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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: [email protected]
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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

REFERENCES

Adriani, A., et al. 2020 Two-year observations of the Jupiter polar regions by JIRAM on board Juno. J. Geophys. Res.: Planet 125 (6), e2019JE006098.CrossRefGoogle Scholar
Adriani, A., et al. 2018 Clusters of cyclones encircling Jupiter's poles. Nature 555, 216–219.CrossRefGoogle ScholarPubMed
Albrecht, T., Blackburn, H.M., Lopez, J.M., Manasseh, R. & Meunier, P. 2015 Triadic resonances in precessing rapidly rotating cylinder flows. J. Fluid Mech. 778, R1.CrossRefGoogle Scholar
Albrecht, T., Blackburn, H.M., Lopez, J.M., Manasseh, R. & Meunier, P. 2018 On triadic resonance as an instability mechanism in precessing cylinder flow. J. Fluid Mech. 841, R3.CrossRefGoogle Scholar
Aldridge, K.D. & Toomre, A. 1969 Axisymmetric inertial oscillations of a fluid in a rotating spherical container. J. Fluid Mech. 27 (2), 307–323.CrossRefGoogle Scholar
Beckebanze, F., Grayson, K.M., Maas, L.R.M. & Dalziel, S.B. 2021 Experimental evidence of internal wave attractor signatures hidden in large-amplitude multi-frequency wave fields. J. Fluid Mech. 915, A41.CrossRefGoogle Scholar
Bellet, F., Godeferd, F., Scott, J. & Cambon, C. 2006 Wave turbulence in rapidly rotating flows. J. Fluid Mech. 562, 83–121.CrossRefGoogle Scholar
Bewley, G.P., Lathrop, D.P., Maas, L.R.M. & Sreenivasan, K.R. 2007 Inertial waves in rotating grid turbulence. Phys. Fluids 19 (7), 071701.CrossRefGoogle Scholar
Boisson, J., Lamriben, C., Maas, L.R.M., Cortet, P.-P. & Moisy, F. 2012 Inertial waves and modes excited by the libration of a rotating cube. Phys. Fluids 24 (7), 076602.CrossRefGoogle Scholar
Bordes, G., Moisy, F., Dauxois, T. & , Cortet, P.-P. 2012 Experimental evidence of a triadic resonance of plane inertial waves in a rotating fluid. Phys. Fluids 24, 014105.CrossRefGoogle Scholar
Bourget, B., Dauxois, T., Joubaud, S. & Odier, P. 2013 Experimental study of parametric subharmonic instability for internal plane waves. J. Fluid Mech. 723, 1–20.CrossRefGoogle Scholar
Boury, S. 2020 Energy and Buoyancy Transport by Inertia-Gravity Waves in Non-Linear Stratifications. Application to the Ocean. Université de Lyon.Google Scholar
Boury, S., Peacock, T. & Odier, P. 2019 Excitation and resonant enhancement of axisymmetric internal wave modes. Phys. Rev. Fluids 4, 034802.CrossRefGoogle Scholar
Boury, S., Peacock, T. & Odier, P. 2021 Experimental generation of axisymmetric internal wave super-harmonics. Phys. Rev. Fluids 6, 064801.Google Scholar
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177–191.CrossRefGoogle Scholar
Bretherton, F.P. 1964 Low frequency oscillations trapped near the equator. Tellus 16, 181–185.CrossRefGoogle Scholar
Brouzet, C., Ermanyuk, E.V., Joubaud, S., Pillet, G. & Dauxois, T. 2017 a Internal wave attractors: different scenarios of instability. J. Fluid Mech. 811, 544–568.CrossRefGoogle Scholar
Brouzet, C., Ermanyuk, E.V., Joubaud, S., Sibgatullin, I.N. & Dauxois, T. 2016 a Energy cascade in internal wave attractors. Europhys. Lett. 113, 44001.CrossRefGoogle Scholar
Brouzet, C., Sibgatullin, I.N., Ermanyuk, E.V., Joubaud, S. & Dauxois, T. 2017 b Scale effects in internal wave attractors. Phys. Rev. Fluids 2, 114803.CrossRefGoogle Scholar
