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MIKE 21 BW User Manual

Boussinesq waves module
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MIKE 21 BW
Boussinesq Waves Module
User Guide
MIKE
2017

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Summary of Contents for MIKE 21 BW

  • Page 1 MIKE 21 BW Boussinesq Waves Module User Guide MIKE 2017...
  • Page 3 PLEASE NOTE COPYRIGHT This document refers to proprietary computer software which is pro- tected by copyright. All rights are reserved. Copying or other repro- duction of this manual or the related programs is prohibited without prior written consent of DHI. For details please refer to your 'DHI Software Licence Agreement'.
  • Page 4 MIKE 21 BW - © DHI...

  • Page 5: Table Of Contents

    ..... . . 17 3.2.2 Check MIKE 21 BW capabilities ....18 3.2.3 Selecting model area spectral and temporal resolution .

  • Page 6: Table Of Contents

    ..........193 MIKE 21 BW - © DHI...

  • Page 7: About This Guide

    21 BW dialogues. It provides more details on specific aspects of the opera- tion of MIKE 21 BW and is what you will normally refer to for assistance if you are an experienced user. The contents of this chapter is the same as found in the Online Help.
  • Page 8 21 Toolbox and the Bathymetry Editor. The documentation for these can be found from the MIKE Zero Documentation Index. A step-by-step training guide on how to set up a MIKE 21 BW for a typical application is also available from the same place.

  • Page 9: Introduction

    General Description Introduction General Description The two modules included in the MIKE 21 BW are based on the numerical solution of time domain formulations of Boussinesq type equations. The Boussinesq equations include nonlinearity as well as frequency dispersion. Basically, the frequency dispersion is introduced in the momentum equations by taking into account the effect of vertical accelerations on the pressure dis- tribution.
  • Page 10 Introduction MIKE 21 BW is capable of reproducing the combined effects of all important wave phenomena of interest in port, harbour and coastal engineering. These include: Shoaling  Refraction  Diffraction  Wave breaking  Bottom friction  Moving shoreline ...

  • Page 11: Application Areas

    With inclusion of wave breaking and moving shoreline MIKE 21 BW is also an efficient tool for the study of many complicated coastal phenomena, e.g.
  • Page 12 This is particularly useful for relative comparisons between different layouts. MIKE 21 BW is also applied for prediction and analysis of the impact of ship- generated waves (also denoted as wake wash). Essential boundary condi-...
  • Page 13 General Description Figure 2.4 Simulation of wave penetration into Frederikshavn harbour, Denmark...
  • Page 14  ments and beaches. The 1DH module can be applied for a number of transects (one spatial dimension) where surf zone dynamics and swash zone dynamics are simu- lated in real-time. MIKE 21 BW - © DHI...
  • Page 15 Transformation of irregular non-linear waves over a natural barred beach profile (upper panel). Offshore (left) and onshore (right) fre- quency wave spectra (lower panels). The spectra are computed using the WSWAT Linear Spectral Wave Analysis module included in MIKE Zero...
  • Page 16 Introduction MIKE 21 BW - © DHI...

  • Page 17: Getting Started

    The purpose of this chapter is to give you a general check list, which you can use for determination and assessment of wave dynamics in ports, harbours and coastal areas using the MIKE 21 Boussinesq Wave model. The work will normally consist of the six tasks listed below: Defining and limiting the wave problem ...

  • Page 18: Check Mike 21 Bw Capabilities

    Chapter 2, which gives a short description of MIKE 21 BW and an overview of the type of applications for which MIKE 21 BW can be used, and by consulting the Scientific Documentation, section 6.

  • Page 19: Check Computer Resources

     An estimate of the required CPU and RAM can easily be obtained using the MIKE 21 BW Model Setup Planner integrated in the Online Help. The disk space is assessed through the MIKE 21 BW Editor. Particularly when wave breaking and moving shoreline are included in the 2DH module (space resolution is 1-2 m and temporal resolution 0.02-0.2 s as...

  • Page 20: Bathymetry

    3.4.3 Sponge layer In practical for all MIKE 21 BW applications you have to prepare maps (2DH, dfs2-file) or profile series (1DH, dfs1-file) for efficient absorbtion of short and long period waves, see section 5.3.11 (Sponge layers).

  • Page 21: Verification

    Running the Production Simulations 3.5.2 Verification The situations which you select for calibration and verification of the model should cover the range of situations you wish to investigate in the production runs. However, as you must have some measurements/observations against which to calibrate and, as the measurements are often only available for short periods, you may only have a few situations from which to choose.

  • Page 22: A Quick Guide For Mike 21 Bw Model Simulation Setup

    Getting Started sis has therefore been placed on the capabilities for graphical presentation in MIKE Zero and it is an area which will be expanded and focused on even fur- ther in future versions (e.g. GIS). Essentially, one plot gives more information than scores of tables and if you can present it in colours, your message will be even more easily understood.
  • Page 23 A Quick Guide for MIKE 21 BW Model Simulation Setup x = 0.1-10 m for the 1DH module (unstructured mesh) with wave – breaking and moving shoreline The next step is to generate a sponge layer map. Sponge (or absorbing) lay- ers are used as wave absorbers.
  • Page 24 Getting Started Wave Generation. Now you are ready to set up up your Boussinesq model run; open MIKE Zero  New  MIKE 21  Boussinesq Waves. It is recommend using the default values in the dialogs in your first model run. If you have decided to include the deep water terms during your model setup (i.e.

  • Page 25: Examples

    Examples General One of the best ways of learning how to use a modelling system like MIKE 21 is through practice. Therefore we have included a number of applications for each of the two modules which you can go through yourself and which you can modify, if you like, in order to see what happens if some of the parame- ters are changed.

  • Page 26: Dh Boussinesq Wave Module - Examples

    Thus, all model boundaries are closed, i.e. considered as land points. At the generation line (j= 12) a time series of fluxes is imposed. This time series is generated using the MIKE 21 Toolbox (wave part) program Random Wave Generation. The significant wave height is H...
  • Page 27 2DH Boussinesq Wave Module - Examples problem can be solved using the classical Boussinesq equations (i.e. the dis- persion coefficient is B= 0). The grid spacing is selected to be 5 m and the time step is 0.5 s. The simula- tion duration is 10 minutes (1201 time steps).

