General Theory of Ocean Currents in a Homogeneous Sea 



385 



is ^0 above the equilibrium level, to another point where this deviation is ^i, it will 

 acquire a final velocity V^ given by the relation 



V,^ = 2g(Co - Ci) (XIII.6) 



if it was at rest at the starting point {Vq = 0). Corresponding values of Fj and ^o — ^i 

 are given in Table 115. 



Table 115 



If a water element glides downwards without friction along an oblique pressure 

 surface through a short vertical distance, it will immediately acquire a very large 

 velocity. If the water masses were not forced by the Coriolis action to move along the 

 lines of equal water level under stationary conditions, even a very small slope would be 

 able to cause enormously intense ocean currents. Equation (XIII. 5) shows that the 

 forces producing the movement {gradient force) do not, in the stationary case, determine 

 the acceleration of the water movement, but solely, due to the Coriolis force, its velocity. 



(b) The Effect of Changing Depth and the Spherical Shape of the Earth 



Equations (XIII.4 and 5) show that the entire water column down to the sea bottom 

 will have the same velocity; it will move hke a solid body with a velocity V in the 

 appropriate direction. This current can only satisfy the continuity equation if the sea 

 bottom is plane. Under stationary conditions {dijdt = 0) according to equation 

 (XII. 16) the continuity equation takes the form 



dv 



cu 



dx 8y 



= 0. 



(XIII. 7) 



It will be satisfied by the values of u and v given by (XIII.4). At constant depth there 

 will thus be no limitation to a geostrophic current. If there are boundaries to the sea 

 in the form of vertical coasts then the boundary condition will require a constant C 

 along them ; the current will then flow only along the coast and there will be no flow 

 perpendicular to the coast. 



If the ocean depth is variable, conditions will be more comphcated. In Fig. 166 

 is shown the case where a given uniform slope of the sea surface (Northern Hemisphere) 



Fig. 166. Deviation of ocean currents for a variable bottom depth. 



