WIND CURRENTS AND WIND WAVES 



125 



Therefore, the wind current is directed 45 degrees cum sole from the 

 direction of the wind. The angle of deflection increases regularly with 

 depth, so that at the depth z = D the current is directed opposite to the 

 surface current. The velocity decreases regularly with increasing depth, 

 and at 2 = D is equal to e~^ times the surface velocity, or one twenty- 

 third of the value at the surface. By far the more important velocities 

 occur above the depth z = D, and Ekman has therefore called this depth 

 "the depth of frictional resistance." It should be observed, however, 

 that according to this solution 

 the velocity of the wind cur- 

 rent never becomes zero, but 

 approaches zero asymptoti- 

 cally, being practically zero 

 below z = D. 



A schematic representation 

 of the pure wind current is 

 given in fig. 30. The broad 

 arrows represent the velocities 

 at depths of equal intervals. 

 Together they form a spiral 

 staircase, the steps of which 

 rapidly decrease in width as 

 they proceed downward. Pro- 

 jected on a horizontal plane, 

 the end points of the vectors 

 lie on a logarithmic spiral. 



The average deflection of 

 the wind current from the di- 

 rection of the wind has been 

 examined (Kriimmel) and 

 found to be about 45° cum sole from the wind direction, independent of 

 latitude, in agreement with Ekman's theory. 



The ratio between the velocity of the wind and that of the surface 

 current, which Thorade has called the wind factor, depends upon the 

 stress of the wind and upon the value of the eddy viscosity — that is, 

 upon D. The stress of the wind is proportional to the square of the 

 wind velocity, Wi] that is, Ta = 3.2 X 10-^2 (p, 120), where W is 

 measured in centimeters per second. Introducing this value into 

 (VII, 19), one obtains, with X = 212 sin v?, 



vo ^ TT 3.2 X 10-^TF 

 W Dp^ sin (p y/2 



On the basis of observations by Mohn and Nansen, Ekman derived the 

 empirical relation 



Fig. 30. Schematic representation of a 

 wind current in deep water, showing the 

 decrease in velocity and change of direction at 

 regular intervals of depth (the Ekman spiral). 

 W indicates direction of wind. 