  • Page 28: Diffraction Test

    The area of interest is the shadow zone behind the breakwater. Due to radiation of energy from the point of diffraction the west- ern boundary has to be placed quite far from this area to avoid reflections. MIKE 21 BW - © DHI...
  • Page 29 2DH Boussinesq Wave Module - Examples Figure 4.3 Model layout. The 10 point wide areas indicate sponge layers and the line at k=0 the open essential boundary. The thickness of the sponge layer is about one times the wave length At the open south boundary a flux boundary is applied.
  • Page 30 The model results are in good agreement with semi-analytical solutions to the Helmholtz equation, see e.g. Shore Protection Manual (1984), see section 5.5.16. List of data and parameter files All data required for this example are included in the default installation: MIKE 21 BW - © DHI...

  • Page 31: Rønne Harbour

    2DH Boussinesq Wave Module - Examples Binary data files Name: Layout.dfs2 Description: Bathymetry and sponge layer coefficients Name: Bc.dfs0 Description: Boundary conditions – time series of surface elevation and its curvature Parameter files Name: Diffraction.bw Description: Diffraction test 4.2.3 Rønne Harbour Purpose of the example The purpose of this example is to simulate the wave disturbance in Rønne harbour, Denmark, situated in the Baltic Sea.
  • Page 32 The maximum water depth is approximately 11 m in the model area. The event to be simulated corresponds to a situation occurring 10 hours per year (on average) and is characterised by having a significant wave height of H MIKE 21 BW - © DHI...
  • Page 33 2DH Boussinesq Wave Module - Examples = 2.65 m with a spectral peak period is T = 8.6 s. The waves are synthesised based on a mean JONSWAP spectrum, as the minimum wave period is set to = 5.7s. The wave disturbance problem can be solved using the classical Boussinesq equations (i.e.
  • Page 34 Examples Figure 4.7 Model results. The upper panel shows the instantaneous surface eleva- tion and the lower panel the wave disturbance Figure 4.8 3D picture of the simulated instantaneous surface elevation in Rønne harbour MIKE 21 BW - © DHI...

  • Page 35: Hanstholm Harbour

    2DH Boussinesq Wave Module - Examples List of data and parameter files All data required for this example are included in the default installation: Binary data files Name: Layout1998.dfs2 Description: Bathymetry, sponge layer and porosity coefficients Name: Ibc.dfs0 Description: Boundary conditions – time series of flux Name: CodeMap.dfs2 Description:...
  • Page 36 Examples Figure 4.9 Hanstholm harbour, Denmark Figure 4.10 Location of Hanstholm harbour Model setup The model setup is illustrated in Figure 4.11. MIKE 21 BW - © DHI...
  • Page 37 (you can modify the specification, if you like, in order to see what hap- pens if e.g. directional waves are applied). The input data files are generated using the Random Wave Generation tool in the MIKE 21 Toolbox (open the file Hanstholm_Harbour_Preprocessing_Data.21T by double clicking).
  • Page 38 Examples than the recommended values (e.g. obtained using the Java Script MIKE 21 BW Model Planner included in the Online Help), which are minimum 7 grid points per wave length and about 35 time steps per minimum wave period. The coarser numerical resolution is chosen in order to reduce the overall computational time and would affect the simulated wave disturbance coeffi- cient marginally.
  • Page 39 2DH Boussinesq Wave Module - Examples Figure 4.14 shows a 3D plot of the instantaneous surface elevation for the entire harbour. Figure 4.13 Model results. Time series of simulated surface elevation at the main harbour entrance (left panel) and at the ferry terminal quay (right panel), see Figure 4.9 Figure 4.14 3D picture of the simulated instantaneous surface elevation in Han-...

  • Page 40: Torsminde Harbour

    Torsminde Harbour Purpose of the example This example illustrates how MIKE 21 BW can be used for simulation of long- period waves (or seiches) inside a harbour. Torsminde Harbour situated at the Danish west coasts (see Figure 4.15) has suffered of seiches causing...
  • Page 41 2DH Boussinesq Wave Module - Examples Figure 4.15 Torsminde Harbour, Denmark. The red dot in the lower panel shows the location In this example the occurrence of the long-period waves is caused by interac- tions of short-period wind waves. The shoaling and breaking of the short- period wave trains are non-linear processes involving a number of compli- cated details.
  • Page 42 The thickness of the sponge layer is here corresponding to one wave length or more. The sponge layer map is generated using the MIKE 21 Toolbox 'Generate Sponge and Porosity Layer Maps' and algebraic manipulations in the Grid Editor.
  • Page 43 At the harbour entrance, along the entrance channel and at northern groin a porosity map is specified for simulation of wave dissipation in the rubble mound structures (see Figure 4.18). A porosity value of 0.85 is used. Also the porosity layer map is generated using the MIKE 21 Toolbox 'Generate...
  • Page 44 Please note that the wave breaking option “exclude wave breaking” is ticked in the MIKE 21 BW Model Setup Planner, see Figure 4.21. This requires an explanation. As stated in the Java Script Note 4 the most important issue is to make sure the breaking waves are well resolved at important areas in the model domain.
  • Page 45 2DH Boussinesq Wave Module - Examples most important issue is to resolved the breaking waves - and you can check this in the section “Check/evaluation of selected T , dx and dt”. Figure 4.19 Numerical parameters Figure 4.20 Wave breaking parameters...
  • Page 46 MIKE 21 BW Model Setup Planner included in the Online Help Model run Before you execute the MIKE 21 BW model simulation you have to provide internal wave boundary data. Simply drag and drop the Torsminde_Har- bour.21t-file into your MIKE Zero shell, go to the 'waves' entry and click on run button, see Figure 4.22.
  • Page 47 2DH Boussinesq Wave Module - Examples Figure 4.22 Generation of internal wave boundary data using the MIKE 21 Toolbox 'Random Wave Generation' tool The length of the simulation is 30 minutes (corresponding to 18001 time steps). The computation time depends on the speed of your PC. For a laptop IBM T40 Pentium M (Centrino, 1.6 GHz and 1GB DDR RAM) the required...
  • Page 48 Examples Roller.lyt' in the MIKE Animator Plus program during or after model execution assuming you have a valid licence for MIKE Animator Plus. From Figure 4.23 and Figure 4.24 is seen that short period wave agitation inside the harbour is very limited.
  • Page 49 Figure 4.25. At the harbour entrance the wave height is reduced to approximately 2 m due to the wave breaking process. Figure 4.25 Map of wave height (upper) and wave disturbance coefficients (lower) simulated by MIKE 21 BW...
  • Page 50 Figure 4.27. In general the agreement is good. MIKE 21 BW pre- dicts slightly higher waves along 600-900 m, which is mainly due to the non- linear shoaling.
  • Page 51 2DH Boussinesq Wave Module - Examples (located in the harbour basin). At Point 3 the dominant wave agitation con- sists of long-period waves, which is even more clearly seen from the normal- ised spectra (lower panel). At Point 3 most of the wave energy is on wave periods within the range 30-60 s, which is in excellent agreement with field measurements.
  • Page 52 Time series of surface elevation at various points (see location map and the output section in DirectionalWaves.BW-file). The lower panel shows the corresponding normalised frequency spectra calculated using the MIKE Zero WSWAT Linear Spectral Analysis Module MIKE 21 BW - © DHI...
  • Page 53 2DH Boussinesq Wave Module - Examples Figures 4.28, 4.29 and 4.30 illustrate further spectral and digital analysis of the MIKE 21 BW model results, which requires a valid license for the WS Wave Analysis Tool included in MIKE Zero. Figure 4.28 Calculated directional spectrum at the Point 1 and Point 2 (see Figure 4.27 for location).
  • Page 54 Calculated bandpass filtered (0.01-0.05 Hz) surface elevation. The pro- file plot shows the long waves along the vertical line depicted in Figure 4.27. The digital filtering is performed using the MIKE Zero WSWAT Digital Filtering Analysis Module List of data and parameter files All data required for this example are included in the default installation: MIKE 21 BW - ©...

