depth exceeds 0.78. To determine the depth at any point along the wave 

 ray, the model uses an algorithm which fits a polynomial to the depth of 

 the surrounding square of eight grid points (relative to that wave ray). 

 Under the rapidly varying bathymetric conditions which exist within the 

 study area, the algorithm often computed nonrepresentative depth values 

 which in turn resulted in offshore wave breaking and caustic (wave 

 crossing) conditions. To help alleviate this problem, the depth grid 

 spacing was increased from 150 meters (500 feet) to 300 meters 

 (1,000 feet), and this modification resulted in a significant reduction 

 in the number of offshore caustics and wave breaking. In addition to 

 this problem, diffraction (i.e., the lateral spreading of energy along 

 the crest of a wave), an important process in "smoothing-out" peaks in 

 wave energy (and height), is ignored by Dobson's model. 



Figures 35 and 36 are two computer-generated wave refraction 

 diagrams for a wave approaching from the east with an offshore wave 

 height of 1.4 meters and a period of 10.5 seconds. Figure 35 shows that 

 many of the wave rays cross before reaching the beach or break offshore. 

 Since each wave ray is propagated independently toward the shoreline, 

 the model is "unaware" of the possibility that any two or more wave rays 

 may cross. Linear wave theory is not valid under these conditions; 

 therefore, all wave rays which crossed before reaching breaking condi- 

 tion must be eliminated from the analysis. Figure 36 shows the same 

 wave propagation as in Figure 35; however, all crossed wave rays have 

 been eliminated. The energy, and therefore, wave properties like 

 height, celerity, and angle along a wave crest between two adjacent 

 noncaustic rays, was assumed to be proportional to the energy values of 

 these noncaustic rays. Hence, breaking wave conditions at all locations 

 along the beach were found by linearly interpolating the values between 

 adjacent noncaustic wave-ray locations. 



Another shortcoming of Dobson's (1967) model is that the influence 

 of tidal jets and currents near inlets on wave refraction is not 

 considered. Together with the fact that bathymetric changes are rapid 

 in the vicinity of inlets, the resulting values of wave height, angle, 

 and celerity at those locations must be considered with some skepticism. 



Computer plots showing the results of the refraction analysis for 

 1.4-meter waves for each wave period and for all four wave approach 

 angles are contained in Appendix G. The difference between the results 

 of waves having the same period and approach direction, but differing in 

 height, is simply a slight difference in the breaking position of the 

 wave along the same wave-ray path. 



3 . Energy Flux Computation . 



The longshore component of wave energy flux, P]_ , is defined as 

 (U.S. Army, Corps of Engineers, Coastal Engineering Research Center, 

 1977; Vitale, 1980) 



p l = ff r2c b sin 2a (9) 



70 



