Ocean Currents in a Non-homogeneous Ocean 



499 



gradient, the upper limit of the H^S-\a.yQV and the reference level are all more or less 

 coincident (except near the coastal areas in the eastern part). All these surfaces join 

 here, forming a single closed system, an almost motionless boundary layer. 



If in an adjacent sea a density discontinuity layer is found everywhere, the deter- 

 mination of the position of a dynamic reference level is considerably simplified, since 

 the lower limit of the top layer is then usually also the lower limit of the upper flow 

 and the discontinuity layer coincides with a layer of no motion. These methods have 

 already been used by Witting (1918) in his investigations on the continental rise 

 around the Baltic. This simple method can, of course, only be used when the thickness 

 of the top layer is not too great ; it is also possible to apply this method with success to 

 shelf areas, having a sharp subdivision in the vertical into two layers. 



A new method for the determination of the depth of no meridional motion has been 

 presented by Stommel (1956). It is of interest in so far as it permits a determination of 

 this depth directly from the observed vertical distribution of the oceanographic 

 factors, and because it also shows that there is in actual fact no depth of no motion in 

 the ocean but rather the depth of no meridional motion always coincides with the 

 layer of maximum vertical velocity. From the general equations for a wind driven 

 motion and the continuity equation cross differentiation leads to the following three 

 relations : 



(XV.20) 



8y 



The quantity pv in the third equation can be ehminated by means of the first equation, 

 giving 



8\p^^^ ^g 8p 8^ 



where 



8z^ 



f(=) 



/2 8x 8z^ 



PCV.21) 



8 

 8x 



(7-) - If) 



This function F(z) is more or less indeterminate, but accord'ng to Ekman differs from 

 zero only in a thin upper layer extending from r = to the depth of frictional influence. 

 F(0) is known in terms of the distribution of the wind stress on the sea surface. If 

 the sea bottom is at —d, then the first integral of equation (XV.2] ) can now be obtained : 



Sz^P^'^^-f 



^(-) + C 



8F 



8z 



(XV.22) 



whereby (f'(r) is defined 