Brouzet, C., Sibgatullin, I.N., Scolan, H., Ermanyuk, E.V. & Dauxois, T. 2016 b Internal wave attractors examined using laboratory experiments and 3D numerical simulations. J. Fluid Mech. 793, 109–131.CrossRefGoogle Scholar
Brunet, M., Dauxois, T. & Cortet, P.-P. 2019 Linear and nonlinear regimes of an inertial wave attractor. Phys. Rev. Fluids 4, 034801.CrossRefGoogle Scholar
Brunet, M., Gallet, B. & Cortet, P.-P. 2020 Shortcut to geostrophy in wave-driven rotating turbulence: the quartetic instability. Phys. Rev. Lett. 124, 124501.Google ScholarPubMed
Busse, F.H. 2010 Mean zonal flows generated by librations of a rotating spherical cavity. J. Fluid Mech. 650, 505–512.CrossRefGoogle Scholar
Cambon, C., Mansour, N.N. & Godeferd, F.S. 1997 Energy transfer in rotating turbulence. J. Fluid Mech. 337, 303–332.CrossRefGoogle Scholar
Cebron, D., Vidal, J., Schaeffer, N., Borderies, A. & Sauret, A. 2021 Mean zonal flows induced by weak mechanical forcings in rotating spheroids. J. Fluid Mech. 916, A39.CrossRefGoogle Scholar
Cho, J.Y.-K. & Polvani, L.M. 1996 The emergence of jets and vortices in freely evolving, shallow-water turbulence on a sphere. Phys. Fluids 8 (6), 1531–1552.CrossRefGoogle Scholar
Dauxois, T. & Young, W.R. 1999 Near-critical reflection of internal waves. J. Fluid Mech. 390, 271–295.CrossRefGoogle Scholar
Davidson, P.A. 2013 Turbulence in Rotating, Stratified and Electrically Conducting Fluids. Cambridge University Press.CrossRefGoogle Scholar
Davis, G. 2019 Attracteurs d'ondes internes de gravité: des résonances en cascade. Une approche expérimentale des régimes linéaire et non-linéaire. Université de Lyon.Google Scholar
Davis, G., Dauxois, T., Jamin, T. & Joubaud, S. 2019 Energy budget in internal wave attractor experiments. J. Fluid Mech. 880, 743–763.CrossRefGoogle Scholar
Davis, G., Jamin, T., Deleuze, J., Joubaud, S. & Dauxois, T. 2020 Succession of resonances to achieve internal wave turbulence. Phys. Rev. Lett. 124, 204502.CrossRefGoogle ScholarPubMed
Deville, M.O., Fischer, P.F. & Mund, E.H. 2002 High-Order Methods for Incompressible Fluid Flows. Cambridge University Press.CrossRefGoogle Scholar
Dintrans, B., Rieutord, M. & Valdettaro, L. 1999 Gravito-inertial waves in a rotating stratified sphere or spherical shell. J. Fluid Mech. 398, 271–297.CrossRefGoogle Scholar
Eriksen, C.C. 1982 Observations of internal wave reflection off sloping bottoms. J. Geophys. Res. 87 (C1), 525–538.CrossRefGoogle Scholar
Fan, B. & Akylas, T.R. 2019 Effect of background mean flow on PSI of internal wave beams. J. Fluid Mech. 869, R1.CrossRefGoogle Scholar
Fan, B. & Akylas, T.R. 2020 Finite-amplitude instabilities of thin internal wave beams: experiments and theory. J. Fluid Mech. 904, A16.CrossRefGoogle Scholar
Fincham, A. & Delerce, G. 2000 Advanced optimization of correlation imaging velocimetry algorithms. Exp. Fluids. 29, 13–22.CrossRefGoogle Scholar
Fischer, P. 1997 An overlapping Schwarz method for spectral element solution of the incompressible Navier–Stokes equations. J. Comput. Phys. 133 (1), 84–101.CrossRefGoogle Scholar
Fischer, P. & Ronquist, E. 1994 Spectral element methods for large scale parallel Navier–Stokes calculations. Comput. Meth. Appl. Mech. Engng 116 (1–4), 69–76.CrossRefGoogle Scholar
Flandrin, P. 1999 Time-Frequency/Time-Scale Analysis, Time-Frequency Toolbox for Matlab. Academic.Google Scholar
