A water wave model with horizontal circulation and accurate dispersion

C. Cotter, Onno Bokhove

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    Abstract

    We describe a new water wave model which is variational, and combines a depth-averaged vertical (component of) vorticity with depth-dependent potential flow. The model facilitates the further restriction of the vertical profile of the velocity potential to n-th order polynomials or a finite element profile with a small number of elements (say), leading to a framework for efficient modelling of the interaction of steepening and breaking waves near the shore with a large-scale horizontal flow. The equations are derived from a constrained variational formulation which leads to conservation laws for energy, mass, momentum and vertical vorticity (or circulation). We show that the potential flow water wave equations and the shallow-water equations are recovered in the relevant limits, and provide approximate shock relations for the model which can be used in numerical schemes to model breaking waves.
    Original languageUndefined
    Place of PublicationEnschede
    PublisherNumerical Analysis and Computational Mechanics (NACM)
    Number of pages15
    Publication statusPublished - Mar 2009

    Publication series

    Name
    PublisherDepartment of Applied Mathematics, University of Twente
    No.1896
    ISSN (Print)1874-4850
    ISSN (Electronic)1874-4850

    Keywords

    • Variational principles
    • Deep and shallow water waves
    • IR-65436
    • EWI-15234
    • METIS-263787
    • New water wave model

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