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Reference Manual

182

MIKE 21 BW - © DHI

5.5.11 Linear dispersion relation

For small amplitude waves, non-linear effects can be neglected and analyti-
cal methods can be used to derive the linear dispersion relation.

The phase celerity using Stokes first order theory is given by 

(5.20)

where 

c

 is the celerity (= L/T), k the wave number (= 2

/L), 

h

 the water depth, 

and 

g

 is the gravitational acceleration (= 9.81 m/s

2

). L and T are the wave 

length and wave period, respectively.

For the calculation of various wave parameters you can use DHI's linear 
wave calculator included in the 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

max

/L

0,min

 < 0.22 

Enhanced Boussinesq equations: h

max

/L

0,min

 < 0.50

Here h

max

 denotes the maximum water depth in the model domain, and L

0,min

 

the minimum wave length in deep water (= gT

2

/2

). T is the minimum wave 

period. A comparison between the phase celerity derived for the Boussinesq 
equations and Stokes first order theory is shown in Madsen et al (1991) and 
Madsen and Sørensen (1992), see Scientific Documentation.

5.5.12 Mesh generation

You can use the MIKE 21 BW 1DH module for either structured or unstruc-
tured meshes. An unstructured mesh is recommended for detailed modelling 
of surf and swash zone dynamics as this allows you to use a high spatial res-
olution in areas of particularly interest. An extracted profile from a e.g. a dfs2 
bathymetry file can be used directly in MIKE 21 BW 1DH as a structured 
mesh having a constant resolution/grid spacing. 

If you would like to increase the spatial resolution in local areas (see e.g. the 
example below) you first have to use the MIKE 21 Toolbox program “Mesh 
Generation for MIKE 21 BW” for generation of an unstructured mesh. Based 
on the structured data (dfs1-type data file) this tool generates a new file con-
taining two items; Item 1: co-ordinate (in length unit) of the node in the mesh 
and Item 2: the corresponding water depth in the node. The second item is 
used as the bathymetry mesh.

c

g tanh(kh)

k

------------------------

=

Содержание 21 BW

Страница 1: ...MIKE 2017 MIKE 21 BW Boussinesq Waves Module User Guide...

Страница 2: ...2...

Страница 3: ...EQUENTIAL DAMAGES OR DAMAGES FOR LOSS OF BUSINESS PROFITS OR SAVINGS BUSINESS INTERRUPTION LOSS OF BUSINESS INFORMA TION OR OTHER PECUNIARY LOSS ARISING OUT OF THE USE OF OR THE INABILITY TO USE THIS...

Страница 4: ...4 MIKE 21 BW DHI...

Страница 5: ...data 20 3 5 Calibrating and Verifying the Model 20 3 5 1 Purpose 20 3 5 2 Verification 21 3 5 3 Calibration parameters 21 3 6 Running the Production Simulations 21 3 7 Presenting the Results 21 3 8 A...

Страница 6: ...ers 148 5 4 Output Parameters 152 5 4 1 Deterministic parameters 152 5 4 2 Phase averaged parameters 158 5 4 3 Wave disturbance parameters 164 5 4 4 Moving shoreline parameters 167 5 4 5 Hot start Par...

Страница 7: ...eters are selected and how the results are presented Chapter 5 Reference Manual p 109 describes the parameters in the MIKE 21 BW dialogues It provides more details on specific aspects of the opera tio...

Страница 8: ...types and file editors the Plot Composer the MIKE Zero Toolbox the MIKE 21 Toolbox and the Bathymetry Editor The documentation for these can be found from the MIKE Zero Documentation Index A step by s...

Страница 9: ...ssinesq type equations originally derived by Madsen et al 1991 and Madsen and S rensen 1992 1 make the modules suitable for simulation of the propagation of directional wave trains travelling from dee...

Страница 10: ...eneration of bound sub harmonics and super harmonics and near resonant triad interactions can also be modelled using MIKE 21 BW Thus details like the generation and release of low frequency oscillatio...

Страница 11: ...IKE 21 BW also includes porosity for the simulation of partial reflection from and transmission through piers and breakwaters Sponge layers are applied when full absorption of wave energy is required...

Страница 12: ...ew harbours is often performed using a combination of simulations with synthetic white noise spectra and simulations with natural wave conditions The purpose of the for mer type of simulations is to i...

Страница 13: ...General Description 13 Figure 2 4 Simulation of wave penetration into Frederikshavn harbour Denmark...

