Bifurcation analysis of double-diffusive convection with opposing horizontal thermal and solutal gradients

Abstract

The onset of convection in double diffusion with equal and opposite thermal and solutal buoyancy forces is studied. Numerical linear stability analyses and integration of the full Boussinesq equations are performed in an infinite vertical fluid layer and in closed rectangular cavities bounded by rigid walls. Detailed study of the subsequent nonlinear evolution is carried out for Le=1.2 and Pr=1. In the infinite vertical layer, the onset of convection is found to correspond to a subcritical circle pitchfork bifurcation. The finite-amplitude branch of steady states in turn loses stability to traveling waves via a supercritical drift pitchfork bifurcation. In a square cavity the bifurcation is transcritical and the full branch of stable and unstable solutions is constructed. With increasing cavity aspect-ratio, we observe alternating transcritical and pitchfork bifurcations, depending on the symmetry of the most unstable eigenvector.