Comptes Rendus
no. S3
Article de synthèse
Internal gravity waves versus inertial waves in the laboratory
[Ondes internes de gravité versus ondes inertielles au laboratoire]
Sylvain Joubaud1  ; Samuel Boury2 ; Philippe Odier1
1 Ens de Lyon, CNRS, Laboratoire de Physique, Lyon, France
2 Université Paris-Saclay, CNRS, FAST, 91405 Orsay, France
Comptes Rendus. Physique, Online first (2024), pp. 1-27.

Les fluides stratifiés en densité et/ou tournants sont très courants dans les écoulements géophysiques et astrophysiques et permettent respectivement la propagation d’ondes internes de gravité et d’ondes inertielles. Mathématiquement, la relation de dispersion particulière a la même forme pour les deux classes d’ondes et peut conduire à des résultats inattendus via amplification, résonance ou non-linéarités. Même si leur relation de dispersion est très similaire, les ondes internes de gravité et les ondes d’inertie ont des caractéristiques structurelles différentes et résultent de mécanismes physiques distincts. Comprendre les analogies et les différences dans leurs dynamiques est crucial pour étudier leurs rôles respectifs. Dans cette revue, nous décrirons des expériences en laboratoire qui ont étudié soit les ondes d’inertie dans un fluide homogène en rotation, soit les ondes internes de gravité dans un fluide stratifié en densité non tournant, afin de mettre en évidence à la fois les similitudes et les divergences entre ces deux types d’ondes. Nous nous concentrerons sur les phénomènes linéaires et non linéaires se produisant pour trois configurations différentes : les faisceaux d’ondes en géométrie 2D et 3D, les ondes axisymétriques, ainsi que les attracteurs d’ondes, spécificité de ces ondes. En particulier, nous décrirons l’influence de ces différentes configurations sur l’instabilité triadique résonante (TRI).

Density-stratified and/or rotating fluids are very common in geophysical and astrophysical flows and enable the propagation of respectively internal gravity waves and inertial waves. Their peculiar dispersion relation has the same mathematical form for both classes of waves and can lead to unexpected outcomes through amplification, resonance or non-linearities. Even though their dispersion relation is very similar, internal gravity waves and inertial waves have different structural characteristics and arise from distinct physical mechanisms. Understanding the analogies and the differences in their behaviors is crucial for studying their respective roles. In this review, we will describe laboratory experiments that have studied either inertial waves in rotating homogeneous fluids or internal gravity waves in non-rotating density stratified fluids to highlight both the similarities and the differences between these two types of waves. We will focus on linear and non-linear phenomena occurring for three different configurations: wave beams in 2D and in 3D geometry, axisymmetric waves, as well as wave attractors, a specific feature for these waves. In particular, we will describe the influence of these various configurations on the Triadic Resonant Instability (TRI).

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Première publication :
DOI : 10.5802/crphys.197
Keywords: Internal gravity waves, Inertial waves, Stratified fluid, Rotating fluid, Triadic Resonant Instability, wave attractors
Mots-clés : Ondes internes de gravité, Ondes inertielles, Fluides stratifiés, Fluides en rotation, Instabilité par résonance triadique, attracteurs d’ondes

Sylvain Joubaud 1 ; Samuel Boury 2 ; Philippe Odier 1

1 Ens de Lyon, CNRS, Laboratoire de Physique, Lyon, France
2 Université Paris-Saclay, CNRS, FAST, 91405 Orsay, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Sylvain Joubaud; Samuel Boury; Philippe Odier. Internal gravity waves versus inertial waves in the laboratory. Comptes Rendus. Physique, Online first (2024), pp. 1-27. doi : 10.5802/crphys.197.

[1] J. Lighthill Waves in fluids, Cambridge University Press, 1978 | Zbl

[2] D. E. Mowbray; B. S. H. Rarity The internal wave pattern produced by a sphere moving vertically in a density stratified liquid, J. Fluid Mech., Volume 30 (1967), pp. 489-495 | DOI

[3] B. R. Sutherland Internal gravity waves, Cambridge University Press, 2010 | Zbl

[4] H. P. Greenspan The Theory of Rotating Fluids, Cambridge University Press, 1968

[5] C. Garrett Internal Tides and Ocean Mixing, Science, Volume 301 (2003) no. 5641, pp. 1858-1859 | DOI

[6] C. Wunsch; R. Ferrari Vertical mixing, energy and the general circulation of the oceans, Annu. Rev. Fluid Mech., Volume 36 (2004), pp. 281-314 | DOI | Zbl

