User`s Manual for NEARCOM Diffractive, Unsteady Wave Driver DUNS
Contents
1. output radiation stress Syz write fnames a8 i1 i1 i1 i1 i1 a4 data sxx c middle lines the same do i 1 nx write 1 rec i pass_sxx i j j 1 ny end do close 1 is appropriate Note that the a8 on the first line would have to be changed if the filename pre fix is not three letters like sxx Other possible desired outputs are pass_sxy pass_syy pass theta pass_ubott pass_height pass_cg pass_wavenum pass_theta pass_c pass mass fluxu pass mass fluxv pass_diss pass_wave ry pass_waverx Not all of these change with time so outputting some would be wasteful 13 4 5 Compilation and Execution A compile command that works on many PC compilers is 90 master f sed f duns f winc f where duns f is the DUNS code Any optimization switches desired may be used To compile the helper program fgen the command 90 fgen f works Fgen may also be compiled as a fortran77 program To execute simply run the master program using whatever format is best on the particular system I find that on a PC running in a DOS window is much better as if the program can t read input or blows up for any reason the window doesn t disappear On Unix or Linux shells this should not be a problem 5 How to get Bad Results These are a few ways in which you can get bad results from the wave driver 5 1 No data subdirectory If you do not have a data subdirectory for out2. A and V correspond to 1 4 The format of the output is open 1 file junk1 out do i 1 nx write 1 100 etac i j j 1 ny end do close 1 100 format 401 f10 4 These can be loaded directly into Matlab or other programs or they may be viewed using a text editor Because they always have the same name they are overwritten every time the wave driver is called 12 4 4 Output After Every ncallwave Times the Wave Driver is Called Binary data files are written to the data subdirectory every ncallwaveth time the wave driver is called or every ncallwave x master_dt x ninterval_callwave seconds These have the form amp00001 out and so on where amp is replaced by eta u or v for other variables The files are written using the commands write fnames a8 i1 i1 i11 i1 i1 a4 data amp amp mod noutskip 10000 10 mod noutskip 1000 10 amp mod noutskip 100 10 amp mod noutskip 10 10 mod noutskip 10 out open 1 file fnames status unknown amp access direct recl 4 ny do i 1 nx write 1 rec i abs amp i j j 1 ny end do close 1 where noutskip 1 2 3 numbers the files sequentially These files may be read using fortran or Matlab If different output data is desired probably the easiest way is to add another output section similar to that above but with the appropriate filename and output variable For example to
3. La A 2iA C k amp amp U o oO F g rak 2Arykl Ayyl 92A i 2 vs eel J iR b A JA K K K 2w 0 1 where amp is the regularised bathymetry and amp K R cos 0 sin 0 is the difference between the actual and regularised wavenumbers multiplied by the wave direction vector The regularised wavenumber k is taken from the regularised depth h This is defined as any depth field for which the underlying wavenumber vector field has no caustics many topographies with submerged shoals will not have well behaved refraction fields so a regularised bathymetry Lateral boundary ee T T gt EN AA a a a O aee gem eae NAS gO ee gi a Be ee 4 sede 57 7 7 Be ae aes eRe ee eee Ee GER ee Le ast Fe ane ee ee Z 7 AD a ae ow i 0 S Beaba oa Figure 1 Definition sketch for wave propagation showing boundaries and sample wavenumbers in the domain is defined with acceptable refraction The regularised wavenumber vector field satisfies the linear dispersion relation o gk tanh Rh 2 and the eikonal wavenumber condition V x K cos 0 sin 0 0 The difference between the regularised and actual bathymetries drives diffractive terms which approximate the effects of the actual bathymetry This approach has been known for some time and is used in well known models such as REF DIF1 In DUNS the regularised bathymetry is computed at each z location as
4. A 1993 Dissipation in random wave groups incident on a beach Coastal Eng 19 1 2 127 150 Svendsen I A Haas K and Zhao Q 2002 Quasi 3D nearshore circulation model SHORE CIRC Version 2 0 Research Report CACR 02 01 Center for Applied Coastal Research University of Delaware Newark Wei G Kirby J T Grilli S T and Subramanya R 1995 A fully nonlinear Boussinesq model for surface waves I Highly nonlinear unsteady waves Journal of Fluid Mechanics 294 71 92 16
5. circulation model we must update on time scales much less than this Typically we recommend passing information to the circulation model at time scales of O 1 2s to ensure good resolution Those with quick eyes will note that this gives the overall model first order accuracy on the time scale of the information passing 1 2s Because of the modular NEARCOM design this is unavoidable but errors introduced here are probably order of magnitude less than errors in estimating for example radiation stresses in breaking waves 3 Examples 3 1 Wave focusing on a submerged shoal This is a nonbreaking example that can not be duplicated here because of the wave breaking in the code but serves to evaluate the accuracy of the basic formulation The focusing shoal of Berkhoff Booiy and Radder 1982 has been used as a test of difraction for many different wave models Figure 2 shows the bathymetry contours and measurement cross sections This topography leads to strong focusing of wave rays with caustics occurring behind the shoal Because of this method 1 may not be used on this topography as an underlying refraction solution does not exist However method 2 is well suited to such a computation The underlying bathymetry was assumed to be a longshore uniform beach whose depth was chosen to be the average over the longshore domain A computational grid size of Ax Ay 0 25m was used with a time step of At 0 025s Lateral boundaries used a re
