MIKE21SW
MIKE21SW
MIKE21SW
User Guide
MIKE 2016
2
PLEASE NOTE
LIMITED LIABILITY The liability of DHI is limited as specified in Section III of your 'DHI
Software Licence Agreement':
3
4 MIKE 21 SW - © DHI
CONTENTS
5
1 ABOUT THIS GUIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2 Assumed User Background . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3 General Editor Layout . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.1 Navigation tree . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.2 Editor window . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.3 Validation window . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.4 Online Help . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2 INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.1 Short Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Application Areas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.3 Computational Features . . . . . . . . . . . . . . . . . . . . . . . . . . 16
3 GETTING STARTED . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3.2 Defining and Limiting the Wave Problem . . . . . . . . . . . . . . . . . . 19
3.2.1 Identify the wave problem . . . . . . . . . . . . . . . . . . . . . 19
3.2.2 Check MIKE 21 SW capabilities . . . . . . . . . . . . . . . . . . 20
3.2.3 Selecting model formulation . . . . . . . . . . . . . . . . . . . . 20
3.2.4 Define computational domain . . . . . . . . . . . . . . . . . . . 20
3.2.5 Check computer resources . . . . . . . . . . . . . . . . . . . . 21
3.3 Collecting Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4 Setting up the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4.1 What does it mean . . . . . . . . . . . . . . . . . . . . . . . . 21
3.4.2 Mesh and bathymetry . . . . . . . . . . . . . . . . . . . . . . . 22
3.4.3 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . 22
3.4.4 Bottom friction coefficients . . . . . . . . . . . . . . . . . . . . . 22
3.4.5 Wind field . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
3.5 Calibrating and Verifying the Model . . . . . . . . . . . . . . . . . . . . . 23
3.5.1 Purpose . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.5.2 Calibration and verification situations . . . . . . . . . . . . . . . . 23
3.5.3 Calibration factors . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.6 Running the Production Simulations . . . . . . . . . . . . . . . . . . . . 24
3.7 Presenting the Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4 EXAMPLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.1 General . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2 Fetch-limited Wave Growth in a Lake . . . . . . . . . . . . . . . . . . . . 27
4.2.1 Purpose of example . . . . . . . . . . . . . . . . . . . . . . . . 27
4.2.2 Defining and limiting the wave problem. . . . . . . . . . . . . . . 27
4.2.3 Presenting the results . . . . . . . .. . . . . . . . . . . . . . . 29
4.2.4 List of data and specification files . .
. . . . . . . . . . . . . . . 32
4.3 North Sea and West-coast Wave Conditions . . . . . . . . . . . . . . . . 33
4.3.1 Purpose of the test . . . . . . . . . . . . . . . . . . . . . . . . 33
4.3.2 Defining and limiting the wave problem. . . . . . . . . . . . . . . 33
4.3.3 Presenting the results . . . . . . . .. . . . . . . . . . . . . . . 36
4.3.4 List of data and specification files . .
. . . . . . . . . . . . . . . 39
6 MIKE 21 SW - © DHI
4.4 Wave Transformation on a Barred Beach . . . . . . . . . . . . . . . . . 39
4.4.1 Purpose of example . . . . . . . . . . . . . . . . . . . . . . . 39
4.4.2 Defining and limiting the wave problem . . . . . . . . . . . . . . 40
4.4.3 Presenting the results . . . . . . . . . . . . . . . . . . . . . . 43
4.4.4 List of data and specification files . . . . . . . . . . . . . . . . . 44
4.5 Wave Transformation Around an Island . . . . . . . . . . . . . . . . . . 45
4.5.1 Purpose of example . . . . . . . . . . . . . . . . . . . . . . . 45
4.5.2 Defining and limiting the wave problem . . . . . . . . . . . . . . 45
4.5.3 Presenting the results . . . . . . . . . . . . . . . . . . . . . . 47
4.5.4 List of data and specification files . . . . . . . . . . . . . . . . . 50
5 BASIC PARAMETERS . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1 Domain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
5.1.1 Mesh and bathymetry . . . . . . . . . . . . . . . . . . . . . . 53
5.1.2 Domain Specification . . . . . . . . . . . . . . . . . . . . . . . 53
5.1.3 Boundary Names . . . . . . . . . . . . . . . . . . . . . . . . 54
5.2 Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
6 SPECTRAL WAVE MODULE . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.1 Basic equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.1.1 Spectral formulation . . . . . . . . . . . . . . . . . . . . . . . 57
6.1.2 Time formulation . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.1.3 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 58
6.2 Time Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.3 Spectral discretization . . . . . . . . . . . . . . . . . . . . . . . . . . 58
6.3.1 Frequency discretisation (fully spectral formulation only) . . . . . . 59
6.3.2 Directional discretisation . . . . . . . . . . . . . . . . . . . . . 59
6.3.3 Separation of Wind-sea and Swell . . . . . . . . . . . . . . . . 59
6.3.4 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4 Solution technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
6.4.1 Instationary formulation . . . . . . . . . . . . . . . . . . . . . 60
6.4.2 Quasi-stationary formulation . . . . . . . . . . . . . . . . . . . 61
6.4.3 Output of convergence information . . . . . . . . . . . . . . . . 64
6.4.4 CFL Number . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.5 Water level conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 65
6.5.1 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 66
6.6 Current conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
6.6.1 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 68
6.7 Wind forcing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
6.7.1 General description . . . . . . . . . . . . . . . . . . . . . . . 70
6.7.2 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 71
6.8 Ice coverage . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
6.9 Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
6.9.1 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 72
6.10 Energy transfer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
6.10.1 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 73
6.11 Wave breaking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7
6.11.1 General description . . . . . . . . . . . . . . . . . . . . . . . . 75
6.11.2 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 76
6.12 Bottom friction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.12.1 General description . . . . . . . . . . . . . . . . . . . . . . . . 77
6.12.2 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 78
6.13 White capping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.13.1 General description . . . . . . . . . . . . . . . . . . . . . . . . 80
6.13.2 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 81
6.14 Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.14.1 Point structures . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.14.2 Line structures . . . . . . . . . . . . . . . . . . . . . . . . . . 84
6.15 Initial conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
6.15.1 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 88
6.16 Boundary conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
6.16.1 Boundary specification . . . . . . . . . . . . . . . . . . . . . . 88
6.16.2 Remarks and hints . . . . . . . . . . . . . . . . . . . . . . . . 94
6.17 Outputs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6.17.1 Geographic View . . . . . . . . . . . . . . . . . . . . . . . . . 95
6.17.2 Output specification . . . . . . . . . . . . . . . . . . . . . . . . 95
6.17.3 Integral wave parameters . . . . . . . . . . . . . . . . . . . . 100
6.17.4 Input parameters . . . . . . . . . . . . . . . . . . . . . . . . 102
6.17.5 Model parameters . . . . . . . . . . . . . . . . . . . . . . . . 103
6.17.6 Spectral parameters . . . . . . . . . . . . . . . . . . . . . . 104
7 SCIENTIFIC DOCUMENTATION . . . . . . . . . . . . . . . . . . . . . . 107
8 LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
8 MIKE 21 SW - © DHI
Purpose
1.1 Purpose
The main purpose of this User Guide is to enable you to use, MIKE 21 Spec-
tral Wave Model FM (MIKE 21 SW), for applications involving the assessment
of wave climates in offshore and coastal areas. The User Guide is comple-
mented by the On-line Help.
9
ABOUT THIS GUIDE
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 work-
ing: mathematical modelling of wave problems.
It is assumed that you are familiar with the basic elements of MIKE 21: file
types and file editors, the Plot Composer, the MIKE Zero Toolbox, the Data
Viewer and the Mesh Generator. The documentation for these can be found
by the MIKE Zero Documentation Index.
To the left is a navigation tree, that shows the structure of the model setup
file, and is used to navigate through the separate sections of the file. By
selecting an item in this tree, the corresponding editor is shown in the central
pane of the setup editor.
The edior for the selected section is shown in the central pane. The content of
this editor is specific for the selected section, and might contain several prop-
erty pages.
For sections containing spatial data - e.g. sources, boundaries and output - a
geographic view showing the location of the relevant items will be available.
The current navigation mode is selected in the bottom of this view, it can be
zoom in, zoom out or recenter. A context menu is available from which the
user can select to show the bathymetry or the mesh, to show the optional GIS
background layer and to show the legend. From this context menu it is also
possible to navigate to the previous and next zoom extent and to zoom to full
extent.
If the context menu is opend on an item - e.g. a source - it is also possible to
jump to this items editor.
Further options may be available in the context menu depending on the sec-
tion being edited.
The bottom pane of the editor shows possible validation errors, and is
dynamically updated to reflect the current status of the setup specifications.
10 MIKE 21 SW - © DHI
Online Help
Open the On-line Help system for browsing manually after a spe-
cific help page:
Open the On-line Help system by selecting “Help Topics” in the main
menu bar.
11
ABOUT THIS GUIDE
12 MIKE 21 SW - © DHI
Short Description
2 INTRODUCTION
The fully spectral formulation is based on the wave action conservation equa-
tion, as described in e.g. Komen et al. (1994) and Young (1999), where the
directional-frequency wave action spectrum is the dependent variable.
13
INTRODUCTION
A major application area is the design of offshore, coastal and port structures
where accurate assessment of wave loads is of utmost importance to the
safe and economic design of these structures. Measured data is often not
available during periods long enough to allow for the establishment of suffi-
ciently accurate estimates of extreme sea states. In this case, the measured
data can then be supplemented with hindcast data through the simulation of
wave conditions during historical storms using MIKE 21 SW.
14 MIKE 21 SW - © DHI
Application Areas
Figure 2.2 A MIKE 21 SW forecast application in the North Sea and Baltic Sea.
The chart shows a wave field illustrated by the significant wave height in
top of the computational mesh. See
http://www.waterforecast.com
15
INTRODUCTION
Figure 2.5 Example of a global application of MIKE 21 SW. Results from such a
model can be used as boundary conditions for regional scale forecast
or hindcast models. See http://www.waterforecast.com
16 MIKE 21 SW - © DHI
Computational Features
17
INTRODUCTION
18 MIKE 21 SW - © 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 when modelling situations involving the growth, decay and transforma-
tion of wind-generated waves and swell in offshore and coastal areas using
the new generation spectral wind-wave models included in MIKE 21 SW.
The work will normally consist of the six tasks listed below:
When preparing to do a study you have to assess the following before you
start to set up the model:
19
GETTING STARTED
Next, check if the MIKE 21 SW module is able to solve your problem. This
you can do by turning to Section 2, which gives a short description of MIKE
21 SW and an overview of the type of applications for which MIKE 21 SW can
be used, and by consulting the Scientific Documentation.
For the assessment of wave conditions in nearshore and coastal areas which
most often involves transformation of known offshore wave statistics (derived
from e.g. measurement, regional/global models, remote sensing data, etc.)
you will typically use the directionally decoupled parametric formulation. It is
important you notice that the wind-wave generation process is presently not
included in this formulation. If this process is important you have to use the
fully spectral formulation, which is more computational demanding, but of
course also more accurate.
