Ejfect of Wind on the Mass Field and on the Density Current 551 



gives 



^+/M, + r, + //, = 0, 



~^-fM, + Ty + Hy = o. 



(XVII.3) 



Therein M is the vector of the mass transport (equation XII. 8, p. 376). To these 

 must be added the continuity equation for an incompressible fluid. 



For a given value of T and ignoring the effects of the horizontal components of the 

 eddy viscosity the three equations (XVII.3 and 4) can be regarded as equations with 

 three unknowns P, M^ and My. Thus, in such a baroclinic current the total pressure P 

 and the mass transport M can be represented as functions of the wind stress. 



Ehmination of P by cross-differentiation, taking into account equation (XVII.4) 

 and putting ^ = df jdy gives 



(f-i)+^-.+rf-t)-- 



According to this vorticity equation the wind-stress vorticity must be balanced at every 

 locality by the vorticity of lateral mixing and by the term /SMy, which is the effect of 

 the change of the Coriolis parameter with latitude. This equation is reminiscent of the 

 equation (XIII. 59a) derived by Ekman who designated the term ^My the planetary 

 vorticity. 



SvERDRUP (1947) and Reid (1948) have applied this equation to the equatorial 

 currents of the eastern Pacific Ocean which correspond closely to the above conditions. 



The X-axis is taken pointing eastward and the >'-axis pointing northward. For the 

 trade wind belt it is possible to put dTy/8x = so that neglecting lateral mixing, 

 (XVII(.5) gives 



^My == - ^' (XVII.6) 



and with (XVII.4) 



and 



M. = .-^(?^' tan + i? ^^) (XVIL7) 



2ajcos0\ej ^ 8y^ / 



cP — dT^ 



ox dy 



and 



dP ^ 8^T^ 



^=-^^^^^^^'^ + ^- 



Thus for X == 0, (at the north-south vertical boundary), M^ = (integration limits 

 to Ax). The bars denote average values of the stress derivatives. The mass transports 

 Mg and My can be found directly from (XVII.3) if dP/dx and 8PJdy are known. 



