All-101 



h2 



9Hq^ = nsyVQ + nseAU^ - (1 + a sinT)cos nsy 



(2^-) 



®^oy = - ^^y^o -^ nse^V^. 



(25) 



Solving for H^, v/e have, (neglecting terms of order e) 



1/3 

 QHq = (1 + a sin t) (cos nsy + nsy sin nsy)( - x + r - e ) 



+ (1 + a sin T)nsy sin nsy 



[ 1/3 (x-r)e"^/3 

 m nsy s e e 



.1/3 ..x,._.xV3e 



+ [ ( e - r)cos(- 



2 



-1/3 " 

 ■) + 



^ (\/3 e^^^ --^)sin(ii^i 

 /3 2 



-1/3 



xe 



-1/3 



•)]. 



> 



(26) 



F irst- Ord er Solution 

 From equations (12) and (15) the terms of first order 

 in 6 are found to be 



£[V, + V. - U, - U, ] - V, = [V - U - yH ]t (27) 

 Ixxx Ixyy Ixxy lyyy 1 ox oy -^ o ^ '^ 



"ix - ^ly 



- H 



OT 



(28) 



The boundary conditions are again U-, = V-, = on x = Ojr, 



In (27) and (28) the right sides of the equations pro- 

 vide the drivin'^ term as did (1 + a sin T:)sin nsy in the zero- 

 order equation. V/e shall proceed with the solution by means of 

 the boundary layer technique. 



For the interior solution we assume that the functions 

 are smooth and hence that the derivatives are of the same order 