The fully spectral model is often used for simultaneous wave prediction and
analysis on large and local scale. Coarse spatial and temporal resolution is
used for the regional (or large) scale part of the computational domain and a
high-resolution boundary- and depth-adaptive mesh is describing the shallow
water environment at the coastline. An example is presented in Section 4
EXAMPLES (p. 27).
Draw up your model domain on a sea chart showing the area of interest and
the area of influence. This is normally an iterative process as on one hand
you should keep the model domain as small as possible, while on the other
hand you have to include the total area of influence. You also have to con-
sider the Boundary Conditions (6.16 Boundary conditions (p. 88)).
The choice of the discrete resolution in the geographic and spectral space
depends on the wave conditions for which simulations are to be performed
and on the bathymetry and forcing fields (wind, current, water level):
20 MIKE 21 SW - © DHI
Collecting Data
tational nodes. Please notice that the CFL number can be saved as a model
output parameter.
Finally, before you start to set up the model, you should check that you are
not requesting unrealistic computer resources:
bathymetric data such as sea charts from local surveys or, for example,
from the Hydrographic Office, UK, or MIKE C-MAP.
wind data; there might be synoptic weather charts, collected cyclone
data, measurement of the wind conditions in selected locations, etc.
current and water level data; if wave-current interaction and/or varying
water level is important for your MIKE 21 SW application you often have
to setup and run a MIKE 21 Flow Model FM simulation prior to the execu-
tion of the wave simulation.
information on sea bed characteristics for assessment of the influence of
bottom dissipation.
calibration and validation data; these might be measured wave parame-
ters at selected locations, e.g. significant wave height, peak wave period
and mean wave direction.
21
GETTING STARTED
Describing the water depth in your defined model domain is one of the most
important tasks in the modelling process. A few hours less spent in generat-
ing the mesh covering the bathymetry may later on mean extra days spent in
the calibration process.
The mesh file including your bathymetry is always generated by MIKE Zero
Mesh Generator, which is a tool for the generation and handling of unstruc-
tured meshes, including the definition and editing of boundaries. The MIKE
Zero Bathymetry Editor can not be used for creating of flexible meshes.
22 MIKE 21 SW - © DHI
Calibrating and Verifying the Model
Please notice that the wind-wave generation in this release is only possible
using the fully spectral formulation.
3.5.1 Purpose
Having completed all tasks listed above you are ready to do the first wave
simulation and to start on the calibration and verification of the model.
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 run your calibration run the first time and compare the simulation
results to your measurements 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. The most important factor in the
calibration is the accuracy of the data. Hence, in order to reduce the differ-
ences, you may have to change the basic model specifications listed in Sec-
tion 3.4.
23
GETTING STARTED
Breaking parameters
– The breaking wave parameters can also be used as calibration fac-
tors in some cases. However, you should be careful in tuning these
parameters. The parameter controls the rate of energy dissipation
after breaking while (depth-induced) controls the amount of depth
related breaking. An increase in increases the rate of energy dissi-
pation. Increasing reduces the amount of depth-related wave
breaking.
– In the directionally decoupled parametric formulation you can also
use the steepness-induced wave breaking parameter to calibrate
your model. By increasing this value the dissipation can be reduced
resulting in increased wave height and wave period.
White capping (fully spectral formulation only)
– In most applications you will apply the default values of the two free
parameters controlling the rate of white-cap (or steepness induced)
dissipation; Cds and . The default values (Cds = 4.5 and = 0.5) are
identical to the recommendations made in Komen et al. (1994).
24 MIKE 21 SW - © DHI
Presenting the Results
selected locations, should you look at the individual numbers. Much empha-
sis has therefore been placed on the capabilities for graphical presentation in
MIKE 21 and it is an area which will be expanded and focused on even fur-
ther in future versions.
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 the cal-
culated wave parameters, e.g. the significant wave heights and the mean
wave periods, and in form of vector plots showing the mean wave directions.
Plotting in MIKE Zero is done by using the Grid Editor, the Plot Composer tool
and the Data Viewer.
Table 6.2 List of tools for viewing, editing and plotting results. (p. 96) provides
you with an overview of the various plotting/viewing tools available in MIKE
Zero.
25
GETTING STARTED
26 MIKE 21 SW - © 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,
which you can go through yourself and which you can modify, if you like, in
order to see what happens if this or that parameter is changed.
The specification data files for the examples are included with the installation
of MIKE 21. For each example a folder is provided. The folder names are as
follows :
27
EXAMPLES
Wind forcing
The wind is blowing from West (270 °N) in 6 hours. Then the wind direction
turns to a south direction (180 °N) from where it blows for 8 hours. The wind
speed is constant U10= 13 m/s. The wind time series is shown in Figure 4.3.
28 MIKE 21 SW - © DHI
Fetch-limited Wave Growth in a Lake
Spectral discretization
The minimum frequency is 0.055 Hz, the frequency ratio is 1.1 and there are
25 discrete frequencies in this case. Hence the frequency spectrum is
resolved within the frequency range [0.055; 0.6] Hz.
Time integration
The time step is 120 s and the simulation period covers 15 hours.
In Figure 4.4 wave growth curves are shown for the significant wave height
and peak wave period (west boundary is to the left). The growth curve at
06:00 hours predicts at fetch 40 km a significant wave height of 1.55 m and a
corresponding spectral peak period of 4.8 s. This prediction is in very good
agreement with Shore Protection Manual (1984) shallow water growth curves
(Hm0 = 1.49 m and Tp = 4.6 s) and the growth curves suggested by Kahma
and Calkoen (in Komen et al., 1994, p. 175-176) (Hm0 = 1.62 m and Tp = 4.9
s).
The maps shown in Figure 4.5 clearly illustrate the influence of the absorbing
boundaries on the wave field. The graphics are created by the MIKE Zero
Data Viewer.
Figure 4.6 shows how the directional spectrum change during the turn of the
wind direction. The graphics are created by the Polar Plot in MIKE Zero Data
Viewer.
29
EXAMPLES
Figure 4.4 Spatial variation of the significant wave height and peak wave period at
two different instances. The results are extracted from the result file
“Wave_line.dfs1”
30 MIKE 21 SW - © DHI
Fetch-limited Wave Growth in a Lake
Figure 4.5 Maps of the significant wave height at two different instances
31
EXAMPLES
Figure 4.6 Evolution of the directional spectrum during a 90° turn of the wind direc-
tion. The plots are made in the Data Viewer. Polar plots can also be
made in the MIKE Zero Plot Composer (Polar Plot control)
The following data files (included in the \sw\Lake folder) are supplied with
MIKE 21 SW:
32 MIKE 21 SW - © DHI
North Sea and West-coast Wave Conditions
DHI has carried out a large number of design studies covering various loca-
tions in the U.K., Norwegian and Danish sectors of the North Sea. These
studies were conducted for Dansk Olie og Naturgas A/S (Denmark), Mærsk
Olie and Gas A/S (Denmark), Hamilton Brothers Oil & Gas Ltd. (U.K.), British
Petroleum (U.K.), Phillips Petroleum Company (Norway) and many others.
Recently, DHI has implemented a forecast model for Eltra A/S (Denmark) for
short and long term wave prediction in connection with planning of installation
and maintenance of an new offshore wind farm located at Horns Rev at the
Danish West-coast. An extensive validation has been carried out for the
MIKE 21 SW model. The present example shows a simulation for the period
5-12 November 2000, where comparison with offshore data (Ekofisk) and
onshore data (Horns Rev) is available.
33
EXAMPLES
Please notice that the bathymetry used in this example and shown in
Figure 4.8 and Figure 4.9 is a modified version of the bathymetry used in the
forecast model.
34 MIKE 21 SW - © DHI
North Sea and West-coast Wave Conditions
Wind forcing
During the peak of the storm (7 November 2000 00:00) the wind is blowing
from easterly directions with a wind speed of about 20 m/s in central North
Sea and about 10 m/s at the West-coast of Jutland, Denmark. An example of
a wind field is shown Figure 4.10.
Figure 4.10 Wind field during the peak for the storm
35
EXAMPLES
Spectral discretization
The minimum frequency is 0.055 Hz, the frequency ratio is 1.1 and there are
25 discrete frequencies in this case. Hence the frequency spectrum is
resolved within the frequency range [0.055; 0.6] Hz.
Time integration
The time step is 900 s (or 15 minutes) and the number of time steps is 672.
This corresponds to a one-week period simulation time.
Figure 4.11 shows a map of the significant wave height for the entire domain,
while Figure 4.12 and Figure 4.13 shows time series of the wave height,
spectral peak wave period and mean wave period at the two measurement
stations. The comparison between model and measured data is seen to be
very good.
Figure 4.11 Maps of the significant wave height at the peak of the storm
36 MIKE 21 SW - © DHI
North Sea and West-coast Wave Conditions
Figure 4.12 Time series of significant wave height (upper), spectral peak wave
period (middle) and mean wave period (lower) at the offshore buoy
(Ekofisk)
37
EXAMPLES
Figure 4.13 Time series of significant wave height, spectral peak wave period and
mean wave period at onshore buoy (Horns Rev)
38 MIKE 21 SW - © DHI
Wave Transformation on a Barred Beach
Figure 4.14 Simulated directional spectra at Horns Rev. The plots are made using
the Polar plot control in the MIKE Zero plot composer
The following data files (included in the \sw\NorthSea folder) are supplied
with MIKE 21 SW:
39
EXAMPLES
40 MIKE 21 SW - © DHI
Wave Transformation on a Barred Beach
41
EXAMPLES
Basic Equations
For this case we want to calculate a stationary solution using the directionally
decoupled parametric formulation. Hence, you should select ´Quasi-station-
ary formulation’ and ‘Directionally decoupled parametric formulation’.
Boundary conditions
The offshore wave condition is Hm0= 2.84 m, Tp= 9.1 s, MWD= 271°N and
directional spreading index n= 7. This condition is applied along the offshore
(west) boundary. A lateral boundary condition is used along the northern and
southern boundary. This type of boundary condition is a good approximation
when the boundary line is almost straight and when the depth contours are
almost perpendicular to the line. This event corresponds to a situation
occurred 28 February 1999 18:00. The corresponding water level is +0.64 m
MSL.
Spectral discretization
The directional sector 240°-300°N is resolved with 13 directions. This results
in a 5° directional resolution.
Solution Technique
The default parameters for the iterative method can be used for this case.
However, you may choose to save information of the iterative procedure.
42 MIKE 21 SW - © DHI
Wave Transformation on a Barred Beach
Figure 4.18 shows a map of the significant wave height for the entire domain.
The convergence of the iterative algorithm is shown in Figure 4.19.
43
EXAMPLES
The following data files (included in the \sw\Fjaltring folder) are supplied with
MIKE 21 SW:
44 MIKE 21 SW - © DHI
Wave Transformation Around an Island
45
EXAMPLES
The unstructured mesh includes 4646 elements. The spatial resolution is 20-
30 m at 16 m depth and 10-15 m at the initial dry points on the island.
