Reflection in variational models for linear water waves


Klopman, Gert and Dingemans, Maarten W. (2010) Reflection in variational models for linear water waves. Wave motion, 47 (8). pp. 469-489. ISSN 0165-2125

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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.

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Copyright:© 2010 Elsevier B.V.
Electrical Engineering, Mathematics and Computer Science (EEMCS)
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