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High-frequency instabilities of Stokes waves

Published online by Cambridge University Press:  28 February 2022

Ryan P. Creedon Open the ORCID record for Ryan P. Creedon [Opens in a new window] ,
Bernard Deconinck  and
Olga Trichtchenko
Ryan P. Creedon*
Affiliation:
Department of Applied Mathematics, University of Washington, Seattle, WA98195, USA
Bernard Deconinck
Affiliation:
Department of Applied Mathematics, University of Washington, Seattle, WA98195, USA
Olga Trichtchenko
Affiliation:
Department of Physics and Astronomy, The University of Western Ontario, London, ONN6A 3K7, Canada
*
†Email address for correspondence: [email protected]
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Abstract

Euler's equations govern the behaviour of gravity waves on the surface of an incompressible, inviscid and irrotational fluid of arbitrary depth. We investigate the spectral stability of sufficiently small-amplitude, one-dimensional Stokes waves, i.e. periodic gravity waves of permanent form and constant velocity, in both finite and infinite depth. We develop a perturbation method to describe the first few high-frequency instabilities away from the origin, present in the spectrum of the linearization about the small-amplitude Stokes waves. Asymptotic and numerical computations of these instabilities are compared for the first time, with excellent agreement.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 937 , 25 April 2022 , A24
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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