All-101 102 



, n r ^ xe-1/3 e ^1 r. ^ ^ xe -1/3 e ^i 



For the boundary near x = r, we now define ^ by 



(x-r) = e'^K 



and specify that the solution vanish as ^-oo, i.e., as the 



distance into the interior part of the ocean increases. By 



a similar analysis, v;e find that near x = r, 



r 27ii 

 ^^b = ^I3(y?'^) + C^^(y,^)e^ + C^^(y,'z)e''^ 3 



+ G^.(y,x)e 3 



In order for ik to tend to zero as Jj-^ - co , it is 

 necessary that C-j_t = C-^^ = C, = 0. Hence 



.1^ = G23(y,'^)e^ = C23(y,T)e^^ ^^ 



The total boundary layer solution can be written 



f x-r) £-1/3 xe-1/3 e--?i 



^l^b = C2(y,T)e^^-^^ + C3(y,T)e^' 3 



-1/3 Itzi 



+ Ci^(y,T)e''' ^ 3 (7) 



The solution throughout the domain consists of (h) and 

 (7) or 



t|j = il)j_ + i|)^ = (1-^ a sln-r )sin nsy|[ - x + C-[_(y, t) ] 



y-p -1/3 e ^+^1 ? 

 + Ci,(y,T)e^^ T" J (8) 



