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Third-order theory for multi-directional irregular waves

Published online by Cambridge University Press:  02 April 2012

Per A. Madsen  and
David R. Fuhrman
Per A. Madsen*
Affiliation:
Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Kgs Lyngby, Denmark
David R. Fuhrman
Affiliation:
Department of Mechanical Engineering, Technical University of Denmark, DK-2800 Kgs Lyngby, Denmark
*
†Email address for correspondence: prm@mek.dtu.dk
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Abstract

A new third-order solution for multi-directional irregular water waves in finite water depth is presented. The solution includes explicit expressions for the surface elevation, the amplitude dispersion and the vertical variation of the velocity potential. Expressions for the velocity potential at the free surface are also provided, and the formulation incorporates the effect of an ambient current with the option of specifying zero net volume flux. Harmonic resonance may occur at third order for certain combinations of frequencies and wavenumber vectors, and in this situation the perturbation theory breaks down due to singularities in the transfer functions. We analyse harmonic resonance for the case of a monochromatic short-crested wave interacting with a plane wave having a different frequency, and make long-term simulations with a high-order Boussinesq formulation in order to study the evolution of wave trains exposed to harmonic resonance.

JFM classification

Waves/Free-surface Flows: Surface gravity waves Waves/Free-surface Flows: Waves/Free-surface Flows

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Type
Papers
Information
Journal of Fluid Mechanics , Volume 698 , 10 May 2012 , pp. 304 - 334
Copyright
Copyright © Cambridge University Press 2012

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