128 



WIND CURRENTS AND WIND WAVES 



observed velocities and the corresponding velocities computed with 

 Fjeldstad's equations and with Ekman's equations, assuming a constant 

 value of He equal to 200. 



The question of the time needed for establishing the assumed sta- 

 tionary conditions has also 

 been examined by Ekman, who 

 has made use of a solution 

 given by Fredholm for the case 

 in which a wind suddenly be- 

 gins to blow with a velocity 

 that later remains constant. 

 It is found that the motion 

 will asymptotically approach 

 a steady state. At each depth 

 the end points of the velocity 

 vectors, when represented as a 

 function of time, will describe 

 a spiral around the end point 

 of the final velocity vector, 

 the period of oscillation being 

 12 pendulum hours, corre- 

 sponding to the period of oscil- 

 lation by inertia movement 

 (p. 94). The average yelocity 

 over 24 hours will be practi- 

 cally stationary from the very 

 beginning, but the oscillations around the mean motion may continue 

 for several days and may appear as damped motion in the circle of inertia. 



Wind Currents in Water in which the Density Increases with Depth 

 In the equations of motion that govern the wind current, the density 

 enters explicitly, and it might therefore be expected that variations of 

 density in a vertical direction would modify the results, but the variations 

 of the density in the ocean are too small to be of importance in this 

 respect. Indirectly, the variations of density do greatly modify the wind 

 current, however, by influencing the eddy viscosity of the water. 



The rate at which a wind current penetrates toward greater depths will 

 depend upon the change of density with depth. Where already an upper, 

 nearly homogeneous layer of considerable thickness has been developed 

 by cooling from above and resulting vertical convection, the wind current 

 will in a short time reach its normal state. Where a light surface layer 

 has been developed because of heating or, in coastal areas, because of 

 addition of fresh water, the wind current will first stir up the top layer and 

 by mixing processes create a homogeneous top layer. When this is 



20m 



Fig. 31. Wind current in shallow water, 

 assuming a constant eddy viscosity (dashed 

 curve) or an eddy viscosity that decreases 

 toward the bottom (full-drawn curve). 

 Observed currents are indicated by crosses. 



