final answer to the general problem of the horizontal and verti- 

 cal current stratification can be given, it is hoped that these 

 notes may serve to stimulate further interest in the subject 

 along lines which will result in a resumption of the problem in 

 the way it was initiated by Walfried Ekman. 



I I . H istorical review 



Approximately 50 years have passed since Walfried Ekman 

 placed our conception of the wind driven ocean currents on a com- 

 pletely new basis. In his well known theory he showed how the 

 effect of the wind goes far beyond the generation of pure drift 

 currents, and how the gradient currents in the deeper layers are 

 maintained by the indirect action of the wind. His studies were 

 directed toward the calculation of the total current system for 

 the given wind system over the oceans. He tried to solve the 

 problem for the vertical and the horizontal velocity distribution. 

 The difficulties which rendered Ekman' s general analysis very dif- 

 ficult have not yet been overcome. Ekman, however, succeeded in 

 solving essential partial problems, and most of his results of 

 the first paper on the subject (1905) have survived half a cen- 

 tury; they still belong to our basic knowledge in dynamical oceano- 

 graphy. 



Ekman was the first to introduce eddy viscosity (virtual 

 friction) into the theory of ocean currents. In a paper from 1923 

 he deduced some important laws which, in the case of steady motion, 

 the currents and particularly their curl must obey. The acceler- 

 ation of the water, originally regarded as effectively eliminated 

 from the equations, was later found to be important as far as the 



