Encyclopedia of Complexity and Systems Science

Living Edition
| Editors: Robert A. Meyers

Nonlinear Internal Waves

  • Moustafa S. Abou-Dina
  • Mohamed A. Helal
Living reference work entry
DOI: https://doi.org/10.1007/978-3-642-27737-5_363-3

Definition of the Subject

The objective of the present work is to study the generation and propagation of nonlinear internal waves in the frame of the shallow water theory. These waves are generated inside a stratified fluid occupying a semi-infinite channel of finite and constant depth by a wave maker situated in motion at the finite extremity of the channel. A distortion process is carried out to the variables and the nonlinear equations of the problem using a certain small parameter characterizing the motion of the wave maker and double series representations for the unknown functions are introduced. This procedure leads to a solution of the problem including a secular term, vanishing at the position of the wave maker. This inconvenient result is remedied using a multiple-scale transformation of variables, and it is shown that the free-surface and the interface elevations satisfy the well-known KdV equation. The initial conditions necessary for the solution of the KdV equations are...


Internal Wave Fluid Layer Boussinesq Equation Secular Term Stratify Fluid 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of ScienceCairo UniversityGizaEgypt