to specify most
of the model parameters (coefficients, initial fields, maps, etc.) separately for
each area. A few comments are listed below:
 For a “cold start”, you first of all specify how many areas you want to
include. Then you select the main area and all sub-areas supplied with
origin in enclosing grid coordinates (integers). Note that the model orien-
tation and origin in geographical coordinates should be supplied with the
type 2 data file for the main area bathymetry.
 For a “hot start”, you select your hot data files, one for each area. The
other information mentioned above is contained in the hot data files and
cannot be changed.
 Specifications given for the simulation period are common to all areas.
123
Reference Manual
 You enter your choice of turbulence formulation which is common to all

areas. Parameters for constant eddy viscosity and for the Smagorinsky
should be specified for each area.
 Bed resistance parameters (constants or maps) should also be specified
for each area. The selected bed resistance formulation (Manning or
Chezy) will be common for all areas.
 Wave radiation stresses can be included in one or more areas.
 Open boundary conditions in the nested MIKE 21 Flow Model are speci-
fied exactly as for the standard MIKE 21 Flow Model. Remember that
open boundaries must be in the main area, see Nested bathymetries
(p. 121).
 Initial surface elevation should be specified for each area. Flooding and
drying depths are common to all areas.
 Source/sink specifications are the same as for the standard MIKE 21
model, except that you also specify the number of the area in which the
source/sink is located. This area number must correspond to the finest
grid covering the source location. Evaporation and precipitation rates are
common to all areas.
 The wind specifications are identical to those in the standard MIKE 21. A
possible type 2 data file is specified for the main area only and the wind
field is interpolated automatically by MIKE 21 NHD to match the finer
grids.
 You specify bridge piers in MIKE 21 NHD as in the standard MIKE 21
and, in addition, you supply the area number for the location(s) of the
pier(s). Bridge piers must be embedded within one area only, i.e. within
the finest grid covering the pier locations, and the line of piers should not
intersect with area borders.
 In the output specifications, each output area must be related to an asso-
ciated model area. For hot files, one file for each area must be specified
Time Step
The time step (which is the same in all areas) to be used in a MIKE 21 Nested
Flow Model simulation is determined in the same way as in the standard
MIKE 21 Flow Model. In the nested version, though, it is necessary to calcu-
late the Courant number within each model area based on the respective grid
spacing and maximum water depth as well as the time step.
CPU Time
The CPU time for a MIKE 21 NHD simulation is proportional to the number of
computational water points in all areas (neglecting the 'hidden' water points
due to nesting). The computational speed (points per second) of MIKE 21
NHD is roughly speaking 10% lower than for the standard MIKE 21 HD due to
an overhead for handling of the nesting.

Structures
Disk Space
The disk space requirements of a MIKE 21 NHD simulation can be deter-
mined in the same way as for a standard MIKE 21 HD simulation, see Disk
Space (p. 96). The system-generated files are the two ASCII files of exten-
sion m21 and log.
6.31.4 Pre- and post-processing tools
All the standard MIKE 21 pre- and post-processing tools (i.e. data file editors,
data type conversion programs, graphics, etc.) can be applied in connection
with MIKE 21 NHD. One tool has been developed especially for nested grid:
 border adjustment: A pre-processing tool developed to aid adjusting

nested bathymetries prior to a MIKE 21 NHD simulation, see Nested
bathymetries (p. 121). This tool takes as input two type 2 bathymetry
data files, corresponding to a fine grid and its enclosing coarser grid, and
produces two new type 2 bathymetry data files. Since the produced mod-
ifications are not necessarily the most ideal, it is strongly recommended
always to check the new bathymetries – coarse as well as fine grid –
along borders that cross a land-water boundary. Possibly you need to
edit the bathymetries using e.g. the GridEdit tool.
If you plan to apply MIKE 21 NHD with more than one sub-level, you
should apply border adjustment 'inside-out'. That is, considering the
example sketched in Figure 6.22, the sequence of border modifications
should contain: Apply the border adjustment program with areas 3 and 5,
then apply border adjustment on the main area (i.e. area 1) and the mod-
ified area 3.
6.32 Structures
6.32.1 Location of a structure
The location of a structure is given by a number of geo-referenced points

which together make up a poly-line. The poly-line defines the width of the
structure perpendicular to the flow direction e.g. for a weir it will describe the
location of the crest in the horizontal plan view. For a culvert the poly-line
should be given as a line perpendicular to the flow direction and further the
line should intersect the mid point of the culvert.
125
Reference Manual
Figure 6.24 The location of a weir. Note the affected cell faces
Figure 6.25 The location of a culvert. Note the affected cell face
A cell face is affected if the defining poly-line intersects the line segment con-
necting the mid points of the two adjacent grid cells. The flow through the
structure is evenly distributed along the affected cell faces.
6.32.2 Weirs
There are three types of weirs available
 Broad crested weir

