Convective Instabilities in Anisotropic Porous Media

This paper addresses the problem of the onset of Rayleigh-Bénard convection in a porous layer using Brinkman's equation and anisotropic permeability. The critical Rayleigh number and wave number at marginal stabilities are calculated for both free and rigid boundaries. In both cases, it is noted that there exist ranges for which the stability criteria is intermediate to the low porosity Darcy approximation and to high porosity single viscous fluid. The permeability anisotropy is found to select the mode of instability.