Anisotropic Porous Penetrative Convection

Dr. Brian Straughan

Department of Mathematics
University of Glasgow

April 17, 1998

Abstract

A linear stability analysis and a nonlinear energy stability analysis is developed for convection in an anisotropic porous medium. The nonlinear analysis is very important since a standard energy method does no in the present situation yield unconditional stability and a weighted analysis must be employed to yield global results. In addition, the nonlinear energy results yield a valuable threshold indicating where possible subcritical instabilities may form. Significantly, we find that when a quadratic density temperature law is used in the anisotropic convection model of Yyvand and Storeslettin (1991), then the growth rate σ is complex provided we are in the anisotropic situation. Thus, the nature of bifurcation into convection is very different from the Boussinesq situation and is lawyers via an oscillatory instability.