Effects of anisotropy on the transition to absolute instability in a porous medium heated from below

Abstract

The emerging instability of a forced throughflow in a fluid saturated horizontal porous duct of rectangular cross section is investigated. The duct is heated from below by assuming the horizontal boundaries to be at different temperatures. Both the horizontal and the vertical boundaries are impermeable and the basic flow is parallel to such boundaries. The porous medium is anisotropic with different permeabilities in the vertical and horizontal directions. The effect of the anisotropy on the onset of the buoyancy driven modal instability and absolute instability is analysed. The parametric conditions leading to the instability of the basic flow are determined by employing an analytical dispersion relation. The different permeabilities in the vertical and horizontal directions come out to play opposite roles in the onset of modal instability and in the transition to absolute instability. It is shown that an increasing vertical permeability has a destabilising effect, while an increasing horizontal permeability has a stabilising effect.