Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation

Abstract

Suppression of chaos in porous media convection under multifrequency gravitational modulation is investigated in this paper. For this purpose, a two-dimensional rectangular fluid-saturated porous layer heated from below subjected to a vertical gravitational modulation will be considered. The model consists of nonlinear heat equation coupled with a system of equations describing the motion under Darcy law. The time-dependent gravitational modulation is assumed to be with two frequencies σ1 and σ2. A spectral method of solution is used in order to reduce the problem to a system of four ordinary differential equations. The system is solved numerically by using the fifth- and a sixth-order Runge-Kutta-Verner method. Oscillating and chaotic convection regimes are observed. It was shown that chaos can be suppressed by appropriate tuning of the frequencies’ ratio η=σ2/σ1.