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Derivation of the nonlinear Schrödinger Equation for shoaling wave-groups

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Abstract

A nonlinear Schrödinger equation with varying coefficients, describing the evolution of surface wave groups moving over an uneven bottom, is derived from Whitham's modulation equations. The derivation yields new expressions for the wave-induced mean flow field.

Zusammenfassung

Ausgehend von Whitham's Modulationsgleichungen wird eine nichtlineare Schrödinger-Gleichung mit veränderlichen Koeffizienten hergeleitet, welche die Entwicklung von Oberflächen-wellengruppen beschreibt, die sich über einen unebenen Boden fortpflanzen. Die Herleitung ergibt neue Ausdrücke für das wellen-induzierte mittlere Strömungsfeld.

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References

  1. A. Davey and K. Stewartson,On three-dimensional packets of surfaces waves. Proc. R. Soc. A338, 101–10 (1974).

    Google Scholar 

  2. V. D. Djordjevic' and L. G. Redekopp,On the deveolpment of packets of surface gravity waves moving over an uneven bottom. J. Appl. Maths. Phys.29, 950–62 (1978).

    Google Scholar 

  3. R. Grimshaw,Slowly varying solitary waves, II. Nonlinear Schrödinger equation. Proc. R. Soc. A368, 377–88 (1979).

    Google Scholar 

  4. M. Stiassnie and U. I. Kroszynski,Long time evolution of an unstable water wave train. J. Fluid Mech.116, 207–25 (1982).

    Google Scholar 

  5. M. Stiassnie and D. H. Peregrine,Shoaling of finite-amplitude surface waves on water of slowly-varying depth. J. Fluid Mech.97, 783–805 (1980).

    Google Scholar 

  6. G. B. Whitham,Linear and nonlinear waves. Wiley-Interscience, New York 1974.

    Google Scholar 

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Authors and Affiliations

  1. Ralph M. Parsons Laboratory, Massachusetts Institute of Technology Cambridge, 02139, MA, USA

    Michael Stiassnie

Authors
  1. Michael Stiassnie
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Additional information

On leave from the Department of Civil Engineering. Technion, I.I.T. Haifa 32000, Israel.

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Stiassnie, M. Derivation of the nonlinear Schrödinger Equation for shoaling wave-groups. Z. angew. Math. Phys. 34, 534–544 (1983). https://doi.org/10.1007/BF00944713

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  • DOI: https://doi.org/10.1007/BF00944713

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