350 FOFONOFF [sect. 3 



serious fault is the implicit assumption that sufficient potential energy is 

 available to allow the circulation to exist as a baroclinic mode. As the processes 

 that control the density are not represented in the linear model, it cannot be 

 taken for granted that enough low-density water will be available to support 

 the transport required to balance the field of surface stress. Although the 

 anomaly of potential energy does not enter explicitly into the vorticity equa- 

 tion for the interior flow or the boundary layer, its distribution in terms of the 

 stress field can be obtained from the momentum equations. Thus, for a given 

 distribution of wind stress, the density field must be capable of producing a 

 distribution of potential energy that is determined by the surface stress. 

 Clearly this will not be possible in every case. 



The frictional model is based on the concept of eddy viscosity. As this 

 concept is, at best, a crude approximation to the dissipative processes in the 

 ocean, the results obtained for the boundary regions must be applied with 

 caution and may be misleading in detail. In the absence of non-linear accelera- 

 tion terms, the frictional effects are the same up-stream as down-stream for 

 flow near the western boundary and give no insight into the processes that 

 enable the Gulf Stream and Kuroshio to separate from the coast before being 

 completely dissipated. Munk, Groves and Carrier (1950) examined the in- 

 fluence of acceleration terms by calculating successive corrections to the linear 

 solution. The main effect of the non-linear terms was to shift the region of 

 highest intensification of the western-boundary current down-stream but the 

 separation of the flow from the coast was not indicated by the analysis. 



The analysis of non-linear acceleration terms in a frictional model is highly 

 complicated and results of a general nature are difficult to obtain. Part of the 

 difficulty in analysing the more complete equation arises because the accelera- 

 tion terms are not small compared to the frictional terms and cannot be 

 considered as small perturbation terms in the equations. Charney (1955) and 

 Morgan (1956) showed that a more realistic theory of the development of the 

 Gulf Stream could be set up by neglecting frictional terms altogether. Thus, 

 although dissipative processes have to be invoked to produce the down-stream 

 deceleration and break-up of the boundary flow, they are apparently not 

 dominant in the up-stream accelerating portion of the flow. The results obtained 

 by Charney and Morgan suggest that considerable insight into the action of the 

 non-linear acceleration terms can be gained by developing the theory of 

 inertial flows in which all dissipative and driving forces are neglected. 



Fofonoff (1954) showed that a simple class of inertial flows can be obtained 

 for a rectangular homogeneous ocean with a level bottom. The equations 

 governing the circulation are of the boundary-layer type provided the interior 

 flow is assumed to be westwards. The westward flow is intensified into a narrow 

 meridional current along the western boundary and returns eastwards as a 

 narrow jet of high velocity. The jet continues along the zonal boundary and is 

 decelerated and turned westwards again in an eastern boundary current. The 

 boundary-layer solutions do not become negligible in the interior of the ocean 

 if there is an eastward component in the interior flow. We shall examine the 



