- 3 - 



After initial transient effects have disappeared, such a 

 current will be in geostrophic balance so that 



where u and v are the ocean velocity components in the x- and y- 

 directions respectively, p' represents the ocean density at a given 

 point (x,y) in the surface layer and p represents pressure. 

 The hydrostatic equation is 



p (z) = po + gP'z , (3) 



where Po is atmospheric pressure at the ocean surface (assumed con- 

 stant here), g is gravity and z is the depth (measured positive 

 downward). We use this equation to obtaini 



V ^ £z-i£i (5) 



^ p'f d X . ^^^ 



This whole process has not affected any pressure below the surface 



layer. Hence there is no ciirrent below the density discontinuity. 



Thus Margules formulae for the slope of density discontinuities on 



a rotating earth with (4) and (5) give the relationship: 



u (H) = _.^^1H = _»1A^' (6) 



P'f oy fay 



and V (H) = -gS-4H = 4 o^ (7) 



p ' f d X f d X , 



where "^ = g 2~P — . These expressions assert that the current in 



P 

 the mixed water at the interface is balanced geostrophically by the 