Страница 14: ...ications related to the 1DH module include computation of wave transformation for nonlinear waves from deep water through the surf zone and all the way up to the beach analysis of generation and relea...

Страница 15: ...of low fre quency energy due to primary wave transformation can be computed This is of significant importance for harbour resonance seiching and coastal pro cesses Figure 2 6 Transformation of irregu...

Страница 16: ...Introduction 16 MIKE 21 BW DHI...

Страница 17: ...he follow ing sections For your particular study only some of the tasks might be rele vant Please note that whenever a word is written in italics it is included as an entry in the Online Help and in t...

Страница 18: ...a under Bathymetry The choice of the grid spacing and time step depends on the wave conditions for which simulations are to be performed and the water depth in the area of interest The ratio of the ma...

Страница 19: ...ke a long time if for example you have to initiate a monitor ing program Alternatively it may be carried out very quickly if you are able to use existing data which are immediately available In all ca...

Страница 20: ...section 5 3 10 Porosity layers 3 4 5 Boundary data In most cases you will force the model by waves generated inside the model domain The internal wave generation of waves allows you to absorb all wav...

Страница 21: ...ts to your measurements or other information you will in many cases see differences between the two The purpose of the calibration is then to tune the model so that these differences become negligible...

Страница 22: ...tion can be accessed online via the Documentation index Providing MIKE21 BW with a suitable bathymetry dfs2 data file for 2DH applications and dfs1 data file for 1DH applications is essential for obta...

Страница 23: ...hment of a porosity map is described in this User Guide see Section 5 3 10 The porosity map is easily created using the MIKE 21 Toolbox Generate Sponge and Porosity Layer Map tool The porosity values...

Страница 24: ...eight For harbour agitation studies also maps of the wave disturbance coefficient should be saved 7 It is recommended to view the results during the model run to make sure everything is as expected Th...

Страница 25: ...directory is provided The directory names are as follows 2DH Boussinesq Wave Module Numerical flume test Examples MIKE_21 BW Flume Diffraction test Examples MIKE_21 BW Diffraction R nne Harbour Examp...

Страница 26: ...d in Figure 4 1 The length in the model east west direction of the flume is 350 m and the width in the model north south direction is 55 m The uniform depth is 10 m Figure 4 1 Model layout The 10 poin...

Страница 27: ...sponding to the spectral peak wave period In this example the thickness of the 10 point wide sponge layer is 0 5 0 6 times the wave length correspond ing to the spectral peak wave period However from...

Страница 28: ...egular wave train Model setup The model setup is illustrated in Figure 4 3 The model size is 1200 m by 700 m with a uniform depth of 40 m Wave absorbing sponge layers are applied at the eastern and no...

Страница 29: ...mulation requires the so called deep water terms to be included i e it is the enhanced Bouss inesq type equations which have to be solved in this case The grid spacing is chosen to be 10 m representin...

Страница 30: ...the wave disturbance coefficient behind a fully reflective breakwater The model results are in good agreement with semi analytical solutions to the Helmholtz equation see e g Shore Protection Manual 1...

Страница 31: ...in R nne harbour Den mark Left panel shows the harbour layout before the cruise terminal was constructed Model setup The model setup is illustrated in Figure 4 6 The model area is chosen based on foll...

Страница 32: ...int wide sponge layer in order to absorb the waves here In reality the waves will break at a small beach here but this will not affect the waves in the central part of the harbour Figure 4 6 Model set...

Страница 33: ...n the deepest part of the model The length of the simulation is 12 minutes corresponding to 1801 time steps Model results The model results are presented in Figure 4 7 showing a contour plot of the in...

Страница 34: ...BW DHI 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 elevati...

Страница 35: ...ration lines for obliquely incident unidirectional waves Hanstholm har bour Denmark situated at the Danish west coast is used in this case see Figure 4 9 and 4 10 In this example the enhanced Boussine...

Страница 36: ...Examples 36 MIKE 21 BW DHI Figure 4 9 Hanstholm harbour Denmark Figure 4 10 Location of Hanstholm harbour Model setup The model setup is illustrated in Figure 4 11...

Страница 37: ...isation purposes oblique incident unidirectional irregular waves are used 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...

Страница 38: ...ed wave disturbance coeffi cient marginally The length of the simulation is 25 minutes corresponding to 7501 time steps Model results The model results are presented in Figure 4 12 showing a contour p...