 Weir formula 1
 Weir formula 2

Structures
The geometry of each of these is to be supplied by the user according to the

sections below.
Broad crested weir

For a broad crested weir the user describes the shape of the “hole” through a
level/width table (see figure below). The datum value for the structure may be
used to shift the levels by a constant amount. The latter is typically used if the
weir geometry has been surveyed with respect to a local benchmark.
Figure 6.26 Definition sketch of broad crested weir geometry
The standard formulations for flow over a broad crested weir are established
automatically by the program on the basis of the weir geometry and the user
specified head loss and calibration coefficients. These formulations assume a
hydrostatic pressure distribution on the weir crests. Different algorithms are
used for drowned flow and free overflow, with an automatic switching
between the two.
Weir formula 1
For the weir formula 1 description the parameters are given by Figure 6.27.
The width is perpendicular to the flow direction. Typically the invert level coin-
cides with the overall datum.
Weir formula 1 is based on a standard weir expression, reduced according to

the Villemonte formula:
H ds – H w 0,385
Q = WC  H us – H w  1 –  ----------------------
k
(6.23)
 H us – H w
where Q is discharge through the structure, W is width, C is weir coefficient, k

is the weir exponential coefficient, Hus is upstream water level, Hds is down-
stream water level and Hw is weir level (see Figure 6.27).
127
Reference Manual
Figure 6.27 Definition sketch for weir flow
Weir formula 2
For the weir formula 2 the geometry is given by a crest level and a width. The
crest level is taken with respect to the global datum. The width is perpendicu-
lar to the flow direction.
Weir formula 2 is the Honma formula:

 C W  H us – H w   H us – H w  for  H ds – H w   H us  2  3
Q =  1 (6.24)
 C 2 W  H ds – H w   H us – H ds  for  H ds – H w   H us  2  3

where Q is the discharge through structure, W is the width, C1 is the weir

coefficient 1, and C2, the weir coefficient 2, is calculated according to
C 2 = 1,5 3C 1 , Hus is the upstream water level, Hds is the downstream water
level and Hw is weir level (see Figure 6.27).
Head Loss Factors

The flow description generally used for a structure is given by:
2
V
H =  t -----s- (6.25)
2g
where DH is the energy loss over the structure, t is the total head loss coeffi-
cient and Vs is the mean cross sectional velocity at the structure.

Structures
The total head loss coefficient (t) is composed of entrance (1) and exit (2)
coefficients. The coefficients are generally related to the input parameters for
Inflow (in) and Outflow (out) and the changes in velocity (v) and area (A):
v A 2
 t =  1 +  2 =  in  ----1- +  out  -----s- (6.26)
 v s  A 2
where suffix '1' and '2' represents velocity and Area on inflow and outflow side
of structure respectively, and 's' represents the velocity and Area in the struc-
ture itself.
For subcritical flow through a structure there is an upstream contraction and a

downstream expansion, so the above equation works fine.
However, in the present implementation, upstream and downstream cross

sections are not extracted and accordingly, tabulated relations on cross sec-
tion areas as function of water levels are not known. Instead, upstream and
downstream areas are set to a large number resulting in a full loss contribu-
tion from the head loss factors defined. Viz,
 t =  1 +  2 =  in +  out (6.27)
Care must be taken when selecting loss coefficients, particularly in situations

where both subcritical and supercritical flow conditions occur. When flow con-
ditions change from subcritical to supercritical (or the Froude number FR
becomes greater than 1), the loss coefficients in and out (specified in the
Head Loss Factors box) are modified:
 If FR > 1 in upstream h-point then in = in / 2

 If FR > 1 in downstream h-point then out = out / 2
Free Overflow Head Loss Factor

