358 FOFONOFF [sect. 3 



Similarly, if we assume that the interior flow is westward and slow enough for 

 relative vorticity to be neglected, the velocity will be geostrophic, so that 



Iu.= -g^ (122) 



and 



For anticyclonic circulation with poleward flow in the western-boundary 

 region, we can assume that the westward drift in the interior extends to the 

 southern boundary {y = 0). Integrating (123), we obtain 





(124) 



hdy 



As (121) and (124) must give the same value for the potential energy at each 

 point in the interior of the ocean, we must have 



ry 



Xb = xbo-fh = Xi = xo-fh+^ h dy (125) 



for ipb = ijji. Hence, the condition 



Xbo = xo + ^ \%idy (126) 



must be satisfied by the boundary solution to be compatible with the interior 

 solution. As xbo cannot become negative, we obtain the inequality 



In order to interpret the meaning of the inequality (127) more completely and 

 to obtain explicit solutions in the boundary region, we have to specify the 

 interior flow. A simple form of interior flow is obtained by assuming ipi to be 

 linear with y, that is, 



ifji = uhy = —Uohoy, (128) 



where Uo is the speed of the westward flow and ^o is the depth of the upper 

 layer at the southern boundary. For this type of flow the transport component is 

 constant at each latitude and the westward velocity is inversely proportional 

 to the depth. Substitution of (128) into the inequality (127) yields 



liAmaxl ^ g'ho^l^yma^x, (129) 



where «/max is the latitude at which xbo is zero. We may express (129) in the 

 alternative form 



ymax2 < g'holUo^ = {Uol^){g'holUo^) - W^/Fr, (130) 