Страница 39: ...sults 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...

Страница 40: ...ng period wave energy on wave periods 30 60 s in the harbour Name Layout dfs2 Description Bathymetry sponge layer and porosity coefficients Name Hanstholm bw Description Wave disturbance test Name Han...

Страница 41: ...ow water lead to substantial cross spectral energy transfer over relatively short dis tances and during shoaling still more energy will be transferred into bound sub harmonics and super harmonics In a...

Страница 42: ...he 20 40 points per wave length at depths 2 10 m where the pri mary part of the waves will break In most practical 2DH applications includ ing wave breaking a grid spacing of 1 2 m is used for peak wa...

Страница 43: ...e coefficient map At the harbour entrance along the entrance channel and at northern groin a porosity map is specified for simulation of wave dissipation in the rubble mound structures see Figure 4 18...

Страница 44: ...ype is set to 3 and the predominant wave direction is set to 270 N Hence we assume the breaking waves rollers mainly propagate in the positive x direction which is a good approximation in this case Th...

Страница 45: ...ule Examples 45 most important issue is to resolved the breaking waves and you can check this in the section Check evaluation of selected Tmin dx and dt Figure 4 19 Numerical parameters Figure 4 20 Wa...

Страница 46: ...uded 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...

Страница 47: ...surface elevation You can make a similar plot by loading drag and drop the PFS file MzPlot Surfaceelevation plc into the MIKE Zero shell during or after model execution From the figure is seen that t...

Страница 48: ...for MIKE Animator Plus From Figure 4 23 and Figure 4 24 is seen that short period wave agitation inside the harbour is very limited Figure 4 23 2D visualisation of instantaneous surface elevation Figu...

Страница 49: ...wave height and wave disturbance coefficient is presented in Figure 4 25 At the harbour entrance the wave height is reduced to approximately 2 m due to the wave breaking process Figure 4 25 Map of wa...

Страница 50: ...line indicated in 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 At the harbour entrance 1100 m...

Страница 51: ...ore 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 Please...

Страница 52: ...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 Modu...

Страница 53: ...WS Wave Analysis Tool included in MIKE Zero Figure 4 28 Calculated directional spectrum at the Point 1 and Point 2 see Figure 4 27 for location The spectrum is calculated using the MIKE Zero WSWAT Dir...

Страница 54: ...ion 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 a...

Страница 55: ...ame Sponge dfs2 Description Map of sponge coefficients Name Porosity dfs2 Description Map of porosity coefficients Name Tools Waves Generation Line 21t Description PFS file generation of internal wave...

Страница 56: ...l waves PFS file RegularWaves bw H 2 m T 8 s and MWD 270 N Irregular directional waves PFS file DirectionalWaves bw Hm0 2 m Tp 8 s Tmin 4 5 s MWD 270 N standard JONSWAP spectrum Cos8 directional sprea...

Страница 57: ...sponge layer is used for efficient wave absorption at the four model boundaries The thickness of the sponge layer is corresponding to one wave length or more The sponge layer map is generated by usin...

Страница 58: ...ue to the smaller wave periods Tmin 4 5 s considered in the directional wave case the time step is reduce accordingly Figure 4 33 shows the wave breaking and moving shoreline parameters used in this a...

Страница 59: ...e 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...

Страница 60: ...GHz and 1GB DDR RAM the required system time is approximately 2 hours the system CPS is approximately 190 000 points second for the regular wave simulation and approximately 5 hours the system CPS is...

Страница 61: ...D visualisation of the simulated instantaneous surface elevation The surface rollers are shown in white You can make a similar plot by loading double click the PFS file Anim Regular Waves with Roller...

Страница 62: ...urface elevation and corresponding wave spectrum are pre sented in Figure 4 37 regular waves and Figure 4 38 irregular waves The spectra are calculated by use of the WSWAT Linear Spectral Wave Analysi...

Страница 63: ...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 upstr...

Страница 64: ...ime series of surface elevation left and corresponding wave spec trum right Irregular directional wave case The data is extracted along the line y 500 m at water depth a 16m b 3m c 1m all upstream isl...

Страница 65: ...ase note wave statistics are calculated only in water points which never dry out The uprush downrush area is shown by white colour in Figure 4 39 lower panel Figure 4 39 Map of wave heights Upper regu...