[7] J. A. MacKinnon; Z. Zhao; C. B. Whalen et al. Climate Process Team on Internal Wave–Driven Ocean Mixing, Bull. Am. Meteorol. Soc., Volume 98 (2017) no. 11, pp. 2429-2454 | DOI

[8] C. de Lavergne; S. Falahat; G. Madec; F. Roquet; J. Nycander; C. Vic Toward global maps of internal tide energy sinks, Ocean Model., Volume 137 (2019), pp. 52-75 | DOI

[9] F. Pollmann Global Characterization of the Ocean’s Internal Wave Spectrum, J. Phys. Oceanogr., Volume 50 (2020) no. 7, pp. 1871-1891 | DOI

[10] U. Achatz; O. Bühler; C. Staquet; W. R. Young Multiscale Wave-Turbulence Dynamics in the Atmosphere and Ocean, Oberwolfach Rep., Volume 19 (2022) no. 3, pp. 2467-2510 | DOI

[11] E. Becker; G. Schmitz Climatological Effects of Orography and Land–Sea Heating Contrasts on the Gravity Wave–Driven Circulation of the Mesosphere, J. Atmos. Sci., Volume 60 (2003) no. 1, pp. 103-118

[12] Y.-J. Kim; S. D. Eckermann; H.-Y. Chun An overview of the past, present and future of gravity‐wave drag parametrization for numerical climate and weather prediction models, Atmosphere-Ocean, Volume 41 (2003) no. 1, pp. 65-98 | DOI

[13] A. de la Cámara; F. Lott; M. Abalos Climatology of the middle atmosphere in LMDz: Impact of source-related parameterizations of gravity wave drag, Journal of Advances in Modeling Earth Systems, Volume 8 (2016) no. 4, pp. 1507-1525 | DOI

[14] L. A. Holt; F. Lott; R. R. Garcia et al. An evaluation of tropical waves and wave forcing of the QBO in the QBOi models, Q. J. R. Meteorol. Soc., Volume 148 (2022) no. 744, pp. 1541-1567 | DOI

[15] R. R. Kerswell; W. V. R. Malkus Tidal instability as the source for Io’s magnetic signature, Geophys. Res. Lett., Volume 25 (1998) no. 5, pp. 603-606 | DOI

[16] G. I. Ogilvie; D. N. C. Lin Tidal Dissipation in Rotating Giant Planets, Astrophys. J., Volume 610 (2004) no. 1, pp. 477-509 | DOI

[17] T. Sidery; N. Andersson; G. L. Comer Waves and instabilities in dissipative rotating superfluid neutron stars, Mon. Not. Roy. Astron. Soc., Volume 385 (2008) no. 1, pp. 335-348 | DOI

[18] M. Le Bars; D. Cébron; P. Le Gal Flows Driven by Libration, Precession, and Tides, Ann. Rev. Fluid Mech., Volume 47 (2015), pp. 163-193 | DOI

[19] M. Bouffard; B. Favier; D. Lecoanet; M. Le Bars Internal gravity waves in a stratified layer atop a convecting liquid core in a non-rotating spherical shell, Geophys. J. Int., Volume 228 (2021) no. 1, pp. 337-354 | DOI

[20] S. Dauxois; P. Odier; A. Venaille Instabilities of Internal Gravity Wave Beams, Ann. Rev. of Fluid Mech., Volume 50 (2018), pp. 131-156 | DOI | Zbl

[21] C. Staquet; J. Sommeria Internal gravity waves: From instabilities to turbulence, Annu. Rev. Fluid Mech., Volume 34 (2002), pp. 559-593 | DOI

[22] G. Veronis The analogy between rotating and stratified fluids, Ann. Rev. Fluid Mech., Volume 2 (1970), pp. 36-67 | DOI

[23] S. Medvedev; V. Zeitlin Parallels between stratification and rotation in hydrodynamics, and between both of them and external magnetic field in magnetohydrodynamics, with applications to nonlinear waves, IUTAM Symposium on Turbulence in the Atmosphere and Oceans (D. Dritschel, ed.) (IUTAM Bookseries), Volume 28, Springer (2010), pp. 27-37 | Zbl

[24] P. Maurer Approche expérimentale de la dynamique non-linéaire d’ondes internes en rotation, Ph. D. Thesis, Université de Lyon, France (2017)

[25] D. E. Mowbray; B. S. H. Rarity A theoretical and experimental investigation of the phase configuration of internal waves of small amplitude in a density stratified liquid, J. Fluid Mech., Volume 28 (1967) no. 1, pp. 1-16 | DOI

[26] T. Peacock; A. Tabaei Visualization of nonlinear effects in reflecting internal wave beams, Phys. Fluids, Volume 17 (2005) no. 6, 061702 | DOI | Zbl

