Effect of amplitude modulation of gravitational vibration on convective instability of reaction fronts in porous media
Karam Allali, Mohamed Belhaq · Applied Mathematical Sciences · 2013
This paper studies the influence of periodic and quasi-periodic amplitude modulations of gravitational vibration on the convective instability of reaction fronts in porous media. Specifically, two cases of amplitude modulation are investigated. In the first case, we consider that the frequency ν2 of the amplitude modulation is either double or half the frequency of the basic gravitational vibration ν1. In this case the modulated gravitational vibration remains periodic. In the second case, we assume that the frequency ν2 is such that ν1 and ν2 are incommensurate which forces the gravitational vibration to be quasi-periodic. The model considered in this study consists of the heat equation, the equation for the depth of conversion and the equations of motion under the Darcy law. The convective instability threshold is obtained. The linear stability analysis of the steady-state solution is performed and the obtained interface problem is solved numerically.