Страница 66: ...ight along two cross sections An excellent agreement is seen at in wave breaking zone x 300 500m upper panel MIKE 21 BW predicts slightly higher waves immedi ately before breaking which is due to nonl...

Страница 67: ...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 mad...

Страница 68: ...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 o...

Страница 69: ...2DH Boussinesq Wave Module Examples 69 Figure 4 42 Wave induced current fields Upper panel regular waves lower panel irregular waves...

Страница 70: ...n regular unidirectional waves Name Setup Directional Waves bw Description PFS file for setup of MIKE 21 BW run irregular directional waves Name Plot RegularWave Disturbance plc Description PFS for 2D...

Страница 71: ...n according to laboratory experiments reported by Hamm 1992a b see reference in S rensen et al 1998 The size of model area is 1200 m x 1200 m and the bathymetry is shown in Figure 4 43 It con sists of...

Страница 72: ...owpass filter is included to remove high frequency waves generated during uprush and downrush at the shoreline and to dissipate the wave energy in areas where the surface roller is not properly resolv...

Страница 73: ...xamples considering wave breaking the deep water terms are included Also in this example we use Simple upwinding at steep gradients and near land for the space discretisation of the convective terms T...

Страница 74: ...he speed of your PC For a laptop IBM T40 Pentium M Centrino 1 6 GHz and 1GB DDR RAM the required system time is approximately 7 hours the system CPS is approximately 180 000 points second You may redu...

Страница 75: ...2DH Boussinesq Wave Module Examples 75 Figure 4 45 Visualisation 2D of instantaneous surface elevation...

Страница 76: ...forcing a current towards the centre line The flow from the two sides join to form a rip current and two symmetrical circulation cells appear A combined vector and contour plot of the nearly steady s...

Страница 77: ...8 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 se...

Страница 78: ...ulated only in water points which never dry out The uprush downrush area is own by white colour in Figure 4 47 and Figure 4 49 Figure 4 49 Map of relative wave height Please note only the lower half o...

Страница 79: ...is considered as a prototype of the laboratory experiments cited above by use of a Froude scaling of 1 40 Model setup The size of model area is 1200 m x 1200 m and the bathymetry is shown in Figure 4...

Страница 80: ...situations Regular unidirectional waves PFS file RegularWaves bw H 3 2 m T 10 7 s and MWD 270 N normal incidence Irregular directional waves PFS file DirectionalWaves bw Hm0 4 6 m Tp 10 7 s Tmin 4 s M...

Страница 81: ...ponge layer offshore from the generation line see Figure 4 52 The absorbing beach on the offshore side of the detached break water is modelled using a sponge layer The thickness of the sponge layer is...

Страница 82: ...stant Manning number of M 35 m1 3 s is used for the bottom friction dissipation Model parameters As in the other examples considering wave breaking the deep water terms are included In this example we...

Страница 83: ...breakwater Hm0 4 6m Tp 10 7s h 13 2m for random wave generation and click on run button The length of the simulation is 42 minutes corresponding to 18001 time steps or approximately 235 peak wave per...

Страница 84: ...averaged velocities under the surface roller obtained by cumulative averaging over approximately 8 peak wave periods starting 7 minutes after simulation start Wave statistics is com puted only in poin...

Страница 85: ...igure 15 p 169 it is seen that the computed eddy structure agrees quite well with the measured structure with respect to the location of eddy the size of the quiescent area in the centre of the eddy a...

Страница 86: ...water for the case of regular unidirectional waves upper panel and irregular directional waves lower panel Computed time averaged of the velocities beneath the surface rollers The time averaging is pe...

Страница 87: ...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...

Страница 88: ...panel model results and lower panel photograph by Mory and Hamm 1997 see S rensen et al 1998 The temporal evolution of the wave induced velocity is shown in Figure 4 59 for the two considered wave si...

Страница 89: ...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 pr...

Страница 90: ...ve 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 exa...

Страница 91: ...on PFS file for setup of MIKE 21 BW run irregular directional waves Name Plot Regular Surface Elevation plc Description PFS file for 2D visualisation the simulated surface elevation using MIKE Zero Pl...

Страница 92: ...sation the simulated wave disturbance coeffi cient using MIKE Zero Plot composer regular unidirectional waves Name Plot Directional Wave Disturbance plc Description PFS file for visualisation the simu...