  • Page 55: Island

    Description: PFS file generation of internal wave boundary data Name: DirectionalWaves.bw Description: PFS file for setup of MIKE 21 BW run Name: Plot Surface Elevation.plc Description: PFS for 2D visualisation of the simulated surface elevation using the MIKE Zero Plot Composer Grid Plot control Name: Plot Wave Disturbance.plc...
  • Page 56 Cos -directional spreading Model setup The size of model area is 1000 m x 1000 m. The bathymetry is an elliptic paraboloid having an elevation of approximately +0.2 m (above the still water MIKE 21 BW - © DHI...
  • Page 57 The thickness of the sponge layer is corresponding to one wave length or more. The sponge layer map is generated by using the MIKE 21 Toolbox 'Generate Sponge and Porosity Layer Maps' and algebraic manipulations in the Grid Editor. Please note the sponge layer map used in the regular wave case is modified compared to the sponge layer map shown in Figure 4.32.
  • Page 58 270 ºN. The remaining parameters are set as recommended in the User Guide and Online Help. Except for the slot depth, which is set to 16 m, default parameters are used for modelling of the moving shoreline. MIKE 21 BW - © DHI...
  • Page 59 Wave breaking and moving shoreline parameters Model run Before you execute the MIKE 21 BW model simulations you have to provide internal wave boundary data. Simply drag and drop the file 'Wave_Genera- tion.21t' into your MIKE Zero shell, go to the 'waves' entry, select the 'Setup...
  • Page 60 Examples Figure 4.34 Generation of internal wave boundary data using the MIKE 21 Toolbox 'Random Wave Generation' and 'Regular Wave Generation' tool The length of the simulation is 8 minutes and 20 seconds (corresponding to 5001 time steps) for the regular wave simulation and 10 minutes for the direc- tional wave simulation.
  • Page 61 The surface rollers are shown in white. You can make a similar plot by loading (double-click) the PFS-file 'Anim Regular Waves with Roller.lyt’ (or 'Anim Directional Waves with Roller.lyt') into the MIKE Animator Plus program during or after model execution assuming you have a valid licence for MIKE Animator Plus.
  • Page 62 Figure 4.37 (regular waves) and Figure 4.38 (irregular waves). The spectra are calculated by use of the WSWAT Linear Spectral Wave Analysis Module. However, the FFT tool included in the MIKE 21 Toolbox may also be used for calculation of raw spectra.
  • Page 63 2DH Boussinesq Wave Module - Examples Figure 4.37 Time series of surface elevation (left) and corresponding wave spec- trum (right). Regular unidirectional wave case. The data is extracted along the line y= 500 m at water depth (a) 16m, (b) 3m, (c) 1m (all upstream island) (d) 1m and (e) 3m (all downstream island)
  • Page 64 (right). Irregular directional wave case. The data is extracted along the line y= 500 m at water depth (a) 16m, (b) 3m, (c) 1m (all upstream island) (d) 1m and (e) 3m (all downstream island) MIKE 21 BW - © DHI...
  • Page 65 2DH Boussinesq Wave Module - Examples The spatial variation of the significant wave height is presented in Figure 4.39. Please note wave statistics are calculated only in water points, which never dry out. The uprush/downrush area is shown by white colour in Figure 4.39 lower panel.
  • Page 66 Examples Results from a MIKE 21 SW simulation have been compared to results from the MIKE 21 BW irregular wave case. Figure 4.40 shows maps of significant wave heights and wave directions. In Figure 4.41 a comparison is made between the two models prediction of the significant wave height along two cross-sections.
  • Page 67 Figure 4.40 Maps of significant wave height and mean wave direction. Upper panel shows MIKE 21 SW results and lower panel shows results for the MIKE 21 BW irregular wave case. The directional analysis of the Boussinesq model results is made by using the WSWAT Directional Wave Analysis...
  • Page 68 Vector plot of the nearly steady state wave-induced velocity field (after 20 minutes) is shown in Figure 4.42 for the two wave cases. For the MIKE 21 BW simulation the velocity is computed as the time-average of the depth- averaged velocity below the surface roller.
  • Page 69 2DH Boussinesq Wave Module - Examples Figure 4.42 Wave induced current fields. Upper panel: regular waves, lower panel: irregular waves...
  • Page 70 Description: PFS file generation of internal wave boundary data Name: Setup Regular Waves.bw Description: PFS file for setup of MIKE 21 BW run (regular unidirectional waves) Name: Setup Directional Waves.bw Description: PFS file for setup of MIKE 21 BW run...