6. put data you will get an error the first time the program tries to write sequential files 5 2 Short longshore domain If you have a short longshore domain the mean angle will not be represented well because of the finite number of possible angles for a given wavenumber in a finite longshore domain To fix this increase domain length 5 3 Very strong longshore bathymetry variations This program is coded only for mild longshore bathymetry variations It is difficult to define mild exactly but a good rule of thumb might be that for a constant x longshore depths should not vary from the mean longshore depth at that location by more than a factor of 2 For very strong longshore variations you will continue to get results but these will become increasingly unreliable 14 5 4 Very wide range of frequencies A good rule of thumb is that frequencies should not vary by more than 15 20 from the underlying frequency Again there will be a continual loss of accuracy as frequency bandwidths increase 5 5 Very wide directional distribution Directions of 30 degrees from the central direction will not show too much error but accuracy decreases quickly after this 5 6 Very strong Currents The model has leading order wave current interaction but will not give good representations of waves anywhere near the blocking point 5 7 Many Input Directions at a Frequency There is a very big difference between a
7. User s Manual for NEARCOM Diffractive Unsteady Wave Driver DUNS Andrew B Kennedy Department of Civil and Coastal Engineering University of Florida Gainesville FL 32611 6590 USA kennedy coastal ufl edu amp James T Kirby Center for Applied Coastal Research University of Delaware Newark DE 19716 USA kirby udel edu 1 Summary This manual gives a brief description of the diffractive unsteady wave driver DUNS for the NEARCOM model suite Examples and sample setups are included The model can predict leading order time varying multidirectional and diffractive behaviour and is thus expected to be useful for the study of wave group forcing on nearshore hydrodynamics Leading order but not full wave current interaction is included Because of assumptions in the derivation and choices made in coding the model is meant for use on open beaches where there is a clear longshore and cross shore direction It should not be used in areas with strongly curved shorelines or in areas with strong diffraction such as inside a harbor 2 Introduction Waves in the ocean are universally acknowledged to be unsteady and multidirectional As they pass from deep water into finite depths and through to the shoreline these variations in shoaling and breaking wave heights and directions will also cause spatial and temporal variations in low frequency waves and currents Despite this the majority of numerical modelling efforts have used either mon
8. flective condition which is considerably different than the physical experiment but as boundaries were far away from the area of interest this was not a concern Formally the physical wave height in computations is not just H 2 A but includes higher order corrections However because of the semi empirical modifications to nonlinear dispersion with unknown effects on surface profiles we use this simpler representation For some situations oa Distance m 0 1 1 1 1 1 0 2 4 6 8 10 12 14 16 18 20 Distance m Figure 2 Contours of bathymetry on BBR shoal showing measurement transects this approximation would be unacceptably crude however for the present case reasonable results may still be obtained Figures 3 4 show computed and measured wave heights along the transects In general agree ment is quite good Both the trend and the magnitude of the refraction and diffraction caused by the shoal are well represented The present results look very similar to those computed using the narrow angle parabolic model given in Kirby and Dalrymple 1986 This is not surprising as with the further assumptions of time invariance weak diffraction in the direction of propagation and negligible current the two models are equivalent Since none of these effects are likely to be highly significant in this case the results are very similar Although the present results are good it is poss
9. he present model and gives confidence that accurate refraction diffraction shoaling results can be obtained in situations for which no direct confirmation is available 3 2 Longshore Current with Unsteady Wave Forcing DUNS is well suited to examine longshore currents in the presence of unsteady wave forcing Here it is used to force the quasi 3D circulation model SHORECIRC Svendsen et al 2002 Figure 5 shows the longshore uniform bathymetry which has a bar trough topography This example is found in the download package All input files for both DUNS SHORECIRC and NEARCOM are included A dummy sediment module is used SHORECIRC here is used in 2D mode as there are unresolved feedback issues between DUNS and the 3D SHORECIRC flow The example is a little contrived with only 5 frequency components used so that users may see easily how the program works and may also modify it easily Still it shows many of the principles and methods required for more complex examples The program runs for 1200 s with Figure 4 Computed and measured x wave heights at transects 6 8 on BBR shoal both SHORECIRC and DUNS providing output We will not worry about the SHORECIRC output as DUNS output provides everything we need First compile and run helper program fgen f This produces the input file freqs dat from the original file spec dat Next compile the master program A compile command that work