Boundary conditions
The offshore wave conditions is Hm0= 2.0 m, Tp= 8 s, MWD = 270 N and
directional spreading index n= 8 (Type 1 boundary formulation). This condi-
tion is applied at the west, north and south boundaries. The east boundary is
a fully absorbing land boundary.
46 MIKE 21 SW - © DHI
Wave Transformation Around an Island
Spectral discretization
The 360° directional space is resolved by 18 directions.
Time integration
The time step is 2 s and the number of time steps is 900 corresponding to a
30-minute simulation time. An instationary time formulation is used in this
case in order to keep the simulation time low. This approach is sufficient for
illustration of the handling of flooding and drying.
Figure 4.22 shows maps of the significant wave height at water level –4 m
MSL (time 12:30) and +2 m MSL (time 12:15). In the last case, the significant
wave height is approximately 1.1 m at the top of the island. This is in excel-
lent agreement with the experience of Hm0 ~ 0.5h ~ 1.1 m (h= 2.2 m is the
water depth) in the breaking zone.
47
EXAMPLES
Figure 4.22 Maps of the significant wave height at two different instances (upper at
water level –4 m MSL and lower at water level +2 m MSL)
1 The model setup used for MIKE 21 BW is included in the installation. Please see
C:\Program Files\DHI\MIKEZero\Examples\MIKE_21\BW\Island
48 MIKE 21 SW - © DHI
Wave Transformation Around an Island
Figure 4.23 Maps of the significant wave height and mean wave direction. Upper
panel shows MIKE 21 SW results and lower panel shows results from a
MIKE 21 BW simulation. The directional analysis of the Boussinesq
model results is made by using the WSWAT Directional Wave Analysis
tool available in MIKE Zero
49
EXAMPLES
is seen in the wave breaking zone (x= 300-500 m, 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 are
caused by reflection from the island bathymetry.
Please note the wave height is reduced to zero at the boundaries as fully
absorbing boundaries (sponge layers) were used in the MIKE 21 BW simula-
tion. 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.
The following data files (included in the \SW\Island folder) are supplied with
MIKE 21 SW:
50 MIKE 21 SW - © DHI
Wave Transformation Around an Island
Figure 4.24 Comparison between modelled significant wave height using a phase-
averaged model (MIKE 21 SW) and a phase-resolving model (MIKE 21
BW). Upper panel shows a comparison along y= 500 m (west-east
direction) and lower panel shows a comparison along x= 500 m (south-
north direction)
51
EXAMPLES
52 MIKE 21 SW - © DHI
Domain
5 BASIC PARAMETERS
5.1 Domain
Providing MIKE 21 SW with a suitable mesh is essential for obtaining reliable
results from your model. Setting up the mesh includes selection of the appro-
priate area to be modelled, adequate resolution of the bathymetry, wave,
wind and flow fields under consideration and definition of codes for open and
land boundaries. Furthermore, the resolution in the geographical space must
also be selected with respect to stability considerations.
You have to generate your mesh file in the MIKE Zero Mesh Generator, which
is a tool for the generation and handling of unstructured meshes, including
the definition and editing of boundaries.
The mesh file is an ASCII file including information of the geographical posi-
tion and bathymetry for each node point in the mesh. The file also includes
information of the node-connectivity in the triangular element mesh.
Map projection
If the mesh is generated by the MIKE Zero Mesh Generator, the map projec-
tion is defined in the mesh file and is only shown for reference. If the map pro-
jection is not defined in the mesh file, you have to select the correct map
projection corresponding to the data in the mesh file.
If you also apply a datum shift - the depth cutoff is relative to the corrected
depths.
For instance - you have a mesh file with values between +2 and -20 meters.
You then shift these to a different datum with a shift of +1 meters. Your cor-
rected bathymetry now ranges between +1 and -21 m. You then cutoff all
depths above -2m, leaving the bathymetry used in the model to range
between -2 and -21 m.
53
BASIC PARAMETERS
Datum shift
You can use any convenient datum for setting up the mesh of your model.
This can be Chart Datum (CD), Lowest Astronomical Tide (LAT) or Mean Sea
Level (MSL). The actual datum is unimportant. What is important is, that for
each simulation, you must provide the model with the correct height of the
model reference level relative to the datum used in the set up of your bathym-
etry. Specifying the datum shift does this. In this way it is possible to carry out
simulations using a range of different water levels without having to alter the
mesh file.
A datum shift of e.g. 2 m (-2 m) means the water depth is increased (reduced)
by 2 m in all node points.
Mesh decomposition
To improve the performance of the numerical scheme it is possible to include
reordering of the mesh (renumbering of the element and node numbers). This
can significantly speed up the computational time by optimizing the memory
access.
Note: When reordering is applied the numbering of the nodes and elements
in the output files has been changed compared to the information in the mesh
file. The information in the log file corresponds to the new ordering.
When you generate your mesh using the MIKE Zero Mesh Generator you
already have defined a code value for open water boundaries. Figure 5.1
shows the definition of codes in a simple application.
54 MIKE 21 SW - © DHI
Time
Figure 5.1 The definition of boundary codes in a mesh is made in the Mesh Gener-
ator
In this case three open boundaries have been detected from the mesh file
specified in the domain parameters; code 2, code 3 and code 4. In the main
Boundary Conditions dialog you can re-name the code values to more appro-
priate names, see Figure 5.2.
Figure 5.2 Change of default code names (from the mesh file) to more appropriate
names
5.2 Time
The period to be covered by the simulation is specified in this dialog. You
have to specify the simulation start date, the overall number of time steps and
the overall time step interval (in seconds).
Using the Instationary formulation (see section 6.4.1) the overall discrete time
steps specified on this page are only used to determine the frequency for
which output can be obtained. The time step used in the calculation is deter-
mined dynamically during the simulation.
Using the Quasi-stationary formulation (see section 6.4.2) the overall discrete
time steps are used to determine the time steps for which a stationary solu-
tion is calculated and thereby the overall frequency for which output can be
obtained.
The simulation always starts with time step number 0 and the simulation start
date is the historical data and time corresponding to time step 0. The simula-
tion end date is presented for reference.
55
BASIC PARAMETERS
56 MIKE 21 SW - © DHI
Basic equations
The relation between the wave energy density spectrum E(, ) and the wave
action density spectrum is given by
N = E
---- (6.1)
The fully spectral formulation is based on the wave action conservation equa-
tion as described in e.g. Komen et al. (1994) and Young (1999), where the
directional-frequency wave action spectrum is the dependent variable.
Quasi-stationary formulation
Instationary formulation
57
SPECTRAL WAVE MODULE
Note, that forcing due to the wind can not be included using the instationary
directionally decoupled parametric formulation.
when the forcing (eg. wind) is slowing varying in space and time
fetch limited wind-wave growth
when individual wave events can be considered as independent
Note: the start time step can only be specified using the MIKE 21/3 Coupled
Model FM.
58 MIKE 21 SW - © DHI
Spectral discretization
The frequency range should cover wave frequencies expected to occur in the
computational domain. For typical offshore applications wave periods from 4
s to 25 s (i.e. frequencies from 0.25 Hz to 0.04 Hz) are found. In enclosed
waters wave periods of 2-3 s (i.e. frequencies from 0.33 Hz to 0.5 Hz) may
also be of interest and should be resolved.
Two types of discretisation are available; 360 degree rose and directional
sector. The 360 degrees compass rose is typically chosen for varying
wind/wave/swell directions. However, if the expected wind/wave/swell direc-
tions fall within a predefined range of directions, the choice of a directional
sector type of discretisation is recommended as it reduce the computational
time.
The separation of wind-sea and swell can be used both in connection with
determination of the maximum prognostic frequency and white capping. As
standard the mean frequency, used in the determination of the maximum
prognostic frequency, is also calculated based on the whole spectrum. For
swell dominated wave conditions this can result in a too low cut-off frequency
and thereby an underestimation of the local generated wind waves. The pre-
dictions can be improved by calculation the mean frequency based on only
the wind-sea part of the spectrum.
59
SPECTRAL WAVE MODULE
No separation
Constant threshold frequency
Dynamic threshold frequency
For details regarding the distinction of wind-sea and swell, see the scientific
documentation (section 5.1 Field Type). The "Dynamic threshold frequency"
used here corresponds to the "Dynamic threshold frequency (version 1)"
described in the scientific documentation.
60 MIKE 21 SW - © DHI
Solution technique
Propagation step
The propagation step is carried out by an explicit Euler scheme. To overcome
the severe stability restriction using an explicit scheme, a multi-sequence
integration scheme is employed following the idea by Vilsmeier and Hänel
(1995). Here, the maximum time step is increased by locally employing a
sequence of integration steps, where the number of levels (steps) may vary
from element to element.
The maximum number of levels (or time steps) in the propagation (transport)
calculation is 32.
In applications with strong wave breaking you should limit the number of time
step levels, say, less than 10. If the maximum number of time step levels is 32
in the breaking zone (information extracted from an initial run) you should
reduce the maximum time step and/or the maximum number of levels.
The steady state solution at each time step in the quasi-stationary time inte-
gration can be solved using the following two methods
61
SPECTRAL WAVE MODULE
F x = 0 (6.2)
where x = x 1 ,x 2 ,... ,x N and F = F 1 x ,F 2 x ,... ,F N x
Set x k + 1 = x k + x k + 1
k+1 k+1 k
F x RMS TOL 1 and H m0 – H m0 max TOL 2 (6.3)
62 MIKE 21 SW - © DHI
Solution technique
N 12
2
xi
i
Root-mean-square norm: x RMS = ----------- (6.4)
N
k+1 k
H m0 – H m0 RMS TOL 1 (6.5)
Recommended Values
The maximum number of iterations has a default value of 500.
Using the modified Newton-Raphson method the default value for the relaxa-
tion factor is 0.1. In general a high factor will give a fast convergence, how-
ever the iteration sequence may diverge. Hence, to ensure convergence a
small value must be used.
Using the method based on iteration in the time domain the maximum num-
ber of iteration must normally be very high to ensure convergence and the tol-
erance must be very small. The maximum number of iteration times the time
step used in the algorithm must be larger that the time it takes for the waves
to propagate through the computational domain. If the tolerance is too high
the algorithm may stop before the steady state solution is obtained. Note that
in case the increment rate of spectral energy in time becomes too large (e.g.
for very high wind speeds), the model will automatically limit the spectral
energy in order to ensure stability in the numerical solution. You can read
more about this in the section Time Integration in the scientific documenta-
tion.
63
SPECTRAL WAVE MODULE
For monitoring the convergence of the iteration procedure used in the quasi-
stationary formulation it is possible to write output of the overall convergence
information and the domain convergence information.
Overall
For the output of overall convergence information you can select the following
three options
No output
Standard output
Standard output and point output
For the standard output the following items for each iteration step is written to
a dfs0-file
If "Standard output and point output" is selected the significant wave height in
a number of user-specified points is also written to the dfs0.
