Let us further assume that the decrease in specific volume of the upper layer is due solely to 

 a change in the temperature =A^. In such a case, the total salinity of the mixed layers can be 

 found from the mixing formula: 



S],2 = , 



Zl + Z-i 



The overall temperature after mixing is found from 



(/l + A/i)Zi+/2Z2 _ /l2l 4-/ 2^2 ^ 



Zi + Z2 ^1 'r ^2 Zi -f- Z^ 



Ml = /i ,2 + 



Zl,2 



A/,, 



(10) 



(11) 



where Si 2 and t^ 2 indicate the mean salinity and the mean temperature, respectively, of the lay- 

 ers up to the start of convective mixing. 



Analogously, provided that the specific volume of the first layer decreases exclusively due to 

 an increase in its salinity by A^-^, we get the total salinity and temperature, after mixing, by the 

 formulas 



SiZ,+ S,z, 

 Zi + 22 



+ 



Zl + Z2 

 '1 Zi "r *2 '2 

 Z1+Z2 



ASi = Si,2 + 



ASi, 



= tl,2. 



(12) 



(13) 



In these formulas, At-^ and AS2 are the changes in temperature or salinity of the first layer 

 necessary for its specific volume to remain equal to the specific volume of the second layer. 



It appears difficult, however, to compute the magnitudes Ati and ASi and therefore, they are 

 usually derived with the help of the TS diagrams. The problem reduces to the following: to find a 

 temperature (or salinity), corresponding to the specific volume of the second layer, from the known 

 temperature (or salinity) of the first layer. Figure 15 shows part of the TS diagram. Let points 

 correspond to elements of the first layer and BC be a portion of the isoline of the specific volume of 

 the second layer. Naturally, for the specific volume of the first layer to become equal to that of 

 the second layer, we must either change the temperature by the magnitude AB = At, or change the 

 salinity by the magnitude AC =AS -i . 



Figure 15. Determination of the TS dia- 

 gram of the change in temper- 

 ature or salinity necessary for 

 a change in the specific volume 

 to a given value . 



72 



