SECT. 3] DYNAMICS OF OCEAN CUKRENTS 341 



the barotropic and baroclinic transports defined previously, we can reduce 

 (57) and (58) to 



U = Ug+Ue+UE 



(61) 



V = Vg+VB+VE. 



Thus, the total transport in the interior of the ocean can be considered to be 

 made up of three types of transport as indicated in (61). Both the barocHnic 

 and barotropic transports are geostrophic, while the Ekman transport repre- 

 sents non-geostrophic deviations of the currents due to stress on the sea 

 surface. Ekman (1905) showed that the surface stress exerted an influence 

 over a layer of thickness {2Avlf)''' which is small compared to the total depth 

 of the ocean. 



The continuity equation (59) requires that the divergence of the sum of the 

 three tjrpes of transport be zero (or equal to rate at which water is added at 

 the surface). However, the divergence of each type does not have to be zero 

 separately. We can calculate the divergence from the definitions of the trans- 

 port components in the form 



f{ 



where p' = pB[l + {Plcc)dal8P]B< pb and ^ = dfldy. We can consider p' to be a 

 close approximation to the mean density pm of the ocean so that 



Vb = pmhuB ~ p'huB, Vb = pmhvB ^ p'hvB, (65) 



where h is the depth of the ocean. As the ocean surface deviates only slightly 

 from a level surface, changes in depth are due to changes of z^, i.e. 



dh dZfj dh dzg 



dx dx dy By 



Substitution of (65) and (66) into (64) yields the alternative form 



(66) 



dx dy 



which must be satisfied by the barotropic transport components. 



We have three basic types of transport represented in the equations. The 

 three types can be combined into eight classes of flows that can occur in 

 interior regions of an ocean. There are three classes in which only one type 



