Heterogeneity and onset of instability in Darcy's flow with a prescribed horizontal temperature gradient

The aim of this study is the analysis of the onset conditions for the thermal instability in a fluid saturated porous medium. The investigation refers to an infinitely wide horizontal porous layer with vertical heterogeneity, such that the lower plane boundary is impermeable and thermally insulated (adiabatic). The temperature distribution on the upper plane boundary is assumed to be prescribed and linearly varying in the horizontal direction. It is shown that these boundary conditions are compatible with a buoyancy-induced parallel-flow solution such that the temperature gradient is inclined with respect to the verticaldirection. The basic parallel flow is perturbed by small–amplitude roll disturbances, so that a linear analysis of the neutral stability is carried out. The local balance equations for the disturbances are solved numerically. The critical conditions for the onset of convection are determined.