430 



General Theory of Ocean Currents in a Homogeneous Sea 



Coast 



Fig. 183. Upper picture: vertical cross-section parallel to the coast through an ocean with 

 increasing depth. Lower picture: horizontal section through the field of the deep current 

 (full line and arrows are valid for a constant frictional depth ; dotted curve and arrows are 

 valid for a variable frictional depth. The arrow at r indicates the assumed direction of the 



wind stress. 



From this it follows easily that 



g Itt g8 2tt 



U^ = Jo and Uy = j- ^ cos j x 



and the stream lines are given by the equation 



81 . In 



y = -^sm -j- X -}- const. 



At a sufficient distance from the coast the current field shows sine waves (Fig. 184) the 

 amplitude of which depends on the absolute size of the bottom waves. The depth of 

 the sea plays no role here; thus the velocity in the direction of the coast is constant, 

 but the total velocity is smaller than in a sea with a constant depth. At the same time 

 the stream lines deviate more and more from a straight course and take on a curvature 

 cum sole as the current passes over decreasing depth and the reverse (contra solem, 

 increasing depth). 



The effect of varying latitude is shown principally by the fact that the deep current is 

 no longer exactly divergence-free. However, this divergence only becomes important 

 in lower latitudes, and in middle and higher latitudes it is always very small. Since in 

 lower latitudes the direction of surface currents is predominantly zonal, this should 

 also apply to deep currents and also here the effect of div U then remains small. 



If all three of the factors influencing the deep current (wind field, bottom topo- 

 graphy and the Earth curvature) are considered at the same time the treatment becomes 



