With these assumptions equations (6) can be written 



: D = 





T x + r 



T y" r 



&- + & 



oy ox 



ox oy 



y » = °. 



(8) 



r and r are the components of the wind stress at the sea sur- 

 x y * 



face in the direction of the x-axis and y-axis, respectively. 

 Cross differentiation of (8), and subtraction leads to 



According to equations (8) 



d£ dD _ Op dD _ 

 ox oy " oy ox 



1^ 



ay 



^ T 3 



~oT 



(9) 



I 45 d!fe_ . £ dD d£_ + Iz & . Ji <& _ £ /dD djL + dD d±_\ (10) 

 D dx Oy D 3y ox D a y D dx Dldy Oy Ox Ox / K±UJ 



By substituting this into equation (9), it follows 



T (£$- + d£\ + (dl .142 . n^\di. + f£^D _ r ap\di. 

 r V ax 2 + dy 2 i + ^dy D dy Ddx^dx + U dx D 37' 3y 



or a t, 



D 



.Is ao 



D dx 



(11) 



~dy~ ~d~x~~ ~d" oy 



With this differential equation and adequate boundary conditions 

 the horizontal mass transport is uniquely determined in the ocean 

 under consideration. The boundary conditions for the North Atlantic 

 Ocean will be specified later. 



In the special case where the depth D is assumed to be constant, 

 it follows from (11) 



r V 2 </> + $£ ^c = " curl z T ' for D = const - 

 This equation is identical with Munk's differential equation for 

 the horizontal mass transport (1950j equ. 6), if the sign of ^ is 

 changed (Munk defined V = d^/dx, U = - d^/dy) and the term rV 2 f 



11 



