MIKE 21 BW
Boussinesq Waves Module
User Guide
MIKE 2017
2
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3
4 MIKE 21 BW - © DHI
1 About This Guide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2 Assumed User Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1 General Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Application Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Getting Started . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
3.2 Defining and Limiting the Wave Problem . . . . . . . . . . . . . . . . . . . . . 17
3.2.1 Identify the wave problem . . . . . . . . . . . . . . . . . . . . . . . 17
3.2.2 Check MIKE 21 BW capabilities . . . . . . . . . . . . . . . . . . . . 18
3.2.3 Selecting model area spectral and temporal resolution . . . . . . . . 18
3.2.4 Check computer resources . . . . . . . . . . . . . . . . . . . . . . . 19
3.3 Collecting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4 Setting up the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4.1 What does it mean . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.4.2 Bathymetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4.3 Sponge layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4.4 Porosity layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.4.5 Boundary data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5 Calibrating and Verifying the Model . . . . . . . . . . . . . . . . . . . . . . . 20
3.5.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
3.5.2 Verification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.5.3 Calibration parameters . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.6 Running the Production Simulations . . . . . . . . . . . . . . . . . . . . . . . 21
3.7 Presenting the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.8 A Quick Guide for MIKE 21 BW Model Simulation Setup . . . . . . . . . . . . 22
4 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
4.2 2DH Boussinesq Wave Module - Examples . . . . . . . . . . . . . . . . . . . 26
4.2.1 Numerical flume test . . . . . . . . . . . . . . . . . . . . . . . . . . 26
4.2.2 Diffraction test . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.2.3 Rønne Harbour . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
4.2.4 Hanstholm Harbour . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
4.2.5 Torsminde Harbour . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.2.6 Island . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
4.2.7 Rip channel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
4.2.8 Detached breakwater . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.2.9 Kirkwall Marina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
4.2.10 Demo-Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.3 1DH Boussinesq Wave Module - Examples . . . . . . . . . . . . . . . . . . . 94
4.3.1 Partial wave reflection . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.3.2 Sloping beach with wave breaking and moving shoreline . . . . . . . 98
4.3.3 Torsminde barred beach . . . . . . . . . . . . . . . . . . . . . . . 102
5
5 Reference Manual . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.2 Basic Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
5.2.1 Module selection . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
5.2.2 Bathymetry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
5.2.3 Type of equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
5.2.4 Numerical parameters (2DH only) . . . . . . . . . . . . . . . . . . 119
5.2.5 Boundary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
5.2.6 Simulation period . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
5.3 Calibration Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
5.3.1 Bathymetric parameters . . . . . . . . . . . . . . . . . . . . . . . 124
5.3.2 Boundary data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
5.3.3 Surface elevation . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
5.3.4 Internal wave generation . . . . . . . . . . . . . . . . . . . . . . . 127
5.3.5 Bottom friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
5.3.6 Eddy viscosity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
5.3.7 Filtering . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 135
5.3.8 Wave Breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5.3.9 Moving shoreline . . . . . . . . . . . . . . . . . . . . . . . . . . . 139
5.3.10 Porosity layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
5.3.11 Sponge layers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148
5.4 Output Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
5.4.1 Deterministic parameters . . . . . . . . . . . . . . . . . . . . . . . 152
5.4.2 Phase-averaged parameters . . . . . . . . . . . . . . . . . . . . . 158
5.4.3 Wave disturbance parameters . . . . . . . . . . . . . . . . . . . . 164
5.4.4 Moving shoreline parameters . . . . . . . . . . . . . . . . . . . . 167
5.4.5 Hot start Parameters . . . . . . . . . . . . . . . . . . . . . . . . . 169
5.5 Entries Arranged Alphabetically . . . . . . . . . . . . . . . . . . . . . . . . 170
5.5.1 Application Progress Visualization (APV) . . . . . . . . . . . . . . 170
5.5.2 Artificial land . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 171
5.5.3 Batch mode . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 172
5.5.4 Blow-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
5.5.5 Boussinesq cross terms . . . . . . . . . . . . . . . . . . . . . . . 177
5.5.6 Courant number . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.5.7 Deep water terms . . . . . . . . . . . . . . . . . . . . . . . . . . 178
5.5.8 First time model set-up . . . . . . . . . . . . . . . . . . . . . . . . 178
5.5.9 Hardware requirements . . . . . . . . . . . . . . . . . . . . . . . 180
5.5.10 High-frequency noise . . . . . . . . . . . . . . . . . . . . . . . . . 181
5.5.11 Linear dispersion relation . . . . . . . . . . . . . . . . . . . . . . 182
5.5.12 Mesh generation . . . . . . . . . . . . . . . . . . . . . . . . . . . 182
5.5.13 Minimum wave period . . . . . . . . . . . . . . . . . . . . . . . . 183
5.5.14 Numerical damping . . . . . . . . . . . . . . . . . . . . . . . . . . 184
5.5.15 Option parameters . . . . . . . . . . . . . . . . . . . . . . . . . . 186
5.5.16 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 186
6 Scientific Documentation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
6 MIKE 21 BW - © DHI
Purpose
1 About This Guide
1.1 Purpose
The main purpose of this User Guide is to enable you to use the Boussinesq
Wave modules included in MIKE 21 BW, for determination and assessment of
wave dynamics in ports, harbours and in coastal areas. The User Guide is
complemented by the Online Help.
Chapter 2 Introduction (p. 9), gives you a general description of the modules
included in MIKE 21 BW and type of typical applications.
Chapter 3 Getting Started (p. 17), contains a step-by-step procedure which
can be followed when working on an application or when writing a proposal. It
is the intention that by following this procedure and by using the Reference
Manual you should be able to get good and reliable results from MIKE 21 BW
although a formal procedure is no substitute for common sense.
Chapter 4 Examples (p. 25) includes a number of simple and more complicated MIKE 21 BW applications. These are chosen to cover typical application areas of MIKE 21 BW. The emphasis in these examples is on how the
parameters are selected and how the results are presented.
Chapter 5 Reference Manual (p. 109) describes the parameters in the MIKE
21 BW dialogues. It provides more details on specific aspects of the operation of MIKE 21 BW and is what you will normally refer to for assistance if you
are an experienced user. The contents of this chapter is the same as found in
the Online Help.
In Chapter 6 Scientific Documentation (p. 191), you can find information on
where to find the scientific background for MIKE 21 BW.
An INDEX is found at the very end of this MIKE 21 BW User Guide.
1.2 Assumed User Background
Although MIKE 21 BW has been designed carefully with emphasis on a logical and user-friendly interface and although the User Guide 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 wave mechanics which
is sufficient for you to be able to check whether the results from MIKE 21 BW
are reasonable or not. This User Guide is not intended as a substitute for and it cannot replace - a basic knowledge of the area in which you are working: mathematical modelling of complex wave problems.
7
About This Guide
It is assumed that you are familiar with the basic elements of MIKE Zero: File
types and file editors, the Plot Composer, the MIKE Zero Toolbox, the MIKE
21 Toolbox and the Bathymetry Editor. The documentation for these can be
found from the MIKE Zero Documentation Index.
A step-by-step training guide on how to set up a MIKE 21 BW for a typical
application is also available from the same place.
8 MIKE 21 BW - © DHI
General Description
2 Introduction
2.1 General Description
The two modules included in the MIKE 21 BW are based on the numerical
solution of time domain formulations of Boussinesq type equations. The
Boussinesq equations include nonlinearity as well as frequency dispersion.
Basically, the frequency dispersion is introduced in the momentum equations
by taking into account the effect of vertical accelerations on the pressure distribution. Both modules solve the Boussinesq type equations using a flux-formulation with improved linear dispersion characteristics. These enhanced
Boussinesq type equations (originally derived by Madsen et al, 1991, and
Madsen and Sørensen, 1992)
the propagation of directional wave trains travelling from deep to shallow
water. The maximum depth to deep-water wave length is h/L
classical Boussinesq equations the maximum depth to deep-water wave
length is h/L
0.22.
0
(1)
make the modules suitable for simulation of
0.5. For the
0
The model has been extended into the surf zone by inclusion of wave breaking and moving shoreline as described in Madsen et al (1997a,b)
Sørensen and Sørensen (2001)
Figure 2.1 MIKE 21 BW is a state-of-the-art numerical tool for studies and ana-
lysis of short and long period waves in ports and harbours and coastal
areas
(1)
and Sørensen et al (1998, 2004).
(1)
,
1 The papers are included in the Scientific Documentation
9
Introduction
MIKE 21 BW is capable of reproducing the combined effects of all important
wave phenomena of interest in port, harbour and coastal engineering. These
include:
Shoaling
Refraction
Diffraction
Wave breaking
Bottom friction
Moving shoreline
Partial reflection and transmission
Non-linear wave-wave interaction
Frequency spreading
Directional spreading
Phenomena, such as wave grouping, surf beats, generation of bound subharmonics and super-harmonics and near-resonant triad interactions, can
also be modelled using MIKE 21 BW. Thus, details like the generation and
release of low-frequency oscillations due to primary wave transformation are
well described in the model. This is of significant importance for harbour resonance, seiching and coastal processes.
Figure 2.2 Simulation of wave propagation and agitation in a harbour area for an
extreme wave event. The breaking waves (surface rollers) are shown in
white
The present release of MIKE 21 BW includes two modules:
2DH Boussinesq Wave Module
1DH Boussinesq Wave Module
10 MIKE 21 BW - © DHI
General Description
The 2DH module (two horizontal space co-ordinates) solves the enhanced
Boussinesq equations by an implicit finite difference technique with variables
defined on a space-staggered rectangular grid.
The 1DH module (one horizontal space co-ordinates) solves the enhanced
Boussinesq equations by a standard Galerkin finite element method with
mixed interpolation for variables defined on an unstructured (or a structured)
grid. Surf zone dynamics and swash zone oscillations can be simulated for
any coastal profile in this module.
Figure 2.3 The MIKE 21 BW includes two modules. The 2DH module (left panel) is
traditionally applied for calculation of wave disturbance in ports and harbours. The 1DH module (right panel) is selected for calculation of wave
transformation from offshore to the beach for the study of surf zone and
swash zone dynamics
MIKE 21 BW also includes porosity for the simulation of partial reflection from
and transmission through piers and breakwaters. Sponge layers are applied
when full absorption of wave energy is required. Finally, MIKE 21 BW also
includes internal generation of waves.
2.1.1 Application Areas
A major application area of MIKE 21 BW is determination and assessment of
wave dynamics in ports and harbours and in coastal areas. The disturbance
inside harbour basins is one of the most important factors when engineers
are to select construction sites and determine the optimum harbour layout in
relation to predefined criteria for acceptable wave disturbance, ship movements, mooring arrangements and handling down-time.
With inclusion of wave breaking and moving shoreline MIKE 21 BW is also an
efficient tool for the study of many complicated coastal phenomena, e.g.
wave induced-current patterns in areas with complex structures.
