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Proceedings Paper

Bichromatic water waves in finite depth
Author(s): Per A. Madsen; David R. Fuhrman
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Paper Abstract

A new third-order solution for bichromatic bi-directional water waves in finite depth is presented. Details of the complete solution can be found in a companion paper. In the present paper, we give the form of the solution, and focus the attention on the nonlinear dispersion relation, which incorporates the effect of an ambient current, with the option of specifying zero net volume flux. The dispersion relation is verified against classical expressions from the literature, and limitations and problems with these classical expressions are identified. Finally, third-order resonance curves for unidirectional and short-crested finite amplitude waves and their three-dimensional perturbations are calculated. Dominant class I and class II wave instabilities (determined by classical stability analyses) are shown to be located close to these resonance curves.

Paper Details

Date Published: 3 February 2006
PDF: 10 pages
Proc. SPIE 5975, Topical Problems of Nonlinear Wave Physics, 597511 (3 February 2006); doi: 10.1117/12.675582
Show Author Affiliations
Per A. Madsen, Technical Univ. of Denmark (Denmark)
David R. Fuhrman, Technical Univ. of Denmark (Denmark)

Published in SPIE Proceedings Vol. 5975:
Topical Problems of Nonlinear Wave Physics
Alexander M. Sergeev, Editor(s)

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