Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation

Karam Allali

Advances in Mathematical Physics, 2018, vol. 2018, issue 1

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.

Date: 2018
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https://doi.org/10.1155/2018/1764182

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:1764182

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