374 FOFONOFF [sect. 3 



to construct a more realistic model, we must introduce barotropic flow and 

 consider a more realistic variation of density or potential energy with latitude. 

 This has been accomplished, in part, by Robinson and Stommel (1959) in their 

 study of the oceanic thermocline and the associated thermal circulation. They 

 assumed that the vertical velocity did not decrease to zero in the deep water 

 but approached a constant value Woo. Thus, for their model, (170) is replaced by 



It can be seen immediately from (181) that solutions with x decreasing eastwards 

 (flow towards the equator) are possible if Wao is greater than zero. The non-zero 

 vertical velocity in the deep water implies the presence of a convergent baro- 

 tropic flow that supplies water to the baroclinic mode. However, Robinson and 

 Stommel ignored the horizontal components of the barotropic flow in the 

 equations. With this simplification, they were able to construct a surprisingly 

 realistic model of the thermocline. 



The presence of an unspecified vertical component of flow in the deep water 

 introduces an indeterminacy into the interior solution. Consequently, choosing 

 a particular form of the interior solution is not sufficient to specify the di- 

 vergence of the Ekman flow or the surface sources. Thus, some freedom is 

 available in choosing the boundary conditions (172) and (173). 



Robinson and Stommel developed their model in terms of temperature and 

 vertical velocity, neglecting lateral diffusion and convection by the zonal 

 component of flow. We shall follow their notation and terminology in describing 

 the model rather than developing their equations in terms of potential energy. 

 The basic equations describing the thermocline model are 



(183) 



(184) 



Clearly, we can replace the temperature T by the apparent temperature T* 

 defined in (160) with no change of the equations or results. Thus, the model 

 can be applied to salinity as well as temperature so long as the linear approxima- 

 tion (157) is admitted. 



Robinson and Stommel looked for solutions of the form 



y ^ (P,i-^ ^ _1_ a^ ^ (185) 



poa poga dz^ 



w = Wo. + -^^^ = H{x)co{^). (186) 



