384 



General Theory of Ocean Currents in a Homogeneous Sea 



where C is the elevation of the sea surface above the undisturbed level (counted 

 positive upwards). Equations (XIII. 1 and 2) then give 



and the condition for non-accelerated (stationary) current is then 



(XIII.3) 





(XIII.4) 



or if the total velocity V = ^y{u^ + y^) and d^fdn is the total pressure gradient {n 

 normal to the lines of equal water level) 



fdn 



(XIII.5) 



For a steady current pressure force and Coriolis force will be in equilibrium. Fig. 165 

 shows diagrams of the forces acting on such currents for both the Northern and the 

 Southern Hemisphere. The currents follow the lines of equal water level which are at 

 the same time isobars on the level surfaces ("Niveau-Flachen") and it follows the 

 proposition: In the Northern Hemisphere when facing downstream for a steady friction- 

 less water movement the higher water level will lie on the right-hand side of the current 

 direction and the lower water level will be on the left-hand side; the slope of the sea surface 

 is a measure of the current intensity. Such a current is termed a geostrophic current. 



Lower water level 





Higher water level 



Lower water level 



Current 



^- 



X 



Higher water level 



Fig. 165. Schematic distribution of the forces for a stationary current in a homogeneous 

 ocean without friction (left side: Northern Hemisphere; right side: Southern Hemisphere). 



Equation (XIII.3) permits integration if the topography of the sea-level is constant 

 in time or unchanged by the current. Multiplying the first equation by u and the second 

 by V, and adding, gives the relation 



¥V^= -gdl 

 If a small water particle moves along a level surface from a point where the sea level 



