Wave groups in uni-directional surface-wave models

E. van Groesen

    Research output: Chapter in Book/Report/Conference proceedingChapterAcademicpeer-review

    Abstract

    Uni-directional wave models are used to study wave groups that appear in wave tanks of hydrodynamic laboratories; characteristic for waves in such tanks is that the wave length is rather small, comparable to the depth of the layer. In second-order theory, the resulting Nonlinear Schrödinger (NLS) equation for the envelope of the wave group contains the dispersion of the group velocity multiplying the linear term and a ‘gen-coefficient’ that results from mode generation multiplying the nonlinear term. The signs of these coefficients determine whether experimentally relevant wave groups are possible or not. If the dispersion is modelled in such a way that it is correct for all wave lengths for infinitesimal waves, relevant wave groups are obtained consisting of constituent waves with a certain maximal wave length; other models for the dispersion (such as in the KdV-equation) lead to different results.
    Original languageEnglish
    Title of host publicationFloating, Flowing, Flying
    Subtitle of host publicationPieter J. Zandbergen’s Life as Innovator, Inspirator and Instigator in Numerical Fluid Dynamics
    EditorsD. Dijkstra, B.J. Geurts, J.G.M. Kuerten, H.K. Kuiken
    Place of PublicationDordrecht
    PublisherSpringer
    Pages215-226
    Number of pages12
    ISBN (Electronic)978-94-017-1564-5
    ISBN (Print)978-90-481-5049-6
    DOIs
    Publication statusPublished - 1998

    Publication series

    NameJournal of engineering mathematics
    PublisherSpringer
    ISSN (Print)0022-0833

    Keywords

    • Wave groups
    • Nonlinear Schrödinger equation
    • Short wave dispersion
    • Towing tanks

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