Variational water-wave model with accurate dispersion and vertical vorticity

Colin Cotter, Onno Bokhove

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    Abstract

    A new water-wave model has been derived which is based on variational techniques 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 modeling 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. It is shown that the potential-flow water-wave equations and the shallow-water equations are recovered in the relevant limits. Approximate shock relations are provided, which can be used in numerical schemes to model breaking waves.
    Original languageUndefined
    Pages (from-to)33-54
    Number of pages22
    JournalJournal of engineering mathematics
    Volume67
    Issue number1-2
    DOIs
    Publication statusPublished - 2010

    Keywords

    • EWI-19297
    • METIS-276287
    • IR-75745
    • Wave-current interactions
    • Coastal engineering
    • Variational principles
    • Bores

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