SECT. 3] DYNAMICS OF OCEAN CUKRENTS 377 



we are able to estimate Wx> and q* (or L). Ths known constants assumed by 

 Robinson and Stommel, except for ky, can be estimated with reasonable ac- 

 curacy from observations of the real oceans, whereas Woo and g* are known only 

 within an order of magnitude. Nevertheless, the thermal circulation is driven 

 by the flow. Wod. and the heat flux, g*, as well as the divergence of the Ekman 

 transports. From the point of view of the thermal mechanism, the vertical flow 

 from the deep water is arbitrary, i.e. the barotropic mode is not controlled by 

 the thermal circulation. 



For Mv> and Q* > 0, we find from (200) and (183) that the horizontal flow 

 is towards the equator if | Wao\ >\We\ and towards the poles if | Woo\ <\We\. As 

 iWxl must exceed \We\ for flow towards the equator, upwelling motion in the 

 deep water is an essential feature of the large anticyclonic gyres in the oceans. 

 However, this feature is not necessarily present for cyclonic gyrals. As has 

 already been indicated in the simple example considered earlier, poleward flow 

 can occur as a purely baroclinic mode {Wao= Wcc = 0). It is interesting to note 

 that if the upward flow in the deep water is sufficiently intense the baroclinic 

 mode occurs as an anticyclonic circulation with flow towards the equator even 

 though the Ekman transport is divergent {we > 0) and the integrated or total 

 transport is poleward. Consequently, we can obtain estimates of Wx, relative to 

 iVe in a region where the curl of wind stress is positive by observing whether the 

 baroclinic flow, calculated from standard oceanographic station data, is 

 cyclonic or anticyclonic. Another consequence of the upward flow in the deep 

 water is that the baroclinic transport, computed from station data, is less than 

 the total transport computed from the distribution of wind stress for cyclonic 

 circulation in the ocean. 



The convergent Ekman transport (mv < 0) presents a more difficult problem. 

 It is clear that downward flow from the Ekman layer cannot extend into the 

 deep water as this would require an increasing vertical gradient of temperature 

 with depth. Hence, we must assume that the downward flow decreases to zero 

 at some depth below the Ekman layer. Below this depth, the vertical flow will 

 be upward. The horizontal flow cannot be poleward under these conditions of 

 vertical flow and we need only consider the case ^ > 0. 



Robinson and Stommel assumed that the downward flow extended to a 

 small, but unknown, depth h and separated the ocean into two layers by the 

 surface of zero vertical flow. They estimated the averages of W and d&ldir] 

 separately in each layer and integrated the linearized equations to obtain 

 relations among the averages and the other parameters describing the model. 

 We shall follow the same procedure but will use slightly different approxima- 

 tions in order to take heat flux into account. 



Anticipating that h will be relatively small and that the temperature will 

 not change rapidly in the upper layer, we assume that the meridional gradient, 

 Ti, does not change appreciably in the upper layer so that its average is approxi- 

 mately Ti. The average of the meridional gradient over a depth interval, L, of 

 the lower layer is approximated by Ti/2. The average of the vertical velocity 

 is of the order of Wel2 in the upper layer and W^I'I in the lower layer. We 



