Suppression of chaos in porous media convection under multifrequency gravitational modulation (Q1629157)

Summary: 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 \(\sigma_1\) and \(\sigma_2\). 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 \(\eta = \sigma_2 / \sigma_1\).