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Vortex cluster arising from an axisymmetric inertial wave attractor

Published online by Cambridge University Press:  06 September 2021

S. Boury Open the ORCID record for S. Boury [Opens in a new window] ,
I. Sibgatullin ,
E. Ermanyuk ,
N. Shmakova ,
P. Odier ,
S. Joubaud Open the ORCID record for S. Joubaud [Opens in a new window] ,
L.R.M. Maas Open the ORCID record for L.R.M. Maas [Opens in a new window]  and
T. Dauxois Open the ORCID record for T. Dauxois [Opens in a new window]
S. Boury*
Affiliation:
Courant Institute of Mathematical Sciences, New York University, New York, NY 10012, USA Univ Lyon, ENS de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
I. Sibgatullin
Affiliation:
P.P. Shirshov Institute of Oceanology, Nahimovskiy prospect 36, Moscow 117997, Russia Ivannikov Institute for System Programming, str. Alexander Solzhenitsyn 25, Moscow 109004, Russia
E. Ermanyuk
Affiliation:
Lavrentyev Institute of Hydrodynamics, av. Lavrentyev 15, Novosibirsk 630090, Russia
N. Shmakova
Affiliation:
Lavrentyev Institute of Hydrodynamics, av. Lavrentyev 15, Novosibirsk 630090, Russia
P. Odier
Affiliation:
Univ Lyon, ENS de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
S. Joubaud
Affiliation:
Univ Lyon, ENS de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France Institut Universitaire de France (IUF), 1 rue Descartes, 75005 Paris, France
L.R.M. Maas
Affiliation:
Institute for Marine and Atmospheric Research, Utrecht University, 3584 CC Utrecht, The Netherlands
T. Dauxois
Affiliation:
Univ Lyon, ENS de Lyon, CNRS, Laboratoire de Physique, F-69342 Lyon, France
*
†Email address for correspondence: sb7918@nyu.edu
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Abstract

We present an experimental and numerical study of the nonlinear dynamics of an inertial wave attractor in an axisymmetric geometrical setting. The rotating ring-shaped fluid domain is delimited by two vertical coaxial cylinders, a conical bottom and a horizontal wave generator at the top: the vertical cross-section is a trapezium, while the horizontal cross-section is a ring. Forcing is introduced via axisymmetric low-amplitude volume-conserving oscillatory motion of the upper lid. The experiment shows an important result: at sufficiently strong forcing and long time scale, a saturated fully nonlinear regime develops as a consequence of an energy transfer draining energy towards a slow two-dimensional manifold represented by a regular polygonal system of axially oriented cyclonic vortices undergoing a slow prograde motion around the inner cylinder. We explore the long-term nonlinear behaviour of the system by performing a series of numerical simulations for a set of fixed forcing amplitudes. This study shows a rich variety of dynamical regimes, including a linear behaviour, a triadic resonance instability, a progressive frequency enrichment reminiscent of weak inertial wave turbulence and the generation of a slow manifold in the form of a polygonal vortex cluster confirming the experimental observation. This vortex cluster is discussed in detail, and we show that it stems from the summation and merging of wave-like components of the vorticity field. The nature of these wave components, the possibility of their detection under general conditions and the ultimate fate of the vortex clusters at even longer time scale remain to be explored.

JFM classification

Geophysical and Geological Flows: Internal waves Geophysical and Geological Flows: Waves in rotating fluids
Type
JFM Papers
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Journal of Fluid Mechanics , Volume 926 , 10 November 2021 , A12
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© The Author(s), 2021. Published by Cambridge University Press

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References

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Boury et al. supplementary movie

Movie illustrating the precession of the Polygonal Vortex Cluster shown in figure 13 of the manuscript.

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