Salvesen 



submergence and for four different speeds. This is, to the author's knowledge, 

 the first time that waves created by a body have been computed to the second 

 order. 



Looking at these wave profiles, we immediately notice the extremely large 

 difference between first-order and second-order waves for the lowest speed of 

 2.5 ft/sec. This seems to violate the original assumption of expansions of the 

 form 



r](x) = eT7(i)(x) + e^T]'^^'>(x) + ... , (25) 



where the second-order term e^r](^\x) was assumed to be one order smaller 

 than the first term er]'- '^x). The experimental results to be discussed will, 

 however, show that the second-order waves agree surprisingly well with the 

 measured waves for these lower speeds. 



It should also be recognized that the shape of the second-order waves 

 downstream are quite the same as given by second-order Stokes waves, as was 

 expected. 



Wave Resistance 



The wave resistance will be obtained from the asymptotic form of the ve- 

 locity potential and the wave elevation. 



It is well known that the first-order wave height, Eq. (22), far downstream 

 takes the simple form 



T7^ ^^(x) = a cos i^x , (26) 



where a is the first-order wave amplitude, and x is an x coordinate so selected 

 that the wave has no phase shift. The second-order part, Eq. (23), can be shown 

 to have far downstream the form 



7?( 2)(x) ^ S COS v(x- r) - -^ i^a^ + i^(77( 1))^ , (27) 



which by Eq. (26) becomes 



T7^^)(x) = S cos v(x-t) + — va^ cos 2z>x , (28) 



where S is of order a^ and t is a phase shift. 



From Eqs. (26) and (28) it can be realized that far downstream we have two 

 Stokes waves. One has the form 



T7j(x) = a cos J>x + — va^ cos 2vx + . . . , K^'^) 



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