SKCT. 3] DYNAMICS OF OCEAN CURRENTS 367 



conclusions based on the application of (146) and (148) depend critically on the 

 assumptions made about the vertical velocity. Nevertheless, it appears reason- 

 able to conclude that strong deep-water currents are induced along some 

 portions of the western boundaries by vertical flow in the interior of the ocean. 



Stommel (1957) suggested that downward flow in the deep water is conflned 

 to relatively small regions in the North Atlantic and Weddell Sea and that, 

 over the remainder of the world ocean, the flow has an upward component. 

 Thus, the deep-water flow is assumed to be driven by concentrated high- 

 latitude sources with the remainder of the ocean acting as a more or less uni- 

 formly distributed sink. The deep water is dissipated by upward flow into the 

 upper layers of the ocean. Assuming tacitly that the western-boundary flow can 

 exist whether or not (151) is satisfied (as, for example, in the purely frictional 

 boundary layer), Stommel and Arons (1960, 1960a) worked out a scheme of 

 interior deep-water circulations connected by western-boundary currents for 

 all of the major oceans. The interior circulation does not cross the equator 

 according to (147). Hence, a separate circulation was assumed in each hemi- 

 sphere. The boundary currents do not depend on the Coriolis parameter but 

 rather on j8, which does not vanish at the equator. Thus, the boundary current 

 is allowed to cross the equator to connect the interior flows in each hemisphere. 

 Its stability at the equator has not apparently been examined. Using these 

 simple arguments, Stommel and Arons were able to make estimates of the 

 magnitude of the deep circulation and also of the length of time required to 

 renew the volume of water in the lower layers of the oceans. Although the 

 circulation scheme proposed by Stommel and Arons is not free from objections, 

 some of which are given here, and has not been confirmed as yet by observations, 

 it illustrates the far-reaching consequences of imaginative application of even 

 the simplest dynamical arguments. 



In order to develop a more satisfying description of the mechanism of 

 convective circulation, we have to introduce conservation equations for heat 

 and salt. As in the momentum equations, we can neglect molecular transport 

 processes in comparison with the turbulent exchange or flux of the properties. 

 Although mixing must occur by molecular diffusion, the diffusion occurs at 

 much shorter length scales than those considered for ocean currents. The flow 

 of heat and salt relative to the mean current is usually approximated by 

 diff'usion equations expressed in terms of eddy diff'usivity coefficients. 



Assuming that the heat content of sea-water is linearly proportional to the 

 temperature and independent of the salinity, we may express the flux of heat 

 Fqi as 



FQi = -K{i)^> (153) 



where K{i) is equal to the horizontal eddy conductivity, Kh, for i=l, 2 and to 

 the vertical eddy conductivity, Kv, for i = 3. Similarly, the flux of salt, Fst, is 



Fsi = -D{i)^, (154) 



OXi 



