Savitsky 



Crest Length Beyond 5 ft« This length of wave crest is 

 always outside of the wake current and thus continuously progresses 

 through still water with no alteration in wave length or speed. 

 During its forward progress, it runs into the caustic area and 

 deflected wave crest originating between 1 ft and 3.5 ft from the 

 wake centerline. 



Application of Analytical Results 



Due to the omission of defraction effects for each wave crest 

 segment, the refraction results discussed in this section are in 

 themselves insufficient to represent the test results. They are 

 nonetheless invaluable in forming the basis for providing qualitative 

 information about the complex processes governing the interaction of 

 a wave system with a finite current field. 



Reflection Effects: The results of the refraction analysis 

 are first used to compute wave heights along crest lines In transverse 

 sections through the wake. The detailed results presented herein 

 are for a transverse section 1 2 f t aft of the grid and for a current 

 field extending 40 ft aft of the grid (as shown in Figs. 23 and 24). 

 Thus, the wave has progressed 28 ft into the wake at the time of com- 

 putation. The grid was 3 ft wide; had a mesh of 2. 7 Inches; a draft 

 of 1.67 ft; and a tow speed of 1 ft sec. Computations were made 

 for 6 ft and 2 ft long waves. The experimental results for these 

 conditions have already been presented In Figs. 19 and 20. 



Since the purpose of this computation Is mainly to compare 

 qualitatively the measured results with elemental analytical results, 

 simplifying assumptions were Introduced. First, It was assumed 

 that the local wave height between adjacent orthogonals Is Inversely 

 proportional to the square root of the distance between these adjacent 

 rays . Thus , 



.1/2 



k -' (t) <'^' 



where: 



io = separation distance between adjacent rays In still water 



i = separation distance between adjacent rays on the de- 

 formed crest line 



Hyy = local wave height In still water 



H^ = local wave height along deformed crest line 



This enabled wave heights to be constructed along a wave crest from 

 the centerline to a distance approximately 6 feet from the centerline. 

 Beyond this point, there is a superposition of the deflected wave seg- 

 ment with the undisturbed length of the Incident wave. In this area. 



434 



