524 EIGHTH PACIFIC SCIENCE CONGRESS 



If we introduce two quantities Di and D^ such that 



D, = .yl^ (") 



P 

 and 



^^1 " \ pw 



P' 



equation (16) becomes 



^\ 



2^ 



/9*£«_ 9^\ _ (25— 1)^ /D, y/ 9'^. a^\ 



cos</> a^g 1 /3t;: axy \ 



R dx pa>h \dy dx / ~ 



(19) 



The quantity Di may be called "the frictional distance", whereas 

 Dj. is the same as Ekman's "depth of frictional influence" except that 

 it does not contain sin ^. 



The coastal conditions which ^^^g should satisfy are 



^, = -^ = (20 



an 



along the coast-lines, where d-^s/dn is the derivative of -^g in the direc- 

 tion normal to the coast-lines. 



If equation (19) can be solved and we can determine the functions 

 ^i{x,y), ■i^2(x,y),^3{x^y)> • • • •, the sum: 



^ (25-l)rf 



*(x,3»,z)= 2^ ■qr^(x,y) cos ^ (21) 



s = 1 



will give the horizontal streamlines at any level z for the wind stresses 

 Tx (x, y) and Ty (x, y). The stream function ■*■ (x, y, z) should, of course, 

 satisfy the condition: 



along the coast-lines and the horizontal streamlines of the currents 

 are given by 



■^{x, y, z) = constant. (23) 



3. Infinitely Deep Ocean 

 If ^\ is the solution of (19) when /z = 1, the solution of (19) will 

 be 



^.(x,>')= ^-^lix^y). (24) 



