General Theory of Ocean Currents in a Homogeneous Sea 419 



The shearing stress of the wind and piling up of water caused by the wind. There are 

 two ways in which the wind stress can be determined. The first is afforded by equation 

 (XIII.41). This requires a knowledge of the frictional coefficient iq, but its dependence 

 on the wind strength is not well-enough known. Ekman has indicated a second possi- 

 bility using the piling up of the water ("Wasserstau") by the wind and using the current 

 produced by the wind over a confined sea. If the effect of the Earth's rotation is dis- 

 regarded (/= 0), and if dpjdx is replaced by the slope / of the sea surface, then the 

 first of the equations (XIII.28) for a variable -q gives the equation 



d I cti] 



This can be integrated considering the boundary conditions 



= -T and (m),=<j = 

 and taking into account the continuity equation 



('9 



2 = 



d 



u dz = 0. 







The frictional coefficient t] increases strongly with distance from the sea bottom. 

 Using the relationship introduced by Fjelstad (see p. 405) 



'» (' - ?T-J 



where « is a positive number smaller than 1 and e is a very small and positive number 

 as compared with d, then the integration, neglecting small terms, gives an approxi- 

 mately valid relation (Palmen, 1932, 1933) 



3 — « T 

 1=--^—.. (XIII.43) 



2 gpd 



For a constant frictional coefficient (« = 0) it transforms to 



i=-l ~. (XIII.44) 



2 gpd 



This equation applies for stationary conditions and a constant density. In the ocean 

 the water is stratified and the wind itself gives rise to changes in the oceanic structure. 

 Thereby solenoid fields are generated and the use of the formulae under these real 

 conditions must necessarily lead to difficulties. To avoid these, Ekman and Palmen 

 (1936) therefore reformulated the equation (XIII.44) 



i = - -, , (XIII.45) 



gpa 



where e is always smaller than 3/2. Assuming that there is no bottom friction (gliding), 

 then e = 1 ; when the depth is large (greater than D) this is only approximately true. 

 If there is adhering ("Haften") of the water at the bottom, then e = 3/2. It is not 

 possible to determine € in each case ; if e = 1 , then T is somewhat too large at shallow 