[27] G. Brethouwer; P. Billant; E. Lindborg; J.-M. Chomaz Scaling analysis and simulation of strongly stratified turbulent flows, J. Fluid Mech., Volume 585 (2007), pp. 343-368 | DOI

[28] G. N. Ivey; K. B. Winters; J. R. Koseff Density stratification, turbulence, but how much mixing?, Annu. Rev. Fluid Mech., Volume 40 (2008), pp. 169-184 | DOI | Zbl

[29] C. P. Caulfield Layering, Instabilities, and Mixing in Turbulent Stratified Flows, Ann. Rev. Fluid Mech., Volume 53 (2021) no. 1, pp. 113-145 | DOI | Zbl

[30] P.-P. Cortet; L. Lanchon Turbulence of internal gravity waves in the laboratory, C. R. Phys (2024) (online first) | DOI

[31] S. Boury Energy and Buoyancy Transport by Inertia-Gravity Waves in Non-Linear Stratifications. Application to the Ocean, Ph. D. Thesis, Université de Lyon, Lyon, France (2020)

[32] D. W. Moore; P. G. Saffman The structure of free vertical shear layers in a rotating fluid and the motion produced by a slowly rising body, Philos. Trans. R. Soc. Lond., Ser. A, Volume 264 (1969) no. 1156, pp. 597-634 | DOI | Zbl

[33] N. H. Thomas; T. N. Stevenson A similarity solution for viscous internal waves, J. Fluid Mech., Volume 54 (1972) no. 3, pp. 495-506 | DOI | Zbl

[34] M. Nikurashin; R. Ferrari Radiation and Dissipation of Internal Waves Generated by Geostrophic Motions Impinging on Small-Scale Topography: Theory, J. Phys. Oceanogr., Volume 40 (2010) no. 5, pp. 1055-1074 | DOI

[35] A. M. M. Manders; J. J. Duistermaat; L. R. M. Maas Wave attractors in a smooth convex enclosed geometry, Phys. D: Nonlinear Phenom., Volume 186 (2003) no. 3-4, pp. 109-132 | DOI | Zbl

[36] P.-Y. Passaggia; P. Meunier; S. Le Dizès Response of a stratified boundary layer on a tilted wall to surface undulations, J. Fluid Mech., Volume 751 (2014), pp. 663-684 | DOI

[37] G. Davis; T. Dauxois; T. Jamin; S. Joubaud Energy budget in internal wave attractor experiments, J. Fluid Mech., Volume 880 (2019), pp. 743-763 | Zbl

[38] E. Horne; F. Beckebanze; D. Micard; P. Odier; L. R. M. Maas; S. Joubaud Particle transport induced by internal wave beam streaming in lateral boundary layers, J. Fluid Mech., Volume 870 (2019), pp. 848-869 | DOI

[39] S. Le Dizès Reflection of oscillating internal shear layers: nonlinear corrections, J. Fluid Mech., Volume 899 (2020), A21 | DOI | Zbl

[40] G. Bordes; F. Moisy; T. Dauxois; P.-P. Cortet Experimental evidence of a triadic resonance of plane inertial waves in a rotating fluid, Phys. Fluids, Volume 24 (2012) no. 1, 014105 | DOI

[41] A. Renaud; A. Venaille Boundary streaming by internal waves, J. Fluid Mech., Volume 858 (2019), pp. 71-90 | DOI | Zbl

[42] M. A. Calkins; J. Noir; J. D. Eldredge; J. M. Aurnou Axisymmetric simulations of libration-driven fluid dynamics in a spherical shell geometry, Phys. Fluids, Volume 22 (2010) no. 8, 086602 | DOI

[43] A. Tilgner Kinematic dynamos with precession driven flow in a sphere, Geophys. Astro. Fluid, Volume 101 (2007) no. 1, pp. 1-9 | DOI | Zbl

[44] C. Morize; M. Le Bars; P. Le Gal; A. Tilgner Experimental Determination of Zonal Winds Driven by Tides, Phys. Rev. Lett., Volume 104 (2010) no. 21, 214501 | DOI

[45] Y. Onuki; S. Joubaud; T. Dauxois Simulating turbulent mixing caused by local instability of internal gravity waves, J. Fluid Mech., Volume 915 (2021), A77 | DOI | Zbl

[46] C. B. Whalen; C. de Lavergne; A. C. Naveira Garabato; J. M. Klymak; J. A. MacKinnon; K. L. Sheen Internal wave-driven mixing: governing processes and consequences for climate, Nat. Rev. Earth Environ., Volume 1 (2020) no. 11, pp. 606-621 | DOI