Friedlander, S. & Siegmann, W.L. 1982 Internal waves in a contained rotating stratified fluid. J. Fluid Mech. 114, 123–156.CrossRefGoogle Scholar
Galtier, S. 2003 Weak inertial-wave turbulence theory. Phys. Rev. E 68, 015301.CrossRefGoogle ScholarPubMed
Godeferd, F.S. & Lollini, L. 1999 Direct numerical simulations of turbulence with confinement and rotation. J. Fluid Mech. 393, 257–308.CrossRefGoogle Scholar
Godeferd, F.S. & Moisy, F. 2015 Structure and dynamics of rotating turbulence: a review of recent experimental and numerical results. Appl. Mech. Rev. 493, 59–88.Google Scholar
Görtler, H. 1943 Über eine schwingungserscheinung in flüssigkeiten mit stabiler dichteschichtung. Z. Angew. Math. Mech. 23, 65–71.CrossRefGoogle Scholar
Gostiaux, L., Didelle, H., Mercier, S. & Dauxois, T. 2006 A novel internal waves generator. Exp. Fluids 42, 123–130.CrossRefGoogle Scholar
Greenspan, H.P. 1968 The Theory of Rotating Fluids. Cambridge University Press.Google Scholar
Grisouard, N., Staquet, C. & Pairaud, I. 2008 Numerical simulation of a two-dimensional internal wave attractor. J. Fluid Mech. 614, 1–14.CrossRefGoogle Scholar
Hazewinkel, J., van Breevoort, P., Dalziel, S. & Maas, L.R.M. 2008 Observations on the wavenumber spectrum and evolution of an internal wave attractor. J. Fluid Mech. 598, 373–382.CrossRefGoogle Scholar
Hazewinkel, J., Maas, L.R.M. & Dalziel, S. 2011 Tomographic reconstruction of internal wave patterns in a paraboloid. Exp. Fluids 50, 247–258.CrossRefGoogle Scholar
Hendershott, M.C. 1969 Impulsively started oscillations in a rotating stratified fluid. J. Fluid Mech. 36 (3), 513–527.CrossRefGoogle Scholar
Hopfinger, E.J. & van Heijst, G.J.F. 1993 Vortices in rotating fluids. Annu. Rev. Fluid Mech. 25, 241–289.CrossRefGoogle Scholar
Hopfinger, E.J., Browand, F.K. & Gagne, Y. 1982 Turbulence and waves in a rotating tank. J. Fluid Mech. 125, 505–534.CrossRefGoogle Scholar
Jeong, J. & Hussain, F. 1995 On the identification of a vortex. J. Fluid Mech. 285, 69–94.CrossRefGoogle Scholar
Jouve, L. & Ogilvie, G.I. 2014 Direct numerical simulations of an inertial wave attractor in linear and nonlinear regime. J. Fluid Mech. 745, 223–250.CrossRefGoogle Scholar
Klein, M., Seelig, T., Kurgansky, M.V., Ghasemi V., A., Dan Borcia, I., Will, A., Schaller, E., Egbers, C. & Harlander, U. 2014 Inertial wave excitation and focusing in a liquid bounded by a frustum and a cylinder. J. Fluid Mech. 751, 255–297.CrossRefGoogle Scholar
Lagrange, R., Meunier, P. & Eloy, C. 2016 Triadic instability of a non-resonant precessing fluid cylinder. C. R. Méc 344, 418–433.CrossRefGoogle Scholar
Lam, F.P.A. & Maas, L.R.M. 2008 Internal wave focusing revisited; a reanalysis and new theoretical links. Fluid Dyn. Res. 40, 95–122.CrossRefGoogle Scholar
Lamriben, C., Cortet, P.-P., Moisy, F. & Maas, L.R.M. 2011 Excitation of inertial modes in a closed grid turbulence experiment under rotation. Phys. Fluids 23 (1), 015102.CrossRefGoogle Scholar
Le Reun, T., Favier, B., Barker, A.J. & Le Bars, M. 2017 Inertial wave turbulence driven by elliptical instability. Phys. Rev. Lett. 119, 034502.CrossRefGoogle ScholarPubMed
Le Reun, T., Favier, B. & Le Bars, M. 2019 Experimental study of the non-linear saturation of the elliptical instability: inertial wave turbulence versus geostrophic turbulence. J. Fluid Mech. 879, 296–326.CrossRefGoogle Scholar
Lin, Y., Noir, J. & Jackson, A. 2014 Experimental study of fluid flows in a precessing cylindrical annulus. Phys. Fluids 26, 046604.CrossRefGoogle Scholar
