Linear stability analysis of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect

Abstract

Temporal and spatiotemporal instabilities of Poiseuille-Rayleigh-Bénard flows in binary fluids with Soret effect have been investigated by a Chebyshev collocation method. Both situations corresponding to the fluid layer heated from below or from above have been studied. When heating is from below and for positive separation factors, the critical thresholds strongly increase when the throughflow is applied, and the boundary curves between absolute and convective instabilities (AI∕CI) increase as well, but more steeply. For large enough positive separation factors, there exist three local minima in the neutral curves Ra(k) (Rayleigh number against wavenumber) for moderate Reynolds numbers (Re), which results in the discontinuity of the critical wavenumber curve and the nonsmoothness of the critical Rayleigh number curve when the Reynolds number is varied. For negative separation factors, there exists a contact point between the critical Rayleigh number curve and the AI∕CI boundary curve at which the fluid system is directly changed from stable to absolutely unstable without crossing the convectively unstable region. This contact point has been characterized and localized for different negative separation factors. When heating is from above, the main observation is that the stationary curve obtained at Re=0 is replaced by two critical curves, one stationary and the other oscillatory, when a throughflow is applied. An energy budget analysis for the binary fluid system is also performed. A better insight into the role played by the solutal buoyancy contribution in the different situations is thus obtained.