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



^'-distribution by the dotted line. In the [J^J-diagram the mixing of the three water 

 types is represented by the broken hne UTZ, but the point Z remains on this [r^]- 

 curve only as long as the core of the intermediate water is not involved in mixing with 

 the water masses U and T. When this happens the Z-point moves into the acute angle 

 and the [TS]-c\xr\c no longer has a peak point at Z but becomes rounded there. 

 The reversal point and the concentration of the depth marks around it shows the core 

 of the intermediate water already affected by mixing, but even at this advanced stage 

 the mixing of the three water masses can be represented by a curve VZT made up of 

 two straight lines. 



Analysis of actual [r5']-curves of the oceans show essentially these main theoretical 

 characteristics; they are remarkably constant over large oceanic regions, they have 

 characteristic reversal points associated with the cores of the individual water types 

 and large parts of these curves often show a surprising approach to a straight line. 

 In these cases the [r5']-curves allow a precise determination of the depth, temperature 

 and salinity of the water masses, which finally combine and form individual water 

 types in the deep layers and they also allow the percentage of the individual compo- 

 nents to be found at all intermediate stages. 



In the foregoing discussion it has so far been assumed only that mixing proceeds 

 according to the usual mixing rules ; the magnitude of the exchange coefficients is not 

 involved. The percentages of the original component-waters before mixing give no 

 information on this point. For obtaining a connection with the [r^j-curve the basic 

 equation given on p. 106 



d^s 8s 



is required. This implies that in order to secure a stationary state the vertical exchange 

 and the horizontal advection must completely balance. By choosing for the origin 

 of the A"-coordinate (pointing positively in the direction of movement of the water 

 mass under consideration in a longitudinal section) that point where the water mass 1 

 is still pure, then the salinity at a distance x will be s^ and at a distance x -{- dx will 

 be Sx+Ax and one obtains with sufficient accuracy: 



8s Az 8^s 



— Ax = s^-\ ^-^ 



8x pu 8z' 



^x-^-Ax — ^x \ a^^-^ ^x y' p_2 ^•^• 



If Sj. is formed from s^ and S2 in the proportion m^ and mg of water masses 1 and 2 

 and Sj._^^x in the proportion m^ — Am and Wg + ^w, then using the mixing rule the 

 above equation transforms to 



(52 — Si)Am Ag 8^s . 

 nil + f^h P" ^^ 



If now m^ + Wg is replaced by the distance D of points 1 and 2 on the [r5']-curve and 

 Am by the distance AD of the point (s -{- As; >& -\- Ad) from the point (5, d), then 



A 2 S2 — Si AD 1 



pu D Ax (8^sl8z^) 