[47] Y. Dossmann; B. Bourget; C. Brouzet; T. Dauxois; S. Joubaud; P. Odier Mixing by internal waves quantified using combined PIV/PLIF technique, Exp. Fluids, Volume 57 (2016) no. 8, 132 | DOI

[48] Y. Dossmann; F. Pollet; P. Odier; T. Dauxois Mixing and Formation of Layers by Internal Wave Forcing, J. Geophys. Res. Oceans, Volume 122 (2017) no. 12, pp. 9906-9917 | DOI

[49] J. M. H. Fortuin Theory and application of two supplementary methods of constructing density gradient columns, J. Polym. Sci., Volume 44 (1960) no. 144, pp. 505-515 | DOI

[50] G. Oster; M. Yamamoto Density Gradient Techniques, Chem. Rev., Volume 63 (1963) no. 3, pp. 257-268 | DOI

[51] D. F. Hill General density gradients in general domains: the “two-tank” method revisited, Exp. Fluids, Volume 32 (2002) no. 4, pp. 434-440 | DOI

[52] K. D. Stewart; C. J. Shakespeare; Y. Dossmann; A. McC. Hogg A simple technique for developing and visualising stratified fluid dynamics: the hot double-bucket, Exp. Fluids, Volume 62 (2021) no. 5, 103 | DOI

[53] S. B. Dalziel; G. O. Hughes; B. R. Sutherland Whole-field density measurements by ‘synthetic schlieren’, Exp. Fluids, Volume 28 (2000) no. 4, pp. 322-335 | DOI

[54] A. M. van Oers; R. de Kat; L. R. M. Maas Whole-field density measurements by digital image correlation, Exp. Fluids, Volume 64 (2023) no. 11, p. 175 | DOI

[55] D. Benielli; J. Sommeria Excitation of internal waves and stratified turbulence by parametric instability, Dynam. Atmos. Oceans, Volume 23 (1996) no. 1-4, pp. 335-343 (4th International Symposium on Stratified Flows, Grenoble, France, Jun 29 - Jul 02, 1994) | DOI

[56] J. Noir; D. Cébron; Mi. Le Bars; A. Sauret; J. M. Aurnou Experimental study of libration-driven zonal flows in non-axisymmetric containers, Phys. Earth Planet. Inter., Volume 204 (2012), pp. 1-10 | DOI

[57] C. Savaro; A. Campagne; M. C. Linares et al. Generation of weakly nonlinear turbulence of internal gravity waves in the Coriolis facility, Phys. Rev. Fluids, Volume 5 (2020) no. 7, 073801 | DOI

[58] C. Pacary; T. Dauxois; E. Ermanyuk; P. Metz; M. Moulin; S. Joubaud Observation of inertia-gravity wave attractors in an axisymmetric enclosed basin, Phys. Rev. Fluids, Volume 8 (2023) no. 10, 104802 | DOI

[59] T. Dauxois; A. Didier; E. Falcon Observation of near-critical reflection of internal waves in a stably stratified fluid, Phys. Fluids, Volume 16 (2004) no. 6, pp. 1936-1941 | DOI | Zbl

[60] B. Voisin; E. V. Ermanyuk; J.-B. Flór Internal wave generation by oscillation of a sphere, with application to internal tides, J. Fluid Mech., Volume 666 (2011), pp. 308-357 | DOI

[61] M. Duran-Matute; J.-B. Flór; F. S. Godeferd; C. Jause-Labert Turbulence and columnar vortex formation through inertial-wave focusing, Phys. Rev. E, Volume 87 (2013) no. 4, 041001 | DOI

[62] E. Monsalve; M. Brunet; B. Gallet; P.-P. Cortet Quantitative experimental observation of weak inertial-wave turbulence, Phys. Rev. Lett., Volume 125 (2020) no. 25, 254502 | DOI

[63] L. Gostiaux; T. Dauxois Laboratory experiments on the generation of internal tidal beams over steep slopes, Phys. Fluids, Volume 19 (2007) no. 2, 028102 | DOI | Zbl

[64] M. M. Scase; S. B. Dalziel Internal wave fields generated by a translating body in a stratified fluid: an experimental comparison, J. Fluid Mech., Volume 564 (2006), pp. 305-331 | DOI

[65] L. Gostiaux; H. Didelle; S. Mercier; T. Dauxois A novel internal waves generator, Exp. Fluids, Volume 42 (2007) no. 1, pp. 123-130 | DOI

[66] T. E. Dobra; A. G. W. Lawrie; S. B. Dalziel The magic carpet: an arbitrary spectrum wave maker for internal waves, Exp. Fluids, Volume 60 (2019), pp. 1-14 | DOI

