444 



General Theory of Ocean Currents in a Homogeneous Sea 



D is the frictional depth and r = {ftjl-n) is the time expressed in units of 12 pendulum 

 hours. The gradual formation of the drift current can be illustrated by plotting the 

 time-variable velocity vector at different depths in the form of the hodograph curves 

 given by Ekman (Fig. 191). For a suddenly starting wind this curve at the surface will 

 have the form of a damped circular oscillation with a period of 12 pendulum hours 

 which is superimposed on the final stationary state of motion. In the deeper layers the 

 oscillation will at first grow somewhat and then regularly decrease again. The velocity 



^=0 



Z = 05D 



z^D 



Z-- 2D 

 1 ^ > 



Fig. 191. Hodograph curves for different depths of the pure drift current which develops 

 due to a wind beginning suddenly (ocean depth unlimited). 



components can also be plotted separately along the time axis thereby obtaining the 

 curves shown in Fig. 192. Each component shows a damped oscillation around a 

 stationary final state and both together show very clearly the characteristics of inertia 

 oscillations. At different depths the oscillations have exactly the same phase but with 

 a decreasing amplitude. If the water depth is less than the frictional depth the close 

 distance from the bottom becomes apparent in the curves, but the oscillation is strongly 

 damped only in the immediate vicinity of the bottom; for hjD = 0-25 the current 

 approaches almost aperiodic the steady state. Solutions can also be found for the case 

 in which the effect of the wind is not applied suddenly but only gradually, and also 

 for the case where the wind maintaining a wind drift current either suddenly or 

 gradually ceases. For more detail see Hidaka (1933), Nomitsu (1933), Fr. Defant 

 (1940). 



The sudden formation of a sea surface slope in a similar way as in the case of a 

 drift current must also give rise for a gradient current to inertia oscillations. Ekman 

 has given the theoretical basis also for this case and has pointed out that for an ocean 

 of greater depth, due to the small frictional effect in the geostrophic current, these 

 inertia oscillations will die away very slowly so that a longer duration of these must 



