p^^'(x,z,t) = -p 



oo 



d2 



(44) 



c-z..o-lf ^-r^ 



d2 



sin (k -x- ojj) (45) 



where W ('2) is governed by 



(/-W dW o /?„ 



with 



(46) 



and 



dW,, gkj^ 



+ — ^ W =0 at 2 = 



dz ojJ- 



W = at 2 = H 



(47) 



(48) 



and represents either surface or internal waves. From (41) to (45) we can derive 

 the driving functions /'^ and ii according to (39) and (40). This includes a great 

 deal of algebra. The final result is 



00 00 



^ m = 1 /! = 1 



(49) 



00 00 



^^ix,%i)=-^ ^ 1^1^1(0) sin[fr+T„).T-^c.„ + <.,)^] 



(50) 



where F- (z)and G~ (0) are given bv 



k -k I 1 cfW 



k. 



1 "W^ r 1 i 



A~^ W„dgr±o.>„,±a,„) -w 



J 02 I J W„ 



1 .. dW^ 



g 1 d^p a;Joj„±6j„) 



t^^ P 



dz~ 



k ^ p dz\ dz dz 



16 