10. ible to achieve slightly greater accuracy by using full time domain systems such as Boussinesq models e g Wei et al 1995 This is because these models do not assume an underlying form for the wave and thus can represent better the strong nonlinear diffraction Still Boussinesq models are computationally an order of magnitude slower than the present model and thus cannot be easily used for long time scales in field situations Wide angle parabolic models can also produce slightly better results in this case e g Kirby 1986 as their treatment of diffraction is more accurate This improvement in accuracy is mainly T lt I EIE z y M y 4 x 0 ji l l j i i i i i 5 6 7 8 9 10 11 12 13 14 15 T T T T T T T T T 2f 2 7 I E e 1k x e I x X gt 0 l l l l i i i i i 5 6 7 8 9 10 11 12 13 14 15 T T T T T T T T T f 3 sxx J I Sik x X I Vane oe cnr x X x x 0 l l l l i i i i i 5 6 7 8 9 10 11 12 13 14 15 H H a k S E k 5 6 7 8 9 10 11 12 13 14 15 T T T T T T T T T gf 5 7 I Sip x x x aes r x x sis 0 1 1 1 1 ll 1 1 1 5 6 7 8 9 10 11 12 13 14 15 y m Figure 3 Computed and measured x wave heights at transects 1 5 on BBR shoal seen in the side lobes of longshore transects 4 5 where the wide angle approximation allows for more accurate diffraction far from the mean wave direction Overall however agreement is quite good using t
11. ochromatic or spectral models neither of which includes the effects of wave groups In this manual we describe a numerical wave driver DUNS that can describe the time varying wave climate in the nearshore on the scale of wave groups The model operates in the time domain and includes leading order multidirectionality diffraction and wave current interaction The ba sic formulation is from Kennedy and Kirby 2003 and comes from a nonlinear multiple scale perturbation expansion Multidirectionality and diffraction are accounted for by making the wave amplitude A complex with both real and imaginary components This leading order multidi rectionality is accurate to approximately 30 degrees from a central direction and diffractive frequency dispersion to perhaps 15 from a peak frequency Accuracy degrades continuously from this peak direction and frequency but is quite accurate near the peak 2 1 Numerical Setup All waves are generated at the offshore boundary as seen in Figure 1 Offshore waves may have any mean angle where the waves travel into the domain rather than out of the domain this is to say that the waves must travel somewhat in the positive x direction rather than the negative x direction The driver has an unstaggered grid and is second order in space and fourth order in time Differences are centered in space The main evolution equation solved by the driver is 2A 2 Cg VA aV lt
12. s on many PC compilers is f90 master f sed f duns f winc f Any optimization switches desired may be used Next run the master program There must be a subdirectory data in the target directory as the program will write output here After the master program has finished the Matlab code readata m will compute and plot the mean current and vorticity averaged from 800 1200s Results are shown in figures 6 7 Note that the 400s averaging period has still not removed all longshore variation in vorticity because of a combination of the shear waves and unsteady forcing Oo N T Elevation m I o 1 50 100 150 200 250 oO Figure 5 Barred bathymetry for test case 4 Inputs and Outputs In addition to data passed from the master program there are two major input files required by DUNS One gives general computational details while the second details input wave parameters 4 1 Input File winput dat The input file winput dat provides the grid sizes time step and boundary conditions for the wave driver A sample file is 3 0 cdx 10 cdy 0 25 l cdt 3 mbcy 15 ncallskip 1 I_hard 1 Ang_use The first two entries are the x and y grid sizes cdx and cdy Theoretically these could be taken from the master grid but we find it useful to make them explicit The next quantity is the model time step The next is the lateral boundary condition for a periodic bo
13. spectral representation with a directional distribution at a given frequency and a deterministic representation with many directions per frequency The difference is that in the spectral representation all of the different directions are assumed to be uncorrelated However with the deterministic representation all components with the same frequency are perfectly correlated throughout all time This can cause problems because of spurious high low areas of breaking waves To get around this say you have 10 directions at a given frequency with frequency bandwidth df Instead use a bandwidth df 10 and give each component its own unique frequency Within the assumptions made to arrive at a spectrum the two are identical but the second option works much better in a deterministic model References Berkhoff J C W Booy N and Radder A C 1982 Verification of numerical wave propaga tion models for simple harmonic linear water waves Coastal Eng 6 255 279 Kennedy A B and Kirby J T 2003 An unsteady wave driver for narrowbanded waves modeling nearshore circulation driven by wave groups Coastal Eng 48 4 257 275 Kirby J T 1986 Higher order approximations in the parabolic equation method for water waves J Geophys Res 91 C1 933 952 15 Kirby J T and Dalrymple 1986 An approximate model for nonlinear dispersion in mono chromatic wave models Coastal Eng 9 545 561 Roelvink J