Lopez, J.M., Hart, J.E., Marques, F., Kittelman, S. & Shen, J. 2002 Instability and mode interactions in a differentially driven rotating cylinder. J. Fluid Mech. 462, 383–409.CrossRefGoogle Scholar
Lopez, J.M. & Marques, F. 2018 Rapidly rotating precessing cylinder flows: forced triadic resonances. J. Fluid Mech. 839, 239–270.CrossRefGoogle Scholar
Maas, L.R.M. 2001 Wave focusing and ensuing mean flow due to symmetry breaking in rotating fluids. J. Fluid Mech. 437, 13–28.CrossRefGoogle Scholar
Maas, L.R.M. 2003 On the amphidromic structure of inertial waves in a rectangular parallelepiped. Fluid Dyn. Res. 33 (4), 373–401.CrossRefGoogle Scholar
Maas, L.R.M. 2005 Wave attractors: linear yet non linear. Intl J. Bifurcation Chaos 15 (9), 2757–2782.Google Scholar
Maas, L.R.M., Benielli, D., Sommeria, J. & Lam, F.P.A. 1997 Observations of an internal wave attractor in a confined stably stratified fluid. Nature 388, 557–561.CrossRefGoogle Scholar
Maas, L.R.M. & Harlander, U. 2007 Equatorial wave attractors and inertial oscillations. J. Fluid Mech. 570, 47–67.CrossRefGoogle Scholar
Maas, L.R.M. & Lam, F.P.A. 1995 Geometric focusing of internal waves. J. Fluid Mech. 300, 1–41.CrossRefGoogle Scholar
Manders, A.M.M. & Maas, L.R.M. 2003 Observations of inertial waves in a rectangular basin with one sloping boundary. J. Fluid Mech. 493, 59–88.CrossRefGoogle Scholar
Manders, A.M.M. & Maas, L.R.M. 2004 On the three-dimensional structure of the inertial wave field in a rectangular basin with one sloping boundary. Fluid Dyn. Res. 35, 1–21.CrossRefGoogle Scholar
Marques, F. & Lopez, J.M. 2015 Precession of a rapidly rotating cylinder flow: traverse through resonance. J. Fluid Mech. 782, 63–98.CrossRefGoogle Scholar
Maurer, P., Ghaemsaidi, S.J., Joubaud, S., Peacock, T. & Odier, P. 2017 An axisymmetric inertia-gravity wave generator. Exp. Fluids 58, 143.CrossRefGoogle Scholar
Maurer, P., Joubaud, S. & Odier, P. 2016 Generation and stability of inertia–gravity waves. J. Fluid Mech. 808, 539–561.CrossRefGoogle Scholar
McEwan, A.D. 1970 Inertial oscillations in a rotating fluid cylinder. J. Fluid Mech. 30 (3), 603–640.CrossRefGoogle Scholar
McEwan, A.D. 1971 Degeneration of resonantly excited standing internal gravity waves. J. Fluid Mech. 50, 431–448.CrossRefGoogle Scholar
Mercier, M.J., Garnier, N.B. & Dauxois, T. 2008 Refection and diffraction of internal waves analysed with the Hilbert transform. Phys. Fluids 20 (8), 086601.CrossRefGoogle Scholar
Mowbray, D.E. & Rarity, B.S.H. 1967 A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid. J. Fluid Mech. 28 (1), 1–16.CrossRefGoogle Scholar
Ogilvie, G.I. 2005 Wave attractors and the asymptotic dissipation rate of tidal disturbances. J. Fluid Mech. 543, 19–44.CrossRefGoogle Scholar
Pedley, T. 1969 On the stability of viscous flow in a rapidly rotating pipe. J. Fluid Mech. 36, 177–191.Google Scholar
Phillips, O.M. 1963 Energy transfer in rotating fluids by reflection of inertial waves. Phys. Fluids 6, 513–520.CrossRefGoogle Scholar
Pillet, G., Ermanyuk, E.V., Maas, L.R.M., Sibgatullin, I.N. & Dauxois, T. 2018 Internal wave attractors in three-dimensional geometries: trapping by oblique reflection. J. Fluid Mech. 845, 203–225.CrossRefGoogle Scholar
Rabitti, A. & Maas, L.R.M. 2013 Equatorial wave attractors and inertial oscillations. J. Fluid Mech. 729, 445–470.CrossRefGoogle Scholar