2DH Boussinesq wave module
Applications related to the 2DH module include:
determination of wave disturbance caused by wind-waves and swell
11
Introduction
analysis of low-frequency oscillations
(seiching and harbour resonance) caused by forcing of e.g. short-wave
induced long waves
wave transformation in coastal areas where reflection and/or diffraction
are important phenomena
Surf zone calculations including wave-induced circulation and run-
up/run-down
simulation of propagation and transformation of transients such as ship-
generated waves and tsunamis
Assessment of low-frequency motions in existing as well as new harbours is
often performed using a combination of simulations with synthetic white-noise
spectra and simulations with natural wave conditions. The purpose of the former type of simulations is to investigate the potential of seiching/resonance
and identification of natural frequencies. This is particularly useful for relative
comparisons between different layouts.
MIKE 21 BW is also applied for prediction and analysis of the impact of shipgenerated waves (also denoted as wake wash). Essential boundary conditions (at open or internal boundaries) for the models can be obtained from 3D
computational fluid dynamic (CFD) models, experimental data, full-scale data
and/or empirical relationships.
12 MIKE 21 BW - © DHI
General Description
Figure 2.4 Simulation of wave penetration into Frederikshavn harbour, Denmark
13
Introduction
Figure 2.5 Wave transformation, wave breaking and run-up in the vicinity of a
detached breakwater parallel to the shoreline. The lower image shows
the associated circulation cell behind the breakwater
1DH Boussinesq wave module
Applications related to the 1DH module include:
computation of wave transformation for nonlinear waves from deep
water, through the surf zone and all the way up to the beach.
analysis of generation and release of low-frequency waves.
assessment of wave breaking, undertow and run-up on dikes, revet-
ments and beaches.
The 1DH module can be applied for a number of transects (one spatial
dimension) where surf zone dynamics and swash zone dynamics are simulated in real-time.
14 MIKE 21 BW - © DHI
General Description
With the inclusion of wave breaking not only the spatial variation of e.g. the
significant wave height, maximum wave height and wave setup on the beach
can be computed, but also details like the generation and release of low-frequency energy due to primary wave transformation can be computed. This is
of significant importance for harbour resonance (seiching) and coastal processes.
Figure 2.6 Transformation of irregular non-linear waves over a natural barred
beach profile (upper panel). Offshore (left) and onshore (right) frequency wave spectra (lower panels). The spectra are computed using
the WSWAT Linear Spectral Wave Analysis module included in MIKE
Zero
15
Introduction
16 MIKE 21 BW - © DHI
General
3 Getting Started
3.1 General
The purpose of this chapter is to give you a general check list, which you can
use for determination and assessment of wave dynamics in ports, harbours
and coastal areas using the MIKE 21 Boussinesq Wave model.
The work will normally consist of the six tasks listed below:
Defining and limiting the wave problem
Collecting data
Setting up the model
Calibrating and verifying the model
Running the production simulations
Presenting the results
Each of these six tasks are described for a “general wave study” in the following sections. For your particular study only some of the tasks might be relevant.
Please note that whenever a word is written in italics it is included as an entry
in the Online Help and in the Reference Manual.
3.2 Defining and Limiting the Wave Problem
3.2.1 Identify the wave problem
When preparing to do a study of e.g. wave disturbance in a harbour, you have
to assess the following before you start to set up the model:
What are the “wave conditions” under consideration in the “area of inter-
est”?
What are the “important wave phenomena”? The following phenomena
should be taken into consideration:
– Shoaling
– Refraction
– Diffraction
– Partial reflection/transmission
– Bottom dissipation
– Wave breaking
– Run-up
– Wind-wave generation
– Frequency spreading
17
– Directional spreading
– Wave-wave interaction
– Wave-current interaction
The MIKE 21 BW module can handle these phenomena with the
exception of wind-wave generation.
3.2.2 Check MIKE 21 BW capabilities
Next, check if the MIKE 21 BW module is able to solve your problem. This
you can do by turning to Chapter 2, which gives a short description of MIKE
21 BW and an overview of the type of applications for which MIKE 21 BW can
be used, and by consulting the Scientific Documentation, section 6.
3.2.3 Selecting model area spectral and temporal resolution
When selecting the model area (or profile) you must consider the area of
interest, the alignment of the model grid relative to the main direction of
approach of the incident wave trains and the position and types of model
boundaries to be used, see Selecting the Model Area under Bathymetry.
Getting Started
The choice of the grid spacing and time step depends on the wave conditions
for which simulations are to be performed and the water depth in the area of
interest.
The ratio of the maximum water depth to the deep water wave length of
waves with the shortest wave period must not become larger than 0.22, if
the deep water correction terms are excluded, and 0.5, if these terms are
included. See Linear Dispersion Relation
The grid spacing is restricted by the resolution of the shortest wave
length or the surface roller, if wave breaking is included. See Selecting
Grid Spacing under Bathymetry
The time step is restricted by the resolution of the shortest wave period.
See Time Step
The Courant number should be kept equal or less than unity (0.5 for the
1DH module) to avoid instability problems. See Courant Number
In practice the choice of the grid spacing and time step is often a compromise
between low computer costs and high accuracy.
The MIKE 21 BW Model Setup Planner (Figure 5.7) is an efficient tool for the
setup of your model.
18 MIKE 21 BW - © DHI
Collecting Data
3.2.4 Check computer resources
Finally, before you start to set up the model, you should check that you are
not requesting unrealistic computer resources:
The CPU time required should be estimated.
The RAM requirements should be estimated.
The Disk Space required should be estimated.
An estimate of the required CPU and RAM can easily be obtained using the
MIKE 21 BW Model Setup Planner integrated in the Online Help. The disk
space is assessed through the MIKE 21 BW Editor.
Particularly when wave breaking and moving shoreline are included in the
2DH module (space resolution is 1-2 m and temporal resolution 0.02-0.2 s as
typically values) the required CPU time and memory demand can be high (>
12 hours) for large computational domains.
3.3 Collecting Data
This task may take a long time if, for example, you have to initiate a monitoring program. Alternatively it may be carried out very quickly if you are able to
use existing data which are immediately available. In all cases the following
data should be collected:
Bathymetric data such as charts from local surveys or, for example, from
the Hydrographic Office, UK, or MIKE C-MAP
Boundary data, which might be measurements (existing or planned spe-
cifically for your model), observations, wave statistics, etc.
Information on type of structures for assessment of the reflection proper-
ties
Calibration and validation data; these might be measured wave parame-
ters at selected locations, observations, etc.
3.4 Setting up the Model
3.4.1 What does it mean
“Setting up the model” is actually another way of saying transforming real
world events and data into a format which can be understood by the numerical model MIKE 21 BW. Thus generally speaking, all the data collected have
to be resolved on the spatial grid selected.
19
3.4.2 Bathymetry
You have to specify the bathymetry as a type 2 or type 1 data file containing
the water depth covering the model area. Describing the water depth in your
model is one of the most important tasks in the modelling process. A few
hours less spent in setting up the model bathymetry may later on mean extra
days spent in the calibration process.
3.4.3 Sponge layer
In practical for all MIKE 21 BW applications you have to prepare maps (2DH,
dfs2-file) or profile series (1DH, dfs1-file) for efficient absorbtion of short and
long period waves, see section 5.3.11 (Sponge layers).
3.4.4 Porosity layer
Modelling of partial reflection/transmission requires preparation of maps
(2DH) or files (1DH) including porosity layers. An efficient procedure is outlined in section 5.3.10 (Porosity layers).
Getting Started
3.4.5 Boundary data
In most cases you will force the model by waves generated inside the model
domain. The internal wave generation of waves allows you to absorb all
waves leaving the model domain (radiation type boundaries).
3.5 Calibrating and Verifying the Model
3.5.1 Purpose
Having completed all the tasks listed above you are ready to do the first timedomain wave simulation and to start on the calibration of the model.
The purpose the calibration is to tune the model in order to reproduce
known/measured wave conditions. The calibrated/tuned model is then verified by running one or more simulations for which measurements are available without changing any tuning parameters. This should ensure that
simulations can be made for any wave conditions similar to the calibration
and verification wave conditions with satisfactory results. However, you
should never use simulation results, whether verified or not, without checking
if they are reasonable or not.
20 MIKE 21 BW - © DHI
Running the Production Simulations
3.5.2 Verification
The situations which you select for calibration and verification of the model
should cover the range of situations you wish to investigate in the production
runs. However, as you must have some measurements/observations against
which to calibrate and, as the measurements are often only available for short
periods, you may only have a few situations from which to choose.
When you have finished the calibration you can run one more simulation for
which you have measurements (or other data) without changing the calibration parameters. If you then get a satisfactory agreement between the simulation results and the measurements you can consider your calibration to be
successful.
3.5.3 Calibration parameters
When you run your calibration run for the first time and compare the simulation results to your measurements (or other information) you will, in many
cases, see differences between the two. The purpose of the calibration is
then to tune the model so that these differences become negligible. You can
change the following model specifications in order to reduce the differences:
Wave conditions
Porosity
Bed resistance
Bathymetry
Wave breaking
Moving shore line
Recommendations on how the specification can be changed are given in the
Reference Manual.
3.6 Running the Production Simulations
As you have calibrated and verified the model you can get on to the “real”
work, that is doing your actual investigation. This will, in some cases, only
include a few runs.
3.7 Presenting the Results
Throughout a modelling study you are working with large amounts of data
and the best way of checking them is therefore to look at them graphically.
Only in a few cases, such as when you check your bathymetry along a
boundary or you want to compare simulation results to measurements in
selected locations, should you look at the individual numbers. Much empha-
21
Getting Started
sis has therefore been placed on the capabilities for graphical presentation in
MIKE Zero and it is an area which will be expanded and focused on even further in future versions (e.g. GIS).
Essentially, one plot gives more information than scores of tables and if you
can present it in colours, your message will be even more easily understood.
A good way of presenting the model results is using contour plots of e.g. the
calculated wave disturbance coefficient by using the Plot Composer tool in
MIKE Zero.
Instantaneous pictures/videos of the simulated surface elevations can also be
generated in the Plot Composer. For 3D visualisation MIKE Animator Plus is
recommended.
3.8 A Quick Guide for MIKE 21 BW Model Simulation Setup
This section includes a chronological list of tasks you should pass through
when setting up a MIKE 21 BW model simulation. Emphasis is put on applications using the 2DH module.
In addition a step-by-step training guide on how to set up a MIKE 21 BW
model for a typical application can be accessed online via the Documentation
index.
Providing MIKE21 BW with a suitable bathymetry (dfs2 data file for 2DH
applications and dfs1 data file for 1DH applications) is essential for obtaining
reliable results from the model. Based on available xyz data for the area of
interest you create the model bathymetry by use of the MIKE Zero tool
Bathymetry Editor. The above mentioned step-by-step guide shows how to
generate a bathymetry from scratch.
1. When setting up the bathymetry it should be kept in mind that the
bathymetry determines which wave conditions that can be modelled. The
maximum water depths restrict the minimum wave period that can be
modelled and the minimum water depth may restrict the wave height if
wave breaking is not included. Therefore it can be necessary to modify
the bathymetry to reach an acceptable compromise between a correct
bathymetry and correct wave conditions. Please use the MIKE 21 BW
Model Setup Planner Java Script embedded in the Online Help when
you are setting up the bathymetry.
