A weakly nonlinear analysis of the effect of vertical throughflow on Darcy-Benard convection

The aim of this paper is to analyze the effect of a downward vertical net mass flow on the type of instability that occurs in a horizontal fluid-saturated porous layer that is heated from below. The strength of the downflow is modelled by Pe, the Peclet number. First, we prove the validity of the principle of exchange of stabilities; consequently, we perform a linear instability analysis of the basic steady flow to determine the critical Darcy-Rayleigh number for the onset of steady convective instability as a function of Pe. Then, a weakly nonlinear stability analysis is performed to determine the smallest value of the Peclet number for which the onset of convection corresponds to a subcritical instability.