338 FOFONOFF [sect. 3 



the mass transport per unit width from the bottom to the surface of the ocean, 

 defined by : 



f/ = pudz, y = \ P^ dz, 



(43) 



and the potential energy, Ep, of a column of water of unit horizontal area, 

 relative to the bottom of the ocean, given by : 



Ep = \ P dz = \ pg{z-ZB)dz, (44) 



where rj is the surface and zb the bottom of the ocean. As in the case of geo- 

 potential, the potential energy can be expressed in terms of the specific volume 

 of sea-water and the pressure by means of the hydrostatic equation. Thus, we 

 obtain 



1 rv 1 rpji 1 cpb 1 cpb 



Ep = -\ {Pa){pg) dz = - \ PadP = -\ PaodP + -\ PS dP 



9 Jzs 9 Jo 9 Jo 9 Jo 



= Ep^ + X, (45) 



where Ep^ is a function of the bottom pressure Pb only and 



V = i r^" PS dP (46) 



9 Jo 



is defined as the anomaly of potential energy. The potential energy anomaly can 

 be evaluated from oceanographic observations in much the same way as the 

 geopotential anomaly. 



Integrating equations (25) through (28) vertically from the bottom to the 

 surface of the ocean and substituting from (43) and (45), we obtain 



8u^ 8uv dx Pbccb (dPB\ ^ . v2TJ ^ (ai\ 



-^- + ^ fV = -^ +AHy^U +rsx-rBx (47) 



dx By dx g \ ox J z 



dx dy ' ^y 9 \ % Jz 



Pb = f ' pg dz (49) 



JZ£ 



f + ^ = 0(orO). (50) 



where Tsx,rsy are components of wind stress at the ocean surface, rBx,rBy com- 

 ponents of bottom stress due to movement of water along the bottom, Ah the 

 kinematic eddy viscosity, piHip, and u^, v^ and uv components of horizontal 

 momentum transport given by integrals of the form 



uv 



= puvdz. (51) 



JZ£ 