Following ranges of grid spacing are typically used in practical applications
– x = 2-10 m for the 2DH module without wave breaking
– x = 1-2 m for the 2DH module including wave breaking and moving
shoreline
22 MIKE 21 BW - © DHI
A Quick Guide for MIKE 21 BW Model Simulation Setup
– x = 0.1-10 m for the 1DH module (unstructured mesh) with wave
breaking and moving shoreline
The next step is to generate a sponge layer map. Sponge (or absorbing) layers are used as wave absorbers. These may be set up along model boundaries to provide radiation boundary conditions, which absorb wave energy
propagating out of the model area. Sponge layers may also be used along
shorelines (see e.g. the Rønne Harbour example and Torsminde Harbour
example in this User Guide). The sponge layer map is easily created using
the MIKE 21 Toolbox Generate Sponge and Porosity Layer Map tool.
2. For simulation of partial wave reflection and/or wave transmission
through various types of structures you would need to create a porosity
layer map. The porosity layer map includes a porosity, which is set to
unity at open water points (no dissipation) and between 0.2 and 1 along
structures where you want to include the dissipation effect of porous flow.
If a porosity value is backed up a land value (> 0), partial reflection will
take place. Conversely, (partial) transmission will also take place if land
points do not back up the porosity values.
An efficient step-by-step procedure for establishment of a porosity map is
described in this User Guide, see Section 5.3.10. The porosity map is
easily created using the MIKE 21 Toolbox Generate Sponge and
Porosity Layer Map tool. The porosity values are calculated using the
MIKE 21 Toolbox Calculation of Reflection Coefficient.
3. If wave breaking and moving shoreline is included you would most often
also have to specify a map (2DH, dfs2 data file) or profile (1DH, dfs1 data
file) including filter coefficients. This lowpass filter is introduced to
remove high-frequency instabilities during uprush/downrush and to dissipate the wave energy in the area where the surface rollers can not be
resolved properly.
4. Next step is to prepare wave boundary conditions for the model. In most
applications you will force the model by waves generated inside the
model domain, i.e. using internal wave generation. Internal wave generation is performed by adding the discharge of an incident wave field along
one or more generation lines. One of the advantages of using internal
generation is that sponge layers can be placed behind the generation
line, to absorb waves leaving the model domain (radiation type boundary).
5. The format of the internal wave generation data depends on type
of
waves; regular, irregular or directional. For generation of regular wave
data you should use the MIKE 21 Toolbox Regular Wave Generation
tool and for irregular and directional waves MIKE 21 Toolbox Random
23
Getting Started
Wave Generation.
6. Now you are ready to set up up your Boussinesq model run; open MIKE
Zero New MIKE 21 Boussinesq Waves. It is recommend using
the default values in the dialogs in your first model run. If you have
decided to include the deep water terms during your model setup (i.e.
allowance of shorter waves) then the deep water terms should of course
be included in the “Type of Equation” dialog. Regarding specification of
output parameters it is recommended to save maps (dfs2 files) and time
series (dfs0 files) of both deterministic parameters (e.g. the surface elevation) and phase-averaged parameters (e.g. the significant and maximum wave height). For harbour agitation studies also maps of the wave
disturbance coefficient should be saved.
7. It is recommended to view the results during the model run to make sure
everything is as expected. This can be made directly from the editor by
clicking on the “View” button, which automatically opens an editor for
viewing the model results.
8. After the simulation you can use various visualization tools included in
MIKE Zero for result presentation. Use e.g. the Plot Composer Grid
Plot for creation of plots and 2D animations of wave disturbance coefficient and instantaneous surface elevation. For 3D visualization MIKE
Animator Plus is recommended (license required).
9. Additional analysis (of both dfs0 and dfs2 data) including spectral, direc-
tional, filtering or crossing analysis of the model output can be made
using the WS Wave Analysis Tool in MIKE Zero (license required).
24 MIKE 21 BW - © DHI
General
4 Examples
4.1 General
One of the best ways of learning how to use a modelling system like MIKE 21
is through practice. Therefore we have included a number of applications for
each of the two modules which you can go through yourself and which you
can modify, if you like, in order to see what happens if some of the parameters are changed.
The specification data files for the examples are included with the installation
of MIKE 21. For each example a directory is provided. The directory names
are as follows:
2DH Boussinesq Wave Module
Numerical flume test:
Diffraction test:
.\Examples\MIKE_21\BW\Flume
.\Examples\MIKE_21\BW\Diffraction
Rønne Harbour:
.\Examples\MIKE_21\BW\Ronne
Hanstholm Harbour:
.\Examples\MIKE_21\BW\Hanstholm
Torsminde Harbour:
.\Examples\MIKE_21\BW\Torsminde_Harbour
Island:
.\Examples\MIKE_21\BW\Island
Rip channel:
.\Examples\MIKE_21\BW\Rip_Channel
Detached breakwater:
.\Examples\MIKE_21\BW\Detached_Breakwater
Kirkwall Marina
.\Examples\MIKE_21\BW\Kirkwall_Marina
Demo-Diffraction
.\Examples\MIKE_21\BW\Demo-Diffraction
1DH Boussinesq Wave Module
Partial reflection test:
.\Examples\MIKE_21\BW\Partial_Reflection
25
Sloping beach with wave breaking and moving shoreline:
.\Examples\MIKE_21\BW\Sloping_Beach
Barred beach with wave breaking:
.\Examples\MIKE_21\BW\Torsminde_Barred_Beach
Please note that the layout of some figures and illustrations presented in this
release of the User Guide is optimised for the integrated Online Help and digital version of this User Guide.
4.2 2DH Boussinesq Wave Module - Examples
4.2.1 Numerical flume test
Purpose of the example
This fairly simple example is included to illustrate the propagation of irregular
waves in a numerical wave flume using the 2DH Boussinesq Wave Module.
Model setup
Examples
The model setup is illustrated in Figure 4.1. The length (in the model
east/west direction) of the flume is 350 m and the width (in the model north
/south direction) is 55 m. The uniform depth is 10 m.
Figure 4.1 Model layout. The 10 point wide areas indicate sponge layers and the
line at j=12 indicates the internal wave generation line
The waves are generated internally inside the model domain, which is the
most common method of forcing a Boussinesq wave model in practical applications. Thus, all model boundaries are closed, i.e. considered as land
points. At the generation line (j= 12) a time series of fluxes is imposed. This
time series is generated using the MIKE 21 Toolbox (wave part) program
Random Wave Generation. The significant wave height is H
spectral peak period is T
=10 s. The waves are synthesised based on a
p
mean JONSWAP spectrum. As the minimum wave period is T
= 1 m and the
m0
= 6 s, the
min
26 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
problem can be solved using the classical Boussinesq equations (i.e. the dispersion coefficient is B= 0).
The grid spacing is selected to be 5 m and the time step is 0.5 s. The simulation duration is 10 minutes (1201 time steps).
Although a 10 point thick sponge layer is used in this example you are in general recommended to apply at least 20 point wide sponge layers in most practical applications of the 2DH Boussinesq Wave Module. Excellent wave
absorbing characteristics have been obtained for sponge layers having a
thickness of 1-2 times the wave length of the most energetic waves (corresponding to the spectral peak wave period). In this example the thickness of
the 10 point wide sponge layer is 0.5-0.6 times the wave length corresponding to the spectral peak wave period. However, from the results shown in
Figure 4.2 (panel showing the significant wave height) it is hard to detect any
spurious reflections from the sponge layers.
Model results
A time series of the simulated surface elevation extracted at point P(35,5) is
shown in Figure 4.2, as well as the spatial variation of the significant wave
height along the channel. Note that the significant wave height is less than 1
m as the incident wave spectrum is not re-scaled.
Figure 4.2 Model results. Time series of simulated surface elevation at a given
point (upper panel) and line series of the stationary significant wave
height along the centre line (lower panel)
27
List of data and parameter files
All data required for this example is included in the default installation:
Binary data files
Name: Layout.dfs2
Description: Bathymetry and sponge layer coefficients
Name: IBC.dfs0
Description: Boundary conditions – time series of flux and surface elevation
Parameter files
Name: Flume.bw
Description: Numerical Flume test
4.2.2 Diffraction test
Purpose of the example
This example is included to illustrate the phenomenon of diffraction. Diffraction is an important process in regions, which are sheltered by barriers such
as breakwaters, jetties or inlets.
Examples
slope
The example describes what happens when a single fully reflecting breakwater interrupts a regular wave train.
Model setup
The model setup is illustrated in Figure 4.3. The model size is 1200 m by 700
m with a uniform depth of 40 m. Wave absorbing sponge layers are applied at
the eastern and northern model boundary, while the western boundary is
treated as fully reflective. The area of interest is the shadow zone behind the
breakwater. Due to radiation of energy from the point of diffraction the western boundary has to be placed quite far from this area to avoid reflections.
28 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.3 Model layout. The 10 point wide areas indicate sponge layers and the
line at k=0 the open essential boundary. The thickness of the sponge
layer is about one times the wave length
At the open south boundary a flux boundary is applied. Sinusoidal waves with
a wave period of 8 s and wave height of 1m is generated. According to linear
theory the wave length is approximately 100 m. Thus, the simulation requires
the so-called “deep-water terms” to be included, i.e. it is the enhanced Boussinesq type equations which have to be solved in this case.
The grid spacing is chosen to be 10 m representing the waves with approximately 10 points per wave length. The time step is chosen to be 0.25 s representing the waves with 32 points per wave period.
The simulation period is chosen to be 200 s corresponding to 800 time steps.
Model results
The model results are presented in Figure 4.4 showing a contour plot of the
instantaneous surface elevation and a map showing the isolines of the wave
disturbance coefficient in the entire domain.
29
Examples
Figure 4.4 Model results. The upper panel shows the instantaneous surface eleva-
tion and the lower panel the wave disturbance coefficient behind a fully
reflective breakwater
The model results are in good agreement with semi-analytical solutions to the
Helmholtz equation, see e.g. Shore Protection Manual (1984), see section
5.5.16.
List of data and parameter files
All data required for this example are included in the default installation:
30 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Binary data files
Name: Layout.dfs2
Description: Bathymetry and sponge layer coefficients
Name: Bc.dfs0
Description: Boundary conditions – time series of surface elevation and its
curvature
Parameter files
Name: Diffraction.bw
Description: Diffraction test
4.2.3 Rønne Harbour
Purpose of the example
The purpose of this example is to simulate the wave disturbance in Rønne
harbour, Denmark, situated in the Baltic Sea. Of special interests is wave disturbance at the new cruise terminal, see Figure 4.5.
Figure 4.5 Right panel shows the new cruise ship terminal in Rønne harbour, Den-
Model setup
The model setup is illustrated in Figure 4.6.
The model area is chosen based on following considerations:
The model is turned –22.5° relative to true north to align the model grid relative to the main direction of the approach of incoming waves.
mark. Left panel shows the harbour layout before the cruise terminal
was constructed
31
Examples
To reduce the number of water points artificial land is introduced outside the
main breakwaters of the entrance leaving only a small area outside the harbour from where the waves can enter the harbour. This limits the application
to unidirectional incoming waves from direction WSW (247.5° N).
Artificial land is also introduced in the innermost part of the harbour. This area
is backup by a 10 point wide sponge layer in order to absorb the waves here.
In reality the waves will break at a small beach here, but this will not affect the
waves in the central part of the harbour.
