342 FOFONOFr [sect. 3 



occurs, three in which two types occur and two in which all three types are 

 either present or absent. In order that we may see the basic restrictions imposed 

 on steady circulation by the simplified momentum equations and continuity, 

 we shall neglect all interactions between the various types of flow and examine 

 briefly each of the eight classes permitted by the simplified equations. 

 The eight classes are : 



(i) Pure Ekman transport. Ekman transport can occur in the absence of 

 baroclinic and barotropic components provided the divergence of the Ekman 

 transport is zero. It will be zero for any wind stress of the form 



JG .dCr 



where O is an arbitrary function of x and y. The fiow is then confined to the 

 upper layer of the ocean and requires no compensating geostrophic flow. The 

 meridional component of transport, Ve, is proportional to the curl of the surface 

 stress. A simple example of this class of flow occurs in an ocean for which the 

 aj-component of surface stress is zero and the ^/-component is a function of y 

 only. The Ekman transport is zonal and non-divergent. This case arises in the 

 study of zonally-uniform ocean circulation. 



(ii) Zonal baroclinic transport. If the baroclinic transport is zonal (Vg — O), 

 its divergence is zero. Hence, both (59) and (62) are satisfied. Thus, the reduced 

 transport equations allow an arbitrary zonal baroclinic flow. The flow is not 

 affected by bottom topography provided the density is uniform near the 

 bottom of the ocean. This class of flow can occur in pure form in an ocean 

 without meridional boundaries. It forms also an essential part of the circulation 

 induced by winds in an ocean with meridional boundaries because winds in a 

 given region of the ocean induce a zonal baroclinic transport westward of the 

 region (Munk, 1950). 



(iii) Pure barotropic transport. Equations (59) and (67) are satisfied by 

 purely barotropic transport if the flow is along contours oi f/h. Otherwise, the 

 flow can be an arbitrary function oifjh. If the bottom is level, the flow will be 

 zonal ; if the bottom rises or drops in a distance over which / does not change 

 appreciably, the flow will be along bottom contours. As fjh is constant along 

 each streamline, the flow is displaced towards the equator in crossing a ridge 

 and towards the poles in crossing a trough in the ocean bottom. 



(iv) Stress-driven baroclinic transport. If the divergence of the Ekman 

 transport is balanced entirely by the divergence of the baroclinic flow, the 

 resultant circulation can persist in the absence of barotropic components. 

 The flow will not extend to the bottom and will not be affected by bottom 

 topography within the restrictions given for class (ii). The sum of the meridional 

 components of Ekman and baroclinic transports will be proportional to the 

 curl of surface stress. This class of flow was assumed by Munk (1950) in his 

 analysis of wind-driven ocean circulation. 



