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

. 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...

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Published inEuropean physical journal plus Vol. 132; no. 12; p. 518
Main Author Seadawy, Aly R.
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2017
Springer Nature B.V
Subjects
Applied and Technical Physics
Atomic
Complex Systems
Condensed Matter Physics
Exact solutions
Fluid pressure
Free surfaces
Internal waves
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Shear flow
Solitary waves
Stability analysis
Theoretical
Water waves
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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.
AbstractList . 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.
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.
ArticleNumber 518
Author Seadawy, Aly R.
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  givenname: Aly R.
  surname: Seadawy
  fullname: Seadawy, Aly R.
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  organization: Mathematics Department, Faculty of Science, Taibah University, Mathematics Department, Faculty of Science, Beni-Suef University
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Snippet . 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...
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...
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StartPage 518
SubjectTerms Applied and Technical Physics
Atomic
Complex Systems
Condensed Matter Physics
Exact solutions
Fluid pressure
Free surfaces
Internal waves
Mathematical and Computational Physics
Molecular
Optical and Plasma Physics
Physics
Physics and Astronomy
Regular Article
Shear flow
Solitary waves
Stability analysis
Theoretical
Water waves
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Title 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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