Страница 93: ...following data files and specification file within the folder of Demo Dif fraction are supplied with MIKE 21 Please note that in order not to overwrite the specification files you should copy them to...

Страница 94: ...e waves are generated inside the model domain which is the most com mon method of forcing the 1DH Boussinesq Wave Module in practical appli cations The two model boundaries i e at j 0 and j jextr are...

Страница 95: ...height and wave period of 1 m and 8 s respectively The model domain is discretized using a structured mesh with 195 elements and 196 nodes The mesh size is 2 m and the integration time step is 0 1 s...

Страница 96: ...lue is a little smaller than the expected value of about 0 40 cf Figure 4 65 which is mainly due to the wave non linearity The incoming waves are not perfectly linear as can be seen from the missing w...

Страница 97: ...the running period from 5 minutes 3001 time steps to 20 minutes 12001 time steps you will obtain a variation of the wave height as shown in Figure 4 66 With an average value of the significant wave he...

Страница 98: ...and a smoothing parameter of 100 default values in MIKE 21 BW A 50 point wide sponge layer is used in the slot in order to damp the oscillations in the slot see Figure 4 67 With respect to the parame...

Страница 99: ...ure 4 68 the spatial variation of a number of phase averaged quantities are presented The maximum wave height is 0 121 m at the generation point and increases towards the break point see Figure 4 68 I...

Страница 100: ...module also allows for an estimate of the depth aver aged undertow which is the return flow below the wave trough Outside the surf zone the undertow is small and equal to Stokes drift The calculation...

Страница 101: ...vertical and horizontal run up height The still water shoreline is located at xr 23 3 m The simulated shoreline motion is converted into a vertical and a horizontal displacement as illustrated in Fig...

Страница 102: ...e default installation Binary data files Parameter files 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 irregula...

Страница 103: ...at spilling breakers would occur for see Madsen et al 1997a 1 p 295 The seaward boundary is treated as nonreflective using sponge layer 100 points Also an absorbing sponge layer is used at the shoreli...

Страница 104: ...shows a line series of the simulated surface elevation on top of the bathymetry Spatial variation of the significant wave height and the maxi mum wave height is shown in Figure 4 75 In Figure 4 76 the...

Страница 105: ...ation 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 origin...

Страница 106: ...75 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...

Страница 107: ...ated using the WS Spectral Analysis module in MIKE 21 Figure 4 78 Model results 3D pictures of the simulated instantaneous surface ele vation Please note that this graph is based on a calculation incl...

Страница 108: ...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 conditio...

Страница 109: ...which they appear in the MIKE 21 BW editor Figure 5 1 Thereafter all other entries are arranged alphabetically in Section 5 5 Figure 5 1 MIKE 21 BW editor The Reference Manual entries are also availa...

Страница 110: ...grid This module is typically selected for calculation of short and long period waves in ports harbours and coastal areas see Examples in Section 4 2 Figure 5 2 Example of a MIKE 21 BW 2DH application...

Страница 111: ...n choosing this option you have to specify a 2D grid for 2DH applications type 2 data file with extension dfs2 or dt2 or a 1D profile for 1DH applications type 1 data file with exten sion dfs1 contain...

Страница 112: ...Figure 5 4 Figure 5 4 Enclosed Harbour In many cases involving breakwaters what happens in part of the area between the outer face of a breakwater and an adjacent model boundary may have no influence...

Страница 113: ...harbour may differ for dif ferent incoming wave directions This is described in Setup of internal gener ation lines section 5 3 4 In other applications such as semi enclosed harbours along exposed coa...

Страница 114: ...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 includ...

Страница 115: ...ed the minimum water depth is theoretically zero and a very small spatial resolution is required to resolve the wave field In practical applications it has been found that the most energetic waves sho...

Страница 116: ...s water points are specified as negative values when they are below the bathymetry datum and positive values when they are above it Note that simulations are carried out using the still water level SW...

Страница 117: ...occurs when the water particle velocity at the crest of the wave begins to exceed the speed of wave propagation Figure 5 9 Wave breaking Boussinesq simulations without wave breaking By comparison the...

Страница 118: ...Sch ffer et al 1993 Madsen et al 1997a b and S rensen et al 2004 see references and scientific documentation Successful modelling of the wave breaking process requires an adequate resolution of the su...

Страница 119: ...tween the maxi mum water depth and the deep water wave length hmax L0 is less than 0 22 The enhanced Boussinesq equations include the so called deep water terms allowing to extend the model into deepe...