14. te simple but there are several subtleties e The first component encountered in the file will be taken to provide the central frequency and direction Note that by giving it zero amplitude here we can define it without messing up any other ordering scheme for frequencies we may wish to use e If a wall lateral boundary condition is used mbcy 1 all components are set to have zero angle e The program fgen f assigns a random phase to each component These are set by the constants at the beginning of the program and can be changed if desired e For a periodic boundary condition and a given wavelength there are only a limited number of angles that are physically possible For an overall longshore domain length of Lyo ny dy the fundamental longshore wavenumber is then kyo 27 Lyo Every wave component must then satisfy k sin mkyo where kj and 6 are the wavenumber and angles of component j and m is an integer This is checked in the main program and angles are adjusted to fit properly Sometimes the jump from one allowable angle to another may be more than might be tolerable in these cases it is best to increase the longshore domain length if possible 4 3 Output after each wave driver call At the end of each wave driver call when control returns to the master program DUNS outputs several ascii files that are useful for examining wave output These are of the form junk out where is an integer n U
15. the longshore average in y of the depth This is the main reason that restricts DUNS to open beaches and is a coding choice not a theoretical restriction Considerably more complex choices could be used as long as they satisfy the eikonal wavenumber relations but would require some recoding The closer the regularised bathymetry is to the actual bathymetry the more accurate the program becomes The group velocity Cy 00 0K and the diffractive coefficient og and nonlinear dispersion coefficient are defined in Kennedy and Kirby 2003 Wave dissipation is represented in equation 1 by w and is taken as that of Roelvink 1993 but would be simple to change to any other desired formulation The program is written in mainly standard fortran77 but on some compilers you will need to compile it as a f90 code because of non standard extensions Sample compiler commands are included in section 4 5 Memory requirements are not large and it can be run easily on any modern PC Because DUNS operates in the time domain it is different from most of the wave drivers that operate with NEARCOM The majority of these provide steady radiation stresses which force the circulation components for a period of minutes to an hour at which time a new wave climate might be applied For wave group forcing this is not at all acceptable Wave group time scales are generally defined to be of O 20 200s so to resolve the temporal variation of wave forcing to the
16. the simple method 4 2 Input Files freqs dat and spec dat and helper program fgen f The input file freqs dat and spec dat define the input wave climate The helper program fgen f is used to convert the more user friendly input spec dat into the DUNS input file freqs dat The input file spec dat looks like 9300 22332 49992 32244 10 0 50 100 150 200 x m Figure 7 Vorticity averaged over 400s Note the presence of shear waves is still noticeable because of the relatively short averaging period 8 6 0 0 15 0 0 10 0 0 1425 0 4 10 0 0 141 0 15 8 0 0 159 0 15 13 0 0 1308 0 15 20 0 0 1712 0 15 7 0 0 155 0 15 10 0 165 0 15 0 The first four entries are seeds for a random number generator used to generate phases for each component They may be changed as desired The next entry is the number of frequency components to be used The maximum number of entries is governed by maxfreq in p1 h and is initially set to 501 This can be changed if desired The line after this is the depth at which these will be generated depth at offshore boundary Each of the next lines contains data about each of the unsteady components The first number on each line is the frequency in Hz The second is the amplitude of each component in m The third is the orientation of each component 11 relative to the x axis in degrees 0 is exactly oriented with the x axis This is qui
17. undary set to mbcy 3 while for a lateral wall boundary condition on both sides set to mbcy 1 We note very strongly that the size of the domain will be different for wall or periodic boundary conditions for a periodic lateral domain the size is ny dy as in a discrete Fourier series while for a wall domain the size is ny 1 x dy because the first and last grid points are exactly at the walls in an unstaggered grid 0 8 F 4 U V m s 0 2 4 0 2 1 1 f 1 0 50 100 150 200 250 Figure 6 Longshore and cross shore velocities averaged in the longshore over 400s The next entry is the output interval The driver will output files every ncallskip times it is called by the master program i e after the ncallskipth call 2 x ncallskipth call etc The entry after this defines the record length for the binary output and may differ between computers For PCs this should be set to 1 while with some unix compilers it should be set to A The final entry chooses the method of calculating angles This actually has no effect on the wave computations but will influence radiation stresses output to other programs Using 1 will use the angle of the underlying wavenumber while 2 attempts to include diffractive effects on the computation of the angle If multidirectional or diffractive effects are important in your computation you should use 2 here but it is somewhat less stable that
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