All-101 22 



choose p = p[z - T(x,y,t)], \iheve the function p of the variable 

 (z - T) can be prescribed to fit observational data. We observe 

 that this functional form for p makes the curves of constant 

 density parallel to each others 



A complete analysis for the unknown quantities as func- 

 tions of the four independent variables x,y,z,t is exceedingly 

 difficult and we are forced to eliminate one variable by inte- 

 grating our equations over the vertical coordinate, z, and then 

 solving for suitably defined integrated quantities. In so doing, 

 we lose information concerning the dependence of the unknowns 

 on z. Since we are primarily concerned with general oceanic 

 circulation and mass transport, however, and since the integra- 

 tion leads to a considerable reduction in diffculty, the advan- 

 tages gained more than balance the loss of information involved. 



Actually we cannot afford a complete loss of information 

 concerning the vertical dependence of velocity. This will become 

 apparent shortly. 



The general density distribution must be specialized in 

 order to permit integration of the equations over the vertical 

 coordinate. Two cases will be considered. 



First, let T be a surface which separates two layers of 

 constant density so that 



p[z - T(x,y,t)] = Pi for z > T(x5y,t) 



and 



p[z - T(x,y,t)] = p2 for z < T(x,y,t). 



For this problem it is convenient to choose the coordi- 

 nate system v/ith the xy-planes parallel to the undisturbed 



