560 



EIGHTH PACIFIC SCIENCE CONGRESS 





Xoo 

 y (A) sin X$dX, 



00 



y (A) = I —sin Xada. 



^C- 



Ca 



Next assume for the wind stress 

 dv 



and 



-A. 



T(A) 



dz 



''I 



T (A) sin A^fiA 



■A. 



dv 



sin Xada 



= I T sin Xada 



J 



1 — COS {XL/D^) 

 = — . 



if T is independent of x. 



Substituting (10), (11) and (12) into (8) and writing 



u^ + iv^ = W 

 the two equations (8) are combined into 



■ d^V , — 



D^r — — (A- + 27rH) W 



^'g 



y(A) = 



(12) 



(13) 



(14) 



(15) 



^ dz^ V . / ^^ g-j^ ^^^ 



and the conditions to be satisfied along the boundaries now become 



z = 0: -A ^ - ^_-_^os(XL/D,) 



(16) 



dz 



and 



A 



It 



(17) 



z = h: \V = 0. (18) 



The solution of the equation (16) subject to the conditions (17) 

 and (18) is 



W := 



+ 



7r^gy(A) 



(A- + 27r-i)co sin (jjDi, 



1 



cos h (VA- + 27r~i z/D,) 



cos ]i (VA- + 2--Z h/D,) 



h — s 



^"^-^vZ-^v 1 — cos (AL/A.) ^"^ ^^ (V^^' + ^TT^'/ --£7 



Va- + ZttH 



) 



cos Ji (VA- + 277-/ ///i),) 

 (19) 