The critical flows (and orifice flows for culverts as well) are multiplied by the
critical flow correction factor, c, specified as the Free Overflow Head Loss
Factor. Typically a value of 1.0 is used.
6.32.3 Culverts
A culvert may be of three different geometries:
 Rectangular
 Circular
 Irregular (A level-width table)
129
Reference Manual
Geometry
With the rectangular and the circular type geometries the width/height or the
diameter is supplied.
For the Irregular type geometry the geometry is to be defined through a level-
width relationship table, see Figure 6.28. Further the user must supply the
invert levels of the culvert on the upstream and on the downstream side. The
invert is the lowest point in the inlet/outlet section. Note that the values in the
level width table are taken with respect to the inverts. Further the user must
supply the length of the culvert (in the flow direction) and the resistance in the
culvert. The latter is defined through the use of Manning's n (=1/M).
Figure 6.28 Definition sketch of irregular level-width culvert geometry
Closed / Open Section switch

A culvert structure can be modelled as an open section if required by setting
the Closed / Open switch. An example where this may be used is a “long”
weir where the friction along the length of the weir is of importance and/or the
flow areas at the entrance and exit are significantly different.
If set to open the culvert will never run full or partially full, therefore only those
flow conditions which represent a free water surface are modelled. When the
water level is higher than the soffit the hydraulic parameters are calculated
based on a section extended vertically upwards with a width equal to that at
the soffit. For example, in the case of a rectangular section the height value is
essentially redundant as the cross-section will be modelled as an open sec-
tion of constant width.
In the case of a circular section, this switch is invalid and will be set to closed.

Structures
Head loss factors

The total head loss, DH through a culvert is given by:
Q  1 f + b 2 
2
H loss = -------  -------
- + ---------------- + -------- (6.28)
2g  A 2 A
2
A 
2
s1 sa s2
where As is the mean cross section area along the length of the culvert and Q
is the discharge, 1 is the entrance or contraction loss, 2 is the outlet or
expansion loss, f is the Friction loss calculated using the Manning formula
and b is the bend loss coefficient.
 As 
 1 =  in  1 – --------1 (6.29)
 A1 
2
 As 
 2 =  out  1 – --------2 (6.30)
 A2 
2
2gLn
 f = ---------------
43
- (6.31)
R
where L is the culvert length, n is Manning's coefficient and R is the mean

Hydraulic Radius along the culvert. The Manning's n-value depends on the
interior surface of the culvert. Table values can be found in literature. For e.g.
a concrete culvert n would typically range from 0.011 to 0.017.
he bend loss coefficient, b, is provided for situations where head losses
other than from the above occur, for example bends, damaged culverts,
trapped debris. For straight culverts in good condition a value of zero would
apply.
Free overflow head loss factor

The critical flows (and orifice flows for culverts as well) are multiplied by the
critical flow correction factor, c, specified as the Free Overflow Head Loss
Factor. Typically a value of 1.0 is used.
131
Reference Manual
6.32.4 Dikes
The flow, Q, over a section of the dike corresponding to an element face with
the length (width), w, is based on a standard weir expression, reduced
according to the Villemonte formula:
3  2 H ds – H w 3  2 0,385
Q = wC  H us – H w  1 –  ----------------------  for H us  H ds  H w
  H us – H w 
(6.32)
32
Q = wC  H us – H w  for H us  H w  H ds
Q=0 for H w  H us  H ds
where Q is discharge through the structure, w is the local width (cell face
width), C is discharge coefficient, Hus is upstream water level, Hds is down-
stream water level and Hw is the crest level taken with respect to the global
datum (see Figure 6.29). The default value of the weir coefficient is 1.838.
Figure 6.29 Definition sketch for Dike Flow
The geometry of a dike is defined as shown below.
Figure 6.30 Definition sketch of spatial varying dike geometry

