Ship Waves and Wave Resistance 



I again thank the author for his significant contribution to a subject of great 

 interest. 



REPLY TO DISCUSSION 



K. W. H. Eggers 



REPLY TO THE DISCUSSION BY WEHAUSEN 



I am pleased to have Prof. Wehausen raise his question. In fact, I tried ap- 

 proach (b) first. In my notati.on, I had to evaluate 



( 3) 



Ej = Ii+ I2 

 where 



,( 1) ,(2) / f r ( 1 



) ,( 2) ( 1) ( 2) ( 1) ( 2) 



i/zy + 02 >/'2 " "^X "^X 



da drj 



and 



f 4''{4'V;czV^o-[g-d0(')]^}d,/: 



i: 



( 1) 



(!)■ 

 0Y 



+ 



( 1) 



,(1) 



dr] 





(1) 



0x 





Ao- 



0x 



Ar\ 



For finite x^, both Ij and 1 2 are difficult to evaluate. Due to tank wall re- 

 flection, there is no decay of first-order flow components. This implies that 

 S(X,Y) has no decay as well; thus i//^ ^^ everywhere includes local components 

 from nearby singularities. Furthermore 1 2, after performing the t? integra- 

 tion on triple products of Fourier terms, leaves us with expressions depending 

 on x^ with an infinite variety of nonrelated periods. 



I met the first difficulty, which arises under approach (c) as well, by trans- 

 forming li to an integral over the undisturbed free surface for -x^-o? (see Eq. 

 (47)). This was possible by use of a peculiar property of the Green's function 

 involved, which appears even in the case of finite depth: If we represent the 

 free wave system of a point source as a Fourier integral in y, then the ampli- 

 tude function (in our case K^/Mj^T, see Eq. (42)) is inverse to the weighting factor 

 of spectral energy (in our case T(2- cos ^(9^), see Eq. (29)) of the expression for 

 wave resistance. 



677 



