General Theory of Ocean Currents in a Homogeneous Sea 



405 



and was then able to obtain a solution for the corresponding equations of motion 

 Fig. 171 presents the vertical distribution of the frictional coefficient as well as of the 

 theoretical current structure, both for a constant frictional coefficient and for a coeffi- 

 cient varying with depth, according to a summary made by Thorade (1931). The 

 observed current values are indicated by crosses. There remains no doubt that agree- 

 ment with the observed data is obtainable only by using coefficients variable with 

 depth. 



20 



(o) 





•0 100 200 300 400 



Bottom 



Fig. 171. (a) Vertical distribution of the turbulent coefficient at a station of the North 



Siberian shelf, (b) Current diagrams: --0--0--, theoretical distribution for a constant 



frictional coefficient ; — o — o — , theoretical distribution for a frictional coefficient as in (a); 



+ + + + + + +, the observed values according to Sverdrup. 



The application of the modern theory for a turbulent flow to drift currents will be 

 discussed later together with its application to gradient currents (see p. 311). 



Effect of stratification. Assuming a horizontal and stratified sea with a normal 

 density increase with depth, then only minor deviations occur as compared with the 

 case for a homogeneous sea (Defant, 1927). However, essentially different conditions 

 appear for sudden vertical density changes (boundary surfaces between different water 

 masses). Here the stratification affects especially the frictional coefficient, which inside 

 the flow of each more or less homogeneous water mass may remain approximately 

 constant and relatively large but may fall almost to zero inside the density transition 

 layer (thermocline). The effect of the wind is thus confined essentially to the top layer 

 and the drift current in this is transmitted only very slowly to the lower water mass 

 across the transition layer. As a boundary condition at the side beneath the top layer 

 it must be assumed, since the water here meets almost no resistance, that there is 

 perfect "gliding" and the drift current in the top layer will thus be different from that 

 over a solid surface. If ^is the thickness of the top layer (z=d) this boundary condition 

 is given by 



7 - = for (z^d). 



cz ^ ^ 



Solutions of this sort have been discussed in greater detail by Nomitsu (1933). The 

 shallower the layer of water in motion the stronger is the current produced by the 

 wind and the larger the angle of deflection; a result which is exactly opposite to that 



