WIND CURRENTS AND WIND WAVES 127 



According to Ekman's theory the angle should remain constant at 

 45 degrees, and the wind factor, according to the empirical results that he 

 used, should be equal to 0.025 in latitude 15° and 0.0136 in latitude 60°. 

 Rossby and Montgomery point out that the wind factor depends upon 

 the depth at which the wind current is measured. Their theoretical 

 values apply to the current at the very surface, but wind currents derived 

 from ships' logs will apply to a depth of 2 or 3 m, depending upon the 

 draft of the vessel. At this depth, their theory gives a wind factor in 

 better agreement with Ekman's value, and they show that their theoretical 

 conclusions are in fair agreement with empirical results. However, the 

 introduction of an eddy viscosity that decreases to zero at the lower limit 

 of the wind-stirred layer is justifiable only if no other currents are present. 

 In the presence of other currents, such as tidal currents or currents related 

 to distribution of mass, the eddy viscosity characteristic of the total 

 motion must be introduced, and the variation of this eddy viscosity 

 probably depends more upon the stability of the stratification than upon 

 the geometric distance from the free surface. A theory of the wind 

 currents must take this fact into account, and cannot be developed until 

 more is known of the actual character of the turbulence. At present, 

 Ekman's classical theory appears to give a satisfactory approximation, 

 especially because no observations are as yet available by means of which 

 the results of a refined theory can be tested. 



So far, it has been assumed that the depth of the water is great com- 

 pared to the depth of frictional resistance. Ekman has also examined the 

 wind currents in shallow water and has determined the constants in 

 (VII, 18) by assuming that at the bottom the velocity is zero. This 

 analysis leads to the result that in shallow water the deflection of the 

 surface current is less than 45 degrees and the turning with depth is 

 slower. In very shallow water the current flows nearly in the direction 

 of the stress at all depths. 



The assumption of an eddy viscosity that is independent of depth is 

 not valid, however, if the water is shallow, because the eddy viscosity 

 must be very small near the bottom, regardless of the character of the 

 current. The effect of a decrease of the eddy viscosity toward the 

 bottom is generally that the angle between wind and current becomes 

 greater at all depths and that the current velocities become greater. This 

 is illustrated by Sverdrup's measurements of wind currents on the North 

 Shelf in latitude 76°35'N, longitude 138°24'E, where the depth to the 

 bottom was 22 m. From these observations, Fjeldstad found that the 

 eddy viscosity could be represented by the formula 



where the distance z from the bottom is in meters. Fig. 31 shows the 



