[TS]-relationship and Connection with Mixing Processes and Large Water Masses 207 



This formula allows the value at any point along the line of spreading of a water type 

 to be calculated from the [^l-curve if the vertical distribution of salinity (or of 

 temperature) is known. In the special case of a tongue-like spreading s is given with 

 sufficient accuracy by the simple form (see p. 106, et seq.) 



•s = -^0 + Rx) cos ^^ z. 



Then 



and for the core layer (z = 0) 



8'^s _ 772 



dh 7r2 



Because 



/(I) = 5o — 5i and /(2) = ^o — Sz, 



and therefore 



S2-s^=f{l)-f(2) 



we obtain 



±,_^ /(I) -/(2) ^J> 



pu TT^D fix) Ax ' 



The application of this equation to the core layer of the subantarctic intermediate 

 water along the western section in the Atlantic gives values for between 0-6 and M 

 which is in rather good agreement with those determined by other methods. However, 

 this method, using the [75]- relationship, also gives only the ratio between vertical 

 exchange and velocity. 



An interesting method that also uses the [r^l-relationship and allows a deeper in- 

 sight into the process of mixing has been given by Jacobsen (1927). Consider a vertical 

 column of water with cross-section of 1 cm^. From this column we consider two 

 cubes (volume 1 cm^) ai A [z = 0) and also at a point J5 at a distance z beneath A. 

 In the course of a mixing process, which should follow the laws valid for diffusion and 

 occurs within the total column which we assume at rest, there will be an exchange of 

 q cm^ of water in the time of / sec between the two cubes. If the displacement of the 

 water quanta during the mixing process follows a Maxwellian distribution then 



q = ke-°-'^\ 



Since there is no increase in mass in the entire water column the integral of qdz from 

 — 00 to +00 must be equal to 1 , This gives a^ = nk^. The amount of salt in cube B 

 is ps X 10~^, where the salinity s is given in per thousand and the increase in salt 

 amount in a small time dt according to the exchange equation is 



Corresponding relationships with Sq and Asq applies to cube A. The sahnity (sq + 

 Asq) in the cube after a time t is the sum of the salt amount originally present and the 



