Effect of a Periodic Gravitational Excitation with Frequency Modulation on Convective Instability in Porous Media

This work deals with the influence of a periodic gravitational excitation on convective instability in porous media. It is assumed that the frequency of the periodic excitation is modulated around a mean value with a certain amplitude and frequency. In the suggested model, we consider the coupling between the heat equation, concentration equation, and the hydrodynamics equations. Two approximations are assumed, the first represents the incompressibility and is formulated by the Boussinesq approach, while the second represents the effect of the porous matrix on the flow and is formulated by Darcy law. Linear stability analysis of the problem is fulfilled and the convective instability boundary is determined using numerical simulations. Results show that the convective instability boundary can be greatly influenced by modulating the frequency of the periodic gravitational modulation. Specifically, it is demonstrated that the modulation of the frequency of the periodic gravitational excitation has a stabilizing or a destabilizing effect depending on its amplitude or frequency.