VERTICAL CIRCULATION IN THE OCEAN 



'47 



does not increase with depth. Consequently we can find a minimum value of the surface 

 velocity when we introduce t^ 



where h is the depth. We obtain: 



3-2 X 10-8 {W - Fmin.)^ h- v^ Fmin. = 0. 



In the first place, it is seen that we always find two values of Fmin. , one which is smaller 

 than W and one which is greater, but only the former is of interest. It is also seen that 

 the velocity of the current at the surface approaches the wind velocity asymptotically 

 when the depth increases towards infinity. 



In order to show the surface velocities which may exist under the above conditions, 

 numerical values have been computed. The values of i',, at different wind velocities are 

 those which have been given by W. Schmidt. We find the following minimum values of 

 the surface velocity (in cm./sec.) at given wind velocities and at given values of the 

 depth of the channel : 



Hence, if the wind velocity is lo m./sec. we should obtain a surface velocity of at least 

 3-32 m./sec. if the depth were looo m. and of 5-99 m./sec. if the depth were 5000 m. 

 These results are quite unreasonable, and the obvious conclusion is that stationary 

 currents, which are due to the effect of the wind on the distribution of density, do not 

 exist in the oceans. 



Ekman has already drawn this conclusion, and the above computation has only been 

 made in order to emphasize a well-known feature. Ekman has, furthermore, pointed 

 out that stationary currents can exist only if they are directed along the parallels of 

 latitude and when the depth is constant. The latter conditions are never fulfilled in the 

 sea and, therefore, no stationary currents can exist. 



The circumstance which must be emphasized here, however, is that a pure drift 

 current must be present unless : 





dv' y 



dz 



where v' represents the velocity of the convection current. The slope current is in- 

 dependent of depth and need not be considered in this connection. This condition 

 leads to a decrease of the velocity near the surface of an order of magnitude which is 