Figure 4.6 Model setup for Rønne Harbour. Upper panel shows the bathymetry,
the middle panel the absorbing sponge layers (10 point wide) and the
lower panel the areas where partial wave reflection is required (3-5
point wide)
The maximum water depth is approximately 11 m in the model area. The
event to be simulated corresponds to a situation occurring 10 hours per year
(on average) and is characterised by having a significant wave height of H
32 MIKE 21 BW - © DHI
m0
2DH Boussinesq Wave Module - Examples
= 2.65 m with a spectral peak period is Tp = 8.6 s. The waves are synthesised
based on a mean JONSWAP spectrum, as the minimum wave period is set to
T
= 5.7s. The wave disturbance problem can be solved using the classical
min
Boussinesq equations (i.e. B= 0). Please note that the truncated wave spectrum is not rescaled, i.e. the incoming wave height is less than 2.65 m.
A grid spacing of 5 m is chosen and a time step of 0.4 s. This results in a
maximum Courant number of 1 in the deepest part of the model. The length
of the simulation is 12 minutes (corresponding to 1801 time steps).
Model results
The model results are presented in Figure 4.7 showing a contour plot of the
instantaneous surface elevation and a map showing the isolines of the simulated wave disturbance coefficients (after 12 minutes).
Figure 4.8 shows a 3D plot of the instantaneous surface elevation for entire
harbour.
The wave disturbance coefficient along the main quay wall of the cruise terminal is 0.05-0.20 for this event. Other statistics (max., min., mean, std. dev.
and number of data) for the two areas defined in the area code map file can
be found in the ASCII file named WaveDisturbanceAlongNewQuay.txt.
33
Examples
Figure 4.7 Model results. The upper panel shows the instantaneous surface eleva-
tion and the lower panel the wave disturbance
Figure 4.8 3D picture of the simulated instantaneous surface elevation in Rønne
harbour
34 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
List of data and parameter files
All data required for this example are included in the default installation:
Binary data files
Name: Layout1998.dfs2
Description: Bathymetry, sponge layer and porosity coefficients
Name: Ibc.dfs0
Description: Boundary conditions – time series of flux
Name: CodeMap.dfs2
Description: Area code map
Parameter files
Name: Ronne1998.bw
Description: Wave disturbance test
4.2.4 Hanstholm Harbour
Purpose of the example
The purpose of this example is primarily to illustrate how to use two internal
generation lines for obliquely incident unidirectional waves. Hanstholm harbour, Denmark, situated at the Danish west coast, is used in this case, see
Figure 4.9 and 4.10. In this example the enhanced Boussinesq type equations are solved, i.e. the deep-water terms are included.
35
Figure 4.9 Hanstholm harbour, Denmark
Examples
Figure 4.10 Location of Hanstholm harbour
Model setup
The model setup is illustrated in Figure 4.11.
36 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.11 Model setup for Hanstholm harbour. Upper panel shows the bathyme-
try, the lower left panel the absorbing sponge layers (20 point wide) and
the lower right panel the areas where partial wave reflection is required
(3-5 points wide)
In this example we consider a case having Hm0= 1.0 m and Tp= 8 s. The
waves are coming from N and the minimum period of interest is set to T
s. As the maximum water depth in the model area is h
sary to include the deep-water terms (h
h
= 4 m. The incoming waves are synthesised based on a mean JON-
min
= 0.45). The minimum depth is
max/Lo
= 17.5m it is neces-
max
min
= 5
SWAP spectrum.
For visualisation purposes oblique incident unidirectional irregular waves are
used (you can modify the specification, if you like, in order to see what happens if e.g. directional waves are applied). The input data files are generated
using the Random Wave Generation tool in the MIKE 21 Toolbox (open the
file Hanstholm_Harbour_Preprocessing_Data.21T by double clicking).
To reduce the computational time artificial land is introduced outside the main
breakwaters of the entrance leaving only a smaller area outside the harbour
from where the waves can enter the harbour.
A grid spacing of 5 m is chosen and a time step of 0.2 s. This results in about
6 grid points per minimum wave length, 25 time steps per minimum period
and a maximum Courant number of 0.52 in the deepest part of the model
area. Please note that the space- and time-resolution in this example is less
37
than the recommended values (e.g. obtained using the Java Script MIKE 21
BW Model Planner included in the Online Help), which are minimum 7 grid
points per wave length and about 35 time steps per minimum wave period.
The coarser numerical resolution is chosen in order to reduce the overall
computational time and would affect the simulated wave disturbance coefficient marginally.
The length of the simulation is 25 minutes (corresponding to 7501 time
steps).
Model results
The model results are presented in Figure 4.12 showing a contour plot of the
instantaneous surface elevation and a map showing the isolines of the simulated wave disturbance coefficients (after 25 minutes). Figure 4.13 shows
time series of the simulated surface elevation inside and outside the harbour.
Examples
Figure 4.12 Model results. The upper panel shows the instantaneous surface eleva-
tion and the lower panel the wave disturbance
38 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.14 shows a 3D plot of the instantaneous surface elevation for the
entire harbour.
Figure 4.13 Model results. Time series of simulated surface elevation at the main
harbour entrance (left panel) and at the ferry terminal quay (right panel),
see Figure 4.9
Figure 4.14 3D picture of the simulated instantaneous surface elevation in Han-
stholm harbour
List of data and parameter files
All data required for this example are included in the default installation:
39
Examples
Binary data files
Name: Layout.dfs2
Description: Bathymetry, sponge layer and porosity coefficients
Parameter files
Name: Hanstholm.bw
Description: Wave disturbance test
Name: Hanstholm_Harbour_Preprocessing_Data.21T
Description: Generation of wave input along the two generation lines. You
have to generate the wave input prior to model execution.
Name: Hanstholm_Harbour_Preprocessing_Plot.plc
Description: Specification for Plot Composer (prior to model run). Please
double-click the file after you have executed Hanstholm_Harbour_Preprocessing_Data.21T.
Name: Hanstholm_Harbour_Postprocessing_Plot.plc
Description: Specification for Plot Composer (after model run). Please dou-
ble-click the file after you have executed Hanstholm.bw.
4.2.5 Torsminde Harbour
Purpose of the example
This example illustrates how MIKE 21 BW can be used for simulation of longperiod waves (or seiches) inside a harbour. Torsminde Harbour situated at
the Danish west coasts (see Figure 4.15) has suffered of seiches causing
moored vessels move to-and-fro from their berthing positions resulting in
breaking of mooring lines, damages on fenders and piers and sometimes collisions of vessels with each other. Field measurements show substantial longperiod wave energy on wave periods 30-60 s in the harbour.
40 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.15 Torsminde Harbour, Denmark. The red dot in the lower panel shows the
location
In this example the occurrence of the long-period waves is caused by interactions of short-period wind waves. The shoaling and breaking of the shortperiod wave trains are non-linear processes involving a number of complicated details. Quadratic interactions between harmonics in shallow water
lead to substantial cross-spectral energy transfer over relatively short distances, and during shoaling still more energy will be transferred into bound
sub-harmonics and super-harmonics. In a number of situations, part of the
energy may be released as free harmonics, e.g. during passage over submerged bars or reefs, during diffraction around a breakwater, or during the
process of breaking. When wave breaking occurs, the primary waves will
start dissipating, and this will allow for a gradual release of the bound subharmonics and result in free long waves moving towards the shoreline and
harbour entrance.
41
Wave breaking is included in this 2DH module application and a wave event
occurring approximately 30 hours/month is considered (H
MWD= 270 ºN).
Model setup
The model bathymetry is illustrated in Figure 4.16 where the maximum depth
is 11.5 m and minimum depth is 1 m. The spatial resolution is 2 m. We will
consider a wave situation where substantial wave breaking will occur:
Examples
= 4.0 m, Tp= 9 s,
m0
Significant wave height, H
Peak wave period, T
Standard JONSWAP spectrum
Minimum wave period T
Mean wave direction, MWD= 270ºN
Cos
8
-directional spreading
p
= 9 s
min
= 4.0 m
m0
= 4.1 s
The most energetic and breaking waves have a period around 9 s and are
resolved by the 20-40 points per wave length at depths 2-10 m, where the primary part of the waves will break. In most practical 2DH applications including wave breaking, a grid spacing of 1-2 m is used for peak wave periods
larger than, say, 7s.
The model bathymetry is generated by using the Bathymetry Editor and algebraic manipulations in the Grid Editor.
As shown in Figure 4.17, a 20-point wide sponge layer has been set up at the
shoreline. Hence wave run-up is not considered in this example. The minimum model depth of 1m is well inside the sponge layer. A 50 points wide
sponge layer is used for efficient wave absorption at the other boundaries.
The thickness of the sponge layer is here corresponding to one wave length
or more. The sponge layer map is generated using the MIKE 21 Toolbox
'Generate Sponge and Porosity Layer Maps' and algebraic manipulations in
the Grid Editor.
42 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.16 Model bathymetry (= 2m) of Torsminde Harbour
Figure 4.17 Sponge coefficient map
At the harbour entrance, along the entrance channel and at northern groin a
porosity map is specified for simulation of wave dissipation in the rubble
mound structures (see Figure 4.18). A porosity value of 0.85 is used. Also the
porosity layer map is generated using the MIKE 21 Toolbox 'Generate
43
Sponge and Porosity Layer Maps' and algebraic manipulations in the Grid
Editor.
Figure 4.18 Porosity coefficient map
Model parameters
Examples
The deep-water terms are included in this example. It is recommended to
always include the deep-water terms when wave breaking (and run-up) is
modelled.
Figure 4.19 shows the numerical parameters used in this example. A similar
set of parameters is recommended for most applications including wave
breaking (and run-up). The use of simple upwinding at steep gradients and
near land and a time extrapolation factor of slightly less than one (0.9 in this
case) has successfully been used in a number of wave breaking applications.
Figure 4.20 shows the wave breaking parameters used in this application.
The roller velocity type is set to 3 and the predominant wave direction is set to
270ºN. Hence we assume the breaking waves (rollers) mainly propagate in
the positive x-direction, which is a good approximation in this case. The
remaining parameters are set as default.
The time step is set to 0.1 s, see Figure 4.21 which shows a snapshot of the
Java Script MIKE 21 BW Model Setup Planner included in the Online Help.
Please note that the wave breaking option “exclude wave breaking” is ticked
in the MIKE 21 BW Model Setup Planner, see Figure 4.21. This requires an
explanation. As stated in the Java Script Note 4 the most important issue is to
make sure the breaking waves are well resolved at important areas in the
model domain. If you use the wave breaking option, the minimum spatial resolution (dx) will be based on hmin and T
breaking option is based on L/dx > 7. If h
(L/dx > 20) whereas the non-
min
is small in an area which is of
min
less importance the planner provides a very small dx (and dt). Hence, the
44 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
most important issue is to resolved the breaking waves - and you can check
this in the section “Check/evaluation of selected T
, dx and dt”.
min
Figure 4.19 Numerical parameters
Figure 4.20 Wave breaking parameters
45
Examples
Figure 4.21 MIKE 21 BW Model Setup Planner included in the Online Help
Model run
Before you execute the MIKE 21 BW model simulation you have to provide
internal wave boundary data. Simply drag and drop the Torsminde_Harbour.21t-file into your MIKE Zero shell, go to the 'waves' entry and click on
run button, see Figure 4.22.
46 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.22 Generation of internal wave boundary data using the MIKE 21 Toolbox
The length of the simulation is 30 minutes (corresponding to 18001 time
steps). The computation time depends on the speed of your PC. For a laptop
IBM T40 Pentium M (Centrino, 1.6 GHz and 1GB DDR RAM) the required
system time is approximately 11 hours (the system CPS is approximately
200,000 points/second).