  • Page 71: Rip Channel

    The thickness of the sponge layer is corresponding to one wave length or more. No sponge layer is used along the lateral boundaries in order to avoid wave radiation into the sponge layer. 1 A link to this paper is available from the MIKE 21 Documentation Index...
  • Page 72 The filter is used at water depths less than approximately 0.5 m, see Figure 4.44. MIKE 21 BW - © DHI...
  • Page 73 2DH Boussinesq Wave Module - Examples Figure 4.44 Map of absorbing sponge layers (left) and map of low-pass filter coeffi- cients (right) A constant Chezy number of C= 35 m /s is used for the bottom friction dissi- pation. This corresponds approximately to a constant wave friction factor of = 0.03 used in Sørensen et al (1998).
  • Page 74 Before you execute the MIKE 21 BW model simulations you have to provide internal wave boundary data. Simply drag and drop the file 'Rip_Channel.21t' into your MIKE Zero shell, go to the 'waves' entry, select the 'Rip channel - H= 2.8m, T= 7.9s, h= 20m and click on run button.
  • Page 75 2DH Boussinesq Wave Module - Examples Figure 4.45 Visualisation (2D) of instantaneous surface elevation...
  • Page 76 Figure 4.46 Visualisation (3D) of instantaneous surface elevation and the surface rollers. The image (and animation) is created in MIKE Animator Plus Due to the increased depth and due to depth refraction by the rip channel, incipient wave breaking is seen to occur comparatively close to the shore along the centre line.
  • Page 77 2DH Boussinesq Wave Module - Examples Figure 4.47 Depth-averaged wave-induced current focusing on the symmetrical cir- culation cell Figure 4.48 Rip current along the rip channel (y= 300 grid points) The rip current significantly affects the wave motion. The large variation of the rip current causes an increase in the wave height, which can be seen in Figure 4.46 (lower panel).
  • Page 78 Map of relative wave height. Please note only the lower half of the com- putational domain is shown Figure 4.50 Variation of relative wave height along rip channel (y= 600 m) and out- side rip channel (y= 200 m) MIKE 21 BW - © DHI...

  • Page 79: Detached Breakwater

    Figure 4.51. It consists of three sections: a 176 m wide horizontal section with a water depth of 13.2 m, a plane sloping beach of 1:50 between the horizon- 1 A link to this paper is available from the MIKE 21 Documentation Index...
  • Page 80 The directional waves will start to break where H ~ 0.5 h, i.e. at water depth 9 m. This means the initial breaking waves are resolved by more than 30 grid points per wave length. MIKE 21 BW - © DHI...
  • Page 81 2DH Boussinesq Wave Module - Examples Figure 4.51 Model bathymetry for the detached breakwater example In the numerical simulations, the physical wave maker is replaced by an inter- nal line of generation, and re-reflection from the boundary is avoided by using a 50 points wide sponge layer offshore from the generation line, see Figure 4.52.
  • Page 82 (0.8 in this case). As discussed in the User Guide we recommend you to use ‘Simple upwinding at steep gradients and near land’ for the space discretisation of the convective terms. However. for numerical MIKE 21 BW - © DHI...
  • Page 83 0.01 default parameters are used for modelling of the moving shoreline. Model run Before you execute the MIKE 21 BW model simulations you have to provide internal wave boundary data. Simply drag and drop the file 'Detached_break- water.21t' into your MIKE Zero shell, go to the 'waves' entry, select the 'Detached breakwater - H= 3.2m, T= 10.7s, h= 13.2m' (for regular wave gen-...
  • Page 84 Examples during or after model execution assuming you have a licence for MIKE Ani- mator Plus. Figure 4.54 Visualisation (2D) of instantaneous surface elevation. Left panel: regu- lar unidirectional waves, right panel: irregular directional waves The computed wave-induced current field for the two cases is shown in Figure 4.56.
  • Page 85 2DH Boussinesq Wave Module - Examples Figure 4.55 Visualisation (3D) of instantaneous surface elevation and the surface rollers. The image (and animation) is created in MIKE Animator Plus. Upper panel: regular unidirectional waves, lower panel: irregular direc- tional waves By comparing Figure 4.56 with the measurements reported in Sørensen et al...
  • Page 86 (upper panel) and irregular, directional waves (lower panel). Computed time-averaged of the velocities beneath the surface rollers. The time-averaging is performed for computational points which always are wet, i.e. outside the swash zone MIKE 21 BW - © DHI...
  • Page 87 2DH Boussinesq Wave Module - Examples Figure 4.57 Circulation cell behind the detached breakwater for the case of direc- tional waves. Computed time-averaged of the velocities beneath the surface rollers. The time-averaging is performed for computational points which can be partly wet, i.e. also inside the swash zone Compared to the case with regular waves, the main features of the eddy structure for random waves are that the quiescent area in the centre of the eddy and the maximum speed is reduced.
  • Page 88 The temporal evolution of the wave-induced velocity is shown in Figure 4.59 for the two considered wave situations. The time series is extracted in a point close to the maximum speed. The figure shows a reduction of approximately MIKE 21 BW - © DHI...
  • Page 89 2DH Boussinesq Wave Module - Examples 30 % in case of irregular, directional waves. The figure also indicates that the time scale for developing the near-steady state flow field is approximately 20 minutes. Figure 4.59 Time series of wave-induced current speed. The time series is extracted at P(375,120) with reference to co-ordinate system shown in Figure 4.56 The spatial variation of the relative wave height is presented in Figure 4.60.
  • Page 90 Relative wave height in circulation cell for the case of regular, unidirec- tional waves (upper panel) and irregular, directional waves (lower panel) List of data and parameter files All data required for this example are included in the default installation: MIKE 21 BW - © DHI...
  • Page 91 Tool Waves Generation line.21t Description: PFS file generation of internal wave boundary data Name: Setup Regular Waves.bw Description: PFS file for setup of MIKE 21 BW run (regular, unidirectional waves) Name: Setup DirectionalWaves.bw Description: PFS file for setup of MIKE 21 BW run...

  • Page 92: Kirkwall Marina

    This example is used in the step-by-step training guide document that can be accessed from the MIKE 21 Documentation Index. The purpose of the step-by-step training guide is to setup a MIKE 21 BW model from scratch and guide you through the various steps in the model setup process, execution and results presentation and visualization.

  • Page 93: Demo-Diffraction

    Council 4.2.10 Demo-Diffraction This simple example simulating wave diffraction is designed for use when running MIKE 21 BW in demo mode. The following data files and specification file (within the folder of Demo-Dif- fraction) are supplied with MIKE 21: Name: Demo-Layout.dfs2...
  • Page 94 At the generation line (j= 21) a time series of fluxes and surface slope is imposed. This time series is generated using the MIKE 21 Toolbox (wave part) program Regular Wave Generation and Random Wave Generation. For...
  • Page 95 Reflection coefficient versus porosity for a 16 m wide absorber in 10 m water depth. The characteristic wave height and wave period is 1 m and 8 s, respectively. Calculated by use of the MIKE 21 Toolbox program Calculation of Reflection coefficient...
  • Page 96 In case of irregular and linear waves the reflection coefficient R can be esti- mated using the formula (based on wave energy considerations):   ----------- - 1 – (4.2)   m0,i MIKE 21 BW - © DHI...
  • Page 97 1DH Boussinesq Wave Module - Examples where H and H are the simulated significant wave height and incident m0,i significant wave height, respectively. From Figure 4.65 is seen that after 5 minutes simulation time the significant wave height is close to one (away from the porosity layer).

