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Resonant triad interactions of gravity waves in cylindrical basins

Published online by Cambridge University Press:  03 July 2023

Matthew Durey Open the ORCID record for Matthew Durey [Opens in a new window]  and
Paul A. Milewski Open the ORCID record for Paul A. Milewski [Opens in a new window]
Matthew Durey*
Affiliation:
School of Mathematics and Statistics, University of Glasgow, University Place, Glasgow G12 8QQ, UK
Paul A. Milewski
Affiliation:
Department of Mathematical Sciences, University of Bath, Claverton Down, Bath BA2 7AY, UK
*
†Email address for correspondence: matthew.durey@glasgow.ac.uk
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Abstract

We present the results of a theoretical investigation into the existence, evolution and excitation of resonant triads of nonlinear free-surface gravity waves confined to a cylinder of finite depth. It is well known that resonant triads are impossible for gravity waves in laterally unbounded domains; we demonstrate, however, that horizontal confinement of the fluid may induce resonant triads for particular fluid depths. For any three correlated wave modes arising in a cylinder of arbitrary cross-section, we prove necessary and sufficient conditions for the existence of a depth at which nonlinear resonance may arise, and show that the resultant critical depth is unique. We enumerate the low-frequency triads for circular cylinders, including a new class of resonances between standing and counter-propagating waves, and also briefly discuss annular and rectangular cylinders. Upon deriving the triad amplitude equations for a finite-depth cylinder of arbitrary cross-section, we deduce that the triad evolution is always periodic, and determine parameters controlling the efficiency of energy exchange. In order to excite a particular triad, we explore the influence of external forcing; in this case, the triad evolution may be periodic, quasi-periodic or chaotic. Finally, our results have potential implications on resonant water waves in man-made and natural basins, such as industrial-scale fluid tanks, harbours and bays.

JFM classification

Waves/Free-surface Flows: Surface gravity waves
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 966 , 10 July 2023 , A25
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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