20 PHYSICAL PROPERTIES OF SEA WATER 



reduces the vertical eddy viscosity. This conclusion has been confirmed 

 by observation. 



The discussion has so far been limited to a consideration of the vertical 

 eddy conductivity, but horizontal eddy conductivity due to horizontal 

 turbulence has also to be introduced. The numerical value of horizontal 

 eddy conductivity must be nearly equal to that of the horizontal eddy 

 viscosity, because the horizontal turbulence is not affected by stable 

 stratification. 



The transfer of salinity or other concentration is similar to the heat 

 transfer. The eddy diffusivity is also proportional to the exchange of 

 mass as expressed by He, the factor of proportionality being a pure num- 

 ber. In sea water of uniform density, r — 1, but, in the case of stable 

 stratification, when complete equalization of concentration does not take 

 place, r < 1 ; that is, the vertical eddy diffusivity is smaller than fie and 

 equals the eddy conductivity. This conclusion has also been confirmed 

 by observation. 



Influence of Stability on Turbulence. The relation between 

 eddy viscosity and eddy diffusion has been examined by Taylor, whose 

 reasoning is based on the fact that in the presence of turbulence the 

 kinetic energy of the system can be considered as composed of two parts : 

 the kinetic energy of the mean motion and the kinetic energy of the super- 

 imposed turbulent motion. In homogeneous water the latter is dissipated 

 by viscosity only, and, if the turbulence remains constant, turbulent 

 energy must enter a unit volume at the same rate at which it is dissipated. 

 Where stable stratification is found, part of the turbulent energy is also 

 used for increasing the gravitational potential energy of the system. In 

 this case the rate at which turbulent energy enters a unit volume, T, must 

 equal the sum of the rate at which the potential energy increases, P, and 

 the rate at which energy is dissipated by viscosity, D. It follows that 

 if the turbulence remains unaltered one must have T > P. 



Taylor shows that the rate at which turbulent energy enters a unit 

 volume equals iie{dv/dzY, where /Xe is the eddy viscosity, and that the rate 

 at which the potential energy increases equals gE fis, where E is the 

 stability (p. 100) and where Ms = rue is the eddy diffusivity. It follows 

 that 



{ti 



>^ = r (II, 9) 



gE tXe 



is a condition which must be fulfilled if the turbulence shall not be 

 destroyed by viscosity and die off. 



Taylor tested the correctness of this conclusion by measurements 

 made by Jacobsen in Danish waters, where Jacobsen found values of 

 At« between 1.9 and 3.8 g/cm/sec. Thus, the eddy viscosity was about 



