512 Ocean Currents in a Non-homogeneous Ocean 



The first expression on the right-hand side is zero, since fj = for z^ and thus using 

 (XV.25) one obtains 



Pi dz ^ b [Pi dz^ ^ 



Po (l-"^ 2 \o.dx 



Pq is the density at the sea surface. The total volume transport through the entire 

 top layer from C to station A is thus finally obtained by integration from x,. to xa 



St 



XA h 



Sdx = ^ 



Pi dz^ , 



~r-dp. 



The integral of (dz'^jdx) dx is equal to Z^ where Z is the depth of the isopycnal at the 

 station A. Finally, on repeating the partial integration, since Z is zero at the sea surface, 

 we have 



St-2f 



'-^^ Pi — P 



dZ\ (XV.26) 



If the transport between two arbitrary verticals A and B is required, then the expres- 

 sions (XV.26) are evaluated at both places and the difference is taken. The water 

 transports obtained in this way are subject to the same limitations for the quantity^. 

 It is noticeable that a knowledge of the mass structure at the two stations is sufficient 

 for the determination of the transport through the vertical section between them, 

 without having a knowledge of the distance between the two stations. Werenskiold 

 offered an explanation for this fact by pointing out that the flux in horizontal direction 

 through the section is unaffected by stretching or shrinking of part of this section, 

 because the pressure gradient and therefore also the current intensity are changed 

 inversely proportional to the current width, and the distance between the two stations 

 is eliminated. It seems, therefore, that only the mass distribution of a single station is 

 required in order to calculate the transport through a vertical section by means of 

 equations (XV.26). However, this is not true at all since a knowledge of the stratifi- 

 cation at two stations C and A is required and, furthermore, the water at C is homo- 

 geneous and has the same density as the deep water at A. 



Since the integration of equation (XV.26) is performed using ordinary metres, the 

 correction required previously for Q is not needed here. 



