Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation
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 c...
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| Language: | English |
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Wiley
2018-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2018/1764182 |
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| author | Karam Allali |
| author_facet | Karam Allali |
| author_sort | Karam Allali |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-5db073f38056400687c1ca10f2dd164b |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-5db073f38056400687c1ca10f2dd164b2025-08-20T03:34:44ZengWileyAdvances in Mathematical Physics1687-91201687-91392018-01-01201810.1155/2018/17641821764182Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational ModulationKaram Allali0Laboratory of Mathematics and Applications, Faculty of Sciences and Technologies, University Hassan II of Casablanca, P.O. Box 146, Mohammedia, MoroccoSuppression 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.http://dx.doi.org/10.1155/2018/1764182 |
| spellingShingle | Karam Allali Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation Advances in Mathematical Physics |
| title | Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation |
| title_full | Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation |
| title_fullStr | Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation |
| title_full_unstemmed | Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation |
| title_short | Suppression of Chaos in Porous Media Convection under Multifrequency Gravitational Modulation |
| title_sort | suppression of chaos in porous media convection under multifrequency gravitational modulation |
| url | http://dx.doi.org/10.1155/2018/1764182 |
| work_keys_str_mv | AT karamallali suppressionofchaosinporousmediaconvectionundermultifrequencygravitationalmodulation |