You must specify the name of the output file and if you choose "Standard out-
put and point output" you must also specify the location of the points. You
must select the map projection (Long/Lat, UTM-32 etc.) in which you want to
specify the horizontal location of the points. The geographical coordinates
are either taken from the dialog or from a file. The file format is an ascii file
with four space separated items for each point on separate lines. The first two
items must be floats (real numbers) for the x- and y-coordinate. The third item
is unused (but must be specified). The last item (the remaining of the line) is
the name specification for each point. The point values in the output file are
determined by piecewise linear interpolation. Hence, the point values are the
discrete values for the element in which the specified point is located.
Domain
For the output of domain convergence information you can select the follow-
ing three options
No output
Output after end calculation
Intermediate output
64 MIKE 21 SW - © DHI
Water level conditions
You must specify the name of the output file and if you choose "Intermediate
output" and you must also specify the frequency by which information should
be stored.
For the fully spectral formulation and Cartesian co-ordinates, the CFL number
is defined as
t t t t
CFL = c x ------ + c y ------ + c ------- + c ------ (6.6)
x y
Selecting the Specified water level variation option you must specify the
water level in m. Note, that the last option is only possible using the MIKE
21/3 Coupled Model FM and only if the Hydrodynamic simulation is included.
65
SPECTRAL WAVE MODULE
For the case with water level varying in time but constant in domain you have
to prepare a data file containing the water level before you set up the spectral
wave simulation. The data file must be a time series file (dfs0). The data must
cover the complete simulation period. The time step of the input data file does
not, however, have to be the same as the time step of the spectral wave sim-
ulation simulation. A linear interpolation will be applied if the time steps differ.
For the case with water level varying both in time and domain you have to
prepare a data file containing the water level before you set up the spectral
wave simulation. The file must be a 2D unstructured data file (dfsu) or a 2D
grid data file (dfs2). The area in the data file must cover the model area. If a
dfsu-file is used piecewise constant interpolation is used to map the data,
while if a dfs2-file is used bilinear interpolation is used. The data must cover
the complete simulation period. The time step of the input data file does not,
however, have to be the same as the time step of the spectral wave simula-
tion. A linear interpolation will be applied if the time steps differ.
A dfsu data file including spatial and temporary varying water level is obtained
by running a MIKE 21 Flow Model FM simulation a priori to the wave simula-
tion.
No current
Specified current variation
Current variation from HD simulation
Selecting the specified current variation option you must specify the velocity
components in m/s. Note, that the last option is only possible using the MIKE
21/3 Coupled Model FM and only if the Hydrodynamic module is included.
66 MIKE 21 SW - © DHI
Current conditions
Blocking factor
For cases with strong apposing current blocking may occur. For wave block-
ing conditions the wave heights can be overestimated. Therefore the wave
action density is set to zero, when the current become to strong, that is when
the following criterion is satisfied
where Cg is the group velocity, (u,v) is the current velocity components, is
the discrete directions of wave propagation and f is the blocking factor. The
default value of the blocking factor is 0.1.
Current data
The format of the current data can be specified in three different ways
For the case with current field varying in time but constant in domain you
have to prepare a data file containing the two velocity components before you
set up the spectral wave simulation. The data file must be a time series file
(dfs0). The data must cover the complete simulation period. The time step of
the input data file does not, however, have to be the same as the time step of
the spectral wave simulation. A linear interpolation will be applied if the time
steps differ.
For the case with current field varying both in time and domain you have to
prepare a data file containing the velocity components before you set up the
spectral wave simulation. The file must be a 2D unstructured data file (dfsu)
or a 2D grid data file (dfs2). The area in the data file must cover the model
area. If a dfsu-file is used piecewise constant interpolation is used to map the
data, while if a dfs2-file is used bilinear interpolation is used. The data must
cover the complete simulation period. The time step of the input data file does
not, however, have to be the same as the time step of the spectral wave sim-
ulation. A linear interpolation will be applied if the time steps differ.
Note, that the two velocity components are interpolated as scalar items.
67
SPECTRAL WAVE MODULE
A dfsu data file including spatial and temporary varying current is obtained by
running a MIKE 21 Flow Model FM simulation a priori to the wave simulation.
Wave blocking is not included in the Spectral Wave Module. When an oppos-
ing current is too strong for the waves to exist the propagation speed is set to
zero.
Please note that wind forcing using the directionally decoupled parametric
formulation is only possible for the quasi-stationary time formulation.
No wind
Wind, speed and direction
Wind, velocity components
Wind data
When the speed and direction option is selected the format of the wind data
can be specified in three different ways
For the case with wind field varying in time but constant in domain you have
to prepare a data file containing the wind speed and direction (in degrees
from true North) before you set up the spectral wave simulation. The data file
must be a time series file (dfs0). The data must cover the complete simulation
period. The time step of the input data file does not, however, have to be the
same as the time step of the spectral wave simulation. A linear interpolation
will be applied if the time steps differ.
For the case with wind field varying both in time and domain you have to pre-
pare a data file containing the wind speed and direction (in degrees from true
North) before you set up the spectral wave simulation. The file must be a 2D
unstructured data file (dfsu) or a 2D grid data file (dfs2). The area in the data
file must cover the model area. If a dfsu-file is used piecewise constant inter-
polation is used to map the data, while if a dfs2-file is used bilinear interpola-
68 MIKE 21 SW - © DHI
Wind forcing
tion is used. The data must cover the complete simulation period. The time
step of the input data file does not, however, have to be the same as the time
step of the spectral wave simulation simulation. A linear interpolation will be
applied if the time steps differ.
When the velocity components option is selected the format of the wind data
must be specified as varying in time and domain. You have to prepare a data
file containing the two velocity components before you set up the spectral
wave simulation. The file must be a 2D unstructured data file (dfsu) or a 2D
grid data file (dfs2). The area in the data file must cover the model area. If a
dfsu-file is used piecewise constant interpolation is used to map the data,
while if a dfs2-file is used bilinear interpolation is used. The data must cover
the complete simulation period. The time step of the input data file does not,
however, have to be the same as the time step of the spectral wave simula-
tion simulation. A linear interpolation will be applied if the time steps differ.
For large scale applications (say, spatial scale > 100 km) it is recommended
to use the coupled formulation with default values. For small scale applica-
tions (say, spatial scale < 10-100 km) the use of the coupled formulation
may result in an overestimation of the sea surface roughness and thus an
overestimation of the significant wave height, see eg, Johnson and Kofoed-
Hansen (2000) and Kofoed-Hansen et al (2000). The overestimation has
mainly been observed for relatively strong winds, say, U10 > 13 m/s.
69
SPECTRAL WAVE MODULE
the directional spreading of the energy from the wind follows a cos2-dis-
tribution
the average frequency is independent of the direction.
The Spectral Wave Module includes the following five wind formulations, see
Johnson (1998) for a thorough description and validation:
SPM73/HBH
Based on expressions derived from the Shore Protection Manual (1973) for-
mulation for the wave growth for fetch-limited sea states in deep water with
coefficients as fitted by Holthuijsen, Booij and Herbers (1989).
SPM84
Based on expressions derived from the Shore Protection Manual (1984) for-
mulation for the wave growth for fetch-limited sea states in deep water using
a power fit for the growth equations.
SPM73
Based on the Shore Protection Manual (1973) using a power fit for the growth
equations instead of tuning as done for SPM73/HBH.
JONSWAP
Same as SPM84, but using U10 instead of Ua. Ua is the adjusted wind speed
as defined in the Shore Protection Manual.
For the fully spectral formulation the wind input source term is parameterized
following Janssen’s formulation and implemented as in WAM cycle 4, see
Komen et al. (1994). For a given wind speed and direction, the growth rate of
waves of a given frequency and direction depends on the friction velocity, u*,
and sea roughness z0. In principle, if the sea roughness is known or assumed
(e.g. the Charnock parameter zch = g.z0/u*2, may be assumed), the wind fric-
tion speed can be estimated using the logarithmic wind profile. Thus, the
growth rate of waves due to wind input can be calculated. Assuming a dimen-
sionless sea roughness (zch = g.z0/u*2) of 0.0144, this formulation was shown
70 MIKE 21 SW - © DHI
Ice coverage
in Komen et al. (1994) to fit the observations compiled by Plant (1982). Note
that the use of a constant Charnock parameter implies that sea roughness is
not coupled with the wave spectrum in the comparison with observations
shown in Komen et al.
The wind direction is defined with respect to true North (coming from). Wind
speeds should be given as U10 (wind speed taken 10 m above the Mean Sea
Level).
Mesh points are taken out of the calculations if the ice concentration (defined
as the fraction of sea covered with ice) becomes larger than a user-defined
concentration (default 0.33). If the ice concentration drops below this value,
the corresponding mesh point is ‘re-activated’. The spectrum is then initial-
ised with a PM spectrum based on a local wind direction with a peak fre-
quency corresponding to the second highest discrete frequency.
Ice data
You have to prepare a data file containing the ice concentration before you
set up the spectral wave simulation. The file must be a 2D unstructured data
file (dfsu) or a 2D grid data file (dfs2). The area in the data file must cover the
model area. If a dfsu-file is used piecewise constant interpolation is used to
map the data, while if a dfs2-file is used bilinear interpolation is used. The
data must cover the complete simulation period. The time step of the input
data file does not, however, have to be the same as the time step of the spec-
tral wave simulation. A linear interpolation will be applied if the time steps dif-
fer.
71
SPECTRAL WAVE MODULE
6.9 Diffraction
Diffraction is included using the phase-decoupled refraction-diffraction
approximation proposed by Holthuijsen et al. (2003). For more details see the
scientific manual.
The approximation is based on the mild-slope equation for refraction and dif-
fraction, omitting phase information. It does therefore not permit coherent
wave fields in the computational domain as in deterministic phase-resolving
models such as Boussinesq type models.
k k –1 k –1
A i , l = 1 – A i , l + A i , l * k = 1 ,nsteps (6.8)
Here k is the number of smoothing steps and a is the smoothing factor. The
smooth approximation, A* , is calculated by first calculating the vertex values
using the pseudo-Laplacian procedure proposed by Holmes and Connell
(1989) and then calculating the cell-centred values by averaging the vertex
values corresponding to each element. By default one filtering step is per-
formed with a smoothing factor of = 1. Note, the smoothing is only used in
the calculation of the diffraction parameter. Increasing the smoothing
(increasing the number of smoothing steps) with reduce the oscillation/con-
vergence problem, but will also has the effect that the diffraction effect will be
reduced.
72 MIKE 21 SW - © DHI
Energy transfer
Quadruplet-wave interaction
The quadruplet-wave interaction controls
Triad-wave interaction
In shallow water triad-wave interaction becomes important. Nonlinear trans-
formation of irregular waves in shallow water involves the generation of
bound sub- and super-harmonics and near-resonant triad interactions, where
substantial cross-spectral energy transfer can take place in relatively short
distance. The process of triad interactions exchanges energy between three
interacting wave modes. The triad-wave interaction is modeled using the sim-
plified approach proposed by Eldeberky and Battjes (1995, 1996).
