428 



General Theory of Ocean Currents in a Homegeneous Sea 



a = TT — ^, this angle will be ^tt — /3 {cum sole). The velocity of the deep current is 

 then 



U 



T . ^ 27tT 

 sin p ^ -7^ cos p. 



bf 



pfD 



The gradient current now extends almost throughout the entire water mass, so that 

 even a low velocity of this current is sufficient to compensate the drift current trans- 

 port. The greater the depth of the water, therefore, the lower will be the velocity of 

 the gradient current, and the less will be the effect of the coasts on the surface current 

 given by the resultant drift and gradient current. As shown by the above equation, 

 containing cos ^ and the frictional depth D in the denominator, the deep current V 

 is very weak. Ekman has calculated numerically three special cases {d — 0-5 D, 

 d = \-25 and 2-5 D). Figure 182 shows the vertical current structure in the usual way 



d=<y^D 



d--V2W . 



cf^2-50 



Fig. 1 82. Vertical structure of the "elementar" current in a water basin with everywhere closed 



(according to Ekman) (the arrow indicates the direction of the water "stau" (direction 



in which the water is piled up by the wind)). 



The uniform deep current can be realized at greater depths, however, it is very weak 

 and at still greater depths vanishes almost entirely. The water is piled up nearly in the 

 wind direction in all cases and is therefore only slightly affected by the Earth's rotation. 

 This may be the reason for the late recognition of the effect of the Earth's rotation on 

 ocean currents. 



( s) Effect of Bottom Topography 



The results so far presented of the theory of steady currents in a homogeneous 

 ocean, of which the most important one is the derivation of the "elementar" current, 

 permit a considerable insight into ocean currents produced by the wind in a homo- 

 geneous sea; however, they can only be applied to smaller oceanic areas over which the 

 effects of latitude variation, as well as that of local variations in depth and wind can 

 still be disregarded. The further development of the theory by Ekman (1923, 1928 a, 

 1932 and Thorade, 1933/)) was devoted primarily to the uniform deep current, 

 and an investigation was made to determine the kind of change which occurs in the 

 deep current when the water masses transported enter 



(1) into areas with non-uniform winds, 



(2) into areas with varying depth, and 



(3) into widely differing latitude regions. 



Thereby conditions become rather complicated, especially with the additional 

 assumption that the upper and lower frictional depth vary, not only from place to 



