26 FOFONOFF [chap. 1 



where Fq is the flux of heat and hg the heat of transfer resulting from the flux 

 of salt. By subtracting the heat of transfer from (63), we obtain the heat flux 

 equation 



Fq = {Lhh — hsLsh)Xh+{Lhs — hsLss)Xs. (67) 



We can express the heat and salt fluxes in more familiar form by substituting 



^ T2 dz 



^ ~ ~d'z [tJ ~ fd^~T7hdz 

 into (64) and (67). Collecting terms, we obtain 



(68) 



(69) 

 az az 



Avhere 



From (65), we may conclude that the coefficients of heat conduction, k, and salt 

 diffusion, D, are positive. 



If a pressure gradient exists within the system, the conditions of final 

 equilibrium, and, hence, the transport processes, are altered slightly. The 

 analysis can be carried out in the same way with the result that the effect of a 

 pressure gradient can be taken into account by replacing dsjdz in (68) and 

 (69) by 



Avhere 



^'~\8pj,- 8f.l8s ^''^ 



The salinity gradient does not vanish in the equilibrium state in the presence 

 of a pressure gradient. The equilibrium salinity gradient for zero salt flux 

 under the hydrostatic pressure gradient is about 3%o to 4%o per 1000 decibars. 

 Vertical gradients of salinity in the deep water of the ocean are usually less 

 than the equilibrium gradient. Consequently, the effect of the pressure gradient 

 in the ocean is to produce diffusion of salt in the direction of increasing salinity. 



None of the coefficients, k, D, Dgs or Ds^, has been measured for sea- water. 

 Estimates of thermal conductivity, k, have been made by Kriimmel (1907) by 



