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Publication - Dr Laura Dickinson

    The near-shore behaviour of shallow-water waves with localised initial conditions


    Pritchard, D & Dickinson, L, 2007, ‘The near-shore behaviour of shallow-water waves with localised initial conditions’. Journal of Fluid Mechanics, vol 591., pp. 413 - 436


    We consider the behaviour of solutions to the nonlinear shallow-water equations
    which describe wave runup on a plane beach, concentrating on the behaviour at
    and just behind the moving shoreline. We develop regular series expansions for
    the hydrodynamic variables behind the shoreline, which are valid for any smooth
    initial condition for the waveform. We then develop asymptotic descriptions of the
    shoreline motion under localized initial conditions, in particular a localized Gaussian
    waveform: we obtain estimates for the maximum runup and drawdown of the wave,
    for its maximum velocities and the forces it is able to exert on objects in its path,
    and for the conditions under which such a wave breaks down. We show how these
    results may be extended to include initial velocity conditions and initial waveforms
    which may be approximated as the sum of several Gaussians. Finally, we relate these
    results tentatively to the observed behaviour of a tsunami.

    Full details in the University publications repository