You may reduce the length of the simulation in order to reduce the overall
CPU time.
Model results
Figure 4.23 shows a 2D visualisation of the simulated instantaneous surface
elevation. You can make a similar plot by loading (drag and drop) the PFS-file
MzPlot.Surfaceelevation.plc into the MIKE Zero shell during or after model
execution. From the figure is seen that the intensity of the high-frequency
waves is larger in the shallow water parts (say, depths less than 6 m) than at
the offshore boundary as the quadratic nonlinear energy transfer is larger in
shallow water than in deep water. Some of the generated high-frequency
waves (say, wave periods less than 2-3 s) may not be properly resolved.
However, they will affect the simulated long waves marginally.
Figure 4.24 shows a 3D visualisation of the simulated instantaneous surface
elevation. The surface rollers are shown in white. You can make a similar plot
by opening (by double-clicking) the PFS-file 'Anim Directional Waves with
'Random Wave Generation' tool
47
Examples
Roller.lyt' in the MIKE Animator Plus program during or after model execution
assuming you have a valid licence for MIKE Animator Plus.
From Figure 4.23 and Figure 4.24 is seen that short period wave agitation
inside the harbour is very limited.
Figure 4.23 2D visualisation of instantaneous surface elevation
Figure 4.24 3D visualisation of instantaneous surface elevation and the surface roll-
ers. The image (and animation) is made in MIKE Animator Plus
48 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
The spatial variation of the significant wave height and wave disturbance
coefficient is presented in Figure 4.25. At the harbour entrance the wave
height is reduced to approximately 2 m due to the wave breaking process.
Figure 4.25 Map of wave height (upper) and wave disturbance coefficients (lower)
simulated by MIKE 21 BW
49
Examples
The results from the phase-resolving MIKE 21 BW model has been compared
to a phase-averaged model MIKE 21 NSW (default model parameters). The
upper panel in Figure 4.26 shows a map of significant wave heights and wave
directions. The lower panel in Figure 4.26 shows a comparison between the
two models prediction of the significant wave height along the horizontal line
indicated in Figure 4.27. In general the agreement is good. MIKE 21 BW predicts slightly higher waves along 600-900 m, which is mainly due to the nonlinear shoaling. At the harbour entrance (1100 m) the two models predict
similar significant wave height.
Figure 4.26 Map of significant wave height simulated by MIKE 21 NSW (upper) and
a comparison between MIKE 21 BW and MIKE 21 NSW along the horizontal line depicted in Figure 4.27 (lower)
Figure 4.27 presents computed time series of water surface elevations at
three different locations. For clarity the vertical scale is change for Point 3
50 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
(located in the harbour basin). At Point 3 the dominant wave agitation consists of long-period waves, which is even more clearly seen from the normalised spectra (lower panel). At Point 3 most of the wave energy is on wave
periods within the range 30-60 s, which is in excellent agreement with field
measurements. Please notice the substantial amount of high-frequency
waves at Point 2 caused by nonlinear wave interactions among the primary
wind waves (see also Figure 4.28).
51
Examples
.
Time series at Point 1 - offshore
Time series at Point 3 - sluice
Time series at Point 5 - basin
Figure 4.27 Time series of surface elevation at various points (see location map and
the output section in DirectionalWaves.BW-file). The lower panel shows
the corresponding normalised frequency spectra calculated using the
MIKE Zero WSWAT Linear Spectral Analysis Module
52 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figures 4.28, 4.29 and 4.30 illustrate further spectral and digital analysis of
the MIKE 21 BW model results, which requires a valid license for the WS
Wave Analysis Tool included in MIKE Zero.
Figure 4.28 Calculated directional spectrum at the Point 1 and Point 2 (see
Figure 4.27 for location). The spectrum is calculated using the MIKE
Zero WSWAT Directional Wave Analysis Module
Figure 4.29 Calculated mean wave direction on top of the bathymetry. The spec-
trum is calculated using the MIKE Zero WSWAT Directional Wave Analysis Module
53
Examples
Figure 4.30 Calculated bandpass filtered (0.01-0.05 Hz) surface elevation. The pro-
file plot shows the long waves along the vertical line depicted in
Figure 4.27. The digital filtering is performed using the MIKE Zero
WSWAT Digital Filtering Analysis Module
List of data and parameter files
All data required for this example are included in the default installation:
54 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Binary data files
Name: Bathymetry.dfs2
Description: Bathymetry data
Name: Sponge.dfs2
Description: Map of sponge coefficients
Name: Porosity.dfs2
Description: Map of porosity coefficients
Parameter files
Name: Tools Waves Generation Line.21t
Description: PFS file generation of internal wave boundary data
Name: DirectionalWaves.bw
Description: PFS file for setup of MIKE 21 BW run
Name: Plot Surface Elevation.plc
Description: PFS for 2D visualisation of the simulated surface elevation
using the MIKE Zero Plot Composer Grid Plot control
4.2.6 Island
Purpose of the example
Name: Plot Wave Disturbance.plc
Description: PFS for 2D visualisation of the simulated wave disturbance
using the MIKE Zero Plot Composer Grid Plot control
Name: Anim Directional Waves with Roller.lyt
Description: PFS for 3D visualisation of the simulated surface elevation
using MIKE Animator Plus
We will consider the transformation of regular unidirectional and irregular
directional waves around an island with a moving shoreline, see Figure 4.31.
The combined effect of most of the wave phenomena of interest in coastal
engineering is included in this example; refraction, shoaling, diffraction,
reflection, bottom friction, nonlinear wave-wave interaction, wave breaking
and run-up.
55
Examples
Figure 4.31 Model bathymetry of an island with an elliptic paraboloid form
We consider two different wave situations:
Regular unidirectional waves (PFS file: RegularWaves.bw)
H= 2 m, T= 8 s and MWD= 270 ºN
Irregular directional waves (PFS file: DirectionalWaves.bw)
H
= 2 m, Tp= 8 s, T
m0
spectrum, Cos
8
-directional spreading
= 4.5 s, MWD= 270 ºN, standard JONSWAP
min
Model setup
The size of model area is 1000 m x 1000 m. The bathymetry is an elliptic
paraboloid having an elevation of approximately +0.2 m (above the still water
56 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
level) at the top point and decreasing to a constant depth of approximately16
m. The bathymetry is shown in Figure 4.31.
The spatial resolution is 2 m. The most energetic waves have a period around
8 s and are resolved by the 17-42 points per wave length at depths 2-16 m.
As the primary part of the waves is expected to break where H
(experience rule), the wave breaking is initiated at approximately 4 m water
depth. At this depth the most energetic waves are resolved by 24 grid points
per wave length. In most practical 2DH applications including wave breaking
and moving shoreline a grid spacing of 1-2 m is used for peak wave periods
larger than, say, 7s.
As illustrated in Figure 4.32 a 50 points wide sponge layer is used for efficient
wave absorption at the four model boundaries. The thickness of the sponge
layer is corresponding to one wave length or more. The sponge layer map is
generated by using the MIKE 21 Toolbox 'Generate Sponge and Porosity
Layer Maps' and algebraic manipulations in the Grid Editor. Please note the
sponge layer map used in the regular wave case is modified compared to the
sponge layer map shown in Figure 4.32.
~ 0.5.h
m0
Figure 4.32 Sponge coefficient map (Directional.Sponge.dfs2)
A lowpass filter is included to remove high-frequency waves generated during
uprush and downrush at the shoreline and to dissipate the wave energy in
areas where the surface roller is not properly resolved. The filter is used at
water depths less than approximately 0.5 m.
Model parameters
The deep-water terms are included in both wave situations. It is recommended to always include the deep-water terms when wave breaking and
run-up is modelled.
57
Examples
Also in this example we use ´'Simple upwinding at steep gradients and near
land' for the space discretisation of the convective terms and a time extrapolation factor of slightly less than one (0.8 in this case). Similar settings are
used for the Torsminde Harbour example presented in section 4.2.5.
The time step is set to 0.1 s for the regular wave simulation and 0.05 s for
directional wave simulation. Due to the smaller wave periods (T
= 4.5 s)
min
considered in the directional wave case the time step is reduce accordingly.
Figure 4.33 shows the wave breaking and moving shoreline parameters used
in this application. The roller velocity type is set to 1 as no predominate direction can be identified for the breaking waves. In the previous example (Torsminde Harbour) the type is set to 3 and the predominant wave direction is set
to 270 ºN. The remaining parameters are set as recommended in the User
Guide and Online Help.
Except for the slot depth, which is set to 16 m, default parameters are used
for modelling of the moving shoreline.
58 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.33 Wave breaking and moving shoreline parameters
Model run
Before you execute the MIKE 21 BW model simulations you have to provide
internal wave boundary data. Simply drag and drop the file 'Wave_Generation.21t' into your MIKE Zero shell, go to the 'waves' entry, select the 'Setup
Name' and click on run button, see Figure 4.34.
59
Examples
Figure 4.34 Generation of internal wave boundary data using the MIKE 21 Toolbox
The length of the simulation is 8 minutes and 20 seconds (corresponding to
5001 time steps) for the regular wave simulation and 10 minutes for the directional wave simulation.
The computation time depends on the speed of your PC. For a laptop IBM
T40 Pentium M (Centrino, 1.6 GHz and 1GB DDR RAM) the required system
time is approximately 2 hours (the system CPS is approximately 190,000
points/second) for the regular wave simulation and approximately 5 hours
(the system CPS is approximately 180,000 points/second) for the directional
wave simulation.
You may reduce the length of the simulations in order to reduce the overall
CPU time.
Model results
Figure 4.35 shows 2D visualisation of the simulated instantaneous surface
elevation for the two wave situations. The most visible wave phenomena are
refraction, shoaling, nonlinear wave-wave interaction (generation of higher
harmonic waves), wave breaking and run-up.
'Random Wave Generation' and 'Regular Wave Generation' tool
60 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.35 Visualisation (2D) of instantaneous surface elevation. Upper: regular
waves and lower: directional waves
Figure 4.36 shows 3D visualisation of the simulated instantaneous surface
elevation. The surface rollers are shown in white. You can make a similar plot
by loading (double-click) the PFS-file 'Anim Regular Waves with Roller.lyt’ (or
'Anim Directional Waves with Roller.lyt') into the MIKE Animator Plus program
during or after model execution assuming you have a valid licence for MIKE
Animator Plus.
61
Examples
Figure 4.36 Visualisation (3D) of instantaneous surface elevation and the surface
rollers. The image (and animation) is made in MIKE Animator Plus.
Upper panel: regular waves, lower panel: directional waves
Time series of surface elevation and corresponding wave spectrum are presented in Figure 4.37 (regular waves) and Figure 4.38 (irregular waves). The
spectra are calculated by use of the WSWAT Linear Spectral Wave Analysis
Module. However, the FFT tool included in the MIKE 21 Toolbox may also be
used for calculation of raw spectra.
Both figures clearly illustrate the effect of wave breaking and nonlinear wavewave interaction (generation of higher harmonic waves).
