Penetrative convection and multi-component diffusion in a porous medium

Linear instability and nonlinear energy stability analyses are developed fo r the problem of a fluid-saturated porous layer stratified by penetrative t hermal convection and two salt concentrations. Unusual neutral curves are o btained, in particular non-perfect 'heart-shaped' oscillatory curves that a re disconnected from the stationary neutral curve. These curves show that t hree critical values of the thermal Rayleigh number may be required to full y describe the linear stability criteria. As the penetrative effect is incr eased, the oscillatory curves depart more and more from a perfect heart sha pe. For certain values of the parameters it is shown that the minima on the oscillatory and stationary curves occur at the same Rayleigh number but di fferent wavenumbers, offering the prospect of different types of instabilit y occurring simultaneously at different wavenumbers. A weighted energy meth od is used to investigate the nonlinear stability of the problem and yields unconditional results guaranteeing nonlinear stability for initial perturb ations of arbitrary sized amplitude. (C) 1998 Elsevier Science Limited. All rights reserved.