Fully dispersive dynamic models for surface water waves above varying bottom, Part 1: Model equations

Embrecht W.C. van Groesen, A. Andonowati

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    5 Citations (Scopus)

    Abstract

    In this paper we formulate relatively simple models to describe the propagation of coastal waves from deep parts in the ocean to shallow parts near the coast. The models have good dispersive properties that are based on smooth quasi-homogeneous interpolation of the exact dispersion above flat bottom. This dispersive quality is then maintained in the second order nonlinear terms of uni-directional equations as known from the AB-equation. A linear coupling is employed to obtain bi-directional propagation which includes (interactions with) reflected waves. The derivation of the models is consistent with the basic variational formulation of surface waves without rotation. A subsequent spatial discretization that takes this variational structure into account leads to efficient and accurate codes, as will be shown in Part 2.
    Original languageUndefined
    Pages (from-to)657-666
    Number of pages10
    JournalWave motion
    Volume48
    Issue number7
    DOIs
    Publication statusPublished - Nov 2011

    Keywords

    • EWI-20967
    • Coastal waves
    • Quasi-homogeneous dispersion
    • AB-equation
    • Variational modeling
    • METIS-281631
    • IR-78967
    • Sloping bottom

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