General Theory of Ocean Currents in a Homogeneous Sea 



433 



20O"''''^30O 



Fig. 185. Topographic influence of a submarine bottom ridge on a current flowing normal 



to the longer axis of the obstacle. Lower picture: vertical profile through the bottom ridge 



(width, 400 km; height, 200 m; water depth, 4 km; p = 30° N.). Upper picture: stream lines 



of the main current (U = 50 cm/sec). 



This gives 





Over the rise the flow thus is subjected to an acceleration acting along the longer axis 

 of the ridge with a maximum value of —/A/// above its highest point. This acceleration 

 gives rise to a curvature of the stream lines cum sole. To the velocity u is added a 

 transverse velocity v which at a point x = ^ — / (^ is the distance of the point under 

 consideration from point A) is given by 



IHl 



H 



F, 



whereby /"denotes the cross-section of the bottom surface for the distance from A to ^. 

 The deflection of the current from the initial x-direction will be vju, and for a small 

 bottom slope is given with sufficient accuracy by vjU. 



The deflection on passing over a bottom ridge is the larger, the smoother the sea, 

 the higher the ridge and the smaller the velocity U. Since in the ocean U is relatively 

 small, it can be expected that the bottom topography will have a stronger eff'ect on 

 the currents. Fig. 185 presents a numerical evaluation of a single case: width of 

 bottom ridge 400 km, its height 200 m, ocean depth 4000 m and = 30° N. while 

 U is taken as 50 cm/sec (somewhat high because of the absence of friction in the 

 current). At the crest of the ridge the deflection will be —37° and in the rear of the 

 rise at its end —55°. The deflection is of course associated with a corresponding change 

 in the sea-level; to the normal slope directed along the crest is now added a slope 

 directed normal to the ridge crest and a corresponding lowering of the sea-level along 

 the .\--direction. If instead of a single ridge the bottom has a series of ridges and troughs 