[67] M. Brunet; T. Dauxois; P.-P. Cortet Linear and nonlinear regimes of an inertial wave attractor, Phys. Rev. Fluids, Volume 4 (2019) no. 3, 034801 | DOI

[68] P. Husseini; D. Varma; T. Dauxois; S. Joubaud; P. Odier; M. Mathur Experimental study on superharmonic wave generation by resonant interaction between internal wave modes, Phys. Rev. Fluids, Volume 5 (2020) no. 7, 074804 | DOI

[69] P. Maurer; S. J. Ghaemsaidi; S. Joubaud; T. Peacock; P. Odier An axisymmetric inertia-gravity wave generator, Exp. Fluids, Volume 58 (2017) no. 10, 143 | DOI

[70] W. V. R. Malkus An experimental study of global instabilities due to the tidal (elliptical) distortion of a rotating elastic cylinder, Geophys. Astrophys. Fluid Dyn., Volume 48 (1989) no. 1-3, pp. 123-134 | DOI

[71] B. Favier; A. Grannan; T. Le Reun; J. Aurnou; M. Le Bars The turbulent response to tidal and libration forcing, Astro Fluid: An International Conference in Memory of Professor Jean-Paul Zahn’s Great Scientific Achievements (EAS Publications Series), Volume 82, EDP Sciences, 2019, pp. 51-58 | DOI

[72] J. R. Munroe; B. R. Sutherland Generation of internal waves by sheared turbulence: experiments, Environ. Fluid Mech., Volume 8 (2008), pp. 527-534 | DOI

[73] V. Dorel; P. Le Gal; M. Le Bars Experimental study of the penetrative convection in gases, Phys. Rev. Fluids, Volume 8 (2023), 103501 | DOI

[74] P. Flandrin Time-Frequency/Time-Scale Analysis, Time-Frequency Toolbox for Matlab©, Wavelet Analysis and Its Applications, 10, Academic Press, San Diego, 1999 | Zbl

[75] Matthieu J. Mercier; Nicolas B. Garnier; Thierry Dauxois Reflection and diffraction of internal waves analyzed with the Hilbert transform, Phys. Fluids, Volume 20 (2008) no. 8, 086601 | DOI | Zbl

[76] M. Mathur; T. Peacock Internal wave interferometry, Phys. Rev. Lett., Volume 104 (2010) no. 11, 118501 | DOI

[77] R. Supekar; T. Peacock Interference and transmission of spatiotemporally locally forced internal waves in non-uniform stratifications, J. Fluid Mech., Volume 866 (2019), pp. 350-368 | DOI

[78] S. Boury; T. Peacock; P. Odier Excitation and resonant enhancement of axisymmetric internal wave modes, Phys. Rev. Fluids, Volume 4 (2019) no. 3, 034802 | DOI

[79] E. Horne; J. Schmitt; N. Pustelnik; S. Joubaud; P. Odier Variational Mode Decomposition for estimating critical reflected internal wave in stratified fluid, Exp. Fluids, Volume 62 (2021), 110 | DOI

[80] S. Boury; B. R. Sutherland; S. Joubaud; T. Peacock; P. Odier Axisymmetric internal wave tunneling (2024)

[81] K. M. Grayson; S. B. Dalziel; A. G. W. Lawrie The long view of triadic resonance instability in finite-width internal gravity wave beams, J. Fluid Mech., Volume 953 (2022), A22 | DOI

[82] J. Hazewinkel; S. B. Dalziel; A. Doelman; L. R. M. Maas Tracer transport by internal wave beams (2010)

[83] B. Bourget; T. Dauxois; S. Joubaud; P. Odier Experimental study of parametric subharmonic instability for internal plane waves, J. Fluid Mech., Volume 723 (2013), pp. 1-20 | DOI | Zbl

[84] B. Bourget; H. Scolan; T. Dauxois; M. Le Bars; P. Odier; S. Joubaud Finite-size effects in parametric subharmonic instability, J. Fluid Mech., Volume 759 (2014), pp. 739-750 | DOI

[85] G. Bordes Interactions non-linéaires d’ondes et tourbillons en milieu stratifié ou tournant, Ph. D. Thesis, Université de Lyon, Lyon, France (2012)

[86] R. E. Davis; A. Acrivos The stability of oscillatory internal waves, J. Fluid Mech., Volume 30 (1967) no. 4, pp. 723-736 | DOI | Zbl

[87] A. D. McEwan; R. M. Robinson Parametric-Instability of Internal Gravity-Waves, J. Fluid Mech., Volume 67 (1975) no. FEB25, pp. 667-687 | DOI | Zbl