Structures
6.32.5 Flow directions for specific structure parameters
Positive and Negative flow directions as referred to in Valve and Head loss
coefficient definitions follows the definition as presented in Figure 6.31. That
is, positive flow direction is defined as the left perpendicular to the direction of
a structure line schematisation.
Figure 6.31 Positive and Negative flow direction definition at structures
To ensure that a structure is mapped properly onto one or more cell faces the
defining poly-line should intersect the line segments connecting the cell cen-
tres. If the latter is not the case a warning is issued in the simulation-log and
the structure is mapped onto the nearest cell face with a similar alignment as
the defining line segment. To ensure a proper mapping simply extent the
poly-line defining the structure location so that it intersects a line segment
connecting cell mid-points, see Figure 6.32
133
Reference Manual
Figure 6.32 Definition of cell mid-points
The affected cell faces are written to the simulation log for inspection. The for-
mat being:
n j k Top Posi
n is an index of the number of cells affected, j and k refers to the individual

cells. The value of Top is either 0 or 1 depending on whether the cell face is
to the right or at the top of the cell. Finally the Posi value indicates whether
the cell is the upstream (1) or the downstream side of the structure. Please
note that the upstream and downstream definition is only of importance if the
loss factors are asymmetric across the structure or the invert levels are differ-
ent upstream and downstream.
6.33 Time Step
6.33.1 Selecting the time step
The time step for your simulation is selected as follows:
 First you determine the grid spacing, x, as described under Nested
bathymetries (p. 121).
 Secondly you decide on the maximum allowed Courant number, Cr, as

described under Courant Number (p. 95).

Velocity
 Then you can determine the maximum time step, tmax, which can be
used in the model from the definition of the Courant number:
C
 t max = x -----r (6.33)
c
where c is the celerity (see Courant Number (p. 95) for a description).
The time step to be used in the model, t, can then be chosen as a “con-
venient” number not greater thantmax.
 Finally you have to check that the Courant number based on the current
speed, (the transport Courant number) Cr,U, instead of the wave celerity,
is less than 1 for the time step chosen. If not, you must reduce the cho-
sen time step. Cr,U is defined as
U- + -----
V-
C r U =  t   ----- (6.34)
 x y
where U,V is the current speed in the x-direction and y-direction. For all
points within the model U and V must follow the above formula. As you
have not yet carried out the simulation you will have to make an estimate
and then check this after the simulation.
Please note that formally U and V in the above expression should be

replaced by P/H and Q/H, respectively, where P and Q are the magnitudes of
the fluxes in the x- and y- directions and H is the local water depth. Often the
two expressions – based on current speeds or on the flux magnitudes – yield
almost the same value, but care should be taken in models with large surface
and/or bottom gradients.
6.34 Velocity
The output velocity is a vector and various types of velocity information may
be selected as output in the HD module:
 U-velocity (in the direction of the x-axis)

 V-velocity (in the direction of the y-axis)
 Current speed (absolute size)
 Current direction (measured positive clockwise from True North)
135
Reference Manual
6.35 Wave Radiation Stresses
You can include the wave induced flow in the model area by specification of
the so called “Wave Radiation Stresses”.
By averaging the equations of motion over depth and time (the wave period)
wave radiation stress terms will be included in the momentum equations.
The additional terms are:
S xx S xy
x-momentum : ----------- + ----------- (6.35)
x y
S yy S xy
y-momentum : ----------- + ----------- (6.36)
y x
where Sxx, Sxy and Syy are the three components of radiation stress.
6.35.2 Specifying the wave radiation stresses.
The inclusion of wave radiation stresses in MIKE 21 should be specified by a

map similar to that for bed resistance except that it should contain three items
(SXX, SXY, SYY) and a prefix item (bathymetry).
The stresses are kept constant in time (steady state wave situation), but by
specifying a so-called soft start, the stresses will be linearly increased from
zero to the input values over the requested number of time steps.
The data file (type 2) containing the wave radiation stresses can be gener-
ated directly by the wave model MIKE 21 PMS. If the file containing wave
radiation stresses is generated another way please ensure that the Data type
value is 930.
Since the wave radiation stresses describe the average flow over one wave
period, the stresses are connected to a certain water depth. Application of the
wave radiation stresses in simulations with time varying water depths (e.g.
tide and/or storm surges) is possible, but the error introduced by the changes
in water depth should be considered.
If the “Flood and Dry” facility is applied, the user should be sure that the wave
radiation stresses are well defined in all grid points which will be flooded dur-
ing the simulation.

