Thermohaline Features 155 



gradients and motions vanish. The components of mass transport per unit 

 width are defined in the following manner: 



M^= pudz, My= I pvdz, 



J -h J -h 



(2) 



and a function P is introduced: 



° pdz. (3) 



J -h 



The equations (1) in the integrated form are as follows: 



(4) 





8P I 



= 2o 



The interchange of integration and difi"erentiation in the pressure terms does 

 not lead to any additional terms, because the lower limit is chosen at zero 

 horizontal pressure gradients, and the terms introduced by the variation 

 in the surface elevation (upper Hmit), —p{Zq) (dzjdx), and so forth, are 

 demonstrably negligible (Munk, 1950). Cross-differentiation of these two 

 equations, and use of the fact that the horizontal divergence of the in- 

 tegrated mass transport vanishes, 



dx dy 



leads to the ' curl ' or vorticity equation now so famihar in theories of wind- 

 driven ocean circulation: ^ 



^My = cvir\T , (5) 



where t is the stress of the wind at the sea surface, and ^ = dfldy. 



In a sense, the simple mathematical manipulation of cross-differentiation 

 tends to obscure the physical meaning of equation (5). Let us therefore 

 begin again with the integrated equations (4) and break each mass-transport 

 component into two parts: one set to represent the Ekman wind-drift 

 transport components M^g, My^, and the other the geostrophic transport 

 components Jf^^, Myg'. 



(6) 



My^My, + My,. 



The equations with which we must deal are the following: 



-fMye = T^\,^,^; fM^,=Ty\,^,^ (7) 



