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Stability of oscillatory gravity wave trains with energy dissipation and Benjamin-Feir instability

Stability of oscillatory gravity wave trains with energy dissipation and Benjamin-Feir instability
Stability of oscillatory gravity wave trains with energy dissipation and Benjamin-Feir instability
The Benjamin-Feir instability describes the instability of a uniform oscillatory wave train in an irrotational flow subject to small perturbation of wave number, amplitude and frequency. Their instability analysis is based on the perturbation around the second order Stokes wave which satisfies the dynamic and kinematic free-surface boundary conditions up to the second order. In the same irrotational flow and perturbation framework of the Benjamin-Feir analysis, the perturbation in the present paper is around a nonlinear oscillatory
wave train which solves exactly the dynamic free-surface boundary condition
and satisfies the kinematic free-surface boundary condition up to the third or-
der. It is shown that the nonlinear oscillatory wave train is stable with respect
to the perturbation when the irrotational flow involves small Rayleigh energy
dissipation.
1531-3492
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Wilson, P.A.
8307fa11-5d5e-47f6-9961-9d43767afa00
Chen, Zhi-Min
e4f81e6e-5304-4fd6-afb2-350ec8d1e90f
Wilson, P.A.
8307fa11-5d5e-47f6-9961-9d43767afa00

Chen, Zhi-Min and Wilson, P.A. (2012) Stability of oscillatory gravity wave trains with energy dissipation and Benjamin-Feir instability. Discrete and Continuous Dynamical Systems - Series B, 17 (7). (doi:10.3934/dcdsb.2012.17.2329).

Record type: Article

Abstract

The Benjamin-Feir instability describes the instability of a uniform oscillatory wave train in an irrotational flow subject to small perturbation of wave number, amplitude and frequency. Their instability analysis is based on the perturbation around the second order Stokes wave which satisfies the dynamic and kinematic free-surface boundary conditions up to the second order. In the same irrotational flow and perturbation framework of the Benjamin-Feir analysis, the perturbation in the present paper is around a nonlinear oscillatory
wave train which solves exactly the dynamic free-surface boundary condition
and satisfies the kinematic free-surface boundary condition up to the third or-
der. It is shown that the nonlinear oscillatory wave train is stable with respect
to the perturbation when the irrotational flow involves small Rayleigh energy
dissipation.

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Accepted/In Press date: 29 March 2012
Published date: 1 October 2012
Organisations: Fluid Structure Interactions Group

Identifiers

Local EPrints ID: 336575
URI: https://eprints.soton.ac.uk/id/eprint/336575
ISSN: 1531-3492
PURE UUID: ea841509-948d-4eac-ad85-ed6a0a3f02b1
ORCID for P.A. Wilson: ORCID iD orcid.org/0000-0002-6939-682X

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Date deposited: 29 Mar 2012 14:59
Last modified: 20 Jul 2019 01:27

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