Transfer coefficient
You can specify the transfer coefficient for triad-wave interaction. This coeffi-
cient controls the magnitude of the interaction. The default value is 0.25.
In very shallow water (say, water depth less than 5 m) triad-wave interactions
may results in the development of secondary peaks at harmonics of the spec-
tral peak frequency as well as the generation of spectral energy within the
infragravity wave frequency band. For further reading reference is made to
Kofoed-Hansen and Rasmussen (1998, 2000).
73
SPECTRAL WAVE MODULE
The formulation used in the spectral wave module is based on the formulation
of Battjes and Janssen (1978). This model has been used successfully in the
past in fully spectral models as well as in parameterized versions.
If wave breaking is included you have to specify the Gamma parameter used
in the breaking formulation. The Gamma parameter can be specified in three
ways
Specified Gamma
Functional form (Ruessink et. al. 2003)
Functional form (Nelson (1987, 1994))
Gamma data
For the case with specified gamma, the Gamma parameter can be specified
in two ways
For the case with values varying in domain you have to prepare a data file
containing the Gamma parameter before you set up the spectral wave simu-
lation. The file must be a 2D unstructured data file (dfsu) or a 2D grid data file
(dfs2). The area in the data file must cover the model area. If a dfsu-file is
used piecewise constant interpolation is used to map the data, while if a dfs2-
file is used bilinear interpolation is used.
Alpha
The alpha controls the rate of dissipation and is a proportional factor on the
wave breaking source function. The default value is 1.
74 MIKE 21 SW - © DHI
Wave breaking
Q b H m 2
E ,
S surf , = – -----------------------
- ------------------- (6.9)
8 E tot
Based on laboratory data and field data it has been shown that the breaking
parameter varies significantly depending on the wave conditions and the
bathymetry. Kaminsky and Kraus (1993) found that values in the range
between 0.6 and 1.59 with an average of 0.79. A number of expressions for
determination of the breaking parameter have been proposed in literature.
Battjes and Stive (1985) found that depends weakly on the deep water wave
steepness. They proposed the following expression
Here s0 = H0 /L0 is the deep water steepness, where H0 and L0 is the wave
height and the wave length, respectively, in deep water. This formulation can
not be used in the present spectral wave model, because the value of is not
determined based on local parameters. Nelson (1987, 1994) found that can
be determined as a function of the local bottom slope, d s , in the mean
wave direction. Nelson suggested the following expression
d
= 0,55 + 0,88exp – 0,012 cotan ------ d 100
s (6.11)
= 0,55 d 100
75
SPECTRAL WAVE MODULE
Recently, Ruessink et al. (2003) have presented a new empirical form for ,
where is determined as a function of the product of the local wave number k
and the water depth d
Ruessink et al. showed that using this formulation for the breaking parameter
the prediction of the wave heights in the breaking zone can be improved for
barred beaches. However, the new formulation is also applicable to planar
beaches.
The default value of 1 for the gamma value controlling the dissipation due to
wave steepness can in some cases give a too strong dissipation. Especially,
when the wind is included. In this case a larger value (2-5) can be used.
Experience has shown that in general the best results are obtained if the
effect of breaking on the mean wave period is excluded.
No bottom friction
Friction coefficient, Cfw
– default value is 0.0077 m/s
– the dissipation coefficient does not depend on the wave hydrody-
namic/sediment conditions
Friction factor, fw
– default value is 0.0212
– the dissipation coefficient does not depend on the wave hydrody-
namic/sediment conditions
Nikuradse roughness, kN
76 MIKE 21 SW - © DHI
Bottom friction
– default value is 0.04 m (this value is often used for offshore applica-
tions using the fully spectral formulation, but is usually too high for
nearshore applications)
– the dissipation coefficient depends on wave hydrodynamic condi-
tions
Sand grain size, d50
– default value is 0.00025 m (median sediment grain size)
– the dissipation coefficient depends on wave hydrodynamic and sedi-
ment conditions
For the case with values varying in domain you have to prepare a data file
containing the bottom friction parameter before you set up the spectral wave
simulation. The file must be a 2D unstructured data file (dfsu) or a 2D grid
data file (dfs2). The area in the data file must cover the model area. If a dfsu-
file is used piecewise constant interpolation is used to map the data, while if a
dfs2-file is used bilinear interpolation is used.
As waves propagate into shallow water, the orbital wave velocities penetrate
the water depth and the source terms due to wave-bottom interaction
become important. Furthermore, the deep-water source terms are modified
because of depth effects. A review of the different wave-bottom interaction
processes is given by Shemdin et al. (1978), who consider dissipation due to
friction in the turbulent boundary layer, percolation into a porous bottom,
motion of a soft bottom and scattering on bottom irregularities. According to
77
SPECTRAL WAVE MODULE
Shemdin et al. (1978) bottom friction is generally dominant when the sedi-
ment is composed of fine sand, d50 = 0.1-0.4 mm or when sand ripples are
present. In this case, the low permeability prohibits percolation and granular
friction prevents viscous flow behaviour (Shemdin et al., 1978). In many prac-
tical cases, the bed is composed of fine sand or wave-generated ripples are
present (e.g. Dingler and Inman (1976) found this to be true on many conti-
nental shelves).
For the fully spectral formulation the bottom dissipation source function is
based on linear theory and can be generalised into Eq. (6.13) below, Weber
(1991)
k
S bot , = – C f --------------------- E , (6.13)
sinh 2kh
12
gk
U bm = 4 --------------------
sinh 2kh
- N , d d (6.14)
The bottom friction in areas dominated by sand depends on the grain size of
the sediment and the presence of bed forms. For the case where there is no
bed form, the Nikuradse roughness parameter kN can be estimated by kN =
2d50, where d50 is the median grain size. In the presence of ripples kN can be
much larger than this value and should be estimated including the ripple char-
acteristics. The bed roughness can be further increased due to the presence
of vegetation. In general, it is quite difficult to assess this parameter; thus it is
used as a calibration factor.
If a variable bottom friction value is used (dfs2/dfsu data file) the spectral
wave module utilises a linear interpolation to obtain the bottom friction values
at the node points.
Experience has shown that in general the best results are obtained if the
effect of bottom dissipation on the mean wave period is included.
78 MIKE 21 SW - © DHI
White capping
If white capping is included you have to specify the two dissipation coeffi-
cients, Cdis and DELTAdis. The Cdis coefficient is a proportional factor on the
white capping dissipation source function and thus control the overall dissipa-
tion rate. The DELTAdis coefficient is controlling the weight of dissipation in
the energy/action spectrum.
For the case with values varying in domain you have to prepare a data file
containing the dissipation coefficient, Cdis, before you set up the spectral
wave simulation. The file must be a 2D unstructured data file (dfsu) or a 2D
grid data file (dfs2). If a dfsu-file is used the mesh in the data file must match
exactly the mesh in the simulation. If a dfs2-file is used the area in the data
file must cover the model area. Bilinear interpolation is used to map the data.
For the case with values varying in domain you have to prepare a data file
containing the dissipation coefficient, DELTAdis, before you set up the spec-
tral wave simulation. The file must be a 2D unstructured data file (dfsu) or a
2D grid data file (dfs2 The area in the data file must cover the model area. If a
dfsu-file is used piecewise constant interpolation is used to map the data,
while if a dfs2-file is used bilinear interpolation is used.
Wave parameters
The values for the mean frequency power and mean wave number power
must be specified as well. The two parameters are used in the definition of
the mean angular frequency and the mean wave number (See General
description below).
79
SPECTRAL WAVE MODULE
Whole spectrum
Wind sea part
2 k k 2
S ds , = – C ds k m 0 1 – --- + --- N ,
2
(6.15)
k k
80 MIKE 21 SW - © DHI
White capping
where Cds (Cdis) and (DELTAdis) are two dispersion coefficients. The mean
angular frequency, , and the mean wave number, k , are calculated as fol-
lows
2 p
p
E f f d f d
= 2f = 2 ------------------------------------------
0 0 (6.16)
2
E f df d
00
2 pk pk
E f k d f d
k = ------------------------------------------------------
0 0 - (6.17)
2
E f df d
0 0
where p and pk are mean angular frequency power and the mean wave
number power. Janssen (See Komen et. al (1994)) proposed to use the fol-
lowing values: Cds= 4.5, = 0.5 and p = p k = – 1 .
Please notice that the white capping dissipation is only relevant for the fully
spectral formulation.
By reducing the Cdis coefficient the overall white capping dissipation can be
reduced resulting in larger waves.
Please notice that the DELTAdis value should be larger than zero and smaller
than one.
A DELTAdis coefficient less than 0.5 correspond to increase the weight of dis-
sipation on lower frequencies resulting in smaller wave periods. A DELTAdis
coefficient lager than 0.5 correspond to increase the weight of dissipation on
higher frequencies resulting in larger wave periods.
81
SPECTRAL WAVE MODULE
6.14 Structures
The horizontal dimension of structures such as piers, offshore wind turbines,
breakwaters, dams and caisons is usually much smaller than the resolution
used in the computational grid. Therefore, the presence of these structures
must be modeled by a subgrid scaling technique. Two different types of struc-
tures can be included in the simulations:
Point structures
Line structures
Two approaches have been developed for taking into account the effect of
point structures:
The source term approach takes the effects of the structures into account by
introducing a decay term to reduce the wave energy behind the structure.
This formulation is only accurate when the energy decay is limited and the
reflection of the wave energy is not taken into account. The convective flux
approach is based on a correction of the convective flux term in geographical
space.
Depending on the choice of property page you can either specify detailed
information for the structures or see a geographic view.
Structure data
The geographical coordinates of the structures are either taken from the dia-
log or from a file. The file format is an ASCII file with two space separated
items for each point on separate lines. The two items must be floats (real
numbers) for the x- and y-coordinate. For each structure you must specify the
type of structure. You can select either "Circular pier" or "User-specified struc-
ture". If "Circular pier" is selected you must also specify the diameter of the
pier. If "User-specified structures" is selected you must enter the file name for
the file containing the reflection factor table. This table should contain the
reflection factor as function of the discrete values of the depth and the mean
wave period. For the description of the format of the file see below. Note that
the format of the table is the same whether you apply a source term approach
or a convective flux approach.
You must also select the map projection (Long/Lat, UTM-32 etc.) in which you
want to specify the horizontal location of the points.
82 MIKE 21 SW - © DHI
Structures
d max – d min
d i = d min + i – 1 ----------------------------
- i = 1 nd (6.18)
nd – 1
T max – T min
T j = T min + j – 1 ----------------------------
- j = 1 nt (6.19)
nt – 1
nd dmin dmax
nt Tmin Tmax
c1,1 c1,2 c1,3 ... c1,nt
c2,1 c2,2 c2,3 ... c2,nt
...