  • Page 98: Sloping Beach With Wave Breaking And Moving Shoreline

    = 0.01 and a smoothing parameter of = 100 (default values in MIKE 21 BW). A 50 point wide sponge layer is used in the slot in order to damp the oscillations in the slot, see Figure 4.67.
  • Page 99 1DH Boussinesq Wave Module - Examples As usual the enhanced Boussinesq equations are solved (i.e. deep-water terms included) in 1DH applications. Figure 4.67 Model setup A structured mesh with elements with an edge length of 0.02 m is used. For the 27.5 m long channel this results in 1375 elements and 1376 nodes.
  • Page 100 Madsen et al (1997a) p. 276ff. An example of the spatial variation of the undertow is shown in Figure 4.70. Paper included in the Scientific Background MIKE 21 BW - © DHI...
  • Page 101 1DH Boussinesq Wave Module - Examples Figure 4.70 Phase-averaged model results. Spatial variation of the undertow Figure 4.71 Moving shoreline model results. Temporal variation of the vertical and horizontal run-up height. The still water shoreline is located at x = 23.3 The simulated shoreline motion is converted into a vertical and a horizontal displacement as illustrated in Figure 4.71.

  • Page 102: Torsminde Barred Beach

    4.3.3 Torsminde barred beach Purpose of the example The purpose of this example is to illustrate how to model wave breaking in case of irregular waves propagating over a natural barred beach profile. The MIKE 21 BW - © DHI...
  • Page 103 1DH Boussinesq Wave Module - Examples beach profile is taken from a 2D-bathymetry map covering the area north of Torsminde harbour, see Figure 5.6. Model setup The model setup is illustrated in Figure 4.73. In the first part of the profile the slope is approximately 1:100, which is increased to approximately 1:50 on the first bar and further to approximately 1:30 on the second bar.
  • Page 104 Spatial variation of the significant wave height and the maxi- mum wave height is shown in Figure 4.75. In Figure 4.76 the variation of the two nonlinear measures, skewness and atiltness are presented. MIKE 21 BW - © DHI...
  • Page 105 1DH Boussinesq Wave Module - Examples Figure 4.74 Deterministic model results. Upper: Line series of surface elevation on top of the bathymetry. Also the simulated extreme levels of the surface elevation (taken throughout the entire simulation time) is indicated. The dashed line indicates the variation of the original bathymetry at the still water shoreline.
  • Page 106 Phase-averaged model results. Spatial variation of the significant and maximum wave height over a barred beach profile Figure 4.76 Phase-averaged model results. Spatial variation of the skewness and atiltness over a barred beach profile MIKE 21 BW - © DHI...
  • Page 107 1DH Boussinesq Wave Module - Examples Figure 4.77 Model results. Offshore (upper) and onshore (lower) wave spectra. The spectra are calculated using the WS Spectral Analysis module in MIKE Figure 4.78 Model results. 3D pictures of the simulated instantaneous surface ele- vation.
  • Page 108 Examples Binary data files Name: Torsminde_mesh.dfs1 Description: Bathymetry Name: Torsminde_model.dfs1 Description: sponge, porosity, resistance and filter coefficients Name: H3.0Tp9Tm2.5.dfs0 Description: Wave Boundary conditions Parameter files Name: Torsminde.bw Description: Torsminde Barred beach MIKE 21 BW - © DHI...

  • Page 109: Reference Manual

    It is intended that you use this manual when you are doing model applications with MIKE 21 BW and need to know how various input, output, etc. are spec- ified or defined. The sections are organised in the order in which they appear in the MIKE 21 BW editor (Figure 5.1).

  • Page 110: Module Selection

    Boundary  Simulation period  5.2.1 Module selection This version of MIKE 21 BW includes two modules: 2DH Boussinesq wave module  1DH Boussinesq wave module  The 2DH module (two horizontal space coordinates) solves the enhanced Boussinesq equations by an implicit finite difference techniques with variable defined on a space-staggered rectangular grid.
  • Page 111 5.2.2 Bathymetry Providing MIKE 21 BW with a suitable model bathymetry is essential for obtaining reliable results from your model. Setting up the bathymetry requires more than just specifying a 2D/1D array of accurate water depths covering the area of interest. It also includes the appropriate selection of the area to be modelled, the grid spacing, location and type of boundaries etc.
  • Page 112 It is stressed that the selection of model area and artificial land areas is closely connected to the wave conditions to be modelled. In this context the wave direction and directional spreading is important (see section 5.3.4 on Setup of internal generation lines). MIKE 21 BW - © DHI...
  • Page 113 Basic Parameters Figure 5.5 Enclosed harbour with reduced computational area In the example, the shallow area inside the harbour is also converted to arti- ficial land values, for two reasons: It is assumed that the shallow area/beach will absorb the wave energy. ...
  • Page 114 A typical situation is schematised in Figure 5.6. Figure 5.6 Selection of a coastal profile for use in MIKE 21 BW 1DH The line on top of the 2D bathymetry plot indicates the location of the extracted profile. It is noticed that the bathymetric profile includes depths larger than zero, which means wave breaking and wave run-up have to be included in this model setup.
  • Page 115 2DH applications and less than about 0.5 in 1DH applications. For an efficient determination of the model setup resolution in space, time and model execution, you can use the MIKE 21 BW Model Setup Planner included in the Online Help.
  • Page 116 Reference Manual Figure 5.7 MIKE 21 BW Model Setup Planner efficient model setup and execution Example A minimum wave period of T = 6 s and a minimum water depth h = 4 m gives a minimum wave length of L = 35 m.
  • Page 117 Wave breaking Boussinesq simulations without wave breaking By comparison, the Boussinesq equations in MIKE 21 BW use the depth-inte- grated velocity as the main velocity variable. This can never exceed the speed of wave propagation. As a consequence, shoaling waves in MIKE 21 BW will continue to shorten and steepen until they can no longer be resolved adequately by the computational grid.
  • Page 118 Boussinesq simulations with wave breaking Wave breaking and moving shoreline have been implemented in a both mod- ules of MIKE 21 BW (1DH and 2DH module). The inclusion of wave breaking is based on the surface roller concept for spilling breakers following the for- mulation by Schäffer et al (1993), Madsen et al (1997a,b) and Sørensen et al...

  • Page 119: Type Of Equation

    Basic Parameters Remarks and Hints Time domain wave modelling including wave breaking and moving shoreline is a difficult numerical task. You may sometimes see numerical instabilities and eventually blow-up in some of your applications. In such case please fol- low the guideline given in Section 5.5.4. We strongly recommend you to carefully walk through the application exam- ples included in this installation prior to your first application with wave break- ing and moving shoreline.
  • Page 120 For stability reasons it is recommended to use the scheme ‘Simple upwinding at steep gradients and near land’ for the space discretisation of the convec- tive terms in connection with simulations including wave breaking (and mov- ing shoreline). MIKE 21 BW - © DHI...

