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Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods

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Abstract.

In this study, we presented the problem formulations of models for internal solitary waves in a stratified shear flow with a free surface. The nonlinear higher order of extended KdV equations for the free surface displacement is generated. We derived the coefficients of the nonlinear higher-order extended KdV equation in terms of integrals of the modal function for the linear long-wave theory. The wave amplitude potential and the fluid pressure of the extended KdV equation in the form of solitary-wave solutions are deduced. We discussed and analyzed the stability of the obtained solutions and the movement role of the waves by making graphs of the exact solutions.

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Authors and Affiliations

  1. Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia

    Aly R. Seadawy

  2. Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

    Aly R. Seadawy

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  1. Aly R. Seadawy
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Correspondence to Aly R. Seadawy.

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Seadawy, A.R. Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods. Eur. Phys. J. Plus 132, 518 (2017). https://doi.org/10.1140/epjp/i2017-11755-6

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  • DOI: https://doi.org/10.1140/epjp/i2017-11755-6

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