Savitsky 



These equations were programmed and evaluated on the 

 PDP-10 computer. Refraction diagrams were obtained for several 

 wave lengths, grid speeds, and initial wake lengths. The present 

 report presents the results for 



\ = 2 , 6 ft 



Grid width = 3 f t 



Grid submiergence = 1.67 ft 



Grid mesh = 2.7 in 



Grid velocity = 1 ft/sec 



Wake length (Xq) = 40 ft 



Actucilly, the empirical formulation for the wake velocity is associ- 

 ated with the above grid geometry. The results for the 2 and 6 ft 

 waves are plotted in Figs. 23 and 24. These refraction diagrams 

 are actually constructed by the so-called "orthogonal" method where- 

 in a wave ray path is obtained from the computer solution. The 

 crest lines shown on the diagrams are everywhere perpendicular to 

 the orthogonals and represent the crest position at times correspond- 

 ing to multiples of the wave period. This time interval, mutliplied 

 by the local wave speed at each point on the crest, determines the 

 position of successive wave crests. 



It is evident, for both wave lengths, that a large distortion 

 of the wave front occurs for the length of wave crest initially located 

 between a point 1 ft from the wake centerline and a point 3. 5 ft from 

 the centerline. In fact, this 2.5 ft length of crest is stretched to 

 nearly eight times this length after the wave has traveled only 30 ft 

 into the wake. The local crest line divergence for the 2 ft wave is 

 larger than that for the 6 ft wave. A similar large stretching is evi- 

 dent for the length of wave crest between 3. 5 and 5.0 ft from the 

 centerline. Because of this extreme divergence of orthogonals for 

 localized lengths of wave crest, it is not expected that refraction 

 techniques alone are sufficient to represent the present wave-current 

 interference effects. In fact, it is expected that diffraction along 

 the wave crest must occur to provide for a flow of wave energy along 

 the crest. This modification will be discussed subsequently. 



The qualitative results obtained from the refraction analysis 

 caji be sum.m.arized by describing the behavior of adjacent finite 

 crest lengths as the wave passes through the wake. The incident 

 wave can be divided into four separate lengths as follows: 



1) Crest length between ^ and i ft. 



2) Crest length between 1 ft and 3.5 ft. 



3) Crest length between 3.5 ft and 5.0 ft. 



4) Crest length beyond 5.0 ft. 



430 



