Sverdrup Balance (1) The large-scale, upper ocean flow in the ...

(3) Geostrophic and Ekman effectsLet u=(u, v) be the horizontal velocity, composed of a geostrophic and anEkman part. Thus, u = u g + u e . The equations of motion then become(4)This can be separated into Ekman and geostrophic parts. The geostrophicpart is(5)The Ekman part is(6)The first set of equations can be solved for v g in terms of w to find thatThis is a simple vorticity equation for the geostrophic, mid-ocean flow. Theleft side is the planetary vorticity; the right side is the vortex stretching.This can be integrated to find thatwhere V is the meridional velocity averaged between the surface and z= D and w E is the Ekman pumping or suction velocity.. The verticalvelocity w is assumed to fall to zero at z = D.(7)(8)2