| Secondary instabilities of linearly heated falling films |
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| 作者姓名： | HU Jun SUN Dejun HU Guohui YIN Xieyuan |
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| 作者单位： | Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China,Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China,Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China,Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China |
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| 基金项目： | 国家自然科学基金，中国科学院资助项目 |
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| 摘 要： | Secondary instabilities of linearly heated failing films are studied through three steps. Firstly, the analysis of the primary linear instability on Miladinova's long wave equation of the linearly heated film is performed. Secondly, the similar Landau equation is derived through weak nonlinear theory, and a two-dimensional nonlinear saturation solution of primary instability is obtained within the weak nonlinear domain. Thirdly, the secondary (three-dimensional) instability of the two-dimensional wave is studied by the Floquet theorem.Our secondary instability analysis shows that the Marangoni number has destabilization effect on the secondary instability.
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| 关 键 词： | linearly heated falling film secondary instability Floquet theorem |
Secondary instabilities of linearly heated falling films |
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| HU Jun,SUN Dejun,HU Guohui,YIN Xieyuan.Secondary instabilities of linearly heated falling films[J].Progress in Natural Science,2005,15(3):205-212. |
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| Authors: | HU Jun SUN Dejun Hu Guohui YIN Xieyuan |
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| Institution: | 1. Department of Modern Mechanics, University of Science and Technology of China, Hefei 230027, China
2. Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China |
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| Abstract: | Secondary instabilities of linearly heated failing films are studied through three steps. Firstly, the analysis of the primary linear instability on Miladinova's long wave equation of the linearly heated film is performed. Secondly, the similar Landau equation is derived through weak nonlinear theory, and a two-dimensional nonlinear saturation solution of primary instability is obtained within the weak nonlinear domain. Thirdly, the secondary (three-dimensional) instability of the two-dimensional wave is studied by the Floquet theorem.Our secondary instability analysis shows that the Marangoni number has destabilization effect on the secondary instability. |
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| Keywords: | linearly heated falling film secondary instability Floquet theorem |
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