A Hamiltonian approach to fairly low and fairly long gravity waves

W.A. van der Veen, F.W. Wubs

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    The propagation of nonlinear dispersive gravity waves in an inviscid irrotational fluid can be described by a Hamiltonian system. The canonical equations contain a boundary integral which is computationally expensive. However, for fairly low and fairly long waves an approximation can be made that gives rise to the solution of computationally more attractive Helmholtz-type equations. In an earlier attempt, canonical equations were derived that are stable for all wavenumbers. However, two Helmholtz-type equations need to be solved per right-hand side evaluation. In this paper, canonical equations are presented with the same qualities, but now only once per right-hand side evaluation a Helmholz-type equation needs to be solved, which is optimal.
    Original languageEnglish
    Pages (from-to)329-345
    Number of pages17
    JournalJournal of Engineering Mathematics
    Issue number4
    Publication statusPublished - Jul-1995

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