Wave Radiation Stresses
In general, it is not recommended to use wave radiation stresses together

with the “Flood and Dry” facility.
The main problems connected to simulations with wave radiation stresses

are related to the open boundary conditions. A MIKE 21 Toolbox program;
Wave Generated Current and Setup, can be used for generation of level or
flux transfer boundary data based on the two dimensional wave radiation
stress data file.
Below is listed a typical sequence step by step to follow in simulations which

include effects from wave radiation stresses:
 A type 2 data file containing the three wave radiation stress components
should be prepared. This file can be generated directly by MIKE 21 PMS.
 Generate transfer boundary data (only contribution from wave radiation
stresses) for all open boundaries in the model area, using “Wave Gener-
ated Current and Setup”.
 Run the HD simulation to obtain the stationary flow field.
The last step is not necessary if for example tide and/or storm surge also
should be included, but it is still recommended for checking purposes
(besides it contributes to the understanding of the final combined flow field).
If additional effects from for example tidal waves should be included in the HD
simulation the following additional steps are typical.
 Run the HD simulation with the tidal effects alone.

Normally this run will be made in a much larger model area (and with
larger grid spacing) than with the wave radiation stresses alone. This is
because the wave generated current is a very local phenomenon (the
surf zone) and accordingly has to be described in a very fine grid (nor-
mally less than 50 m in grid spacing), whereas the tide (long waves) can
be described with a much larger grid spacing. Very often the tidal infor-
mation to be used as boundary conditions is only known at stations rela-
tively far away from the local area of interest, and accordingly the model
area needs to be extended.
 Generate transfer boundary data (only contribution from the tide) for all
open boundaries in the local model area using the data transfer tool in
the MIKE 21 Toolbox.
 Superimpose the two contributions to the boundary data, using “Wave

Generated Current and Setup”.
 Run the final HD simulation.

Please note that this simulation needs a warm-up period before the wave
generated flow has become stationary. The length of the warm-up period
137
Reference Manual
is approximately the simulation period until stationarity has been

obtained in the HD simulation with the wave radiation stresses alone.
6.36 Wind Conditions
You can include the effects of a wind blowing over the model area in the fol-
lowing way. The driving force due to this wind is calculated from the following
quadratic law:
 air 2
C w --------------- W (6.37)
 water
where CW is the wind friction coefficient,  is the density (the ratio equals
1/800) and W is the wind velocity in m/s 10 m above the sea surface.
Note that the direction of the wind is given in degrees blowing from (relative
to true north (see Figure 6.33)).
Figure 6.33 Definition of wind direction
6.36.2 Specifying the wind conditions
The wind conditions can be specified in three ways:
 As a wind which is blowing from the same direction and with the same
magnitude over the whole model area for the whole simulation period.
 As a wind where the magnitude and direction varies during the simula-
tion period but is the same over the whole model area.
You have to prepare a data file (type 0) containing the wind speed and
direction before you set up the hydrodynamic simulation. This can be
done by entering the data in an ASCII file using your normal editor and

Wind Conditions
then reading this file into the standard data file format from the data file
editor.
The wind speed and wind direction must be given as two separate items
in the data file. The time step of the wind input data file does not, how-
ever, have to be the same as the time step of the hydrodynamic simula-
tion. A cubic interpolation will be applied if the time steps differ. The only
requirement is that the wind data be specified for the complete simulation
period.
In both cases you can specify a start up period during which the wind speed
is increased linearly from 0 to the specified wind speed in order to avoid
shock waves being generated in the model.
 As a wind where the magnitude and direction varies during the simula-
tion period and over the model area.
You have to prepare a data file (type 2) containing the wind speed com-
ponents and air pressure before you set up the hydrodynamic simulation.
This can be done by either using one of the two MIKE 21 wind generat-
ing programs (cyclone generated wind and pressure, or wind generated
on the basis of digitised pressure fields). Or you can enter the data in an
ASCII file using your normal editor and then reading this file into the
standard data file format from the data file editor.
The wind speed and pressure must be given as three separate items in
the data file. The first item should be the pressure in hPa, the two next
ones should be the wind speed in the x-direction and y-direction, respec-
tively. The time step of the wind input data file does not, however, have to
be the same as the time step of the hydrodynamic simulation.
A linear interpolation will be applied if the time steps differ. The only
requirements are that the wind map matches the bathymetry map and
that the wind data covers the complete simulation period.
In addition to the name of the wind data file you have to specify a refer-
ence or neutral pressure level. It is the pressure at the start of the simula-
tion when it is assumed to be constant over the whole model and the
initial surface is horizontal.
6.36.3 Specifying the wind friction
Normally a wind friction coefficient of 0.0026 will give good results for moder-
ate and strong winds in the open sea. For weak winds, however, smaller
coefficients can be used.
139
Reference Manual
If you specify a varying wind speed you might also need to specify a varying
friction coefficient. Consequently, the possibility of varying the friction coeffi-
cient linearly as a function of the wind speed is included, yielding