...
cnd,1 cnd,2 cnd,3 ... cnd,nt
General description
Source term approach
The source term due to the effect of a structure can be written
c
s = – ---- c g E (6.20)
A
where A is the area of the cell/element in the mesh in which the structure is
located, c is the reflection factor, cg is the group celerity and E(,) is the
energy density.
1
– ---- F n l (6.21)
A
83
SPECTRAL WAVE MODULE
where A is the area of the cell/element in the mesh in which the structure is
located and the normal flux through the element edge, Fn, is multiplied with
the length l and summed over the number of edges.
Depending on the choice of property page you can see a Geographic View or
a List View of the Line structures.
There are two different methods for specification of the line structure.
In the List View you can create a new line structure clicking on the "New line"
button. By selecting a Line structure in the Line list and clicking on the "Delete
line" button you can remove this line structure. For each line structure you
can specify the name of the line structure and whether the line structure
should be active or not. The specification of detailed information for each line
structure is made subsequently. From the List View page you can navigate to
the dialog for specification by clicking on the "Go to ..".
Data
The type of transmission can be specified as
84 MIKE 21 SW - © DHI
Structures
Kr = 1 – Kt (6.22)
Figure 6.1 The location of a line structure. Note the affected cell faces.
The crest level of the structure has to be specified when "Goda's formula" is
selected for the "Transmission type". This crest level can be specified as
Constant
Varying in domain
When Constant is specified you have to specify the constant crest level. The
geographical coordinates and the crest level, when "Varying in domain" is
selected for the crest level, are taken from the dialog or from an ASCII file.
The file format is three space separated floats (real numbers) for the x- and y-
coordinate and the crest level on separate lines for each of the points. The
faces defining the line section are listed in the log-file.
You must also select the map projection (Longitude/Latitude, UTM etc.) in
which you want to specify the location of the line section for the structure.
85
SPECTRAL WAVE MODULE
Constant
Constant in time and varying along line
Varying in time and varying along line
When "Constant in time and varying along line" and "Varying in time and var-
ying along line" is specified you have to prepare a data file containing crest
level correction before you set up the wave simulation. The file must be a
dfs1 file, where the number of grid points corresponds to the number of
points, which is used to define the input polyline. The data must cover the
complete simulation period when "Varying in time and varying along line" is
specified for the format. The time step of the input data file does not, how-
ever, have to be the same as the time step of the hydrodynamic simulation. A
linear interpolation will be applied if the time steps differ.
General description
The energy balance equation for the physical process of a wave encounter-
ing a structure can be stated as
2 2 2
Kt + Kr + Kl = 1 (6.23)
f f-
K t = K t max ----- ----
H i H i min
---- f
- +
1 i H f
---- f f
K t = --- 1 – sin --- --------------- - ----- ----- (6.24)
2 2 H i min H i H i max
f f-
K t = K t min ----- ----
H i H i max
86 MIKE 21 SW - © DHI
Initial conditions
where a and b are two fitting coefficients and Kt,min and Kt,max are the mini-
mum and maximum transmission coefficients. Hi is the incoming wave height
and f is the freeboard which is determined as the crest level minus the sur-
face elevation. The minimum and maximum relative freeboard is given by
f
----
- = 2 --- asin 1 – 2K t max – (6.25)
H i min
f-
----
= 2 --- asin 1 – 2K t min – (6.26)
H i max
Zero spectra
– the wave action is set to zero in all node points
87
SPECTRAL WAVE MODULE
When the quasi-stationary formulation is used the specified type of initial con-
dition is used as the initial guess for the iterative procedure for the first time
step only. For subsequent time steps the initial guess for the iterative proce-
dure is based on the solution obtained from the previous time step. However,
you have the option to apply the initial conditions as starting guess for the
iterative procedure for all time steps. This is recommendable if you model a
time series of representative independent waves.
If the simulation includes wind effect the Zero spectra should not be used.
Depending on the choice of property page you can get a geographic view or a
list view of the boundaries.
You can choose between the following nine different types of boundary condi-
tions
Closed boundary
Wave parameters (Version 1)
Wave parameters (version 2)
Wind-sea and swell parameters (Version 1)
Wind-sea and swell parameters (Version 2)
Wave action spectrum
Wave energy spectrum
Lateral boundary
Reflective boundary
88 MIKE 21 SW - © DHI
Boundary conditions
Closed boundary
Specifying a closed boundary corresponds to having land along the bound-
ary, i.e. no waves enter the model domain through this boundary and the out-
going waves are fully absorbed. This type of boundary is utilized if no wave
data is available.
For the fully spectral formulation the distribution in the frequency domain is a
JONSWAP spectrum with standard shape parameters (=3.3, a=0.07 and
b=0.09).
DSD = 2 1 – a2 + b2
where
2 n
1
a = -------
m0 cos E , d d
0 0
89
SPECTRAL WAVE MODULE
2 n
1
b = -------
m0 sin E , d d
0 0
The relationship between the directional spreading index and the directional
standard deviation is presented in Table 6.1 below.
Table 6.1 The relationship between the directional spreading index and the direc-
tional standard deviating
1 39.15
2 32.52
3 28.36
4 25.45
5 23.28
6 21.58
7 20.20
8 19.05
9 18.08
10 17.24
11 16.52
12 15.87
13 15.30
14 14.78
15 14.31
16 13.88
17 13.49
18 13.13
19 12.80
20 12.49
40 8.94
60 7.33
80 6.36
100 5.70
The energy spectrum at the boundary is scaled so that the energy in the dis-
crete part of the spectrum corresponds to the specified energy at the bound-
ary.
90 MIKE 21 SW - © DHI
Boundary conditions
spectra determined from the wave parameters for wind-sea and the wave
parameters swell. Both spectra are determined as described in the precious
section "Wave parameters (Version 1 and 2)". For the wind-sea part of the
spectrum the standard shape parameters for a JONSWAP spectrum are used
and for the swell part the peakedness parameter is changed to =5.0.
Note, that this type of boundary conditions can only be used for the fully spec-
tral formulation.
Lateral boundary
For this type of boundary condition a one-dimensional calculation of the basic
equations is solved along the boundary line. The information of the incoming
waves in the start point and the end point of the line are obtained from the
connected boundary lines.
Reflective boundary
When specifying a reflective boundary no waves can enter the model domain
through this boundary, and the outgoing waves are reflected from the bound-
ary. The amount of wave reflection is controlled by the specified reflection
coefficient, R. When the value is 0 the outgoing waves are fully absorbed,
and when the value is 1 outgoing waves are fully reflected. In between the
waves are partial reflected.
91
SPECTRAL WAVE MODULE
Boundary Data
Wave parameters (Version 1 and 2) data
The wave parameters can be specified in three different ways
For the case with waves varying in time but constant in along the boundary
you have to prepare a data file containing the boundary values before you set
up the wave simulation. The data file must be a time series file (dfs0). The
data must cover the complete simulation period. The time step of the input
data file does not, however, have to be the same as the time step of the
hydrodynamic simulation. You can choose between different type of interpo-
lation (see Interpolation type below).
For the case with waves varying both in time and along the boundary you
have to prepare a data file containing the boundary values before you set up
the wave simulation. The file must be a profile file (dfs1). The mapping from
the input data file to the boundary section is described in Interpolation Type.
The data must cover the complete simulation period. The time step of the
input data file does not, however, have to be the same as the time step of the
wave simulation. You can choose between different type of interpolation (see
Interpolation type below).
For the case with waves varying in time but constant in along the boundary
you have to prepare a data file containing the boundary values before you set
up the wave simulation. The data file must be a time series file (dfs0). The
data must cover the complete simulation period. The time step of the input
data file does not, however, have to be the same as the time step of the
hydrodynamic simulation. You can choose between different type of interpo-
lation (see Interpolation type below).
For the case with waves varying both in time and along the boundary you
have to prepare a data file containing the boundary values before you set up
the wave simulation. The file must be a profile file (dfs1). The mapping from
the input data file to the boundary section is described in Interpolation Type.
The data must cover the complete simulation period. The time step of the
input data file does not, however, have to be the same as the time step of the
wave simulation. You can choose between different type of interpolation (see
Interpolation type below).
92 MIKE 21 SW - © DHI
Boundary conditions
In both cases you have to prepare a data file containing the boundary values
before you set up the wave simulation. Using the directionally decoupled par-
ametric formulation the file must contain the zero-th moment m0(q ), e.g.
expressed by [m2/rad], of the normal wave action spectrum and the first-order
moment m1(q ), e.g. expressed by [m2s/rad], of the normal wave action spec-
trum. Using the fully spectral formulation, the file must contain the normal
wave action spectrum N(s,q ), e.g. expressed by [m2s2/rad].
For the case "Varying in time, constant along line" the file must be a dfsu file
or a dfs1 or a dfs2 file, respectively, for the two different formulations. For the
case "Varying in time and along line" the file must be a dsu file containing line
information of the spectral parameters. The data file can be obtained from a
previous spectral wave simulation when you have saved spectral information
in a selected point or along a line. Using the directionally decoupled paramet-
ric formulation linear interpolation is used to map the data in the directional
domain. Using the fully spectral formulation bilinear interpolation is used to
map the data in the frequency-directional domain. The mapping in the geo-
graphical domain for the case "Varying in time and along line" is described in
Interpolation Type.
The data must cover the complete simulation period. The time step of the
input data file does not, however, have to be the same as the time step of the
hydrodynamic simulation. A linear interpolation will be applied if the time
steps differ.
You have to prepare a data file containing the energy spectrum E(f ,q ), e.g.
expressed by [m2s/rad], before you set up the wave simulation.
For the case "Varying in time, constant along line" the file must be a dfsu file
or a dfs2 file. For the case "Varying in time and along line" the file must be a
dsu file containing line information of the energy spectrum. The data file can
be obtained from a previous simulation using the fully spectral formulation
when you have saved the energy spectrum in a selected point or along a line.
The mapping in the geographical domain for the case "Varying in time and
along line" is described in Interpolation Type.
Using the directionally decoupled parametric formulation the zero-th and first-
order moment of the action density directional spectrum is obtained from the
93
SPECTRAL WAVE MODULE
Soft start
The soft start time interval is time over which the forcing functions are gradu-
ally increased from the reference significant wave height to 100% of the true
value. The increase can either be linear or follow a sinusoidal curve.
When the Wind-sea and swell parameters (Version 1 and 2) is selected the
wind-sea part is soft started using the specified reference value for the signif-
icant wave height, while the swell part always is soft started using a reference
value of 0 for the significant wave height.
Interpolation type
For the two cases with values varying in time two types of time interpolation
can be selected:
linear
piecewise cubic
In the case with values varying along the boundary two methods of mapping
from the input data file to the boundary section are available:
normal
reverse order
Using normal interpolation the first and last point of the line are mapped to the
first and the last node along the boundary section and the intermediate
boundary values are found by linear interpolation. Using reverse order inter-
polation the last and first point of the line are mapped to the first and the last
node along the boundary section and the intermediate boundary values is
found by linear interpolation.
