Thermal convection in superposed fluid and porous layers subjected to a plane Poiseuille flow

Abstract

Thermal convection in a two-layer system comprised by a fluid layer overlying a layer of porous media saturated with the same fluid has been investigated. The system is heated from below and subjected to a horizontally plane Poiseuille flow. The interaction between both instability mechanisms, the unstably stratification and the shear arising from the plane Poiseuille flow, is studied and a completely linear stability analysis has been carried out by considering both longitudinal rolls (LRs) and transverse rolls (TRs). It is found that the neutral curves of both modes may be bimodal, which is dependent on the depth ratio, the ratio of the depth of fluid layer to that of the porous layer. The stability characteristics of LRs are found to be invariant with the Reynolds number based on the horizontal Poiseuille velocity and the Prandtl number of the fluid, and the instability is always dominated by this mode if the Reynolds number is within low or moderate strength. The superimposed Poiseuille flow seems to exert a stabilizing effect on the traveling TRs and the critical transverse mode tends to be within the porous layer with low propagating speed. However, if the Reynolds number is sufficiently large, a shear instability mode appears abruptly with higher propagating speed and then dominates the system instability.