PHYSICAL PROPERTIES OF SEA WATER 19 



The distinction between vertical and horizontal turbulence is particu- 

 larly significant where the density of the water increases with depth, 

 because such an increase influences the two types of turbulence in a 

 different manner. Where the density of the sea water increases with 

 depth (disregarding the effect of pressure), vertical random motion is 

 impeded by Archimedean forces, because a mass that is brought to a 

 higher level will be surrounded by water of less density and will tend to 

 sink back to the level from which it came, and, conversely, a water mass 

 moving downward will be surrounded by denser water and will tend to 

 rise. In this case the stratification of the water is called stable, because 

 it cannot be altered unless work against gravity is performed. Stable 

 stratification reduces the vertical turbulence, and, where the stability is 

 very great, the vertical turbulence may become nearly suppressed and the 

 eddy viscosity very small. The effect of stability on the horizontal 

 turbulence, however, is probably negligible, because the horizontal 

 random motion takes place mainly along surfaces of equal density. It 

 has even been suggested that the horizontal turbulence increases with 

 increasing stability. 



Similar reasoning is applicable to eddy conductivity. In the case of 

 eddy viscosity, it was assumed that the exchange of mass leads to a 

 transfer of momentum from one layer to another, which is expressed 

 by means of Me. Correspondingly, when dealing with eddy conductivity, 

 one can assume that the transfer of heat through a unit surface in unit 

 time, dQ/dt, is proportional to the exchange of mass through the surface, 

 as expressed by He, and to the gradient of the potential temperatures, 

 di^/dn; that is, dQ/dt = rixe dT^/dn, where r is a factor that depends upon 

 the specific heat of the fluid and upon the manner in which the heat 

 contents of the moving masses are given off to the surroundings. A mass 

 which is transferred to a new level may break down at that level into 

 smaller and smaller elements, so that equalization of temperature ulti- 

 mately takes place by molecular heat conduction between the smallest 

 elements and the surroundings. If such is the case, both the difference in 

 momentum and the difference in heat content are given off, and the 

 proportionality factor, r, is equal to the specific heat of the liquid. Since the 

 specific heat of water is nearly unity, the numerical values of eddy con- 

 ductivity and eddy viscosity would be practically equal. However, 

 where stable stratification prevails, the elements, being lighter or heavier 

 than their surroundings, may return to their original level before comple- 

 tion of temperature equalization, whereas equalization of momentum may 

 have been accomplished by collision. In this case, the factor of propor- 

 tionality, r, will be smaller than the specific heat of the liquid; that is, in 

 the sea, r will be smaller than unity and the eddy conductivity will be 

 smaller than the eddy viscosity. Thus, it may be concluded that stable 

 stratification reduces the vertical eddy conductivity even more than it 



