Section 29. Convective Mixing 



As has already been pointed out, stable equilibrium of the stationary horizontal layers may 

 exist under the condition that the lighter layers lie above the heavier ones. Being more exact, it is 

 necessary that the stability of the layers be positive for equilibrium. As soon as this condition is 

 disrupted, eddies occur on the surfaces of separation, mixing these layers. Thus, by its very na- 

 ture, convective mixing is also a turbulent process.* 



Let us assume that the specific volume of topmost layer begins to decrease for some reason. 

 At the same time the stability between the first and second layers from the top will begin to 

 decrease. 



The stability depends on two factors — on the vertical specific volume gradient (without cor- 

 rection for compressibility) and on the adiabatic correction. In our discussion we will disregard 

 the latter, due to its small size in comparison with the specific volume gradients of the upper lay- 

 ers, and we will consider that for mixing to be possible it is necessary that the specific volume of 

 the first layer becomes equal to the specific volume of the second layer from the top. 



A decrease in the specific volume of sea water may be caused either by an increase in the sa- 

 linity or by a change in temperature which would bring the water closer to the temperature of 

 greatest density. 



An increase in the salinity of the surface layers of the sea water, regardless of the mixing of 

 waters of different salinity, may be caused either by ice formation, or by evaporation. 



Let us assume that a layer of Ice of thickness i and salinity S-^ forms from a uniform layer of 

 thickness p, whose salinity at the initial moment was 5, 5 j < S. 



If we melt this layer of ice of thickness i, we will obtain a column of water of height h, 

 whereupon 



~ S,.. ' (1) 



where 6 j = the density of the ice, 



6 = the density of water. 



w 



Naturally, after the ice is formed, the salinity of the remaining water column will increase 



by A^. 



From the mixing law, we get 



S2= ftSi +(2 — /!) (S+AS), (2) 



from which the increase in salinity will be 



AS = ^ y— . (3) 



* Theoretically, in the absence of turbulence, equilibrium may exist even with some negative 

 stability. 



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