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Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system

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  • A. A. Halim
  • S. P. Kshevetskii
  • S. B. Leble

Abstract

We consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is numerically solved via a finite-difference scheme for which we prove the convergence and stability. Together with the solution of the Sturm-Liouville problem, the stream functions give the internal waves profile.

Suggested Citation

  • A. A. Halim & S. P. Kshevetskii & S. B. Leble, 2003. "Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2003, pages 1-15, January.
    • Handle: RePEc:hin:jijmms:731659
    DOI: 10.1155/S0161171203212242
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