Страница 120: ...g with simple upwinding at steep gradients and near land quadratic upwinding with simple upwinding at steep gradients and near land simple upwinding differencing All three schemes are characterised by...

Страница 121: ...ency noise appears in the computational domain with the largest water depth typically near an internal generation line or at an open boundary As explained in Blow up after some time steps see link bel...

Страница 122: ...simulation Number of time steps The number of time steps is the total simulation time divided by the time step The total simulation time should allow for waves to reach all model areas and from this...

Страница 123: ...tep in combination with the grid spacing is selected so that the Cou rant number is less than or equal to 1 Including the deep water terms To avoid numerical damping and instability the minimum wave p...

Страница 124: ...3 1 Bathymetric parameters On this dialog you specify information related to the bathymetry i e the defini tion of land points and shift of reference level if any Bathymetry value representing land Th...

Страница 125: ...hange accordingly to the change in water level Often the safest thing to do is to make new copies of the bathymetry files and change the depths in the different bathymetry files Figure 5 12 Example of...

Страница 126: ...dary conditions such as surface elevations can not be specified Absorbing boundary An absorbing boundary allows wave energy to pass out of the model area without reflections propagating back into the...

Страница 127: ...eration line One of the advantages of using internal generation is that sponge layers can be placed behind the gen eration line to absorb waves leaving the model area The wave data needed depends on t...

Страница 128: ...generation line The use of directional waves requires a reasonably wide model area and a generation line depending on the specified directional distribution This is illustrated in Figure 5 14 The mai...

Страница 129: ...ases An example is shown in Figure 5 14 where it can also be seen that the area with artificial land on the right hand side of the harbour entrance has been enlarged compared to the example above In F...

Страница 130: ...rner Grid spacing You must also specify the grid spacing in the x and y directions correspond ing to the bathymetry used for the Boussinesq wave simulation Figure 5 16 Definition of main wave directio...

Страница 131: ...ve to the generation line open boundary In both cases a dfs0 data file is used as input An example is shown in Figure 5 19 Figure 5 19 Boussinesq wave simulation using one dimensional wave generation...

Страница 132: ...inesq wave simulation using directional wave generation input dfs1 see the MIKE 21 Toolbox tool Random Wave Generation 5 3 5 Bottom friction Short periodic waves Usually the effects of bottom friction...

Страница 133: ...Chezy number formulation 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 t...

Страница 134: ...some hydraulic text books 5 3 6 Eddy viscosity The decomposition of the prognostic variables into a mean quantity and a tur bulent fluctuation leads to additional stress terms in the governing equati...

Страница 135: ...n 5 5 It is not recommended to use eddy viscosity to damp out numerical instabili ties in MIKE 21 BW simulations Remarks and hints Eddy viscosity is mainly introduced in MIKE 21 BW for modelling of wa...

Страница 136: ...dertaken in the Grid Editor dfs2 or in the Profile Editor dfs1 To obtained a smooth transition between 0 and 0 25 it is recommended to delete some 0 s around the area with filter coef ficient 0 25 and...

Страница 137: ...ac tor The default value is 1 5 For plunging breakers see section Type of breakers Ozanne et al 2000 suggest a value of about 2 0 Type of roller celerity The roller celerity is assumed to be proportio...

Страница 138: ...waves relative to true North The default direction is 270 N corresponding to waves from West Type of breakers Depth induced wave breaking of individual waves starts when the wave height becomes great...

Страница 139: ...pness induced wave breaking which occurs on deeper water when the wave height becomes to large compared to the wave length White caps can be observed in the figure below Figure 5 27 White caps in open...

Страница 140: ...nd a dis turbance of the flow in the physical domain On the other hand the numerical solution becomes unstable for extreme values of the slot width In practice it turns out that the slot width should...

Страница 141: ...ty values at open water grid points should be set to unity i e porosity 1 0 The porosity should only be set to less than unity along structures where you want to include the dissipation effect of poro...

Страница 142: ...sired reflection coefficient can be determined by the use of the MIKE 21 Toolbox program Calculation of Reflection Coefficients Important The porosity should never be smaller than 0 2 For impermeable...

Страница 143: ...porous struc ture In most practical cases the pore sizes are relatively large typically 0 1 m to 1 0 m and the turbulent losses will dominate The laminar loss term has also been included to allow the...

