Instability in heated water-porous system

Abstract

This paper investigates the stability in a heated fluid-porous system. Darcy’s law is used for the flow in the porous medium. Previous studies indicate that the classical Rayleigh–Bénard instability in this flow is independent of the mutual positions of the fluid layer and porous layer. This paper demonstrates that the instability depends on the mutual positions of the fluid layer and porous layer when the liquid density is nonlinearly dependent on temperature. When porous medium is located at the bottom of the system, onset of convection may occur in lower porous layer (pure-porous mode), upper water layer (pure-water mode) or across both layers (porous-water mode). However, onset of convection cannot take place only in the upper porous layer when porous medium is placed at the top of the system. The influence of depth ratio $\hat{d}$ and the density inversion parameter ${\theta }_M$ on instability of bilayer system are investigated in detail and dependence of critical modes on parameters are summarized in phase diagrams. In addition, direct numerical simulation is used to analyse the instability mechanism and identify subcritical or supercritical instability for bilayer systems.