62 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.37 Time series of surface elevation (left) and corresponding wave spec-
trum (right). Regular unidirectional wave case. The data is extracted
along the line y= 500 m at water depth (a) 16m, (b) 3m, (c) 1m (all
upstream island) (d) 1m and (e) 3m (all downstream island)
63
Examples
Figure 4.38 Time series of surface elevation (left) and corresponding wave spec-
trum (right). Irregular directional wave case. The data is extracted along
the line y= 500 m at water depth (a) 16m, (b) 3m, (c) 1m (all upstream
island) (d) 1m and (e) 3m (all downstream island)
64 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
The spatial variation of the significant wave height is presented in
Figure 4.39. Please note wave statistics are calculated only in water points,
which never dry out. The uprush/downrush area is shown by white colour in
Figure 4.39 lower panel.
Figure 4.39 Map of wave heights. Upper: regular waves and lower: irregular waves.
Please note the directional wave simulation was extended to 20 minutes simulation time
65
Examples
Results from a MIKE 21 SW simulation have been compared to results from
the MIKE 21 BW irregular wave case. Figure 4.40 shows maps of significant
wave heights and wave directions. In Figure 4.41 a comparison is made
between the two models prediction of the significant wave height along two
cross-sections. An excellent agreement is seen at in wave breaking zone (x=
300-500m, upper panel). MIKE 21 BW predicts slightly higher waves immediately before breaking which is due to nonlinear shoaling. The observed oscillations offshore the breaking point is caused by reflection from the island.
Behind the island the phase-resolving model (MIKE 21 BW) results in larger
waves than the phase-averaged model (MIKE 21 SW) which is caused by
effects of diffraction, reflection and nonlinearities.
66 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.40 Maps of significant wave height and mean wave direction. Upper panel
shows MIKE 21 SW results and lower panel shows results for the MIKE
21 BW irregular wave case. The directional analysis of the Boussinesq
model results is made by using the WSWAT Directional Wave Analysis
Module available in MIKE Zero
67
Examples
Figure 4.41 Comparison between modelled significant wave height using a phase-
resolving model (MIKE 21 BW) and a phase-averaged model (MIKE 21
SW). Upper panel shows a comparison along y= 500 m (west-east
direction) and lower panel shows a comparison along x= 500 m (southnorth direction)
Vector plot of the nearly steady state wave-induced velocity field (after 20
minutes) is shown in Figure 4.42 for the two wave cases. For the MIKE 21
BW simulation the velocity is computed as the time-average of the depthaveraged velocity below the surface roller. As expected the current speeds
are significant larger in case of regular waves. No data is available for qualitative and quantitative comparisons. Sections 4.2.8 (Detached breakwater) and
4.2.7 (Rip channel) deal with examples where experimental data is available.
68 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.42 Wave induced current fields.
Upper panel: regular waves, lower panel: irregular waves
69
List of data and parameter files
All data required for this example are included in the default installation:
Binary data files
Name: Bathymetry.dfs2
Description: Bathymetry data
Name: Sponge Directional Waves.dfs2
Description: Map of sponge coefficients (irregular directional waves)
Name: Sponge Regular Waves.dfs2
Description: Map of sponge coefficients (regular unidirectional waves)
Name: Filter.dfs2
Description: Map of lowpass filter coefficients
Parameter files
Name: Tool Waves Generation Lines.21t
Description: PFS file generation of internal wave boundary data
Examples
Name: Setup Regular Waves.bw
Description: PFS file for setup of MIKE 21 BW run
(regular unidirectional waves)
Name: Setup Directional Waves.bw
Description: PFS file for setup of MIKE 21 BW run
(irregular directional waves)
Name: Plot RegularWave Disturbance.plc
Description: PFS for 2D visualisation of the simulated wave disturbance
using the MIKE Zero Plot Composer Grid Plot control (regular
unidirectional waves)
Name: Plot Directional Wave Disturbance.plc
Description: PFS for 2D visualisation of the simulated wave disturbance
using the MIKE Zero Plot Composer Grid Plot control (irregular
directional waves)
Name: Anim Regular Waves with Roller.lyt
Description: PFS for 3D visualisation of the simulated surface elevation
using MIKE Animator Plus (regular unidirectional waves)
Name: Anim Directional Waves with Roller.lyt
Description: PFS for 3D visualisation of the simulated surface elevation
using MIKE Animator Plus (irregular directional waves)
70 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
4.2.7 Rip channel
Purpose of the example
The next two examples concentrate on wave breaking, run-up and waveinduced currents. This can be done without the traditional splitting of the phenomena into a wave problem and a current problem. In both examples we
consider waves normally incident on a plane sloping beach, but with some
alongshore non-uniformity to trigger nearshore circulation. In the first example, a rip channel is present while the second example (section 4.2.8) concerns a detached breakwater parallel to the shoreline.
Laboratory experiments are available for both examples as described in
Sørensen et al (1998)
Boussinesq model results and laboratory measurements. The two examples
included in the DHI Software installation are very similar to the cases considered in Sørensen et al (1998). However, the examples here are considered
as prototypes of the laboratory experiments by use of a Froude scaling of
1:40.
Model setup
The first example is chosen according to laboratory experiments reported by
Hamm (1992a, b), see reference in Sørensen et al (1998). The size of model
area is 1200 m x 1200 m and the bathymetry is shown in Figure 4.43. It consists of a plane sloping beach of 1:30 with a rip channel excavated along the
centre line. The maximum water depth is 20 m at the offshore boundary.
We will consider regular, unidirectional incident waves with a period of 7.9 s
(1.25 s in the laboratory) and a wave height of 2.8 m (0.07 m in the laboratory) at the offshore boundary. Wave direction is 270 ºN.
The spatial resolution is 2 m. As the primary part of the waves is expected to
break where Hmax ~ 0.8
breaking is initiated at 3.5-4 m water depth. At this depth the waves are
resolved by approximately 25 grid points per wave length.
(1)
. This paper includes detailed comparisons between
.
h (experience rule for regular waves), the wave
As illustrated in Figure 4.44 a 50 points wide sponge layer is used for wave
absorption at the offshore boundary and behind the slot used to modelling the
run-up process. The thickness of the sponge layer is corresponding to one
wave length or more. No sponge layer is used along the lateral boundaries in
order to avoid wave radiation into the sponge layer.
1 A link to this paper is available from the MIKE 21 Documentation Index
71
Examples
Figure 4.43 Model bathymetry for rip channel example
A lowpass filter is included to remove high-frequency waves generated during
uprush and downrush at the shoreline and to dissipate the wave energy in
areas where the surface roller is not properly resolved. The filter is used at
water depths less than approximately 0.5 m, see Figure 4.44.
72 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.44 Map of absorbing sponge layers (left) and map of low-pass filter coeffi-
cients (right)
A constant Chezy number of C= 35 m
pation. This corresponds approximately to a constant wave friction factor of
f
= 0.03 used in Sørensen et al (1998).
m
As opposed to the shore-normal case steady solutions for the mean flow can
only exists when the forcing by radiation stress is balanced by bottom friction
and mixing processes. Mixing processes are usually modelled by means of
an eddy viscosity. In the breaking zone, the viscous shear is to some extent
take into account by the additional convective terms due to the surface roller.
Outside the breaking zone, the eddy viscosity is usually very small. Hence no
eddy viscosity is included in the simulation.
Model parameters
As in the other examples considering wave breaking the deep-water terms
are included.
Also in this example we use ´'Simple upwinding at steep gradients and near
land' for the space discretisation of the convective terms. The time extrapolation factor is set to zero, which will not cause numerical damping of waves as
they propagate in the x-direction. If directional waves are considered a nonzero value close to one should be used.
The time step is set to 0.1 as in the previous two examples.
1/2
/s is used for the bottom friction dissi-
The roller velocity type is set to 3 and the predominant wave direction is set to
270 ºN. Hence we assume the breaking waves (rollers) will mainly propagate
in the positive x-direction, which is a good approximation in this example. The
remaining parameters are set as recommended in the User Guide and Online
Help. The time scale for the roller is set to T/5= 1.58 s.
Except for the slot depth, which is set to 12 m and the slot width is set to 0.05
default parameters are used for modelling of the moving shoreline. The slot
width is fairly large compared to recommendations (0.001-0.01), which will
73
results in a smaller run-up than if a value within the recommended interval
was used. The large value was choosing for numerical stability reasons and
will affect the wave-induced current pattern marginally.
Model run
Before you execute the MIKE 21 BW model simulations you have to provide
internal wave boundary data. Simply drag and drop the file 'Rip_Channel.21t'
into your MIKE Zero shell, go to the 'waves' entry, select the 'Rip channel - H=
2.8m, T= 7.9s, h= 20m and click on run button.
The length of the simulation is 20 minutes (corresponding to 12001 time
steps or approximately 150 wave periods).
The computation time depends on the speed of your PC. For a laptop IBM
T40 Pentium M (Centrino, 1.6 GHz and 1GB DDR RAM) the required system
time is approximately 7 hours (the system CPS is approximately 180,000
points/second).
You may reduce the length of the simulations in order to reduce the overall
CPU time.
Examples
Model results
Figure 4.45 shows a 2D visualisation of the simulated instantaneous surface
elevation. The most visible wave phenomena are refraction, shoaling, nonlinear wave-wave interaction (generation of higher harmonic waves).
Figure 4.46 shows 3D visualisations of the simulated instantaneous surface
elevation. The surface rollers are shown in white. You can make a similar plot
by loading (double-click) the PFS-file 'Anim Regular Waves with Roller.lyt'
into the MIKE Animator Plus program during or after model execution assuming you have a valid licence for MIKE Animator Plus.
74 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.45 Visualisation (2D) of instantaneous surface elevation
75
Examples
Figure 4.46 Visualisation (3D) of instantaneous surface elevation and the surface
rollers. The image (and animation) is created in MIKE Animator Plus
Due to the increased depth and due to depth refraction by the rip channel,
incipient wave breaking is seen to occur comparatively close to the shore
along the centre line. Here, the wave setup is quite small and the larger setup
appearing away from the rip channel gives an alongshore gradient in the
mean water surface forcing a current towards the centre line. The flow from
the two sides join to form a rip current and two symmetrical circulation cells
appear.
A combined vector and contour plot of the nearly steady state wave-induced
velocity field is shown Figure 4.47. The velocity is computed as the time-average of the depth-averaged velocity below the surface roller. A pronounced rip
current is seen along the centre line of the bathymetry (y= 300 grid points).
Figure 4.48 shows the cross-shore variation of the rip current. A maximum of
approximately 1 m/s for the mean depth-averaged return current is seen,
which is in good agreement with the experiments reported by Hamm (1992b),
see Sørensen et al (1998).
76 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.47 Depth-averaged wave-induced current focusing on the symmetrical cir-
culation cell
Figure 4.48 Rip current along the rip channel (y= 300 grid points)
The rip current significantly affects the wave motion. The large variation of the
rip current causes an increase in the wave height, which can be seen in
Figure 4.46 (lower panel). The rip current also causes a small local bend in
the wave crest occurring at the centre line as observed by Hamm.
77
Examples
The spatial variation of the relative wave height is presented in Figure 4.49.
Please note wave statistics are calculated only in water points, which never
dry out. The uprush/downrush area is own by white colour in Figure 4.47 and
Figure 4.49.
