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Triadic resonant instability in confined and unconfined axisymmetric geometries

Published online by Cambridge University Press:  21 February 2023

S. Boury Open the ORCID record for S. Boury [Opens in a new window] ,
P. Maurer ,
S. Joubaud Open the ORCID record for S. Joubaud [Opens in a new window] ,
T. Peacock Open the ORCID record for T. Peacock [Opens in a new window]  and
P. Odier
S. Boury*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA CNRS, Laboratoire de Physique, ENS de Lyon, F-69342 Lyon, France Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
P. Maurer
Affiliation:
CNRS, Laboratoire de Physique, ENS de Lyon, F-69342 Lyon, France
S. Joubaud
Affiliation:
CNRS, Laboratoire de Physique, ENS de Lyon, F-69342 Lyon, France Institut Universitaire de France (IUF), 1 rue Descartes 75005 Paris, France
T. Peacock
Affiliation:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
P. Odier
Affiliation:
CNRS, Laboratoire de Physique, ENS de Lyon, F-69342 Lyon, France
*
†Email address for correspondence: sb7918@nyu.edu
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Abstract

We present an investigation of the resonance conditions governing triad interactions of cylindrical internal waves, i.e. Kelvin modes, described by Bessel functions. Our analytical study, supported by experimental measurements, is performed both in confined and unconfined axisymmetric domains. We are interested in two conceptual questions: can we find resonance conditions for a triad of Kelvin modes? What is the impact of the boundary conditions on such resonances? In both the confined and unconfined cases, we show that sub-harmonics can be spontaneously generated from a primary wave field if they satisfy at least a resonance condition on their frequencies of the form $\omega _0 = \pm \omega _1 \pm \omega _2$. We demonstrate that the resulting triad is also spatially resonant, but that the resonance in the radial direction may not be exact in confined geometries due to the prevalence of boundary conditions – a key difference compared with Cartesian plane waves.

JFM classification

Geophysical and Geological Flows: Stratified flows Geophysical and Geological Flows: Internal waves Instability: Nonlinear instability
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 957 , 25 February 2023 , A20
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Copyright
© The Author(s), 2023. Published by Cambridge University Press

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