426 



General Theory of Ocean Currents in a Homogeneous Sea 



Table 127. Energy Dissipation in Ocean Currents 



(according to Schmidt) 

 (Values in erg cm"- sec~^) 



(/) The Effects of Coasts on the ''Elementar''' Current 



The vertical structure of the "elementar" current depends essentially on the direction 

 of the wind relative to the general outline of the coast, since this has a large effect on 

 the equation expressing the condition that for stationary conditions the transport 

 component at right angles to the coast must be zero. Ekman (1923) has presented a 

 solution in two simple and very instructive cases. The first case assumes an extended 

 oceanic region off a long straight coast over which blows a wind of constant force 

 and direction. The water depth d is assumed to be constant and greater than 2D. The 

 sea-level will fall uniformly from the coast towards the open sea and the pressure 

 gradient produced by the piling up of water by the wind ("Windstau") will be at right 

 angles to the coast. With an arbitrary orientation of the co-ordinate system the trans- 

 port components M'^ and Afy will be given by equation (XIII.27). The transport 

 components of the gradient current are given by 



M'^ = bU^ - BUy and W; = BU^ + bUy, (XIII.54) 



whereby U^ and Uy are the components of the uniform deep current and 



(- - S) 



5 = V- and b = \ pd 



If the X-axis is oriented along the coast, then f/,, = and from continuity equation 

 M'y X M"y = is obtained 



T 



Bf pcoD sin 



r.. 



For a given T and a given angle between wind and coast the drift current and the 

 gradient current is fully determined. Ekman has given a simple graphical method for 

 the construction of the total current structure in this case. Figure 1 8 1 shows this current 

 structure in some special cases. The current arrows have to be visualized as drawn 

 from the point o to the points on the curve and the small points refer to heights of 

 0-1, 0-2 D etc., above the sea bottom and to depths of 0, 0-1 D, 0-2 D etc., below the 

 sea surface. The wind direction is indicated by the arrow. The cases correspond to 

 angles of /S = 0, +45° and -45°.* 



There is a considerable difference between conditions when the water flow is un- 

 hindered in all directions or when it is adhered due to any kind of influence. In the 



* ^ = indicates a wind direction parallel to the coast ; the increase in j3 is positive to the right and 

 negative to the left. 