Figure 4.49 Map of relative wave height. Please note only the lower half of the com-
putational domain is shown
Figure 4.50 Variation of relative wave height along rip channel (y= 600 m) and out-
side rip channel (y= 200 m)
78 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
List of data and parameter files
All data required for this example are included in the default installation:
Binary data files
Name: Bathymetry.dfs2
Description: Bathymetry data
Name: Sponge.dfs2
Description: Map of sponge coefficients
Name: Filter.dfs2
Description: Map of lowpass filter coefficients
Parameter files
Name: Tool Wave Generation line.21t
Description: PFS file generation of internal wave boundary data
Name: Setup Regular Waves.bw
Description: PFS file for setup of MIKE 21 BW run
Name: Anim Regular Waves with Roller.lyt
Description: PFS for 3D visualisation of the simulated surface elevation
4.2.8 Detached breakwater
Purpose of the example
In this example we shall consider wave transformation and wave-induced
currents around a detached breakwater parallel to the shoreline.
Comprehensive hydrodynamic measurements around a detached breakwater on a plane beach have recently been reported by Mory and Hamm (1997)
and Hamm et al (1995), see references in Sørensen et al (1998)
paper also includes detailed comparisons between Boussinesq model results
and laboratory measurements.
The present example is considered as a prototype of the laboratory
experiments cited above by use of a Froude scaling of 1:40.
Model setup
The size of model area is 1200 m x 1200 m and the bathymetry is shown in
Figure 4.51. It consists of three sections: a 176 m wide horizontal section with
a water depth of 13.2 m, a plane sloping beach of 1:50 between the horizon-
using MIKE Animator Plus
(1)
. This latter
1 A link to this paper is available from the MIKE 21 Documentation Index
79
Examples
tal section and the shoreline, and an emerged plan beach with a slope of
1:20. A half detached breakwater approximately 266 m long and 35 m wide is
placed parallel to the shoreline along a vertical wall. The onshore side of the
breakwater is located approximately 373 m from the shoreline. An absorbing
beach is placed on the offshore side of the breakwater and along the vertical
wall opposite to the breakwater.
We will consider two different wave situations:
Regular unidirectional waves (PFS file: RegularWaves.bw)
H= 3.2 m, T= 10.7 s and MWD= 270 ºN (normal incidence)
Irregular directional waves (PFS file: DirectionalWaves.bw)
H
= 4.6 m, Tp= 10.7 s, T
m0
= 4 s, MWD= 270 ºN, standard
min
JONSWAP spectrum, cos2-directional spreading (normal incidence)
The spatial resolution is set to 2 m. As the primary part of the waves is
expected to break where Hmax ~ 0.8
.
h (experience rule for regular waves),
the wave breaking is initiated at 4 m water depth in case of regular waves.
The directional waves will start to break where H
~ 0.5.h, i.e. at water depth
m0
9 m. This means the initial breaking waves are resolved by more than 30 grid
points per wave length.
80 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
Figure 4.51 Model bathymetry for the detached breakwater example
In the numerical simulations, the physical wave maker is replaced by an internal line of generation, and re-reflection from the boundary is avoided by using
a 50 points wide sponge layer offshore from the generation line, see
Figure 4.52. The absorbing beach on the offshore side of the detached breakwater is modelled using a sponge layer. The thickness of the sponge layer is
corresponding to one wave length or more. Only in case of directional waves
a sponge layer is used along the lateral boundaries.
A lowpass filter is included to remove high-frequency waves generated during
uprush and downrush at the shoreline and to dissipate the wave energy in
81
Examples
areas where the surface roller is not properly resolved. The filter is used at
water depths less than approximately 0.7 m, see Figure 4.53.
Figure 4.52 Map of absorbing sponge layers for regular wave simulation (left) and
directional wave simulation (right)
Figure 4.53 Map of low-pass filter coefficients used for both type of waves
A constant Manning number of M= 35 m
1/3
/s is used for the bottom friction
dissipation.
Model parameters
As in the other examples considering wave breaking the deep-water terms
are included.
In this example we use ‘Simple upwinding differencing’ for the space discretisation of the convective terms. The time extrapolation factor is set to a value
of slightly less than one (0.8 in this case). As discussed in the User Guide we
recommend you to use ‘Simple upwinding at steep gradients and near land’
for the space discretisation of the convective terms. However. for numerical
82 MIKE 21 BW - © DHI
2DH Boussinesq Wave Module - Examples
stability reasons it is sometimes necessary to use the slightly more dissipative simple upwind scheme. As long as the waves are properly resolved the
dissipation is usually small.
The time step is set to 0.14 s.
The roller velocity type is set to 3 and the predominant wave direction is set to
270 ºN. Hence we assume the breaking waves (rollers) will mainly propagate
in the positive x-direction, which is a good approximation in this example. The
remaining parameters are set as recommended in the User Guide and Online
help including the time scale for the roller which is set to T/5= 2.14 s.
Except for the slot depth, which is set to 13.2 m and the slot friction coefficient
is 0.01 default parameters are used for modelling of the moving shoreline.
Model run
Before you execute the MIKE 21 BW model simulations you have to provide
internal wave boundary data. Simply drag and drop the file 'Detached_breakwater.21t' into your MIKE Zero shell, go to the 'waves' entry, select the
'Detached breakwater - H= 3.2m, T= 10.7s, h= 13.2m' (for regular wave generation) and 'Detached breakwater - Hm0= 4.6m, Tp= 10.7s, h= 13.2m' (for
random wave generation) and click on run button.
The length of the simulation is 42 minutes (corresponding to 18001 time
steps or approximately 235 (peak) wave periods).
The computation time depends on the speed of your PC. For a laptop IBM
T40 Pentium M (Centrino, 1.6 GHz and 1GB DDR RAM) the required system
time is approximately 13 hours (the system CPS is approximately 130,000
points/second).
You may reduce the length of the simulations in order to reduce the overall
CPU time.
Model results
Figure 4.54 shows 2D visualisation of the simulated instantaneous surface
elevation for the two wave situations. The most visible wave phenomena are
refraction, shoaling, diffraction, nonlinear wave-wave interaction (generation
of higher harmonic waves), wave breaking and run-up. You can make a similar plot by loading (drag and drop) the PFS-file 'MzPlot.Elevation.Regular.plc'
or 'MzPlot.Elevation.Directional.plc' into the MIKE Zero shell during or after
model execution.
Figure 4.55 shows 3D visualisations of the simulated instantaneous surface
elevation. The surface rollers are shown in white. You can make a similar plot
by loading (double-click) the PFS-file 'Anim Regular Waves with Roller.lyt’ (or
‘Anim Directional Waves with Roller.lyt’) into the MIKE Animator Plus program
83
Examples
during or after model execution assuming you have a licence for MIKE Animator Plus.
Figure 4.54 Visualisation (2D) of instantaneous surface elevation. Left panel: regu-
lar unidirectional waves, right panel: irregular directional waves
The computed wave-induced current field for the two cases is shown in
Figure 4.56. Here, the velocities are the depth-averaged velocities under the
surface roller obtained by cumulative averaging over approximately 8 (peak)
wave periods starting 7 minutes after simulation start. Wave statistics is computed only in points outside the swash zone, which is the white area shown in
Figure 4.56. As described in the User Guide it is possible (through a batch
execution) to include calculation of wave statistics in the swash zone and an
example is shown in Figure 4.57. As the number of sampling values is varying in this wetting and drying zone care should be taken when the results are
interpreted.
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2DH Boussinesq Wave Module - Examples
Figure 4.55 Visualisation (3D) of instantaneous surface elevation and the surface
rollers. The image (and animation) is created in MIKE Animator Plus.
Upper panel: regular unidirectional waves, lower panel: irregular directional waves
By comparing Figure 4.56 with the measurements reported in Sørensen et al
(1998, figure 15 p 169) it is seen that the computed eddy structure agrees
quite well with the measured structure with respect to the location of eddy, the
size of the quiescent area in the centre of the eddy and the maximum speed.
As reported in Sørensen et al (1998) the main discrepancy is in the area outside the lee of the breakwater. The model results show that the strong jet
along the wall of the breakwater is only slowly disintegrated and bent towards
the shoreline, while in the experiment, the jet is bent very strongly at the tip of
the breakwater.
85
Examples
Figure 4.56 Circulation cell behind the detached breakwater for the case of regular,
unidirectional waves (upper panel) and irregular, directional waves
(lower panel). Computed time-averaged of the velocities beneath the
surface rollers. The time-averaging is performed for computational
points which always are wet, i.e. outside the swash zone
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2DH Boussinesq Wave Module - Examples
Figure 4.57 Circulation cell behind the detached breakwater for the case of direc-
tional waves. Computed time-averaged of the velocities beneath the
surface rollers. The time-averaging is performed for computational
points which can be partly wet, i.e. also inside the swash zone
Compared to the case with regular waves, the main features of the eddy
structure for random waves are that the quiescent area in the centre of the
eddy and the maximum speed is reduced.
Figure 4.58 shows a snapshot of the surface elevation for the case of regular
waves. A forward bend in the wave fronts can be seen near the breakwater.
This phenomenon is caused by the strong following current with a maximum
Froude number of 0.2-0.3.
87
Examples
Figure 4.58 Instantaneous surface elevation for the case of regular, unidirectional
waves. Upper panel: model results and lower panel: photograph by
Mory and Hamm (1997), see Sørensen et al (1998)
The temporal evolution of the wave-induced velocity is shown in Figure 4.59
for the two considered wave situations. The time series is extracted in a point
close to the maximum speed. The figure shows a reduction of approximately
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2DH Boussinesq Wave Module - Examples
30 % in case of irregular, directional waves. The figure also indicates that the
time scale for developing the near-steady state flow field is approximately 20
minutes.
Figure 4.59 Time series of wave-induced current speed. The time series is
extracted at P(375,120) with reference to co-ordinate system shown in
Figure 4.56
The spatial variation of the relative wave height is presented in Figure 4.60. In
general, the breaking zone is wider for the case with random waves than for
the case with regular waves and the relative wave height variation is seen to
be smoother for the random waves.
89
Examples
Figure 4.60 Relative wave height in circulation cell for the case of regular, unidirec-
tional waves (upper panel) and irregular, directional waves (lower
panel)
List of data and parameter files
All data required for this example are included in the default installation:
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2DH Boussinesq Wave Module - Examples
Binary data files
Name: Bathymetry.dfs2
Description: Bathymetry data
Name: Sponge Regular Waves.dfs2
Description: Map of sponge coefficients (regular, unidirectional waves)
Name: Sponge Directional Waves.dfs2
Description: Map of sponge coefficients (irregular, directional waves)
Name: Filter.dfs2
Description: Map of lowpass filter coefficients
Parameter files
Name: Tool Waves Generation line.21t
Description: PFS file generation of internal wave boundary data
Name: Setup Regular Waves.bw
Description: PFS file for setup of MIKE 21 BW run
(regular, unidirectional waves)
Name: Setup DirectionalWaves.bw
Description: PFS file for setup of MIKE 21 BW run
(irregular, directional waves)
Name: Plot Regular Surface Elevation.plc
Description: PFS-file for 2D visualisation the simulated surface
elevation using MIKE Zero Plot composer
(regular, unidirectional waves)
Name: Plot Directional Surface Elevation.plc
Description: PFS-file for 2D visualisation the simulated surface
elevation using MIKE Zero Plot composer
(irregular, directional waves)
Name: Plot Regular Wave Induced Currents.plc
Description: PFS-file for 2D visualisation the simulated wave-induced current
field using MIKE Zero Plot composer
(regular, unidirectional waves)
Name: Plot Directionalr Wave Induced Currents.plc
Description: PFS-file for 2D visualisation the simulated wave-induced current
field using MIKE Zero Plot composer
(irregular, directional waves)
Name: Plot Regular Wave Disturbance.plc
91
Description: PFS-file for visualisation the simulated wave disturbance coeffi-
Name: Plot Directional Wave Disturbance.plc
Description: PFS-file for visualisation the simulated wave disturbance coeffi-
Name: Anim Regular Waves with Roller.lyt
Description: PFS-file for 3D visualisation of the simulated surface
Name: Anim Directional Waves with Roller.lyt
Description: PFS-file for 3D visualisation of the simulated surface
4.2.9 Kirkwall Marina
Examples
cient using MIKE Zero Plot composer
(regular, unidirectional waves)
cient using MIKE Zero Plot composer
(irregular, directional waves)
elevation using MIKE Animator Plus
(regular, unidirectional waves)
elevation using MIKE Animator Plus
(irregular, directional waves)
Purpose of the example
This example is used in the step-by-step training guide document that can be
accessed from the MIKE 21 Documentation Index.