  • Page 121: Boundary

    Basic Parameters Time discretisation of cross-Boussinesq terms The representation of the Boussinesq cross terms (i.e. Q and Q the x-sweep and P and P in the y-sweep) has required special atten- tion. Time-extrapolation factor of 1 In order to obtain the correct time-centering, we have used linear time-extrap- olation of these terms.

  • Page 122: Simulation Period

    Recommendations As open boundaries are treated as fully reflective in MIKE 21 BW it is recom- mended to use internal wave generation. In 2DH applications involving wave- current interaction an open boundary may be used, e.g. an open flux bound- ary.
  • Page 123 25-35 time steps. Again it should be checked if the Courant criterion is fulfilled. It is recommended to use the MIKE 21 BW Model Setup Planner for determination of the optimal time step. Including wave breaking and moving shoreline: ...

  • Page 124: Calibration Parameters

    This may for example be Chart Datum, lowest astronomical tide (LAT), or mean sea level (MSL). The actual datum you use is not important. What is important, is that for each simulation you must provide the model with MIKE 21 BW - © DHI...

  • Page 125: Boundary Data

    Calibration Parameters the correct height of the still water level, i.e. the model reference level, rela- tive to the datum used in setting up your bathymetry, see the figure below. This is done by specifying the Shift of Reference Level. Then, the model will automatically make any internal adjustments necessary for that particular model simulation.

  • Page 126: Surface Elevation

    This is the main reason that internal wave generation is often preferred as opposed to 'open boundary wave generation'. To prepare the boundary input files the wave tools in the MIKE 21 Toolbox may be applied. Closed boundary A closed boundary (land points) does not allow for flow across the boundary.

  • Page 127: Internal Wave Generation

    To prepare the wave input data the wave tools in the MIKE 21 Toolbox should be applied. You specify the number of internal generation lines to be used in your simula-...
  • Page 128 The useful model area is further restricted due to diffraction of waves into the shadow area outside the thin red lines. Note, that the directional information on the waves is specified when generat- ing the input wave files using the MIKE 21 Toolbox tool Random Wave Gen- eration. Figure 5.14 Model setup for modelling directional waves MIKE 21 BW - ©...
  • Page 129 Calibration Parameters The correct generation of the incident wave conditions can only be obtained on the assumption that the water depth is constant along the open boundary or the internal generation line. Therefore, the open boundaries and internal generation lines should be placed in areas where there is a small variation in the water depth.
  • Page 130 . Please note that the co-ordinate system refers to the general (or global) co-ordinate system.  Figure 5.17 Definition of generation lines and main wave directions , when main using two generation lines to generate a wave field. MIKE 21 BW - © DHI...
  • Page 131 How to join internal generation lines in a corner Examples of wave fields MIKE 21 BW can model regular as well as irregular waves. Normal incident irregular waves Irregular waves can be applied both using internal wave generation and an open boundary in case of normal incidence, i.e.

  • Page 132: Bottom Friction

    Reference Manual Figure 5.20 Boussinesq wave simulation using unidirectional wave generation input (dfs1), see the MIKE 21 Toolbox tool Random Wave Generation Incident directional irregular waves For incident directional irregular waves, i.e. waves having an angle different from 90 degrees relative to the generation line, only internal wave generation is possible.
  • Page 133 Manning number formulation  Chezy number The bottom friction formulation used in MIKE 21 BW has been set up using the Chezy bed friction rule. With the Chezy bed friction rule, the shear stress at the bed can be expressed in terms of the Chezy number, C, as gU U...

  • Page 134: Eddy Viscosity

    Manning number has the unit [m /s], and h is the water depth. Please note that the Manning number used in MIKE 21 BW is the reciprocal value of the Manning number described in some hydraulic text books.

  • Page 135: Filtering

    MIKE 21 BW simulations. Remarks and hints Eddy viscosity is mainly introduced in MIKE 21 BW for modelling of wave-cur- rent interaction, where sub grid effects in the current field are not resolved. Please also note that a wave-induced flow field can only exist when the forc- ing by radiation stress is balanced by bottom friction and mixing processes.

  • Page 136: Wave Breaking

    0.25 and subsequently make an interpolation. 5.3.8 Wave Breaking The incorporation of wave breaking in MIKE 21 BW is based on the concept of surface rollers. Surface roller concept The wave breaking is assumed initiated if the slope of the local water surface exceeds a certain angle, in which case the geometry of the surface roller is determined.
  • Page 137 Calibration Parameters made to Schäffer et al (1993) and Madsen et al (1997a). The latter paper is included in the scientific documentation. Although the breaker model is not designed for to handle plunging breakers, successful results have been obtained even with the default breaker parameters listed below. Figure 5.23 Cross-section of a breaking wave and the assumed vertical profile of the horizontal velocity components...
  • Page 138 Spilling takes place when steep waves propagate over a flat shoreface. Spill- ing breaking is a gradual breaking process which takes place as a foam bore on the front topside of the wave over a distance of 6-7 wave lengths. Figure 5.25 Plunging MIKE 21 BW - © DHI...

  • Page 139: Moving Shoreline

    5.3.9 Moving shoreline The incorporation of a moving shoreline in MIKE 21 BW is based on the fol- lowing approach: the computation domain is extended artificially by replacing the solid beach by a permeable beach characterised by a very small porosity.
  • Page 140 Please note Numerical modelling of a moving shoreline is a very difficult task. You may sometimes see numerical instabilities and eventually blow-up in some of your MIKE 21 BW - © DHI...

  • Page 141: Porosity Layers

    Calibration Parameters applications. In such situations we recommend you to introduce a slot friction coefficient, e.g. 0.01-0.1. You may also increase the width and/or the depth of the slot. 5.3.10 Porosity layers Porosity values are used to model either partial reflection and/or transmission through structures.
  • Page 142 For a given set of porous flow parameters (see section Recommended poros- ity layer parameters below), the porosity values required to obtain a desired reflection coefficient, can be determined by the use of the MIKE 21 Toolbox program Calculation of Reflection Coefficients.
  • Page 143 For Boussinesq wave simulations, the equations in MIKE 21 BW have been modified to include porosity and the effects of non-Darcy flow through porous media. In this way, it is possible for MIKE 21 to model partial reflection, absorption and transmission of wave energy at porous structures such as rubble mound breakwaters (see e.g.
  • Page 144 Recipe for generation of porosity maps An effective procedure for establishment of porosity maps in connection with application of MIKE 21 BW 2DH in wave disturbance analysis is outlined below. Step 1 Open your bathymetry file (dfs2-file) and change the land value (e.g.
  • Page 145 Figure 5.31 The MIKE 21 Toolbox programme Calculation of Reflection Coefficients is used to estimate the porosity value to be used in MIKE 21 BW. Step 3 The next step is to establish the porosity map. Most often this is generated using the MIKE 21 Toolbox programme Generate Porosity Map as shown in Figure 5.31.
  • Page 146 (typically 10-20 sub-areas). For each of these sub-areas a porosity value is determined using the MIKE 21 Toolbox programme Calculation of Reflection Coefficient. For each of the defined sub-areas the original porosity (0.5 in this example) is replaced by the...
  • Page 147 Calibration Parameters Figure 5.34 Example of porosity map correction at harbour entrance areas. Hint In order to obtain a quick rough estimate of the wave disturbance inside a harbour it is a good idea to run a simulation using a porosity map with a con- stant porosity along all porous structures.

