CONVECTIVE INSTABILITY IN SUPERPOSED FLUID AND ANISOTROPIC POROUS LAYERS

The onset of thermal convection due to heating from below in a system consisting of a fluid layer overlying a porous layer with anistropic permeability and thermal diffusivity is studied. Flow in the porous medium is assumed to be governed by Darcy's law; the Beavers-Joseph condition is applied at the interface between the two layers. The linear perturbation equations are solved numerically. It is found that the effects of anisotropy on the onset of thermal convection are most profound for small values of the depth ratio zeta (ratio of fluid layer thickness to porous layer thickness), since in that case, the onset of convection corresponds to significant motion in both layers. For fixed values of the vertical permeability in the porous medium, decreasing the value of zeta (ratio of horizontal to vertical permeability) leads to stabilization of the superposed layer configuration because of increased resistance to motion in the porous medium. For larger values of zeta, the onset of motion is increasingly confined to the fluid layer, with the transport of heat through the porous layer occurring primarily by conduction. Accordingly, the influence of zeta on the stability characteristics for larger zeta is less significant than the effects of an anisotropic thermal conductivity.