Density inversion phenomenon in porous penetrative convection

Abstract

Penetrative convection occurs in many natural phenomena where an unstable stratified fluid moves into a stable one. This topic is of interest in many research fields like, for example, in geophysics and astrophysics. In the present paper, on taking into account for quadratic density law, the onset of penetrative convection in a horizontal porous layer is investigated. For the problem at stake, since the principle of exchange of stabilities has been proved, the convection can occur only through a secondary stationary motion. The critical Rayleigh numbers for the onset of stationary convection have been found via the linear instability analysis of the conduction solution. Moreover, the nonlinear stability of the motionless state has been investigated via the energy method. Numerical simulations have been performed through Chebyshev-τ spectral method in order to analyse the behaviour of stability and instability thresholds with respect to the upper plane temperature.