All-101 kl 



i' = T\i =0 onx = 0,r 



\\^ =^ = on y = 0,1 (20. a) 



yy -^9 



can be solved for i) by applying the boundary- layer technique" 



to the boundaries x = 0,r« The solution is 



ijj = (1 + a sin T;)sin nsy 1 -x + r - e + e /■->Q\^-'r) 



.r: -1/3 

 1/3 X y3 e 



+ [(e -r)cos(— — — ) + 



£-V3 



\/3 



^/3 ..-1/3. 



1/3 X V J e - ^ 



+ (^,/3£ -'-_IL.)sin( -_)]e ^ ^ 



From (19) U and V^ are found to be 



) 1/3 1/-^ (x-r)£ 



U = - ns(l +a sin t)cos nsy -i-x + r-e -^+£'^-'6 



r . ^ -1/3 



"- -■-' X 



-l/3i 



-1/3 \/'\ T- -1/3 X£ 



+ [(el/3.r)cos(2LN/l£ _.)+( V3 £ - -X)sin(£lli )] e"""^ 



^ 1/3 ^ . , . 



.22) 



r (x-r)s-l/3 



Vq = ( 1 4- a sin t ) sin nsy ■ - 1 + e 



-1/31 

 r -1/3 -1/3 r- -1/3 ^£ V 



+ [cos(— rr ) +( — V'3)sin( ~ -)je '^ I 



n/3 ^ 



■^ (23) 



The zero-order equations derived from (I3) and (1^) are 



* The problem defined by equations (20), (20, a) is solved in 

 detail in Appendix 5 by means of the boundary layer technique, 

 The method used in the remainder of this paper is described 

 in detail in that section. Munk and Carrier [6] used this 

 method for solving the steady problem in a triangular ocean. 