The directional spreading index is typically within the interval 2-8 for wind
waves and larger than 10 for swell.
6.17 Outputs
Standard data files with computed results from the simulation can be speci-
fied here. Because result files tend to become large, it is nomally not possible
94 MIKE 21 SW - © DHI
Outputs
to save the computed discrete data in the whole area and at all time steps. In
practice, sub areas and subsets must be selected.
In the main Outputs dialog you can add a new output file by clicking on the
"New output" button. By selecting a file in the Output list and clicking on the
"Delete output" you can remove this file. For each output file you can specify
the name (title) of the file and whether the output file should be included or
not. The specification of the individual output files is made subsequently. You
can go to the dialog for specification by clicking on the "Go to .." button.
Finally, you can view the results using the relevant MIKE 21 viewing/editing
tools on the "View" button during and after the simulation.
For each selected output file the field type, the output format, the treatment of
flood and dry, the output file (name and location), and time step must be
specified. Depending on the output format the geographical extend of the out-
put data must also be specified.
Field type
You can choose between the following types of data
Parameters
– Integral wave parameters
– Input parameters
– Model parameters
Output format
You can choose between following types of output formats
95
SPECTRAL WAVE MODULE
The file type depends on the field type as described in Table 6.2.
Table 6.2 List of tools for viewing, editing and plotting results.
96 MIKE 21 SW - © DHI
Outputs
Viewing/ Profile - - -
Series Edi-
editing
tor
tools
Plotting Plot - - -
tools Composer
(Line Series
Plot)
Viewing/ Data - - -
Viewer/
editing
Data
tools
Manager
Plotting Data - - -
tools Viewer/ Plot
Composer
(dfsu Plot)
Output file
A name and location of the output file must be specified along with the type of
data (file type)
Whole area
Only wet area
Only real wet area
Selecting the Only wet area option the output file will contain delete values for
land points. The land points are defined as the points where the water depth
is less than a drying depth. The drying depth is by default set to zero. When
the spectral wave module is dynamic coupled with the hydrodynamic module
and flood and dry is included in the hydrodynamic simulation the drying depth
for the spectral wave module is set equal to the drying depth in the hydrody-
namic module. Selecting the Only real wet area option the output file will con-
tain delete values not only on land but also in points covered by ice and
97
SPECTRAL WAVE MODULE
points for which the water depth is smaller then the minimum water depth for
which calculations is performed. The minimum depth is 0.01 m.
Time step
The temporal range refers to the overall time steps specified under Simula-
tion period in the Time dialog.
Point series
If "Parameters" is selected for the field type you must specify the type of inter-
polation. You can select discrete values or interpolated values. If "Spectral
parameters" is selected for the field type the interpolation type is always set
to discrete values.
The geographical coordinates of the points are either taken from the dialog or
from a file. The file format is an ascii file with four space separated items for
each point on separate lines. The first two items must be floats (real num-
bers) for the x- and y-coordinate. For 3D field data the third item must be an
integer for the layer number if discrete values are selected and a float (real
number) for the z-coordinate if interpolated values are selected. For 2D field
data the third item is unused (but must be specified). The last item (the
remaining of the line) is the name specification for each point.
You must also select the map projection (Long/Lat, UTM-32 etc.) in which you
want to specify the horizontal location of the points.
If "discrete values" is selected for the type of interpolation, the point values
are the discrete values for the elements in which the points are located. The
element number and the coordinates of the center of the element are listed in
the log-file.
If "interpolated values" is selected for the type of interpolation, the point val-
ues are determined by 2nd order interpolation. The element in which the point
is located is determined and the point value is obtained by linear interpolation
using the vertex (node) values for the actual element. The vertex values are
calculated using the pseudo-Laplacian procedure proposed by Holmes and
Connell (1989). The element number and the coordinates are listed in the
log-file.
Line series
You must specify the first and the last point on the line and the number of dis-
crete points on the line. The geographical coordinates are taken from the dia-
log or from a file. The file format is an ascii file with three space separated
items for each of the two points on separate lines. The first two items must be
floats (real numbers) for the x- and y-coordinate. For 3D field data the third
item must be a float (real number) for the z-coordinate. For 2D field data the
third item is unused (but must be specified). If the file contains information for
98 MIKE 21 SW - © DHI
Outputs
more than two points (more than two lines) the information for the first two
points will be used.
You must also select the map projection (Long/Lat, UTM-32 etc.) in which you
want to specify the horizontal location of the points.
If "Parameters" is selected for the field type the values for the points on the
line are determined by 2nd order interpolation. The element in which the point
is located is determined and the point value is obtained by linear interpolation
using the vertex (node) values for the actual element. The vertex values are
calculated using the pseudo-Laplacian procedure proposed by Holmes and
Connell (1989). The element number and the coordinates are listed in the
log-file.
If "Spectral parameters" is selected for the field type values for the points on
the line are determined by piecewise linear interpolation. Hence, the point
values are the discrete values for the elements in which the specified points
are located. The element number and the horizontal coordinates of the center
of the element and z-coordinate are listed in the log file.
Area series
The discrete field data within a polygon can be selected. The closed region is
bounded by a number of line segments. You must specify the coordinates of
the vertex points of the polygon. Two successive points are the endpoints of a
line that is a side of the polygon. The first and final point is joined by a line
segment that closes the polygon. The geographical coordinates of the poly-
gon points are taken from the dialog or from a file. The file format is an ascii
file with three space separated items for each of the two points on separate
lines. The first two items must be floats (real numbers) for the x- and y-coordi-
nate. For 3D field data the third item must be a float (real number) for the z-
coordinate. For 2D field data the third item is unused (but must be specified).
You must also select the map projection (Long/Lat, UTM-32 etc.) in which you
want to specify the horizontal location of the points.
99
SPECTRAL WAVE MODULE
Dconvergence is the angle from true North to projection North (positive clock-
wise).
Using the fully spectral formulation the integral parameters can be deter-
mined for the total spectral, the wind sea part or the swell part.
Type of Spectrum
The type of spectrum can be defined in four different ways:
Whole spectrum
Frequency range
Directional range
Frequency and directional range
You have to make sure the frequency range is within the selected discrete
frequencies. A frequency range is often relevant when simulated results are
compared with measured data.
where
= 0.7
= 0.31
g
f p PM = 0.14 -------- (6.27)
U 10
U 10 4
E PM = ---------
- (6.28)
1.4g
101
SPECTRAL WAVE MODULE
Thus, for a fully developed sea state the threshold frequency is 70% of the
peak frequency for the wind-sea.
U 10
-------- cos – w 0.83 (6.29)
c
where U10 is the wind speed, c the phase speed and and w is the wave
propagation and wind direction, respectively.
Ice concentration c -
The input parameters are identical to the forcing used in the wave model.
Length l m Characteristic
mesh length
Area a m2 Characteristic
mesh area
The first three parameters are related to bottom friction and wave breaking,
respectively. The Courant number and time step factor is related to the inte-
gration of the wave action balance equation. The length and area are related
to the mesh used. The last four parameters are all typically used in connec-
tion with detailed studies of air-sea interaction processes.
Dconvergence is the angle from true North to projection North (positive clock-
wise).
103
SPECTRAL WAVE MODULE
Using the fully spectral formulation the wave energy can be determined for
the total spectral, the wind sea part or the swell part.
Using the directional decoupled parametric formulation you can save the dis-
tribution of wave energy E() with discrete directions as well the directional
distribution of zero-th m0() and first-order moment m1() of wave action.
The discrete directions are defined positive clockwise from projection North
(coming from).
The discrete directions are defined positive clockwise from projection North
(coming from).
Please notice that the output file extension may be either .dfsu or .dfs2:
Using .dfsu (default) the underlying mesh visualise the spectral discreti-
sation (, ) and each element contains the related computed value.
Using .dfs2 the data will be structured in 2D with the axis defining and
, respectively. This file can be visualised using Polar plot in Plot Com-
poser.
105
SPECTRAL WAVE MODULE
107
SCIENTIFIC DOCUMENTATION
Battjes, J.A. and J.P.F.M., 1978: Energy loss and set-up due to breaking of
random waves, in Proc. 16th Int. Conf. On Coastal Eng., ASCE, NY, 569-587.
Battjes, J.A. and M.J.F. Stive, 1985: Calibration and verification of a disper-
sion model for random breaking waves, Geophys. Res., 90, 9159-9167.
Bouws, E. and G.J. Komen, 1983: On the balance between growth and dissi-
pation in an extreme, depth-limited wind-sea in the southern North Sea.
J. Phys. Oceanogr., 13, 1653-1658.
Booij, N., R.C. Ris and L.H. Holthuijsen, 1999: A third-generation wave model
for coastal regions. 1. Model description and validation. J. Geophys. Res.,
104, 7649-7666.
Charnock, H., 1955: Wind Stress on a water surface. Quart. J. Roy. Meteorol.
Soc., 81, 639-640.
Collins, J.I., 1972: Prediction of shallow water spectra. J. Geophys. Res., 77,
2693-2707.
Dingler, J. R., 1974: Wave formed ripples in nearshore sands. PhD. Thesis,
Univ. of California, San Diego, CA, 136pp.
Donelan, M.A., F.W. Dobson, S.D. Smith and R.J. Anderson, 1993: On the
dependence of sea surface roughness on wave development. J. Phys.
Oceanogr., 23, 2143-2149.
109
LIST OF REFERENCES
Geernaert, G.L., K.B. Katsaros and K. Richter, 1986: Variation of the drag
coefficient and its dependency on sea state. J. Geophys. Res., 91C, 6, 7667-
7669.
Garratt, J.R., 1977: Review of drag coefficients over oceans and continents,
Monthly Weather Review, 105, 915.
Günther, H., S. Hasselmann and P.A.E.M. Janssen, 1992: The WAM model
cycle 4. DKRZ Technical Report No 4, Hamburg.
Gulev, S.K. and L. Hasse, 1998: North Atlantic wind waves and wind stress
fields from voluntary observing ship data. J. Phys. Oceanogr., 28, 1107-1130.
Holthuijsen, L.H., N. Booij, and T.H.T Herbers, 1989, A prediction model for
stationary, short crested waves in shallow water with ambient currents.
Coastal Eng., 13, 23-54.
Holthuijsen L.H., Herman A., Booij N. and Cieslikiewicz W., 2002, Diffraction
in SWAN, Proceedings 28th International Conference Coastal Engineering,
Cardiff, 405-412.
Janssen, P.A.E.M., 1989: Wave induced stress and the drag of airflow over
sea waves. J. Phys. Oceanogr., 19, 745-754.
Janssen, P.A.E.M., 1998: On the effect of ocean waves on the kinetic energy
balance and consequences for the initial dissipation technique. J. Phys.
Oceanogr., 30, 1743-1756.
Johnson, H.K., J. Højstrup, H.J. Vested and S.E. Larsen, 1998: On the
Dependence of Sea Surface Roughness on Wind Waves. J. Phys. Ocean-
ogr., 28, 1702-1716.
