Convective instabilities for reacting viscous fluids far from equilibrium

Abstract

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 and 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 doublediffusive context was investigated by (Veronis, 1965; Veronis, 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. The boundary layer analysis of (Proctor, 1981) is an interesting one and provides some explanation for the energy results of (Shir and Joseph, 1968). The phenomenon of double diffusive convection and even multi-diffusive convection is examined in detail in the next chapter.