ATl-lCl 51 



+ ^ "^"^ '^ nsy sin nsy e 



-2/-^ f 2/3 ^ 1/3 ,^ -1/3 



l- /3 3 '/3 3V^ 2 



o 1/3 2/3 ,/~ -1/3 \/-> r- -V3 



. [(^ - ^)x . l_]cos(f4.^™) - ~2-^^^2- l/3C3)cos(2Sfii-) 



+ (C^ - 1/3 C2)sin( )] >e 2 + iL-|os_'L nsy sin nsy • 



1 r 1/3n -1/3 , I (x-r)e" 



•i (x - r - e ) + An |"e • (50) 



.3 ^J 



The terms U-, and V^ do not satisfy the boundary con- 

 ditions V-, = -^- = on y = Ojl* V/e must recall that these 

 boundary conditions were chosen rather arbitrarily as being 

 plausible ones for the type of wind distribution specified, and 

 the y dependence of the zero-order solution was accordingly 

 chosen as sin nsy, VJe cannot expect such a y dependence to 

 satisfy all the conditions for each set of equations. The fact 

 that U-1 and V-, do not satisfy the boundary conditions does not 

 seem to be very serious since we do not really know what con- 

 ditions are appropriate. 



If we next consider the equations resulting from equat- 

 ing the coefficients of 6 to zero, we obtain from (8) and (11), 



= f^2xxx * ^2W - ^2xxy - "2yyy ^ " ^2 = (^i^ - Ui^-yH,)^ 



'J2X + V2y = - H-, • 



In the boundary layer, near x = 0, V^ is of order e . 

 Thus V7e can expect Vp to be of order £"* in that region. By a 

 similar argument, we can expect V-^ to be of order e '^--'5 Vk to 

 be of order e -^,etc. If we therefore write out the series 



