348 roFONOFF [sect. 3 



possible to show that a counterflow can be developed under part of the Kuroshio 

 system with a deep-water source in the Southern Hemisphere. Confirmation by 

 direct measurement has not yet been made. 



E. Zonal Boundaries 



Munk (1950) did not consider explicitly the influence of zonal boundaries in 

 his analysis of wind-driven circulation. The meridional extent of the circulation 

 in his treatment was determined by latitudes at which the curl of wind stress 

 was zero. We shall examine briefly the type of boundary layer that is formed 

 along a solid zonal boundary. i 



We assume that, if the curl of the wind stress does not vanish along a zonal 

 boundary, there will be a boundary layer of characteristic width W formed in 

 the vicinity of the boundary. Introducing the non-dimensional variables 

 rj = ylW, ^ = xjL, where L is the zonal extent of the ocean, and using the ncn- 

 dimensional form of the transport function and wind stress introduced pre- 

 viously, we obtain the boundary-layer equation 



AH terms in (80) will be of unit magnitude if we choose 1^= (J/zL/^S)'/* ~ 

 200 km. The solutions differ from those obtained for meridional boundaries 

 because the equation depends on both ^ and 17. The presence of both independent 

 variables in the boundary-layer equation prevents us from obtaining simple 

 general solutions. However, we can obtain some of the features of the solutions 

 by assuming that the curl of wind stress is independent of 17 in the boundary 

 layer. The solution can then be written in the form 



ifj' = ijj'i + tfj'h, (80) 



where ifj'i is the interior solution and ijj'n is a solution of the homogeneous 

 equation obtained by dropping the curl term in (79). The boundary conditions 

 are that i/j' and its derivative with respect to rj are zero at the zonal boundary 

 (^y = -q = 0) and that the boundary-layer solution remains finite as 17 increases. 



The simplest class of solutions of (80) is that for which the variables are 

 separable, i.e. </«' can be written in the form tp' = X{$)Y{r]). The functions X{$) 

 and Y{r]) satisfy the equation 



Two cases are possible depending on whether A is negative or positive. If A is 

 negative, the solutions are of the form 



f^ = e-lAli^^^e""", (82) 



1 Munk and Carrier (1950) showed that the characteristics of the western -boundary 

 current are not changed appreciably if the western boundary is incHned to the y-axis. 

 They obtained the boundary -layer solution for a triangular ocean. 



