Gravity modulation and cross-diffusion effects on the onset of multicomponent convection.

A linear stability analysis is undertaken to investigate the effects of cross-diffusion and gravity modulation on the onset of convective instability in horizontally unbounded multiply diffusive fluid layers. We consider layers of incompressible Boussinesq fluid in which all thermophysical properties are constant except for the density insofar as it contributes to a buoyant force. It is assumed that the density is a linear function of the various components present and the fluxes are linear combinations of all the gradients of those components. We begin with a study of the effects of coupled molecular diffusion in a triply diffusive fluid layer under a constant gravity field. The bounding surfaces are perfectly conducting, perfectly permeable, and free of stresses. Stability is determined by way of temporal eigenvalues of a linear system of ODE's. We find that the off-diagonal elements of the diffusivity matrix may strongly affect the linear stability criteria, regardless of their relative value (as long as they do not vanish) as compared to the main-diagonal elements. We also investigate the combined effects of a sinusoidally varying gravity field and cross-diffusion in several doubly diffusive configurations. In particular, we consider: (1) stress-free and rigid boundaries with imposed gradients, and (2) stress-free and rigid boundaries when a solute gradient is induced by Soret separation. Stability is determined by way of Floquet multipliers of a linear system of ODE's with periodic coefficients. The topology of neutral curves and stability boundaries exhibits features not found in the modulated singly diffusive or unmodulated multiply diffusive fluid layers. In a gravity modulated doubly diffusive layer with cross-diffusion, when one Rayleigh number, say R₂, is fixed or induced, neutral curves spanned by the other Rayleigh number (R₁) and the horizontal wavenumber are in general multivalued. In addition, finite as well as semi-infinite R₁ stability ranges can be found. A notable feature is the occurrence of double minima, each one corresponding to a different asymptotically stable neutral response. A temporally and spatially quasi-periodic bifurcation from the basic state is possible when the Rayleigh numbers of the double extrema coincide. In this situation, there are two incommensurate critical wavenumbers at two incommensurate onset frequencies at the same Rayleigh number