Reinaud, J.N. 2019 Three-dimensional quasi-geostrophic vortex equilibria with m-fold symmetry. J. Fluid Mech. 863, 32–59.CrossRefGoogle Scholar
Richet, O., Muller, C. & Chomaz, J.-M. 2017 Impact of a mean current on the internal tide energy dissipation at the critical latitude. J. Phys. Oceanogr. 47, 1457–1472.CrossRefGoogle Scholar
Rieutord, M., Georgeot, B. & Valdettaro, L. 2000 Inertial waves in a rotating spherical shell: attractors and asymptotic spectrum. J. Fluid Mech. 85, 4277–4280.Google Scholar
Rieutord, M., Georgeot, B. & Valdettaro, L. 2001 Wave attractors in rotating fluids: a paradigm for ill-posed cauchy problems. Phys. Rev. Lett. 435, 103–144.Google Scholar
Rieutord, M. & Valdettaro, L. 1997 Inertial waves in a rotating spherical shell. J. Fluid Mech. 341, 77–99.CrossRefGoogle Scholar
Rieutord, M. & Valdettaro, L. 2010 Viscous dissipation by tidally forced inertial modes in a rotating spherical shell. J. Fluid Mech. 643, 363–394.CrossRefGoogle Scholar
Rossby, C.G. 1939 Relation between variations in the intensity of the zonal circulation of the atmosphere and the displacements of the semi-permanent centers of action. J. Mar. Res. 2, 38–55.CrossRefGoogle Scholar
Sauret, A., Cébron, D., Le Bars, M. & Le Dizès, S. 2012 Fluid flows in a librating cylinder. Phys. Fluids 24, 026603.CrossRefGoogle Scholar
Scolan, H., Ermanyuk, E. & Dauxois, T. 2013 Nonlinear fate of internal waves attractors. Phys. Rev. Lett. 110, 234501.CrossRefGoogle Scholar
Scott, R.K. & Polvani, L.M. 2007 Forced-dissipative shallow-water turbulence on the sphere and the atmospheric circulation of the giant planets. J. Atmos. Sci. 64, 3158–3176.CrossRefGoogle Scholar
Sibgatullin, I.N. & Ermanyuk, E.V. 2019 Internal and inertial wave attractors: a review. J. Appl. Mech. Tech. Phys. 60, 284–302.CrossRefGoogle Scholar
Sibgatullin, I.N., Ermanyuk, E.V., Maas, L.R.M., Xu, X. & Dauxois, T. 2017 Direct numerical simulation of three-dimensional inertial wave attractors. In IEEE Xplore. Proceedings 2017 Ivannikov ISPRAS Open Conference (ISPRAS), 30 November–1 December 2017, Moscow, Russia, pp. 137–143.Google Scholar
Stern, M.E. 1963 Trapping of low frequency oscillations in an equatorial boundary layer. Tellus 15, 246–250.CrossRefGoogle Scholar
Stewartson, K. 1971 On trapped oscillations of a rotating fluid in a thin spherical shell. Tellus 23, 506–510.CrossRefGoogle Scholar
Stewartson, K. 1972 On trapped oscillations of a rotating fluid in a thin spherical shell II. Tellus 24, 283–287.CrossRefGoogle Scholar
Thomas, N.H. & Stevenson, T.N. 1972 A similarity solution for viscous internal waves. J. Fluid Mech. 54, 495–506.CrossRefGoogle Scholar
Waleffe, F. 1993 Inertial transfers in the helical decomposition. Phys. Fluids A 5, 677–685.CrossRefGoogle Scholar
Wu, K., Welfert, B.D. & Lopez, J.M. 2020 a Precessing cube: resonant excitation of modes and triadic resonance. J. Fluid Mech. 887, A6.CrossRefGoogle Scholar
Wu, K., Welfert, B.D. & Lopez, J.M. 2020 b Reflections and focusing of inertial waves in a librating cube with the rotation axis oblique to its faces. J. Fluid Mech. 896, A5.CrossRefGoogle Scholar
Yarom, E. & Sharon, E. 2014 Experimental observation of steady inertial wave turbulence in deep rotating flows. Nat. Phys. 10, 510–514.CrossRefGoogle Scholar

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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