414 General Theory of Ocean Currents in a Homogeneous Sea 



This vertical current stratification was termed by Ekman the ''elementar" current. 

 In limited seas the condition of continuity must also be satisfied. For stationary 

 conditions where everything remains invariable with time the inflow and outflow must 

 balance for a given oceanic space. The drift current is determined by the wind, thus 

 the slope of the sea surface and hence the gradient current must be such as to maintain 

 the constancy of the current system in time. The continuity equation and the boundary 

 conditions in this way determine the structure of the "elementar" current. A simple 

 case can be taken to illustrate these conditions (Fig. 177, right-hand side). A wind 

 parallel to a long straight coast will produce a drift current through which a total 

 water transport away from the coast down to the upper frictional depth is initiated. 

 This causes the surface of the sea to lower along the entire coast and will thus produce 

 a gradient current. The uniform deep current extending downwards from the surface 

 to the lower frictional depth D" will run parallel to the coast and thus cannot com- 

 pensate the removal of water away from the coast accomplished by the wind current. 

 This compensation must be provided for by the bottom current which carries water 

 towards the coast in the direction of the pressure gradient. The slope of the sea surface 

 will thus increase continuously, until the removal of water from the coast, due to the 

 drift current, is exactly balanced by the bottom current. The current in the top layer 

 will then be a vector composition of drift and deep current. The angle of deflection 

 at the surface will thus decrease from 45° to 18°. The current vectors are shown in 

 Fig. 177 for depth intervals of 0-2Z), with the same for the bottom current (at D' = D"). 

 The uniform deep current occupying the deepest water layer between surface current 

 and bottom current is shown by the thick arrow; it is non-divergent and because of its 

 thickness is the decisive current component for the water transport in the oceans. 

 Further interesting cases of "elementar" currents in oceanic regions of special shapes 

 will be discussed in the following section. 



It is of some interest to deal in some detail with the diagrams of forces for the three 

 layers of "elementar" currents. Since the vectors of Coriolis force and gradient force 

 are fixed by the current vector at the point under consideration, and by the sea surface 

 slope the primary task is to fix the frictional vector. This can be done in the following 

 way. If the current vector is denoted by t) (components u and v), the vector of the 

 deep current by 33 {U,V) and the difference vector by lu (h'^., n'j,)=(tu— 3.^). 

 (m— U, V— V), then the equations of motion will have the form 



~f^= - Sq^-^ J^x and fu=-g~-i-Ry, 



whereby -i^(/?a;, Ry) is the frictional vector. 

 However, for the uniform deep current 



-fV=-g~ and fU=-g^. 

 ■' dx dy 



Subtraction gives 



— fWy = R^ and fw^^Ry 



so that w'x Rx + »*'i/ Ry = 0. 



This, however, is the necessary condition for the vector of the frictional force 

 ^{Rx, Ry) to be at right angles to the direction of the difference vector tu. Thus the 

 direction of the vectors of all three forces involved are known and therefore a diagram 



