All-101 9 



z = T] , viz. , T = - Pq/^p r] - C (where Ap =p_j-^ ~Po ^^^ T = -C 

 when r] - 0). Thus, if the velocities are negligible in the 

 depths of the ocean, the therraocline must respond inimediately 

 to a change in the shape of the free surface in order to main- 

 tain negligible pressure gradients at these depths. 



The three assumptions, (a) hydrostatic pressure, 

 (b) negligible velocities in the ocean depths, and (c) con- 

 stant density belov/ the thermocline, are crucial for the present 

 case. It is, of course, possible that any one or a combination 

 of these three assumptions may be incorrect. If this be the 

 case, then the thermocline need not respond to the free surface 

 immediately. The frequency of the wind variation which we shall 

 consider later in our development will be small so that assump- 

 tions (a) and (b) seem plausible. Thus the only motion exist- 

 ing below the thermocline is caused by vertical shear and this 

 motion decays exponentially with increasing depth according to 

 Ekman [ l3 . 



The equations of motion are then integrated from the 

 depth z = - h to the free surface z = t] . This problem will be 

 called the one-layer problem because of the single integration* 

 The depth, z = - h, does not appear explicitly in the integrated 

 equations. 



In both cases, the effect of the wind is represented 

 by the shear stress at the ocean surface and appears in the 

 evaluation of the vertical viscous terms at the upper limit of 

 integration (free surface). 



An additional difference between the two problems is 



