Submerged Two-Dimensional Bodies 



The solution to the differential system of Eqs. (19) is therefore the same as 

 the well-known solution to the moving pressure distribution problem, given by 

 Wehausen and Laitone (6b), namely. 



w(2) (z) = _L. r ds f(s) I [izy (z- ib- s)] 



(20) 



where the function f(s) is defined in Eqs. (19) and can be written by virtue of 

 Eq. (17) as 



f(s) = pUM2i 





+ 2 





With 



+ 4 



r 10 



j = 



^ 27tU\ , ,2 



j = \(S.2 + b^) 



s/ + b' 



(21) 



The wave height can now be obtained easily. The first-order wave eleva- 

 tion is, by Eqs. (13a) and (17), 



^(1) 



('') = E rr? I'" I 



rrU 



iv X - — - ib 

 10 



(22) 



and the second-order wave is 



7^(2) (x) = j ds f(s) Re I [i2^ (X- s+ iO)] + i^ [t]^ ^>j^ , (23) 



where f(s) is given by Eq. (21). Note that 



\^—\ Re I [i2>(x- s+ iO)] 



is the wave height created by an integral pressure P concentrated on an infi- 

 nitely narrow band of the free surface at x = s . A detailed discussion of this is 

 given by Lamb (7). A plot of Re i[iiv(x- s+ iO)] is seen in Fig. 2. 



603 



