340 FOFONOFF [sect. 3 



contours of x- Furthermore, the transport between two contours xi and ^2 is 

 equal to (x2 — xO//' where/ is the mean vakie of the Coriohs parameter between 

 the two contours. If the contours do not he along lines of equal Coriolis para- 

 meter, the baroclinic flow must be divergent. For example, if the contours xi 

 and X2 cross latitudes for which the Coriolis parameters are /i and/2 respectively, 

 the difference in transport Ai/jg, where 



^<pg = ^^2-Xi)(^-f) = -(X2-Xi)7-F' 



represents the mass of water that has been converted to, or from, the baroclinic 

 mode. The baroclinic flow between contours of x decreases with latitude if the 

 flow is polewards and increases with latitude if the flow is towards the equator. 



C. Interior Transport Equations 



We have seen from the analysis of the magnitudes of the various terms in 

 the momentum equations that non-linear accelerations and Reynolds stresses 

 are small relative to the pressure gradient and Coriolis forces except in regions 

 where the currents are sharply confined spatially. We can formulate a simplified 

 model of transport by neglecting accelerations and frictional forces due to 

 horizontal gradients of velocity. However, in doing so, we eliminate all second- 

 order derivatives of velocity and transport. Consequently, we will not be able 

 to satisfy all the necessary boundary conditions along the lateral boundaries 

 of the ocean in terms of the reduced system of equations. We will have to re- 

 introduce the higher-order terms in the boundary region to complete the 

 system. The simplification will work if it can be shown that the higher-order 

 terms decrease in magnitude with distance from the boundary and become 

 small in the interior of the ocean. The separation of the ocean into an interior 

 and boundary region enables us to consider more general types of flow. 



Assuming that we can neglect friction and accelerations in some region of the 

 ocean, we obtain the reduced system of transport equations : 



ex cy 

 By introducing the transport components Ue and Ve defined by 



Ue = Tsylf, Ve = -Ts,lf, (60) 



which will be referred to as Ekman trans'port components, and substituting 



