364 FOFONOFF [sect. 3 



occur even though the interior transport, as determined by wind stress, is 

 westward. If sufficient water is available, the wind-induced circulation could 

 be strong enough to drive the interface to the surface at some point along the 

 western boundary. The flow beyond this point would not be attached to the 

 boundary and could not be entirely inertial. The intensified current could 

 continue into higher latitudes only if water is removed from the coastal side of 

 the current by dissipative processes. The current could extend into regions 

 where the interior flow is eastward provided a seaward counter-current can be 

 developed. The counter-current could be an inertial recirculation of water 

 from an eastward jet as suggested in the discussion of the homogeneous ocean. 

 Stommel (1958) has suggested that the flow in the western-boundary current 

 can become unstable if the interface approaches sufficiently close to the surface. 

 The internal Froude number, u^lg'h, becomes greater than unity as the current 

 becomes more intense. The instability can presumably take the form of a 

 meander of entire current or the formation of hydraulic jumps along the inter- 

 face. If hydraulic jumps are formed, water would tend to be dissipated from 

 the coastal side of the intensified current where the depth of the upper layer is 

 least. 



6. Conveetive Circulation 



We have seen in the preceding sections that models of steady circulation can 

 be constructed provided we assume that either the barotropic or baroclinic 

 mode is absent from the flow. Both modes can be present in the steady state 

 if processes are present to convert flow from one mode to the other. The ex- 

 istence of such processes was assumed in setting up the various classes of 

 motion allowed by the integrated momentum and continuity equations for the 

 interior of the ocean. Clearly, the processes must alter the density of sea-water 

 along a stream-line and, hence, consist basically of the convection and diffusion 

 of heat and salt in the interior of the ocean. Because of the extreme complexity 

 of the complete system of conservation equations, progress in obtaining an 

 understanding of the influence of conveetive and diffusive processes on the 

 general circulation in the ocean has been slow. It is only in recent years that 

 theoretical investigations carried out on simplifled models have indicated the 

 importance of these processes, particularly in determining the steady circula- 

 tion of deep water. 



Two approaches to the problem of understanding conveetive circulations 

 have been made. The first consists basically of the relaxation of the condition 

 that no flow normal to a surface of constant density can occur. Thus, in the 

 two-layer ocean model, vertical flow across the interface is allowed even 

 though the conservation equations for heat and salt are violated. By ignoring 

 the additional conservation equations, we are able to examine the dynamical 

 effects introduced by the vertical flow in terms of elementary models. The 

 presence of a vertical velocity makes the set of momentum and continuity 

 equations indeterminate. Solutions cannot be obtained in terms of the boundary 



