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Stability of waves on fluid of infinite depth with constant vorticity

Published online by Cambridge University Press:  17 February 2022

M.G. Blyth Open the ORCID record for M.G. Blyth [Opens in a new window]  and
E.I. Părău Open the ORCID record for E.I. Părău [Opens in a new window]
M.G. Blyth*
Affiliation:
School of Mathematics, University of East Anglia, NorwichNR4 7TJ, UK
E.I. Părău
Affiliation:
School of Mathematics, University of East Anglia, NorwichNR4 7TJ, UK
*
†Email address for correspondence: [email protected]
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Abstract

The stability of periodic travelling waves on fluid of infinite depth is examined in the presence of a constant background shear field. The effects of gravity and surface tension are ignored. The base waves are described by an exact solution that was discovered recently by Hur and Wheeler (J. Fluid Mech., vol. 896, 2020). Linear growth rates are calculated using both an asymptotic approach valid for small-amplitude waves and a numerical approach based on a collocation method. Both superharmonic and subharmonic perturbations are considered. Instability is shown to occur for any non-zero amplitude wave.

JFM classification

Waves/Free-surface Flows: Waves/Free-surface Flows
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 936 , 10 April 2022 , A46
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Copyright
© The Author(s), 2022. Published by Cambridge University Press

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References

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