354 FOFONOFF [sect. 3 



theory, discussion of its features is given in the section deahng with time- 

 dependent motion. 



There are several important characteristics of the inertial flow for negative 

 values of uq that we will note before examining the two-layer ocean. The 

 stream-function ip is symmetrical with respect to the central meridian of the 

 ocean. Hence, u and rj are also symmetrical and v is antisymmetrical. As 

 the equations for the two-layer ocean are basically the same as those for the 

 homogeneous ocean, we anticipate the same symmetries in the solutions. The 

 width of the boundary region depends only on the interior velocity and jS. It 

 does not depend on the size of the ocean and is least for the slowest interior 

 velocities. As in the frictional model, no eastward acceleration of the flow is 

 present. Acceleration takes place only along the western boundary where the 

 pressure gradient has a down-stream component. Deceleration occurs along 

 the eastern boundary where the flow is against the pressure gradient. 



An eastern-boundary current can occur only if it is fed by a jet of high 

 velocity and high relative vorticity. Because of the concentration of the flow 

 into a narrow jet, any dissipation in the system would have a drastic effect on 

 the flow. If relative vorticity is lost in the zonal jet not all of the stream-lines 

 will be able to regain their original latitude and the flow will shift toward the 

 jet. We may speculate that if friction were suddenly to act on an inertial flow 

 with a jet along the northern boundary, the flow would cease first along the 

 southern boundary, and the region of no motion would grow northwards as 

 relative vorticity is removed from the jet. The inertial circulation would finally 

 be confined to the north-west corner of the ocean before ceasing altogether. If 

 this speculation is correct in a gross sense, we can interpret qualitatively the 

 action of non-linear terms in the frictional model. The solutions for inertial 

 flow indicate that no western-boundary currents can exist at latitudes for 

 which the interior flow is eastward as the eastward flow would require the 

 boundary current to decelerate. Thus, the boundary current can extend into 

 latitudes of eastward interior flows only if there is an inertial recirculation so 

 that the boundary current is not decelerated. Thus, immediately seaward of 

 the boundary current there should be a counterflow with a westward component 

 of velocity. On the basis of these qualitative arguments, it appears that the 

 counterflow suggested by the frictional model is essential to the stability of 

 the western-boundary currents. However, more detailed and rigorous analyses 

 would have to be carried out before the conjectures given here could be sub- 

 stantiated. 



A. Inertial Baroclinic Flow 



The non-linear momentum equations examined for the homogeneous ocean 

 can be solved also for simple classes of baroclinic flow in a two-layer ocean by 

 applying approximate boundary-layer techniques. The two-layer ocean model 

 is a better approximation to the real ocean than the homogeneous model in that 

 both barotropic and baroclinic motion can exist. Yet, the model is sufficiently 



