Bifurcation and Stability of Two-Dimensional Double-Diffusive Convection

Details Bifurcation and Stability of Two-Dimensional Double-Diffusive Convection Bifurcation and Stability of Two-Dimensional Double-Diffusive Convection

2006-11-11

arxiv.org/abs/physics/0611111v1

Comm Pure and Appl Anal., 7:1(2008), 23-48

Physics

Atmospheric and Oceanic Physics

Scientific paper

In this article, we present a bifurcation and stability analysis on the double-diffusive convection. The main objective is to study 1) the mechanism of the saddle-node bifurcation and hysteresis for the problem, 2) the formation, stability and transitions of the typical convection structures, and 3) the stability of solutions. It is proved in particular that there are two different types of transitions: continuous and jump, which are determined explicitly using some physical relevant nondimensional parameters. It is also proved that the jump transition always leads to the existence of a saddle-node bifurcation and hysteresis phenomena.

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