Страница 144: ...is outlined below Step 1 Open your bathymetry file dfs2 file and change the land value e g 5 along all structures having partial reflective properties to another value code e g 3 This is illustrated i...

Страница 145: ...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 In this tool you specify the calculated porosity value o...

Страница 146: ...s 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 th...

Страница 147: ...e structures If no porosity values are specified the reflection will be 100 from land points As the porosity results in dissipation of energy the reflection may be con trolled by the porosity values a...

Страница 148: ...s to repre sent a given transmission coefficient the MIKE21 Toolbox tool Calculation of Reflection Coefficients should be used 5 3 11 Sponge layers Sponge or absorbing layers can be used as efficient...

Страница 149: ...eline see right hand figure below Figure 5 37 Example of sponge layer profiles The panel to the left shows a profile without moving shoreline and the right panel shows profile including moving shoreli...

Страница 150: ...s 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 Genera...

Страница 151: ...and zero flux If you require a radiation boundary with another reference value you can specify the relevant level most often you only specify a surface elevation through an option Grid Point Sponge Va...

Страница 152: ...such as skewness kurtosis and atiltness is calcu lated The temporal averaging can be performed on cumulative or subseries basis including or excluding the swash zone Wave disturbance parameters A comm...

Страница 153: ...ies data dfs2 file 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 butt...

Страница 154: ...2DH module only Roller angle 2DH module only Roller celerity cx 2DH module only Roller celerity cy 2DH module only Water level roller 2DH module only Surface elevation The surface elevation is a basi...

Страница 155: ...include this parameter in the output Auxiliary variable 1DH module only This prognostic variable is relevant to save in connection with debugging model results The auxiliary variable is defined as 5 9...

Страница 156: ...e scientific documentation Usually you would not save this information Water level roller 2DH module only The water level including rollers is mainly used in connection with 3D visualis ation of the i...

Страница 157: ...to a grid having the constant spatial resolution of Jlast Jfirst 1 Npoints In case you use a structured mesh of the bathymetry we recommend you to use the suggested default value of Npoints Jlast Jfi...

Страница 158: ...a name and title of the file Figure 5 44 The list of phase averaged output parameters includes various varia bles for detailed analysis and presentation Wave statistics You can select between followin...

Страница 159: ...r level first time Most often you should keep the default value Output type You can choose between following output types type 0 point series data dfs0 file type 1 line series data dfs1 file type 2 gr...

Страница 160: ...zero crossing wave height within a specified time period Maximum surface elevation The maximum surface elevation max is defined as the maximum value of the surface elevation within a specified time p...

Страница 161: ...ler thickness The mean roller thickness can be interpreted as a time averaged measure of the intensity of wave breaking Outside the surf zone the mean roller thick ness is zero The definition of the r...

Страница 162: ...tiltness The atiltness A is defined by 5 13 where E denotes the mean operator The atiltness is a higher order integral measure of the lack of vertical wave profile symmetry The parameter takes a posit...

Страница 163: ...Output Parameters 163 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...

Страница 164: ...ed meshes to save the entire profile of data i e keep the default values of Jfirst and Jlast 5 4 3 Wave disturbance parameters Figure 5 47 A number of wave disturbance parameters can be extracted from...

Страница 165: ...e performed You must also specify the interval in number of time steps for which the 2D map is updated A typical value is 1 2 minutes Area statistics When wave dist coeff is set in your dialog setting...

Страница 166: ...s a setup which you may use for reference Remarks and hints Start up period Regular waves Start up period For irregular waves in ports and harbours it is important to specify the simula tion time long...

Страница 167: ...be started at arrival of e g wave No 30 and the calculation period should normally cover the time step range specified on the Simulation Period dialog The start up period should not be confused with...

Страница 168: ...eous cross shore displace ment of the still water shoreline The initial value equals the x co ordinate of the still water shoreline Vertical run up The vertical run up is defined as the vertical displ...

Страница 169: ...s a continuation of an earlier run For this to be possible details of the finishing conditions of the earlier simulation must have been saved in a hot data The information stored in the hot data file...

Страница 170: ...zation APV Artificial land Batch mode Blow up Boussinesq cross terms Courant number Deep water terms First time model set up Hardware requirements High frequency noise Linear dispersion relation Mesh...

Страница 171: ...as land Artificial land should only be applied to water areas which have no influence on the wave conditions in areas of interest The idea of applying artificial land is to save computational time In...