 c0 ; W  W0


Cw =  c +  c – c  -----------------------------
W – W0 
- ; W0  W  W1 (6.38)
 0 1 0
W1 – W0

 c1 ; W  W1

You can use the wind friction factor as a parameter in your model calibration.
Level boundaries can optionally be adjusted according to
level = boundary data –  P – P neutral    g  (6.39)
when you use pressure or elevation boundary variations.
6.37 List of References

Aupoix, B. Eddy Viscosity Subgrid Scale Models for Homogeneous Turbu-
lence, in Macroscopic Modelling of Turbulent Flow, Lecture Notes in Physics,
Proc. Sophie-Antipolis, France, 1984.
Fredsøe, J. Turbulent boundary layers in Combined Wave Current Motion. J.

Hydraulic Engineering, ASCE, Vol 110, No. HY8, pp. 1103-1120, 1984.
Horiuti, K. Comparison of Conservative and Rotational Forms in Large Eddy

Simulation of Turbulent Channel Flow, Journal of Computational Physics, 71,
pp 343-370, 1987.
Hungr, O. (1995). A model for the runout analysis of rapid flow slides, debris
flows, and avalanches. Canadian Geotechnical Journal, 32(4), 610-623.
Jeyapalan, J. K., Duncan, J. M., & Seed, H. B. (1983). Investigation of flow

failures of tailings dams. Journal of geotechnical engineering, 109(2), 172-
189.
Jones, O., Zyserman, J.A. and Wu, Yushi. Influence of Apparent Roughness
on Pipeline Design Conditions under Combined Waves and Current, Pro-
ceedings of the ASME 2014 33rd International Conference on Ocean, Off-
shore and Arctic Engineering, 2014.

List of References
Julien, P.Y. (2010) Erosion and Sedimentation, Second Edition. Cambridge

University Press. 2010.
Kofoed-Hansen, H., Giménez, E.C. and Kronborg, P. Modelling of landslide-

generated waves in MIKE 21, 4th DHI Software Conference, 2001.
Leonard, A. Energy Cascades in Large-Eddy Simulations of Turbulent Fluid

Flows, Advances in Geophysics, 18, pp 237-247, 1974.
Lilly, D.K. On the Application of the Eddy Viscosity Concept in the Inertial
Subrange of Turbulence, NCAR Manuscript No. 123, National Center for
Atmospheric Research, Boulder, Colorado, 1966.
Madsen, P.A., Rugbjerg, M. and Warren, I.R. Subgrid Modelling in Depth Inte-
grated Flows, Coastal Engineering Conference, 1, pp 505-511, Malaga,
Spain, 1988.
Naef, D., Rickenmann, D., Rutschmann, P., & McArdell, B. W. (2006). Com-
parison of flow resistance relations for debris flows using a one-dimensional
finite element simulation model. Natural Hazards and Earth System Science,
6(1), 155-165.
Pastor, M., Quecedo, M., González, E., Herreros, M. I., Merodo, J. F., & Mira,
P. (2004). Simple approximation to bottom friction for Bingham fluid depth
integrated models. Journal of Hydraulic Engineering, 130(2), 149-155.
Rodi, W. Turbulence Models and Their Application in Hydraulics - A State of

the Art Review, Special IAHR Publication, 1980.
Smagorinsky, J. General Circulation Experiment with the Primitive Equations,

Monthly Weather Review, 91, No. 3, pp 99-164, 1963.
Wang, J.D. Numerical Modelling of Bay Circulation, The Sea, Ocean Engi-
neering Science, 9, Part B, Chapter 32, pp 1033-1067, 1990.
141
Reference Manual

