Convection induced by inclined thermal and solutal gradients, with horizontal mass flow, in a shallow horizontal layer of a porous medium

Abstract

A theoretical examination is made of convection, induced by applied thermal and solutal coplanar gradients inclined to the vertical and with net horizontal mass flux, in a shallow horizontal layer of a saturated porous medium. The horizontal components of these gradients induce a Hadley circulation superimposed on the net horizontal flow. The combined flow becomes unstable when the vertical components are sufficiently large. The solid matrix of the saturated medium is assumed adiabatic (heat capacity ratio/porosity = 1). A linear stability analysis is carried out, and calculations are made using Galerkin approximation for the various modes of instability. The orientation of the preferred mode and the other critical quantities are determined for representative parameter values. Our results, when complemented with results found in the literature for different parameter values, indicate that the horizontal gradient effect switches from stabilizing to destabilizing as the magnitude of the gradient increases.