[88] D. Benielli; J. Sommeria Excitation and breaking of internal gravity waves by parametric instability, J. Fluid Mech., Volume 374 (1998), pp. 117-144 | DOI | Zbl

[89] S. Joubaud; J. Munroe; P. Odier; T. Dauxois Experimental parametric subharmonic instability in stratified fluids, Phys. Fluids, Volume 24 (2012) no. 4, 041703 | DOI

[90] J. A. MacKinnon; M. H. Alford; O. Sun; R. Pinkel; Z. Zhao; J. Klymak Parametric subharmonic instability of the internal tide at 29 N, J. Phys. Oceanogr., Volume 43 (2013) no. 1, pp. 17-28 | DOI

[91] Q. Hu; X. Huang; Q. Xu; C. Zhou; S. Guan; X. Xu; W. Zhao; Q. Yang; J. Tian Parametric Subharmonic Instability of Diurnal Internal Tides in the Abyssal South China Sea, J. Phys. Oceanogr., Volume 53 (2023) no. 1, pp. 195-213 | DOI

[92] C. Brouzet; E. V. Ermanyuk; S. Joubaud; I. Sibgatullin; T. Dauxois Energy cascade in internal-wave attractors, Europhysics Letters, Volume 113 (2016) no. 4, 44001 | Zbl

[93] P. Maurer; S. Joubaud; P. Odier Generation and stability of inertia-gravity waves, J. Fluid Mech., Volume 808 (2016), pp. 539-561 | DOI | Zbl

[94] D. O. Mora; E. Monsalve; M. Brunet; T. Dauxois; P.-P. Cortet Three-dimensionality of the triadic resonance instability of a plane inertial wave, Phys. Rev. Fluids, Volume 6 (2021) no. 7, 074801 | DOI

[95] S. J. Ghaemsaidi; M. Mathur Three-dimensional small-scale instabilities of plane internal gravity waves, J. Fluid Mech., Volume 863 (2019), pp. 702-729 | DOI

[96] K. N. Kumar; T. K. Ramkumar; M. Krishnaiah MST radar observation of inertia-gravity waves generated from tropical cyclones, J. Atmos. Sol.-Terr. Phys., Volume 73 (2011), pp. 1890-1906 | Zbl

[97] W. H. Schubert; J. J. Hack; P. L. Silva Dias; S. R. Fulton Geostrophic adjustment in an axisymmetric vortex, J. Atmos. Sol.-Terr. Phys., Volume 37 (1980), pp. 1464-1484

[98] T. N. Stevenson Axisymmetric Internal Waves Generated by a Travelling Oscillating Body, J. Fluid Mech., Volume 35 (1969), pp. 219-224 | DOI

[99] M. R. Flynn; K. Onu; B. R. Sutherland Internal wave excitation by a vertically oscillating sphere, J. Fluid Mech., Volume 494 (2003), pp. 65-93 | DOI | Zbl

[100] J. K. Ansong; B. R. Sutherland Internal gravity waves generated by convective plumes, J. Fluid Mech., Volume 648 (2010), pp. 405-434 | DOI | Zbl

[101] S. Boury; P. Maurer; S. Joubaud; T. Peacock; P. Odier Triadic resonant instability in confined and unconfined axisymmetric geometries, J. Fluid Mech., Volume 957 (2023), A20 | DOI

[102] E. V. Ermanyuk; J.-B. Flór; B. Voisin Spatial Structure of First and Higher Harmonic Internal Waves from a Horizontally Oscillating Sphere, J. Fluid Mech., Volume 671 (2011), pp. 364-383 | Zbl

[103] S. J. Ghaemsaidi; H. V. Dosser; L. Rainville; T. Peacock The impact of multiple layering on internal wave transmission, J. Fluid Mech., Volume 789 (2016), pp. 617-629 | DOI

[104] T. Peacock; P. Weidman The Effect of Rotation on Conical Wave Beams in a Stratified Fluid, Exp. Fluids, Volume 39 (2005), pp. 32-37 | DOI

[105] E. V. Ermanyuk; N. D. Shmakova; J.-B. Flór Internal Wave Focusing by a Horizontally Oscillating Torus, J. Fluid Mech., Volume 813 (2017), pp. 695-715 | Zbl

[106] D. Guimbard L’instabilité elliptique en milieu stratifié tournant, Ph. D. Thesis, Université du Sud Toulon Var, France (2008)

[107] D. Guimbard; S. Le Dizès; M. Le Bars; P. Le Gal; S. Leblanc Elliptic instability of a stratified fluid in a rotating cylinder, J. Fluid Mech., Volume 660 (2010), pp. 240-257 | DOI