Johnson, H.K., H.J. Vested, H. Hersbach, J. Højstrup, and S.E. Larsen, 1999:
On the coupling between wind and waves in the WAM model, To appear in
Journal of Atmospheric and Oceanic Technology.
111
LIST OF REFERENCES
Kahma, K.K. and C.J. Calkoen, 1994: Growth curve observations, In Dynam-
ics and Modelling of Ocean Waves by Komen et al., Cambridge University
Press, 174-182,
Kudryatsev, V.N. and V.K. Makin (1996): Transformation of wind in the coastal
zone. KNMI, Scientific Report WR 96-04.
Large, W.G. and S. Pond, 1981: Open ocean momentum flux measurements
in moderate to strong winds. J. Phys. Oceanogr., 14, 464-482.
Makin V.K., V.N. Kudryatsev and C. Mastenbroek, 1995: Drag of the sea sur-
face. Boundary-Layer Meteorol., 73, 159-182.
Merzi, N. and W.H. Graf, 1985: Evaluation of the drag coefficient considering
the effects of mobility of the roughness elements. Ann. Geophys., 3, 473-478.
Nelson, R.C., 1987: Design wave heights on very mild slopes: An experimen-
tal study, Civil. Eng. Trans., Inst. Eng., Aust., 29, 157-161.
Nelson, R.C., 1994: Depth limited wave heights in very flat regions, Coastal
Eng., 23, 43-59.
Nielsen, P., 1979: Some basic concepts of wave sediment transport. Series
paper 20 Institute of Hydrodynamic and Hydraulic Engineering, Technical
University of Denmark,160pp.
Nordeng, T.E., 1991: On the wave age dependent drag coefficient and rough-
ness length at sea. J. Geophys. Res., 96, 7167-7174.
Oost, W.A., 1998: The Knmi HEXMAX stress data – a reanalysis. Boundary-
Layer Meteorology, 86, 447-468.
Phillips, O.M., 1981: The structure of short gravity waves on the ocean sur-
face. In: Spaceborn Synthetic Aperture Radars for Oceanography, the Johns
Hopkins Press.
Resio, D.T., B. Tracy, C.L. Vincent, and J.H. Rasmussen (1999): Non-linear
energy fluxes and the finite-depth equilibrium range in wave spectra. Submit-
ted to J. Phys. Oceanogr.
Ris, R.C. 1997: Spectral modelling of wind waves in coastal areas, PhD. the-
sis, Delft 1997.
Ris, R.C., L.H. Holthuijsen and N. Booij, 1999: A third-generation wave model
for coastal regions. 2. Verification. J. Geophys. Res., 104C, 7667-7681.
Ruessink, B.G., Walstra, D.J.R. and Southgate, H.N. 2003: Calibration and
verification of a parametric wave model on barred beaches, Coastal Eng., 48,
139-149.
113
LIST OF REFERENCES
through the sea surface, Wave Dynamics and Prediction. NATO Conf. Ser. V,
1, 347-365.
Smith, S.D., 1988: Coefficients for sea surface wind stress, heat flux and
wind profiles as function of wind speed and temperature. J. Geophys. Res.,
93C, 15,467 - 15,472.
Smith, S.D. and E.G. Banke, 1975: Variation of the sea surface drag coeffi-
cient with wind speed. Quart. J. Roy. Meteor. Soc, 101, 665-673.
Smith, S.D. 1980: Wind stress and heat flux over the open ocean in gale
force winds. J. Phys. Oceanogr.,10, 709-726.
Smith, S.D., Katsaros, K.B., Oost, W.A. and Mestayer, P., 1996: The impact of
the HEXOS Programme. Boundary-Layer Meteorol.,78, 109-142.
Taylor, P.A. and R.J. Lee, 1984: Simple guidelines for estimating wind speed
variations due to small-scale topographic features, Climatol Bull, 18, 3-32.
Toba, Y., N. Iida, H. Kawamura, N. Ebuchi and I.S.F. Jones, 1990: Wave
dependence on sea-surface wind stress. J. Phys. Oceanogr., 20, 705-721.
Tolman, H. L., 2003: Treatment of unresolved islands and ice in wind wave
models. Ocean Modelling, 4, 219-231.
Tolman, H. L., 2002: Alleviating the Garden Sprinkler Effect in wind wave
models. Ocean Modelling, 4, 269-289.
Troen, I. and E.L. Petersen, 1989: European Wind Atlas, Risø National Labo-
ratory. 656pp.
Weber, S.L., 1991: Bottom friction for wind sea and swell in extreme depth-
limited situations, J. Phys. Oceanogr., 21, 149-172.
Weber, S.L., 1988: The energy balance of finite depth gravity waves. J. Geo-
phys. Res. 93, C4, 3601-3607.
Wu, J., 1980: Wind stress coefficients over sea surface near neutral condi-
tions. A revisit, J. Phys. Oceanogr., 10, 727-740.
Yelland, M. and P.T. Taylor, 1996: Wind stress measurements from the open
ocean. J. Phys. Oceanogr., 26, 1712-1733.
Yelland, M., B.I. Moat, P.K. Taylor, R.W. Pascal, J. Hutchings and V.C. Cor-
nell, 1998: Wind stress measurements from the open ocean corrected for air-
flow distortion by the ship. J. Phys. Oceanogr., 28, 1511-1526.
Taylor, P.K. and M.J. Yelland, 1999: The dependence of sea surface rough-
ness on the height and steepness of the waves. Manuscript submitted to. J.
Phys. Oceanography, July 1999.
Young, I.R., 1999: Wind generated ocean waves, in Elsevier Ocean Engi-
neering Book Series, Volume 2, Eds. R. Bhattacharyya and M.E. McCormick,
Elsevier.
115
LIST OF REFERENCES
117
Index
A
About this guide . . . . . . . . . . . .9
Alpha data . . . . . . . . . . . . . . 74
Ambient flow . . . . . . . . . . . . . 16
Application areas . . . . . . . . . . .9
Assessment of wave climates . . . . .9
B
Background roughness Charnock parameter 69
Basic equations . . . . . . . . . . . 57
Boundary-fitted unstructured mesh . 16
Breaking parameters . . . . . . . . 24
C
Calibration and verification . . . . . 23
Calibration factors . . . . . . . . . . 23
CFL number . . . . . .20, 65, 103, 104
Charnock constant . . . . . . . . . . 69
Check list . . . . . . . . . . . . . . 19
Computational features . . . . . . . 16
Computer resources . . . . . . . . . 21
Convergence angle . . . . . . . . 103
Coordinate type . . . . . . . . . . . 53
Coupled formulation . . . . . . . . . 69
Coupling . . . . . . . . . . . . . . . 16
Courant number . . . . . . . . . . 103
Cyclone generated waves . . . . . . 39
D
Datum shift . . . . . . . . . . . . . 54
Depth-adaptive . . . . . . . . . . . 20
depth-adaptive . . . . . . . . . . . . 14
Design . . . . . . . . . . . . . . . . .9
Directional decoupled parametric formulation 13
Directional discretisation . . . . . . . 59
Directional resolution . . . . . . . . 59
Directional spectra . . . . . . . . . . 39
Directional spectrum . . . . . . . 29, 32
Directionally decoupled parametric formulation 20, 57
Directionally decoupled parametric formulations 16
Discrete Interaction Approximate (DIA) 73
Domain parameters . . . . . . . . . 55
E
Ekofisk . . . . . . . . . . . . . . 33, 37
Energy transfer . . . . . . . . . . . 73
Examples . . . . . . . . . . . . . . 27
Extreme sea states . . . . . . . . . 14
F
Fetch-limited wave growth in a lake 27
Fetch-limited wave growth test . . . 27
Fjaltring . . . . . . . . . . . . . . . 39
Flooding and drying . . . . . . . . . 45
Frequency discretisation . . . . . . 59
Frequency range . . . . . . . . . . 59
Fully spectral formulation . . 13, 20, 57
G
Gamma data . . . . . . . . . . . . 74
Getting started . . . . . . . . . . . 19
Global models . . . . . . . . . . . 20
Global scale . . . . . . . . . . . . 16
H
Horns Rev . . . . . . . . . . . . . 33
I
Ice coverage . . . . . . . . . . . . 71
Ice data . . . . . . . . . . . . . . . 71
Input parameters . . . . . . . . . . 102
Integral parameters . . . . . . . . . 100
Island . . . . . . . . . . . . . . . . 45
L
Local depth-adaptive refinement of mesh 42
Local depth-adaptive
refinement of the mesh . . . . . . 42
M
Mesh decomposition . . . . . . . . 54
Mesh file . . . . . . . . . . . . . . 53
MIKE Zero Mesh . . . . . . . . . . 53
Minimum depth cutoff . . . . . . . . 53
Model formulation . . . . . . . . . . 20
Model parameters . . . . . . . . . 103
N
North Sea . . . . . . . . . . . . 14, 33
wave conditions . . . . . . . . . 33
119
Index
O
Offshore buoy . . . . . . . . . . . . 37
Offshore wind farm . . . . . . . . . 33
Offshore wind turbine . . . . . . . . 82
On-line help . . . . . . . . . . . . 9, 11
Onshore buoy . . . . . . . . . . . . 38
Output format . . . . . . . . . . . . 95
P
Presenting the results . . . . . . 19, 24
Production simulations . . . . . . . 24
Propagation step . . . . . . . . . . 61
Q
Quadruplet wave-wave interaction . 73
Quadruplet-wave interaction . . . . . 73
R
Regional scale . . . . . . . . . . . . 14
Reordering . . . . . . . . . . . . . . 54
S
Sediment transport . . . . . . . . . 15
Setting up the model . . . . . . . . . 21
Soft start interval . . . . . . . . . . . 66
Solution technique . . . . . . . . . . 60
Spectral discretization . . . . . . . . 58
Spectral parameters . . . . . . . . 104
Swell . . . . . . . . . .17, 19, 101, 102
T
Time parameters . . . . . . . . . . 55
Torsminde . . . . . . . . . . . . . . 39
Triad-wave interaction . . . . . . . . 73
Type of air-sea interaction . . . . . . 69
U
Uncoupled formulation . . . . . . . . 69
Unstructured meshes . . . . . . . . 13
User background . . . . . . . . . . .9
W
WAM Cycle 4 . . . . . . . . . . . . 69
Water level conditions . . . . . . . 65
Water level data . . . . . . . . . . 65
Wave action conservation equation 13
Wave breaking . . . . . . . . . . . 74
Wave breaking source function . . . 74
Wave phenomena . . . . . . . . . 19
wave phenomena . . . . . . . . . . 19
Wave-induced currents . . . . . . . 15
Wind data . . . . . . . . . . . . . . 68
Wind field . . . . . . . . . . . . 22, 35
Wind forcing . . . . . . . . . . . . 28
Wind sea . . . . . . . . . . . . . . 101
Wind-generated waves . . . . . . . 19
Wind-wave generation . . . . . 20, 23
121
Index