Surfrider Foundation: Mitigation Through Surf Enhancement

APPENDIX A
Modeling Ocean Gravity Waves with REF/DIF 1
(Page 1 of 2)

REF/DIF 1 represents a new breed of ocean wave models that have a number of strengths over traditional modeling methods. It is important to remember that REF/DIF is a model with limitations and assumptions that may divorce model results from actual wave responses. These strengths and weaknesses are discussed below. Included is a section on program input particular to the modeling efforts of this study. REF/DIF is capable of modeling many situations that are more involved than those presented here. The interested reader should consult the users manual (Kirby and Dalrymple, 1994) for additional information about REF/DIF 1.

Strengths:
REF/DIF 1 is a weakly non-linear combined refraction and diffraction model which incorporates the shoaling, refraction, energy dissipation and diffraction of propagating waters waves. REF/DIF 1 models wave heights and directions on a model grid rather than on irregularly spaced rays, this is a major strength because it avoids the difficulties associated waving ray crossing that may lead to uninterpretable results (Kirby and Dalrymple, 1994). Traditionally models had to suspend refraction in areas were diffraction is dominant. Far from the diffraction area, refraction is resumed. Although this technique allows inclusion of diffraction in an approximate way, it is clearly an inaccurate method. REF/DIF 1 combines both refraction and diffraction explicitly, thus permitting the modeling of waves in regions where the bathymetry is irregular and where diffraction is important (Kirby and Dalrymple, 1994).

Assumptions:
REF/DIF 1 propagates monochromatic waves across the bathymetry grid. Because waves in most natural situations are Rayleigh distributed in height and frequency and also have a complex directional component, it is important to recognize that REF/DIF 1 results presented in this study are based on a single wave with a specific height and frequency. In addition REF/DIF propagates waves in one direction per run. The model, in parabolic form, ignores reflection. This may be an important omission when investigating an artificial reef with a steep toe angle such as the reefs modeled in this study.

The REF/DIF 1 model, in parabolic form, has a number of assumptions:
(1) Mild Bottom Slope. The mathematical derivation of the model assumes that the variations of the bottom occur over distances which are long in comparison to a wave length. It was found that for bottom slopes up to 1:3 the mild slope model was accurate and for steeper slopes it still predicted the trends of wave height changes correctly. The reef bathymetries are in violation of the mild bottom slope (Kirby and Dalrymple, 1994). A toe angle of 80° has a bottom slope of over 1:0.17 (significantly steeper than 1:3). It is unknown how this violation affects the model results.

(2) Weak nonlinearity. Strictly the model is based on a Stokes perturbation expansion and therefore is restricted to applications where Stokes waves are valid, unless the Stokes-Hedges nonlinear model dispersion relationship is selected. In this case, a heuristic dispersion relationship developed by Hedges (1976) is used. In shallow water this relationship matches that of a solitary waves. This hybrid model is discussed in more detail in Kirby and Dalrymple (1986). In this study the Stokes-Hedges dispersion relationship is always turned on because the waves are propagating over a shallow reef (discussed below).

(3) The wave direction is confined to a sector ą70° to the principal assumed wave direction. This did not present a limitation to this study because no wave direction that lead to an angle larger than 40° was considered.

Program Input: Model Control and Wave Data:

In order to operate the REF/DIF 1 on a bathymetry grid several files must be created. A file called param.h must be created which is used to store the dimension of the grid. The grid sized used in this study was 200 by 200 cells for all model runs. Next a file must be created that includes information about the bathymetry grid and the wave climate for each run. Once the program called datgen25.f is edited for the appropriate grid size (the file contains code specific to the grid size), compiled and run, this data is easily input for each model run via the executable form of datgen25.f. The file that is generated is called indat.dat. The example below is the input instructions and inputs for a typical model run from the datgen25.f executable. The bold text are the instructions and the italic text are the users input responses.

enter name for .dat file containing reference grid in' single quotes
'reef8.dat'
enter name for output data file
'output.dat'
enter grid dimensions mr, nr
200
200
enter grid spacings dxr, dyr and depth tolerance dt
5
5
5
input iu: 1=mks, 2=english
1
input dispersion relationship; ntype: 0=linear,
1=composite, 2=stokes
1
input lateral boundary condition; ibc: 0=closed
1=open
1
input ispace (0=program picks x spacing, 1=user chooses)
0
input nd (# y divisions, 1 is minimum)
1
input if(1) turbulent, if(2) porous, if(3) laminar
standard choice: 1, 0, 0
0
0
0
input isp (subgrid features) :standard 0
0
input values of iinput, ioutput:
iinput: 1 standard, i.e., not starting from previous run
2 if starting from previous run
ioutput: 1 standard, not saving restart data
2 if saving restart data
1
1

input value of isurface:
isurface = 0: no surface picture generated
isurface = 1: surface picture generated
0
input iwave (1 discrete, 2 directional spread)
1
input nfreq (# of frequencies)
1
input wave period and tide stage
12
0
input # of waves per frequency, nwavs
1
input amplitude and direction
.762
0

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