[108] S. Boury; T. Peacock; P. Odier Experimental generation of axisymmetric internal wave super-harmonics, Phys. Rev. Fluids, Volume 6 (2021) no. 6, 064801 | DOI

[109] N. D. Shmakova; J.-B. Flór Nonlinear aspects of focusing internal waves, J. Fluid Mech., Volume 862 (2019), R4 | DOI

[110] G. Michel Three-wave interactions among surface gravity waves in a cylindrical container, Phys. Rev. Fluids, Volume 4 (2019), 012801 | DOI

[111] L. E. Baker; B. R. Sutherland The evolution of superharmonics excited by internal tides in non-uniform stratification, J. Fluid Mech., Volume 891 (2020), R1 | DOI | Zbl

[112] T. Dauxois; W. R. Young Near-critical reflection of internal waves, J. Fluid Mech., Volume 390 (1999), pp. 271-295 | DOI

[113] O. M. Phillips Energy Transfer in Rotating Fluids by Reflection of Inertial Waves, The Physics of Fluids, Volume 6 (1963) no. 4, pp. 513-520 | DOI | Zbl

[114] C. C. Eriksen Observations of internal wave reflection off sloping bottoms, J. Geophys. Res. Oceans, Volume 87 (1982) no. C1, pp. 525-538 | DOI

[115] A. M. M. Manders; L. R. M. Maas On the three-dimensional structure of the inertial wave field in a rectangular basin with one sloping boundary, Fluid Dyn. Res., Volume 35 (2004) no. 1, pp. 1-21 | DOI | Zbl

[116] G. Pillet; L. R. M. Maas; T. Dauxois Internal wave attractors in 3D geometries : A dynamical systems approach, Eur. J. Mech. B Fluids, Volume 77 (2019), pp. 1-16 | DOI | Zbl

[117] B. Favier; S. Le Dizès Inertial wave super-attractor in a truncated elliptic cone, J. Fluid Mech., Volume 980 (2024), A6 | DOI | Zbl

[118] L. R. M Maas; F. P. A Lam Geometric focusing of internal waves, J. Fluid Mech., Volume 300 (1995), pp. 1-41 | DOI | Zbl

[119] J. Bajars; J. Frank; L. R. M. Maas On the appearance of internal wave attractors due to an initial or parametrically excited disturbance, J. Fluid Mech., Volume 714 (2013), pp. 283-311 | DOI | Zbl

[120] Y. Colin de Verdière; L. Saint-Raymond Attractors for Two-Dimensional Waves with Homogeneous Hamiltonians of Degree 0, Commun. Pure Appl. Math., Volume 73 (2020) no. 2, pp. 421-462 | DOI | Zbl

[121] Z. V. Makridin; A. K. Khe; I. N. Sibgatullin; E. V. Ermanyuk Forced internal wave attractors: Linear inviscid theory, Phys. Rev. Fluids, Volume 8 (2023) no. 8, 084801 | DOI

[122] I. N. Sibgatullin; E. V. Ermanyuk Internal and Inertial Wave Attractors: A Review, J. Appl. Mech. Tech. Phys., Volume 60 (2019) no. 2, pp. 284-302 | DOI

[123] M. E. Stern Trapping of low frequency oscillations in an equatorial boundary layer, Tellus, Volume 15 (1963), pp. 246-250 | DOI

[124] F. P. Bretherton Low frequency oscillations trapped near the equator, Tellus, Volume 16 (1964) no. 2, pp. 181-185 | DOI

[125] K. Stewartson On trapped oscillations of a rotating fluid in a thin spherical shell II, Tellus, Volume 24 (1972), pp. 283-287 | DOI

[126] M. Rieutord; L. Valdettaro Inertial waves in a rotating spherical shell, J. Fluid Mech., Volume 341 (1997), pp. 77-99 | Zbl

[127] M. Rieutord; B. Georgeot; L. Valdettaro Wave attractors in rotating fluids: a paradigm for ill-posed Cauchy problems, Phys. Rev. Lett., Volume 435 (2001), pp. 103-144 | DOI

[128] M. Rieutord; L. Valdettaro Viscous dissipation by tidally forced inertial modes in a rotating spherical shell, J. Fluid Mech., Volume 643 (2010), pp. 363-394 | DOI | Zbl

[129] A. Rabitti; L. R. M. Maas Equatorial wave attractors and inertial oscillations, J. Fluid Mech., Volume 729 (2013), pp. 445-470 | DOI

[130] B. Favier; A. J. Barker; C. Baruteau; G. I. Ogilvie Non-linear evolution of tidally forced inertial waves in rotating fluid bodies, Mon. Not. R. Astron. Soc., Volume 439 (2014), pp. 845-860 | DOI