The purpose of the step-by-step training guide is to setup a MIKE 21 BW
model from scratch and guide you through the various steps in the model
setup process, execution and results presentation and visualization.
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2DH Boussinesq Wave Module - Examples
Figure 4.61 Aerial image of Kirkwall Marina, UK. Photo courtesy Orkney Islands
Council
4.2.10 Demo-Diffraction
This simple example simulating wave diffraction is designed for use when
running MIKE 21 BW in demo mode.
The following data files and specification file (within the folder of Demo-Diffraction) are supplied with MIKE 21:
Name: Demo-Layout.dfs2
Description: Bathymetry and sponge layer
Name: BC.dfs0
Description: Boundary conditions
Name: Demo-Diffraction.bw
Task: Model: MIKE 21 BW Boussinesq Waves
Description: Demo simulation, wave diffraction
Please note that in order not to overwrite the specification files you should
copy them to your own working folder or rename them.
93
4.3 1DH Boussinesq Wave Module - Examples
4.3.1 Partial wave reflection
Purpose of the example
This fairly simple example is included to illustrate the process of wave propagation and partial reflection of regular and irregular waves in a numerical
wave flume using the 1DH Boussinesq Wave Module. The enhanced Boussinesq equations are solved in this example (as in practically all applications of
the 1DH Boussinesq Wave Module), i.e. the deep-water terms are included.
Model setup
The model setup is illustrated in Figure 4.62. The length of the flume is 390 m
with a uniform depth of 10 m.
Examples
Figure 4.62 Model setup (vertical cross-section). A 20 point wide sponge layer is
used at the left-hand side boundary and a 8 point wide porosity layer at
the other model extreme. The waves are generated internally at node j
= 21
The waves are generated inside the model domain, which is the most common method of forcing the 1DH Boussinesq Wave Module in practical applications. The two model boundaries (i.e. at j= 0 and j= jextr) are considered
closed. Opposite to applications of the 2DH Boussinesq Wave Module you do
not have to specify land points at the two model extremes.
Although a 20 point thick sponge layer is used in this example, you are in
general recommended to apply a sponge layer thickness corresponding to at
least once the wave length of the most energetic waves (corresponding to the
spectral peak wave period). In practice (with mesh size in the order of 1 m)
this means a 50-200 point thick sponge layer. In this example the thickness of
the 20 point wide sponge layer is 0.5-0.6 times the wave length corresponding to the spectral peak wave period.
At the generation line (j= 21) a time series of fluxes and surface slope is
imposed. This time series is generated using the MIKE 21 Toolbox (wave
part) program Regular Wave Generation and Random Wave Generation. For
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1DH Boussinesq Wave Module - Examples
the regular waves the wave height is H = 1 m and the wave period T =8 s. For
the irregular waves the significant wave height is H
peak period T
= 8 s. The waves are synthesised based on a mean JON-
p
SWAP spectrum. The minimum wave period T
can be solved using the enhanced Boussinesq type equations with a dispersion coefficient of B= 1/15.
The thickness of the porosity layer (8 point wide) is about one-quarter of the
wave length and the porosity value is set to 0.70. From the reflection-porosity
curve shown in Figure 4.63 it is seen that a porosity of 0.70 corresponds to a
reflection coefficient of about 0.4, assuming a characteristic wave height and
wave period of 1 m and 8 s, respectively.
= 1 m and the spectral
m0
= 4 s. Hence the problem
min
The model domain is discretized, using a structured mesh
and 196 nodes. The mesh size is 2 m and the integration time step is 0.1 s
corresponding to a maximum Courant number of about 0.5 s. The simulation
duration is 5 minutes (3001 time steps).
Figure 4.63 Reflection coefficient versus porosity for a 16 m wide absorber in 10 m
Model results
with 195 elements
water depth. The characteristic wave height and wave period is 1 m and
8 s, respectively. Calculated by use of the MIKE 21 Toolbox program
Calculation of Reflection coefficient
Time series of the simulated surface elevation extracted at point P(150) is
shown in Figure 4.64 for irregular waves and regular waves. In case of regular waves it is seen that the resulting wave height is increased due to the
wave reflection. It is more difficult to identify the increased wave height in
case of irregular incident waves.
95
Examples
R
a
maxamin
–
a
maxamin
+
-----------------------------=
R
H
m0
H
m0,i
------------
2
1–=
Figure 4.64 Model results. Time series of input and simulated surface elevation at a
P(150) for irregular (left panels) and regular waves (right panels)
The wave reflection coefficient can be estimated from the model results
shown in Figure 4.65. In case of monochromatic and linear waves the reflection coefficient R can be estimated, using the formula:
(4.1)
where a
amplitude, respectively. From Figure 4.65 is found that a
max
and a
is the maximum and minimum value of the envelope
min
0.65 m and a
max
min
0.32, which results in a reflection coefficient of about 0.34. This value is a
little smaller than the expected value of about 0.40 cf. Figure 4.65, which is
mainly due to the wave non-linearity. The incoming waves are not perfectly
linear (as can be seen from the missing wave profile symmetry in
Figure 4.65), which is assumed in the theory for the Calculation of Reflection
coefficient program and for the above formula.
Figure 4.65 Model results. The left panel shows an envelope plot of the surface ele-
vation (corresponding to one wave period) in case of regular waves.
The right panel shows line series of the significant wave height at two
different times in case of irregular waves
In case of irregular and linear waves the reflection coefficient R can be estimated using the formula (based on wave energy considerations):
96 MIKE 21 BW - © DHI
(4.2)
1DH Boussinesq Wave Module - Examples
where Hm0 and H
are the simulated significant wave height and incident
m0,i
significant wave height, respectively. From Figure 4.65 is seen that after 5
minutes simulation time the significant wave height is close to one (away from
the porosity layer). This clearly shows that you need to run the model for a
longer period to be able to carry out a proper statistical analysis. If you
change the running period from 5 minutes (3001 time steps) to 20 minutes
(12001 time steps) you will obtain a variation of the wave height as shown in
Figure 4.66. With an average value of the significant wave height of 1.07-1.08
m and the incident significant wave height of 1.0 m the wave reflection coefficient is estimated to 0.38-0.41. This estimate is in excellent agreement with
the theory.
Figure 4.66 Model results. 3D pictures of the simulated instantaneous surface ele-
vation. Upper: regular waves. Lower: irregular waves
List of data and parameter files
All data required for this example are included in the default installation:
97
Binary data files
Name: Partial_Reflection_mesh.dfs1
Description: Mesh
Name: Partial_Reflection_model.dfs1
Description: Sponge and porosity layer coefficients
Name: RegularWave_H1.0T8.0h10.0.dfs0
Description: Wave generation data in case of regular waves
Name: IrregularWave_Hs1.0Tp8.0h10.0
Description: Wave generation data in case of irregular waves
Parameter files
Name: Regular_wave_simulation.bw
Description: PFS-file for the regular wave case
Name: Irregular_wave_simulation.bw
Description: PFS-file for the irregular wave case
Examples
4.3.2 Sloping beach with wave breaking and moving shoreline
Purpose of the example
Wave breaking and wave run-up on a gently sloping plane beach is considered in this example. The example concentrates on shoaling of regular waves
and spilling type of wave breaking.
Model setup
The model setup follows the experimental setup by Ting and Kirby (1994).
They presented measurements for spilling and plunging type of breakers on a
plane sloping beach with a slope of 1/35 starting in depth of 0.40 m. The
model setup is illustrated in Figure 4.67. Waves are generated at internal
points by source terms, representing the volume flux in progressive waves.
The wave period is 2.0 s and the wave height 0.121 m. The seaward boundary is treated as nonreflective, using sponge layer (100 points). A moving
shoreline is included in the simulation, using a slot width of = 0.01 and a
smoothing parameter of = 100 (default values in MIKE 21 BW). A 50 point
wide sponge layer is used in the slot in order to damp the oscillations in the
slot, see Figure 4.67. With respect to the parameters of the breaker model
the following standard (default) values are applied: initial breaking angle
20, final breaking angle
roller form factor f
= 1.5. An explicit filter is introduced near the still water
d
shoreline to remove short-wave instabilities during uprush and downrush and
to dissipate the wave energy in the model area where the surface roller cannot be resolved.
= 10, half-time for cut-off roller t
o
= T/5 = 0.4 and
1/2
=
b
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1DH Boussinesq Wave Module - Examples
2
As usual the enhanced Boussinesq equations are solved (i.e. deep-water
terms included) in 1DH applications.
Figure 4.67 Model setup
A structured mesh with elements with an edge length of 0.02 m is used. For
the 27.5 m long channel this results in 1375 elements and 1376 nodes. The
time step is 0.005 s and the simulation duration 50 s (10001 time steps).
Model results
Figure 4.68 shows a line series of the simulated surface elevation on top of
the bathymetry. The wave breaking and wave run-up processes are clearly
seen on this figure.
In Figure 4.68 the spatial variation of a number of phase-averaged quantities
are presented. The maximum wave height is 0.121 m at the generation point
and increases towards the break point, see Figure 4.68. Inside the surf zone
the wave height is decreasing. The significant wave height is times larger
than the regular (linear) wave height. Figure 4.68 also shows the spatial variation of the crest and trough elevation and of the mean water level. In
Sørensen and Sørensen (2001)
(1)
a comparison is made between measure-
ments and simulated results for the crest and trough elevation.
In Figure 4.68 is also seen that the mean water level increases in the surf
zone in order to balance the decrease in momentum due to the wave height
decay.
1 Paper included in the Scientific Background
99
Examples
Figure 4.68 Deterministic model results. Line series of surface elevation on top of
the bathymetry
Figure 4.69 Phase-averaged model results. Line series of various quantities
The 1DH Boussinesq module also allows for an estimate of the depth-averaged undertow, which is the return flow below the wave trough. Outside the
surf zone the undertow is small and equal to Stokes drift. The calculation and
verification of the undertow inside the surf zone is presented in Madsen et al
(1997a)
(1)
p. 276ff. An example of the spatial variation of the undertow is
shown in Figure 4.70.
1 Paper included in the Scientific Background
100 MIKE 21 BW - © DHI
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