All-101 3^- 



layers of the oceans Is negligible, but no definite conclusions 

 have been established to this effect* It Is because of this 

 uncertainty that v/e consider the two separate problems, 1 and 

 2« If the motion of deep v;ater is really negligible, the pres- 

 sure gradient in deep water is also negligible and the assump- 

 tions of Problem 1 are justified with the result that the thermo- 

 cline responds instantaneously to a change in the free surface 

 height provided the hydrostatic pressure assumption is also 

 valid. Consequently, the only motion existing in the layer 

 below the bottom of the thermocline is that due to the shear 

 force exerted by the water at the depth z = T - d onto the water 

 below it. Vertical shear will extend the motion to lower depths 

 but the velocities will decay exponentially in the vertical 

 direction [l] until they become negligible. 



If the motion of deep water is not negligible, then we 

 must consider Problem 2 v;here no such assumption is made. In 

 that case, the thermocline does not necessarily respond imme- 

 diately to a change in the free surface and, consequently, a 

 pressure gradient may result. Since the fluid in the bottom 

 layer is homogeneous and since the wave length of the thermo- 

 cline is large compared to the depth of the lower layer, a 

 velocity with uniform vertical profile is set up, (hydrostatic 

 pressure being again assumed). The shear stress, 'Cpx' exerted 

 by the water of the upper layer onto the surface of the lower 

 layer also causes a velocity in the lower layer. This velocity 

 is not uniform vertically. The problem including the effect of 