[131] J. He; B. Favier; M. Rieutord; S. Le Dizès Internal shear layers in librating spherical shells: the case of attractors, J. Fluid Mech., Volume 974 (2023), A3 | DOI | Zbl

[132] A. M. M. Manders; L. R. M. Maas; T. Gerkema Observations of internal tides in the Mozambique Channel, J. Geophys. Res. Oceans, Volume 109 (2004) no. C12 | DOI

[133] W. Tang; T. Peacock Lagrangian coherent structures and internal wave attractors, Chaos, Volume 20 (2010) no. 1, 017508 | DOI | Zbl

[134] G. Wang; Q. Zheng; M. Lin; D. Dai; F. Qiao Three dimensional simulation of internal wave attractors in the Luzon Strait, Acta Oceanologica Sinica, Volume 34 (2015) no. 11, pp. 14-21 | DOI

[135] L. R. M. Maas; D. Benielli; J. Sommeria; F. P. A. Lam Observations of an internal wave attractor in a confined stably stratified fluid, Nature, Volume 388 (1997), pp. 557-561 | DOI

[136] L. R. M. Maas Wave focusing and ensuing mean flow due to symmetry breaking in rotating fluids, J. Fluid Mech., Volume 437 (2001), pp. 13-28 | Zbl

[137] J. Hazewinkel; P. van Breevoort; S. Dalziel; L. R. M. Maas Observations on the wavenumber spectrum and evolution of an internal wave attractor, J. Fluid Mech., Volume 598 (2008), pp. 373-382 | DOI

[138] N. Grisouard; C. Staquet; I. Pairaud Numerical simulation of a two-dimensional internal wave attractor, J. Fluid Mech., Volume 614 (2008), pp. 1-14 | DOI

[139] L. Jouve; G. I. Ogilvie Direct numerical simulations of an inertial wave attractor in linear and nonlinear regime, J. Fluid Mech., Volume 745 (2014), pp. 223-250 | DOI

[140] K. Wu; B. D. Welfert; J. M. Lopez Inertial wave attractors in librating cuboids, J. Fluid Mech., Volume 973 (2023), A20 | DOI | Zbl

[141] C. Brouzet; I. N. Sibgatullin; H. Scolan; E. V. Ermanyuk; T. Dauxois Internal wave attractors examined using laboratory experiments and 3D numerical simulations, J. Fluid Mech., Volume 793 (2016), pp. 109-131 | DOI

[142] F. Beckebanze; C. Brouzet; I. N. Sibgatullin; L. R. M. Maas Damping of quasi-two-dimensional internal wave attractors by rigid-wall friction, J. Fluid Mech., Volume 841 (2018), pp. 614-635 | DOI | Zbl

[143] G. Pillet; E. V. Ermanyuk; L. R. M. Maas; I. N. Sibgatullin; T. Dauxois Internal wave attractors in three-dimensional geometries: trapping by oblique reflection, J. Fluid Mech., Volume 845 (2018), pp. 203-225 | DOI

[144] C. Brouzet; E. Ermanyuk; S. Joubaud; G. Pillet; T. Dauxois Internal wave attractors: different scenarios of instability, J. Fluid Mech., Volume 811 (2017), pp. 544-568 | DOI

[145] A. Swart; A. Manders; U. Harlander; L. R. M. Maas Experimental observation of strong mixing due to internal wave focusing over sloping terrain, Dynam. Atmos. Oceans, Volume 50 (2010) no. 1, pp. 16-34 | DOI

[146] M. Klein; T. Seelig; M. V. Kurgansky et al. Inertial wave excitation and focusing in a liquid bounded by a frustum and a cylinder, J. Fluid Mech., Volume 751 (2014), pp. 255-297 | DOI

[147] I. Sibgatullin; X. Xu; A. Tretyakov; E. Ermanyuk Influence of geometry on energy flow and instability in inertial wave attractors for rotating annular frustum, AIP Conf. Proc., Volume 2116 (2019) no. 1, 030034 | DOI

[148] S. Boury; I. Sibgatullin; E. Ermanyuk et al. Vortex cluster arising from an axisymmetric inertial wave attractor, J. Fluid Mech., Volume 926 (2021), A12 | DOI

[149] N. Lanchon; D. O. Mora; E. Monsalve; P.-P. Cortet Internal wave turbulence in a stratified fluid with and without eigenmodes of the experimental domain, Phys. Rev. Fluids, Volume 8 (2023) no. 5, 054802 | DOI

[150] S. Galtier Inertial Wave Turbulence, Physics of Wave Turbulence, Cambridge University Press, 2022, pp. 155-178 | DOI

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