  • Page 148: Sponge Layers

    2DH Boussinesq wave module In the figure below sponge layers are used to model a fully absorbing beach and to absorb waves radiating out of the harbour area. MIKE 21 BW - © DHI...
  • Page 149 Calibration Parameters Figure 5.36 Example of a sponge layer map 1DH Boussinesq wave module In connection with modelling of non-linear wave transformation on coastal profiles sponge layers are usually applied at the two model domain extremes. As for 2D applications the sponge layers at j= 0 are used for absorption of wave energy propagation out of the model domain.
  • Page 150 Given the guidelines above, you are free to select your own values for the sponge layer (damping) coefficients. Tool for generation of files including sponge layers Most often you will use the MIKE 21 Toolbox program Generate Sponge and Porosity Layer Maps for generation of sponge layers: Recommended sponge values...
  • Page 151 Calibration Parameters square root for the subsequent points. The following values are obtained: Grid Point Sponge Value Land Point Land Point 3.9045 2.5947 1.9492 1.5955 1.3868 1.2572 1.1738 1.1187 1.0816 1.0565 1.0392 1.0273 1.0190 1.0132 1.0092 1.0064 1.0045 1.0031 1.0022 Open Water Remarks and hints An absorbing sponge layer damps the waves (per default) relative to the still...

  • Page 152: Output Parameters

    Output Parameters Deterministic parameters The basic results from a MIKE 21 BW simulation consist of arrays containing the total water depth, h, the depth-integrated velocity, P, in the x-direction, and the depth-integrated velocity, Q, in the y-direction. For the 1DH module an auxiliary variable, w, is saved as well.
  • Page 153 For point series data (type 0) you can choose a number of different points in each file. You can view the results easily using the relevant MIKE Zero tools by clicking on the “View” button or by e.g. presenting the results using Plot Composer as in Figure 5.38.
  • Page 154 The surface elevation is a basic model parameter and should always be included in your model specifications. It is calculated on basis of computed water depth and bathymetry. You can use this item for 3D visualisation of the instantaneous surface elevation (see e.g. Figure 5.40) using MIKE Animator Plus. Water depth The water depth is a prognostic variable similar to the P flux and Q flux.
  • Page 155 Output Parameters Figure 5.40 Visualisation (3D) of instantaneous surface elevation using MIKE Ani- mator Plus, where input is a dfs2 file including the surface elevation. P flux The prognostic variable P flux is the depth-integrated flux density in x-direc- tion.
  • Page 156 Figure 5.41) using MIKE Animator Plus. For generation of 3D images and animations you have to save the water level and water level (roller) into two separate dfs2 files. You may use the MIKE Animator Plus setup included in the examples as an template.
  • Page 157 Output Parameters Figure 5.42 Example of 2D map and time series of surface elevation in two selected points Remarks and hints When you specify the spatial range of your output data you also have to specify the number of points you would like to save, N .

  • Page 158: Phase-Averaged Parameters

    In case of “subseries statistics” your output items will be set to zero at the update inter- val. In most cases you would select “Cumulative statistics”. NOTE: MIKE 21 BW - © DHI...
  • Page 159  For point series data (type 0) you can choose a number of different points in each file. You can view the results easily using the relevant MIKE Zero tools by clicking on the “View” button. Output parameters You can choose following output parameter types: Significant wave height ...
  • Page 160 Usually you will include this out- put item in your model specifications when wave breaking and moving shore- MIKE 21 BW - © DHI...
  • Page 161 Output Parameters line is included. The wave set-down and wave setup can be calculated from this item. Mean flux, P The mean flux P is defined as time averaged depth-integrated flux density in x-direction Mean flux, Q The mean flux Q is defined as time averaged depth-integrated flux density in y-direction.
  • Page 162 For further informa- tion on this output type please see Goda and Morinobu (1998) p. 314ff. Usually you will not include this quantity in your model output specifications. MIKE 21 BW - © DHI...
  • Page 163 Output Parameters Figure 5.46 Example of phase-averaged output showing the wave-induced current (upper). The lower figure shows the instantaneous surface elevation on top of the bathymetry...

  • Page 164: Wave Disturbance Parameters

    Figure 5.47 A number of wave disturbance parameters can be extracted from a MIKE 21 BW simulation including detailed sub-area statistics The wave disturbance coefficient is defined as the ratio of the significant wave height relative to the incoming significant wave height. If e.g. the wave height at a given position is 0.5 m and the incoming (offshore) wave height is...
  • Page 165 Output Parameters Figure 5.48 An example of a 2D map of wave disturbance coefficients Type of scaling You must specify whether the scaling of the coefficients should be relative to a user defined incoming wave height or relative to the wave height in a spe- cific grid point.
  • Page 166 (statistically speaking). If the calculation is started at arrival of the first wave (wave No. 1) the calculated wave disturbance coeffi- cients inside the harbour may be underestimated. MIKE 21 BW - © DHI...

  • Page 167: Moving Shoreline Parameters

    Note that for regular waves the significant wave height is a factor larger than the wave height. 5.4.4 Moving shoreline parameters The moving shoreline output MIKE 21 BW 1DH application only consists of time series containing the following three output items: Horizontal run-up  Vertical run-up ...
  • Page 168 Vertical run-up The vertical run-up is defined as the vertical displacement of the still water level. Total run-up The total run-up is defined as the run-up distance measured along the a swash profile. MIKE 21 BW - © DHI...

  • Page 169: Hot Start Parameters

    Output Parameters Figure 5.52 Example of moving shoreline output. Upper panel shows the coastal profile, middle the vertical run-up and lower panel the total run-up measured along the profile 5.4.5 Hot start Parameters The hot start facility allows you to start a simulation as a continuation of an earlier run.

