554 Ejfect of Wind on the Mass Field and on the Density Current 



3° the value of h\/a is already large enough to allow equation (XVII.6) to be used 

 instead of (XVII. 10). 



For a sufficiently narrow belt on both sides of the equator expansion into a power 

 series with respect to h\/a gives, neglecting higher order terms 



t^o = :^ (^ - lb A + Ab,h^ + . . . (XVII. 1 1) 



If lateral mixing is neglected (// = 0) the equations (XVII. 3) become 



T = AP-^ifM (XVII. 12) 



and (XVII. 1 1) with (XVI.31) becomes 



Vo - 4boh^ + — ^ + . . . (XVII. 13) 



Po 



Since M remains finite at the equator this gives finally by means of (XVI.31) and 

 (XVII. 12) 



%Th 

 Vo=--F~ • (XVII. 14) 



The behaviour of v^ can be illustrated in the following way. If the first term on the 

 right-hand side of (XVII. 10) is the drift current and the remainder of ^o is taken as the 

 slope current, then both components tend to infinity on approaching the equator, 

 but due to the coupling between these two components they behave in such a way 

 that their sum remains finite and approaches the vector (XVII. 14) as a limit of zero 

 latitude. The surface current, the wind stress and the surface pressure gradient all 

 have the same direction at the equator. Figure 255 illustrates their behaviour near 

 the equator. 



wind 



Fig. 255. The two components (vwind and Wgrad) of the current velocity (ftot) somewhere 



near the equator. Exactly at the equator the vectors of the current velocity, the pressure 



gradient Ap and the wind stress T fall all in the same direction. 



More recently Yoshida (1955) has shown that the model used by Weenink and Groen 

 apparently leads to a solution involving a discontinuity in the vicinity of the equator. 

 This singularity originates in the assumptions of the model. A modification of the 

 model which seems more realistic in the light of recent observations appears to give 

 a reasonable solution. 



