366 FOFONOFF [sect. 3 



of water flowing across the surface, zq, between the two latitudes. If the integra- 

 tion is extended to the hmits of the ocean, the integral in (146) must vanish. 

 Hence, both positive and negative values of wq must occur. 



If we cross-differentiate the geostrophic equations in (34) to eliminate 

 pressure, we see that the horizontal velocities in the interior of the ocean must 

 also satisfy the equation 



Integration of (147) over the zonal section yields 



-fpoWoL+^Tg = 0, (148) 



where Tg is the geostrophic transport of mass through the zonal section. As 

 the continuity equation (28) is satisfied by the intensified boundary currents, 

 whereas (147) is not, the geostrophic transport will not, in general, be equal to 

 the total transport T. The difference T — Tg can be interpreted as the mass 

 transport of the boundary flow Tb if the boundary flow can exist as a steady 

 current. 



Solving for the diff'erence, Tb, from (146) and (148), we obtain 



Tb= T-Tg = To-T poWoLdy-fpoWoLlp. (149) 



We have seen from the analysis of the inertial boundary flow that the western- 

 boundary current is stable and can exist in the steady state only if it accelerates 

 along the western boundary. The difference, Tb, will represent an accelerating 

 flow if dTbjdy is positive. In this case the interior flow adjacent to the western 

 boundary is westward and directed into the boundary region. Differentiating 

 (149), we see that the condition for an accelerating boundary flow is 



— = -V„,.„i-^^^>0 (150) 



or 



-^-- + —^- < 0. (151) 



By integrating (151), we can see that the acceleration is zero if 



poWoL = {poWoL)yJo^lf^. (152) 



Hence, for a constant vertical velocity, the boundary flow is unaccelerated, i.e. 

 constant, if the width of the ocean decreases with latitude as I//2. If the width 

 decreases more rapidly, the boundary flow is accelerated and, if less rapidly, 

 the flow is decelerated. However, if wq is assumed to vary with latitude, the 

 stable regions could only be determined from the exact distributions of wq and 

 L. In the extreme case, given any variation of L with latitude, it is possible to 

 choose Wq so that (151) is either satisfied or violated at every latitude. Hence, 



