Gravity Waves and Finite Turbulent Flow Fields 



the two waves are combined in proper phase as indicated by the 

 crest line plots in Figs. 23 and 24. The section of wave crest that 

 develops into a caustic has not been included in this elemental con- 

 struction. The results of this simple refraction analysis are 

 plotted in Figs, 25 and 26 for the 6 ft and 2 ft wave lengths. It is 

 seen that this procedure results in essentially unmodified crest 

 heights just aft of the physical grid; then large reductions in wave 

 height for areas trajisverse to the grid and, finally, increases in 

 wave height in those areas where the deflected segment of the wave 

 combines with the undeformed segment of the incident wave. The 

 results of the refraction computations do not entirely agree with the 

 experimental data -- particularly in the region of the grid waJke where 

 the test results show significant attenuations in wave height while 

 the computed results show no wave height attenuation. 



Considering the variation of computed wave height along the 

 crest line (Figs. 25 and 26), it is seen that there is a large increase 

 in wave height for positions less than and greater than approximately 

 6 ft from the grid centerline. At this 6 ft point, the computed wave 

 height is a minimum. These transverse gradients cannot remain in 

 equilibrium and thus represent a source of energy flow along the 

 wave crest from the regions of large wave height to the point of low 

 wave height. This is a diffraction phenomenon which exists simul- 

 taneously with refraction effects. A rigorous theoretical analysis 

 of this problem appears to be extremely complex and is yet to be 

 developed. For the purposes of the present study, a simplified 

 analysis is developed which combines the results of elemental solu- 

 tions of wave refraction, diffraction and superposition. Although 

 not completely rigorous, this simplified approach is tenable and 

 relatively easily applied. 



Diffraction Effects: As normally considered, wave diffraction 

 occurs when part of a wave is "cut off" as it moves past an obstruc- 

 tion such as a breakwater. The portion of the wave moving past the 

 tip of the breakwater will be the source of a flow of energy in the 

 direction essentially along the deformed wave crest and into the 

 region In the lee of the structure. As explained by Wiegel, the "end" 

 of the wave will act somewhat as a potential source and the wave in 

 the lee of the breakwater will spread out with the amplitude decreas- 

 ing exponentially along the deformed crest line. The mathematical 

 solution of this phenomenon, which is taken from the theory of 

 acoustic and light waves. Is described by Penny and Price [ 1952] , 

 Johnson [ 1952] and Wiegel [ 1964] . The solutions for two basic 

 diffraction phenomenon are presented by Wiegel: one Is the case of 

 a seml-lnflnlte breakwater and the other Is for the case of waves en- 

 countering a single gap In a very long breakwater. The solution for 

 both cases are presented by Wiegel In the form of contour plots of 

 equal diffraction coefficient, K, defined as the ratio of the wave 

 height In the area aifected by diffraction to the wave height in the 

 area unaffected by diffraction. For the case of the wave passing 

 through a single gap, the solutions are presented for various ratios 

 of wave length to gap width. 



435 



