Studies on the Motion of Viscous Flows— VI 



VI — Convective Instability of a Horizontal Layer 



of Fluid with Maintained Concentration of 



Diffusive Substance and Temperature 



at the Boundaries ■. ■■ , :> 



Paul Lieber 



University of California 



Berkeley, California 



and 



Lionel Rintel 



William and Mary College 



Williamsburg, Virginia 



ABSTRACT* 



The critical conditions for the convective instability of a horizontal 

 layer of fluid which has constant gradients of temperature and con- 

 centration of a diffusive substance are derived. The parameter de- 

 termining the stability is a sum of two dimensionless parameters of the 

 form of Rayleigh numbers, one based on the quantities determining the 

 nnolecular heat transfer across the layer, and the second based on those 

 quantities determining the molecular transfer of the diffusive sub- 

 stance. For liquids, a strong stabilizing or destabilizing action of the 

 nnolecular diffusion results, which depends on the sign of the gradient 

 of the salt concentration. When the gradient of salt concentration sta- 

 bilizes, overstable oscillations are found to provide the mechanism of 

 the stabilization. 



INTRODUCTION 



Convective vortices in fluids are associated with unstable equilibria of 

 forces which act on and/or are produced by the motion of the fluid. It has been 

 found that a class of convection-causing agents, characterized by transfer 



*This paper is based on a technical report issued under the same title by the 

 Institute of Engineering Research, University of California, Berkeley, as Report 

 Nonr ZZ2(87), MD-63-6, in November 1963. 



693 



