Floquet instability of a gravity modulated Rayleigh–Benard problem in an anisotropic porous medium

Abstract

This work deals with the effect of gravity modulation on the onset of convection in a horizontal porous layer subjected to an adverse temperature gradient. Low amplitude gravity modulations are considered. The analysis is linear and specific attention is paid to the boundary effects of Brinkman's model and anisotropies of the porous medium in permeability and thermal conductivity. A Floquet analysis is applied and critical values of the parameters are found analytically using stability charts. The emergence of instability through the synchronous and subharmonic modes, transition between them and their dependence discussed for physically realistic values of control parameters. The findings of this analysis may be useful in controlling convective plumes during fabrication which develop into freckles in the ground grown crystals.