Lieber and Rintel 



Since Eq. (10) differs from Rayleigh's equation determining the convective 

 instability of a layer of fluid heated from below only by a virtual temperature 

 gradient as defined by Eq. (12), critical conditions are (Pellew and Southwell, 

 1940): 



Two rigid boundaries Rg = 1708 



Upper boundary free from 



tangential stresses and Rg = 1100 (13) 



boundary rigid 



Two free boundaries Ra = 658 



CONCLUSIONS 



The critical conditions of Eqs. (13) are valid both for gases and liquids; in 

 the latter case the diffusive substance is dissolved salts. For this case, since 

 ttj < and ttj > 0, the following situations are possible: 



(a) /3' > 0, fi" < Both gradients, that of the temperature and that 



of the concentration of the dissolved salts, are 

 destabilizing. 



(b) /3' > 0, /?" > The temperature gradient destabilizes, while that 



of concentration of salts stabilizes. 



(c) /S' < 0, p" < The gradient of salt concentration destabilizes, 



while that of temperature stabilizes. 



(d) /3' < 0, /5" > The basic solution of Eqs. (2) is stable with 



respect to convection. 



Moreover, the stabilization or destabilization of the gradients of concentra- 

 tion of salts and temperature are respectively weighted by the reciprocals of 

 k' and k". Since for common salts the numerical value of k' is two orders of 

 magnitude larger than that of k", in case (b) above a very small gradient of 

 concentration of salts can stabilize a much larger adverse temperature gradi- 

 ent and, vice versa in case (c) a very small decrease in salt concentration with 

 depth can destabilize a fluid layer with density increasing with depth. This 

 particular case has been considered in detail by Stern (1960). For case (b) 

 the result can be interpreted as follows: 



Convection is a mechanism of heat transfer by means of vortices of finite 

 dimensions. The heat into (from below) and out of (from above) the convective 

 vortices is supplied by the molecular diffusion. In the case of gradients of tem- 

 perature and concentration of salts, the convective vortex transfers salts and 

 heat upward, as represented schematically in Fig. 1. 



In state 1 of the figure, salts and heat are diffusing into the vortex at 

 point a and out of it at point b. The resulting buoyancy forces cause the 



698 



