Absolute/Convective Instabilities Analysis in a Double Diffusive Environment

Abstract

This paper presents the instability analysis of the buoyancy layers that exists near a vertical impermeable wall of constant temperature and mass flux situated in a linearly mass stratified fluid (the Prandtl number). The dimensionless parameter separates the two possible equilibrium situations: a heat driven convection (HDC) regime along the wall if M³1 and a HDC-MDC (mass driven convection) regimes succession if M<1.

Two particular parameter sets are considered for the two situations.

The HDC regime generated by the case I parameter set is convectively unstable no matter where the instantaneous perturbation is applied, while an absolutely unstable situation appears for the HDC-MDC regime of case II when the perturbation is applied in the HDC region.