A weakly nonlinear analysis of the effect of vertical throughflow on Darcy–Bénard convection

Abstract

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 [Formula: see text], the Péclet 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 [Formula: see text]. Then, a weakly nonlinear stability analysis is performed to determine the smallest value of the Péclet number for which the onset of convection corresponds to a subcritical instability.