1 26 WIND CURRENTS AND WIND WAVES 



vo 0.0127 



from which follows 



w /-■ — (V"' 20) 



D = 7.6 Z— ; (VII, 21) 



Vsin (p 



and this value is in fair agreement with observed values of the upper 

 homogeneous layer in the sea that is interpreted as the layer which is 

 stirred up by the wind. At wind velocities below 3 Beaufort (about 

 6m/sec) the above formula, according to Thorade, should be replaced by 



D = MT^l (VII, 22) 



vsin (f 



The last two formulas give the depth of frictional resistance in meters for 

 wind velocities in meters per second. The latter formula gives smaller 

 values of D than Ekman's formula when the wind velocity is below 4.3 

 m/sec, perhaps because the stress of the wind is relatively smaller at low 

 wind velocities (p. 120). 



From equations (VII, 17), (VII, 21), and (VII, 22), one obtains (see 

 table 1, p. 23) 



Me = 1.02 W {W ^Q m/sec), 

 Me = 4.3 W (TF > 6 m/sec). 



From these relations the following corresponding values are computed: 



Wind velocity (m/sec) 2 4 6 8 10 15 20 



fjLe (g cm/sec) 8 65 (218) 375 430 970 1720 



Rossby and Montgomery have developed a new theory of the wind 

 currents by introducing an eddy viscosity depending upon a mixing 

 length that is small near the surface, increases to a maximum at a short 

 distance below the surface, and then decreases linearly to zero at the 

 lower boundary of the wind-stirred layer. The variation with depth 

 of the mixing length is assumed to be entirely determined by means of 

 dimensionless numerical constants. The theory leads to a series of 

 complicated expressions for the angle between surface current and stress, 

 the wind factor, and the depth of the wind current. These quantities all 

 depend both on latitude and on wind velocity. Rossby and Montgomery 

 give their final results in the form of tables, according to which the deflec- 

 tion of the wind current in latitude 5° increases from 35 degrees at a wind 

 velocity of 5 m/sec to 43 degrees at a wind of 20 m/sec, and in latitude 60° 

 from 42 to 52.7 degrees. In the same latitude the wind factors decrease 

 from 0.0317 at a wind velocity of 5 m/sec to 0.0266 at a velocity of 

 20 m/sec and from 0.0273 to 0.0228, respectively. 



