General Theory of Ocean Currents in a Homogeneous Sea 



All 



Fig. 181. Vertical structure of the "elementar" current for different orientations of the coast 

 relative to the wind (according to Ekman) (the arrow indicates the wind direction). 



first case only a pure drift current is formed and the effect of the wind is restricted to 

 a relatively thin top layer. At coasts, however, the effect of the current-producing 

 wind extends almost down to the sea bottom due to the generation of deep currents. 

 Their velocity is not insignificant and may be as much as half of that of the surface 

 current. The second case is that of a sea enclosed by land, with a wind of constant 

 direction and constant speed blowing over its entire surface. Here the continuity 

 condition requires that the transport in all directions should be zero, that is, that the 

 total gradient current transport must be the same as that of the drift current and 

 directed oppositely. The boundary condition equations are now 



^/■x + ^x = and My + My = 0. 



Taking the positive j'-axis along the direction of the wind stress, then Ta- = and 

 Ty = T. This gives 



Tlf-i-bU^-BUy^O and BU^ + bUy = 



from which it follows that 



bT . __ BT 



U.= - 



and Uy = 



f(b^ + B') ^' f{b^ + B^) 



If the angle {cum sole) between the gradient current transport and the pressure 

 gradient is denoted by fi and if Uy — 0, then 



My^-B "°^ ^^tan-^. 



This angle is almost 90°, if the depth of the sea is not too small (for djD = 1, 2, 10, 

 ^ is approx. 79°, 85° and 89°, respectively). However 



^ = -^=tana, 



where a is the angle between the direction of the deep current and that of the wind, or 

 a — |7T is the angle between the directions of pressure gradient and wind. Since 



