A Hamiltonian Boussinesq model with horizontally sheared currents

Elena Gagarina, Jaap van der Vegt, Vijaya Ambati, Onno Bokhove

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    Abstract

    We are interested in the numerical modeling of wave-current interactions around beaches’ surf zones. Any model to predict the onset of wave breaking at the breaker line needs to capture both the nonlinearity of the wave and its dispersion. We have formulated the Hamiltonian dynamics of a new water wave model. This model incorporates both the shallow water model and the potential flow model as limiting systems. The variational model derived by Cotter and Bokhove (2010) is such a model, but the variables used have been difficult to work with. Our new model has a three-dimensional velocity field consisting of the full three-dimensional potential field plus horizontal velocity components, such that the vertical component of vorticity is nonzero. Our aims are to augment the new model locally with bores and to derive a numerical finite element discretization of the new model including the capturing of bores. As a preliminary step, the variational finite element discretization of Miles’ variational principle coupled to an elliptic mesh generator is shown.
    Original languageEnglish
    Place of PublicationEnschede
    PublisherUniversity of Twente, Department of Applied Mathematics
    Publication statusPublished - Feb 2012

    Publication series

    NameMemorandum / Department of Applied Mathematics
    PublisherUniversity of Twente, Department of Applied Mathematics
    No.1977
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • (Dis)Continuous finite elements
    • Hamiltonian dynamics
    • Water wave model
    • Compatible schemes

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