Effect of Wind on the Mass Field and on the Density Current 553 



TsucHiVA (1955fl, b) who made a second approximation to the geostrophic current 

 equation for/ = 0. For the surface velocity of a drift current and a frictionless gradient 

 current the equations (XIII.26 and 31) give 



Tcos(ifj — 77/4) 



- - ("A 



rsin(iA-7T/4) 

 V(fpoV) ~^ fp< 



r 



(XVII.6) 



where is the angle between the wind stress and the direction of the ^-current; the 

 subscript zero refers to the sea surface. Indeterminate solutions are obtained from 

 (XVII. 6) for the equator. If an exact solution is required the eddy viscosity cannot be 

 taken as insignificant by comparison with the pressure gradient and the Coriolis 

 force. Only in this way there is an equilibrium between the wind stress, the pressure 

 force and the vertical friction in the equatorial belt. The simple equation of motion 

 (corresponding to (XIII. 23fl) and (XIII. 30) is now 



where 



V = Vjc ^ iVy and p ~ Po- 



The boundary conditions are 



L^] =.-T=-iT, + iTy) and y(z = O)) = (XVII.8) 



(XVII.7) is identical with 



ry9 



" av^b, (XVII.9) 



cz 



where 



a = — and d = [^ + ' ^ 



7] 7] \dx cy 



If b{z) is known from observations then, taking equation (XVII.8) into account and 

 since a is independent of z this can be solved. To determine b{z) Weenink and Groen 

 used the Reid model (1948) which gives a good approximation for the equatorial 

 regions. This postulates a homogeneous layer of thickness h below which the density 

 of the water increases with depth according to an exponential function (see XVI. 30). 

 For this model (as in XVI. 31) one obtains 



ldp\ Ap8h /8p\ Apdh 



and the solution of (XVII.9) at the surface (z = 0) will be 



„„ = Jl _ *« (, - 1+^%-H A (XVII.IO, 



7]^/a a \ 1 + h\/a J 



When the value of h\/a or of /is large the expression in brackets will equal 1 and 

 (XVII.IO) will be nearly equal to (XVII.6). It is thus apparent that at a latitude of 2° to 



