Wave groups in uni-directional surface-wave models

E. van Groesen*

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    20 Citations (Scopus)

    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
    Pages (from-to)215-226
    Number of pages12
    JournalJournal of engineering mathematics
    Volume34
    Issue number1-2
    DOIs
    Publication statusPublished - 1 Jul 1998

    Keywords

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

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