Страница 172: ...he extension bat in a text editor The bat file should include a path to the bin directory and lines for each specification file default 64bit installation path path C Program Files x86 DHI year bin x6...

Страница 173: ...caused by an inconsistency in the simulation setup Therefore please check your model specifications carefully Near the end of the log file you get the message BLOW UP detected In other words you have...

Страница 174: ...simulation may also be the result of inconsistencies in your input specifications This is because the Boussinesq wave model is relatively robust and it can take some time before the effects of inconsi...

Страница 175: ...d absorb the breaking wave energy by introducing sponge layers You may also reconsider you model setup and include wave breaking As you have to resolve the individual breaking waves you would probably...

Страница 176: ...ow in Figure 5 54 Then the time step should be reduced to a temporal resolution of 50 points per wave period If instabilities still appear then you may try using a partly lin ear time extrapolation of...

Страница 177: ...u may also try to use a smaller number by trial and error If all your efforts fail you can contact you local DHI Software Support Centre 5 5 5 Boussinesq cross terms The representation of the Boussine...

Страница 178: ...ction of the classical form of the Boussinesq equations is the shallow water limitation in terms of the water depth to deep water wave length ratio h L0 Celerity errors gradually increase for increasi...

Страница 179: ...Setup Planner for the minimum wave period 4 Find the time step for the numerical time integration Beside fulfilling the CFL criterion first expression in bracket the minimum wave period has to be res...

Страница 180: ...ram For a 4 500 MHz Pentium II processor the CPS is in order of 100000 points second for 2D applications and about 15000 points second for 1D applications including surf zone dynamics When you know th...

Страница 181: ...times result in instabilities which eventually may cause a model blow up An example is illustrated in the figure below Figure 5 56 High frequency noise Often the instability high frequency noise appea...

Страница 182: ...r gT2 2 T is the minimum wave period A comparison between the phase celerity derived for the Boussinesq equations and Stokes first order theory is shown in Madsen et al 1991 and Madsen and S rensen 19...

Страница 183: ...57 Example of spatial resolution for a barred coastal profile Conditions Spectral peak period 8 s 40 nodes per wave length and minimum mesh spacing 0 2 m 5 5 13 Minimum wave period The minimum wave pe...

Страница 184: ...esult 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...

Страница 185: ...Entries Arranged Alphabetically 185 Figure 5 58 Application of different time extrapolation factors...

Страница 186: ...sion 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 ble to the Boussinesq wave module Application verific...

Страница 187: ...Waters editor M B Fischer Academic Press New York Abbott M B Petersen H M Skovgaard O 1978 On the Numerical Model ling of Short waves in Shallow Water Journal of Hydraulic Research 16 3 Boussinesq typ...

Страница 188: ...E F H S Chen and L L Hadley 1996 Validation of numerical model for wind waves and swell in harbours Journal of Waterway Port Coastal and Ocean Engineering 122 5 245 257 Sponge Layers and Radiation Bou...

Страница 189: ...ption and Modelling of Direc tional Seas Lyngby Paper No C 2 p 11 Mei C C 1983 The applied dynamics of ocean surface waves John Wiley Sons New York Svendsen I A and Jonsson I G 1980 Hydrodynamics of C...

Страница 190: ...Reference Manual 190 MIKE 21 BW DHI...

Страница 191: ...dsen P A S rensen O R and Sch ffer H A 1997a Surf zone dynam ics simulated by a Boussinesq type model Part I Model description and cross shore motion of regular waves Coastal Eng 32 255 288 Madsen P A...

Страница 192: ...Scientific Documentation 192 MIKE 21 BW DHI...

Страница 193: ...193 INDEX...

Страница 194: ...e step 177 Cross momentum derivatives 120 Cross section of a breaking 137 Cruise terminal 31 D 1DH module 110 2DH module 110 Deep water terms 178 Deep water terms 37 Deterministic parameters 152 DHI s...

Страница 195: ...d interactions 10 Non Darcy flow 143 Non Gaussian characteristics 162 Normal incident irregular waves 131 Numerical damping 184 Numerical dissipation 120 Numerical instabilities 140 Numerical instabil...

Страница 196: ...onics 10 Super harmonics 10 Surf similarity parameter 103 Surface elevation 126 Surface roller concept 118 136 Surging 139 T Temporary file 111 Text books 188 Time of arrival 164 Time step interval 12...

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