Impact of boundary excitation on stability of a diffusive boundary layer in porous media

Abstract

We study the effects of boundary excitation on the onset of natural convection and the dynamics of subsequent convective mixing by conducting linear stability analysis (LSA) and direct numerical simulations (DNS). A detailed parametric analysis on the stability of a diffusive boundary layer in porous media subject to three different types of linear decline, linear decline followed by constant concentration, and symmetric flat floored valley shape boundary conditions is presented. We propose scaling relations based on results of LSA to describe the critical time and the associated wavenumber of convective instabilities that incorporate the effect of the boundary parameters. The LSA results show that the classic onset criterion is applicable when decline factors (α) is smaller than 10−4. The results also demonstrate that α does not play a significant role in the instability of the system unless it is greater than 10−4. The results show that in systems with linear concentration decline followed by constant concentration, the impact of decline on the stability of the system decreases as α increases. Based on the LSA results, a system with α>10−2 leads to unified stability criteria at different constant concentration (χ) similar to the classic problem, when the transient time (τ) and the wavenumber (κ) are rescaled by χ as τχ2 and κ/χ, respectively. Our results also show that the duration of the flat portion in symmetric flat floored valley shape boundary condition is the main factor controlling the stability behavior of the system. The DNS results reveal that the dynamics of the buoyancy-driven mixing is also significantly influenced by the temporal variation of concentration at the boundary. These findings improve our understanding of buoyancy-driven instabilities in the presence of boundary excitation and finds applications in thermal and solutal convection in porous media.