  • Page 170: Entries Arranged Alphabetically

    The model simulation log file is shown at all time. The log file is an ASCII file and has the same name as the input PFS-file, but the suffix is “.log”. This file MIKE 21 BW - © DHI...

  • Page 171: Artificial Land

    Entries Arranged Alphabetically contains a list of all the specifications used for the execution, plus information about the input data and the output data. If a Blow-up is detected, then the error messages will appear in the log file. Right clicking on the log file in the progress windows, you may use the "Find…"...

  • Page 172: Batch Mode

    Following this procedure your runs will be execute in a row as described in the run.bat file. Batch execution can also be initiated using the Launch Simulation Manager available in Start -> All Programs -> MIKE [year] -> MIKE Zero -> Tools -> Launch Simulation Engine. MIKE 21 BW - © DHI...

  • Page 173: Blow-Up

    5.5.4 Blow-up MIKE 21 BW checks the requests and input from you as much as possible, but in order to minimise the number of restrictions on potential applications, it is allowed to request MIKE 21 BW to perform unrealistic simulations. Also, MIKE 21 BW is an advanced numerical model, which means that the possibil- ity of numerical instabilities (“blow-ups”) exists.
  • Page 174 The plots not only show you where the instability starts, they may also be used as a guide to determine the cause. What action needs to be taken will depend on the main cause of the instability. MIKE 21 BW - © DHI...
  • Page 175 Entries Arranged Alphabetically Blow-up near porosity layers The reason for the blow-up may be application of too small porosity values. Most often the porosity should be larger than 0.2. If you still have a blow-up, you can try to use a larger value or increase the number of porosity layers in front of the structure.
  • Page 176 In order to avoid an instability you may consider generating new open bound- ary or internal generation data using a different initial random seed. The over- all statistics of the data will not change (it is just a different realisation). MIKE 21 BW - © DHI...

  • Page 177: Boussinesq Cross Terms

    Entries Arranged Alphabetically Reducing the wave height As long as the problem you would like to model is not strongly non-linear you may reduce the incident significant wave height. Crash before the first time step General description You have started the execution of a simulation and it stops immediately after. A typical message will be: Figure 5.55 Stack overflow problem...

  • Page 178: Courant Number

    5.5.7 Deep water terms MIKE 21 BW solves the classical form and an enhanced form of the Boussin- esq equations. The enhanced equations are different from the classical for- mulation as a number of new Boussinesq correction terms (so-called deep water terms) are included.
  • Page 179 In case of breaking waves and moving shoreline boundary 20-40 grid points are required for the most energetic waves (20 points are assumed in the MIKE 21 BW Model Setup Planner) for the minimum wave period. Find the time step for the numerical time integration. Beside fulfilling the...

  • Page 180: Hardware Requirements

    You can evaluate the required computational time if you know the computa- tional speed (CPS) of your PC running MIKE 21 BW. An estimate is given in the pop-up dialog when you start executing the program. For a 4-500 MHz...

  • Page 181: High-Frequency Noise

    Entries Arranged Alphabetically include the calculation of the wave disturbance coefficients.  Note that an estimate of the required storage for your specified output data is provided through the graphical user interface. RAM requirements You can evaluate the required internal memory by 4 –...

  • Page 182: Linear Dispersion Relation

    Online Help. Boussinesq equations You can use this dispersion relation as a good approximation to the phase celerity of the Boussinesq equations used in MIKE 21 BW as long as you fulfil the requirements: Classical Boussinesq equations: h <...

  • Page 183: Minimum Wave Period

    For generation of files including sponge, porosity, bed friction and filter coeffi- cients you have to use the original bathymetry/profile file (as used as input to the MIKE 21 Toolbox program “Mesh Generation for MIKE 21 BW”). Linear interpolation is used to obtain the respective values at the non-uniformed dis- tributed node points.

  • Page 184: Numerical Damping

    The first panel shows the result of a simulation with time-extrapolation (default in MIKE 21 BW, time-extrapolation factor = 1). On the second panel the time-extrapolation has been omitted corresponding to a backward time- centring of the cross-terms (time-extrapolation factor = 0). Finally, the third panel shows the results of using a mixture, i.e.
  • Page 185 Entries Arranged Alphabetically Figure 5.58 Application of different time-extrapolation factors...

  • Page 186: Option Parameters

    Name_of_Text_Editor is set to “Textpad.exe” (see section 5.2.1). The default value is one. Figure 5.59 Inclusion of an option parameter in a MIKE 21 BW PFS-file 5.5.16 References The references listed below provide you with more basic information applica-...
  • Page 187 Entries Arranged Alphabetically Ozsanne, F, Chadwick, A J, Huntley, D A, Simmonds, D J and Lawrence, J (2000) Velocity predictions for shoaling waves with a Boussinesq-type model. Coastal Eng., 41, 361-397. Kuang-ming, Y, M Rugbjerg and A Kej, (1987) Numerical modelling of har- bour disturbance in comparison with physical modelling and field measure- ments.
  • Page 188 The Sea, Ocean Engineering Science, 9, Part B, Chapter 33, pp 1067-1103. Eagleson, P S & Dean, R G (1966) Small Amplitude Wave Theory. In: Estu- ary and Coastline Hydrodynamics, editor A T Ippen, McGraw-Hill, New York. MIKE 21 BW - © DHI...
  • Page 189 Entries Arranged Alphabetically Hamm, L, Madsen, P A & Peregrine, D H (1992) Non-linear wave dynamics in the near-shore zone. A review paper on MAST Morphodynamics. Larsen, J, Madsen, P A & Abbott, M B (1984) Numerical modelling of direc- tional seas in deepwater.
  • Page 190 Reference Manual MIKE 21 BW - © DHI...

  • Page 191: Scientific Documentation

    Scientific Documentation Scientific documentation for MIKE 21 BW can be accessed online via the Documentation index. Likewise the following papers are available: Abbott, M B, McCowan, A D & Warren, I R (1984): "Accuracy of Short-wave Numerical" Models. J. Hydr. Eng., 110, 173-197.
  • Page 192 Scientific Documentation MIKE 21 BW - © DHI...

  • Page 193: Index

    INDEX...
  • Page 194 Initial breaking angle ..137 1DH module ....110 Initial surface elevation ..126 MIKE 21 BW - © DHI...
  • Page 195 ... 161 Mesh generation ... 182 MIKE 21 BW Model Setup Planner 115 Quadratic upwinding ..120 MIKE 21 Toolbox .
  • Page 196 ... . 143 Two generation lines ..129 Two internal generation lines ..35 MIKE 21 BW - © DHI...

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