Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods
Mathematics Department, Faculty of Science, Taibah University, Al-Madinah Al-Munawarah, Saudi Arabia
2 Mathematics Department, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt
* e-mail: Aly742001@yahoo.com
Accepted: 24 October 2017
Published online: 12 December 2017
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.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2017