Convective Instabilities for Reacting Viscous Fluids Far from Equilibrium
The phenomenon of double-diffusive convection in a fluid layer, where two scalar fields (such as heat and salinity concentration) affect the density distribution in a fluid, has become increasingly important in recent years. The behaviour in the double-diffusive case is much more diverse than for the Bénard problem. In particular, linear stability theory, cf. Baines & Gill (1969), predicts that the first occurrence of instability may be via oscillatory rather than stationary convection if the component with the smaller diffusivity is stably stratified. Finite amplitude convection in the double-diffusive context was investigated by Veronis (1965, 1968a) whose results suggested steady finite amplitude motion could occur at critical values of a Rayleigh number much less than that predicted by linearized theory. Several later papers confirmed this, usually by weakly nonlinear theory, see e.g., Proctor (1981) and the references therein. Proctor’s (1981) boundary layer analysis is an interesting one and provides some explanation for the energy results of Shir & Joseph (1968).
KeywordsRayleigh Number Viscous Fluid Convective Instability Entropy Inequality Linear Stability Theory
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