Reflection in variational models for linear water waves

G. Klopman, Maarten W. Dingemans

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    4 Citations (Scopus)


    The reflection characteristics are analysed for a series of Hamiltonian water-wave models. These variational models have been derived by applying a Boussinesq-like approach to the vertical flow-structure. Both parabolic and hyperbolic-cosine approximations to the vertical structure are considered. Mild-slope approximations are made for the flow velocities, by neglecting horizontal derivatives of the mean water depth in the Hamiltonian density. In all cases, a positive-definite Hamiltonian is ensured, contributing to the good dynamical behaviour of the resulting flow equations. It is found that, in general, the mild-slope approximation results in less good predictions of the reflections, as compared to the steep-slope variants – i.e. without the mild-slope approximation – and the accurate model results of Porter and Porter [13]. However, by carefully choosing the normalisation for the mild-slope models, good reflection characteristics can be obtained while maintaining the simpler structure of the mild-slope model, as compared with the steep-slope variants.
    Original languageEnglish
    Pages (from-to)469-489
    JournalWave motion
    Issue number8
    Publication statusPublished - 2010


    • IR-73909
    • Boussinesq-like wave model
    • Hamiltonian
    • METIS-296883
    • Sloping bottom
    • Linear theory
    • Water waves
    • Reflection


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