Reflection in variational models for linear water waves

  • Klopman G
  • Dingemans M
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Abstract

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. © 2010 Elsevier B.V.

Author-supplied keywords

  • Boussinesq-like wave model
  • Hamiltonian
  • Linear theory
  • Reflection
  • Sloping bottom
  • Water waves

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Authors

  • Gert Klopman

  • M. W. Dingemans

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