THEORY OF UPWELLING AND COASTAL CURRENTS 



559 



where - is the stress of \vind and may be either a constant or a function 

 of X. On the bottom ;ve must have no motion, because of the vertical 

 friction at z = Ji: 



M = t; = 0, (4) 



and along the coast, which is considered to consist of vertical cliffs, we 

 have because of the horizontal friction at x = 0: 



u = V = 0. (5) 



In the region very far from both the coast and wind region, we have 

 at .V = oo: 



0. 



dx 



Let us define D^ and Di^ by 



-Dv = 77\/A^./po) sin 6; -On = -V^u/p^ sin 0. 



(6) 



(7) 



Dy is the depth of frictional influence defined by Ekman (1905) in his 

 theory of ocean currents, and D^, is a quantity having a dimension of 

 a length and may be called "frictional distance." This is a measure 

 of the horizontal turbulence. Then the equations (1) now become 



where 



(8) 



i = 



Du 



(9) 



In order to solve the equations (8), suppose 

 « = J- Cih (A) sin \^dX, 



CO 



Wi (A) = C u {a, z) sin Xada 



J 00 

 Vi (A.) sin X^dX, 



00 



V^ (A) = Cv (a, z) sin Xada 



(10) 



(11) 



