On long waves in shallow water with shear flow |
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| Affiliation: | 1. Institute of Applied Physics and Computational Mathematics, Beijing 100088, PR China;2. Graduate School of China Academy of Engineering Physics, Beijing 100088, PR China;1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan, Hubei 430074, China;2. Department of Mathematics, University of Texas-Pan American, Edinburg, Texas 78541, USA;3. College of Sciences, China University of Mining and Technology, Xuzhou, Jiangsu 221116, China |
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| Abstract: | Various evolution equations for long interfacial waves with shear flow are derived with the assumptions that: (1) the wavelength of the interfacial waves is much larger than the total depth of the fluids, and (2) that the spanwise dependence is much weaker than the streamwise dependence. A particular case of interest occurs when the interfacial waves are at or near direct resonance. In this case the Boussinesq equation replaces the Korteweg-de Vries equation. Various special solutions in two dimensions are discussed. |
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