INDEX
143
Index
B Speed . . . . . . . . . . . . . . . . 135
Bridge . . . . . . . . . . . . . . . . 72
U
C Urban area . . . . . . . . . . . . . .50
Cell face . . . . . . . . . . . . 64, 133
Cold start . . . . . . . . . . . . . . . 49 V
Composite structures . . . . . . . . . 72 Velocity . . . . . . . . . . . . . . . 135
Culvert . . . . . . . . . . . . . . . . 67
Current . . . . . . . . . . . . . . . 135 W
Weir . . . . . . . . . . . . . . . . . .64
D
Data type . . . . . . . . . . . . . . 112
Dike . . . . . . . . . . . . . . . . . 69
E
Evaporation . . . . . . . . . . . . 57, 99
F
Froude number . . . . . . . . . . . 102
H
Hot start . . . . . . . . . . . . . . . 49
I
Infiltration . . . . . . . . . . . . . . . 58
Inland flooding . . . . . . . 48, 99, 101
Inundation statistics . . . . . . . . . 105
L
Landslide . . . . . . . . . . . . . 50, 84
Leakage . . . . . . . . . . . . . . . 59
M
Multi-cell overland solve . . . . . . . 109
Multi-cell overland solver . . . . . . . . 50
N
Nested model . . . . . . . . . . . . . 76
P
Precipitation . . . . . . . . . . . 57, 116
R
Rating curve . . . . . . . . . . . . . 56
Rural area . . . . . . . . . . . . . . 50
S
Shear stress . . . . . . . . . . . . 117

MIKE 21 Flow Model: Hydrodynamic Module

Uploaded by

Copyright:

Available Formats

MIKE 21 Flow Model: Hydrodynamic Module

Uploaded by

Document Information

Original Title

Copyright

Available Formats

Share this document

Share or Embed Document

Sharing Options

Did you find this document useful?

Is this content inappropriate?

Copyright:

Available Formats

MIKE 21 Flow Model: Hydrodynamic Module

Uploaded by

Copyright:

Available Formats

MIKE 21 Flow Model

COPYRIGHT This document refers to proprietary computer software which is pro-

'IN NO EVENT SHALL DHI OR ITS REPRESENTATIVES

6 MIKE 21 Flow Model - © DHI

8 MIKE 21 Flow Model - © DHI

10 MIKE 21 Flow Model - © DHI

1 About This Guide

This User Guide is complemented by the Online Help.

1.2 Assumed User Background

In this case, “common sense” means a background in coastal hydraulics and

12 MIKE 21 Flow Model - © DHI

2.1 General Description

The hydrodynamic module simulates water level variations and flows in

 bottom shear stress

2.1.1 Application areas

MIKE 21 Flow Model, Hydrodynamic Module, can be applied to a wide range

 modelling of tidal hydraulics

As mentioned previously, the MIKE 21 HD output results are also used as

As MIKE 21 HD is a very general hydraulic model, it can easily be set up to

 secondary circulations, eddies and vortices

14 MIKE 21 Flow Model - © DHI

 Wind set-up example:

Note: The Sound example is described in a separate document, which can

MIKE 21 Flow Model, Hydrodynamic Module, Step-by-Step Training Guide

3.2 Wind Set-up in a Rectangular Lake

3.2.1 Defining the model

The problem is to determine the wind set-up in a lake.

The test conditions are:

 The lake is rectangular in shape with a length of 5 km in the east/west

Figure 3.1 Wind set-up in a small lake, model layout

Additional information required by MIKE 21 is:

3.2.2 Extracting data for plotting

16 MIKE 21 Flow Model - © DHI

Figure 3.2 Time series of the wind set-up in a rectangular lake

3.2.3 Evaluating the results

3.3 Donegal Bay

3.3.1 Purpose of the study

From the specifications for the study we quote:

“The existing drainage system in Donegal town is a combined system

In order to do the required investigation a number of different MIKE 21 mod-

3.3.2 Defining the hydrodynamic model

The model area was chosen based on the following considerations:

18 MIKE 21 Flow Model - © DHI

The time step was chosen to be 60 seconds, as this results in a maximum

3.3.3 Collecting data

Tidal measurements, collection of wind data and measurements of flow in the

3.3.4 Setting up the model

Figure 3.4 Model bathymetry, Donegal Bay

Simultaneous measurements of the water level close to the open boundary

3.3.5 Calibrating and verifying the model

20 MIKE 21 Flow Model - © DHI

Figure 3.5 Flow pattern during verification simulation at Donegal Bay

Most of the calibration work consisted of obtaining a correct schematisation of

3.3.6 Running the production simulations

3.3.7 Presenting the results

3.3.8 List of data and specification files

The following data files are supplied with MIKE 21:

22 MIKE 21 Flow Model - © DHI

3.4 Retention Basin by River