[La turbulence d’ondes internes de gravité au laboratoire]
Dans cet article, nous passons en revue les efforts récents de plusieurs équipes visant à observer au laboratoire une turbulence d’ondes internes de gravité dans un fluide stratifié en densité dans le régime faiblement non-linéaire. Ces études ont en commun d’adopter la même stratégie consistant à injecter l’énergie dans des ondes faiblement non-linéaires avant d’augmenter l’amplitude du forçage afin de déclencher une transition vers un régime de turbulence d’ondes. La motivation à ces travaux est double. D’une part, il est depuis longtemps proposé que la dynamique des petites échelles océaniques soit pilotée par le régime de turbulence d’ondes internes faiblement non-linéaire, sans toutefois qu’une confirmation définitive n’ait pour l’instant pu être apportée. Une meilleure compréhension de la turbulence d’ondes internes faiblement non-linéaire apparaît ainsi comme un levier important pour améliorer la paramétrisation des petites échelles océaniques dans les modèles climatiques. D’autre part, l’identification de solutions valides à la théorie de la turbulence d’ondes internes de gravité reste un problème ouvert et l’observation expérimentale de ce régime apparaît donc d’un grand intérêt pour guider les développements théoriques. Nous concluons que deux caractéristiques doivent être améliorées dans les expériences afin d’accéder à un véritable régime de turbulence d’ondes faiblement non-linéaire au laboratoire. Il faut d’une part contrôler les effets de taille finie et en particulier empêcher la concentration de l’énergie dans les modes propres d’ondes du domaine fluide. Il convient d’autre part d’augmenter sensiblement la longueur d’onde à laquelle l’énergie est injectée afin d’accéder à des nombres de Reynolds plus élevés et des nombres de Froude plus faibles pour construire une turbulence avec des spectres en loi de puissance développés tout en restant dans un régime faiblement non linéaire.
In this article, we review the recent efforts of several teams that aimed at observing in the laboratory a turbulence of internal gravity waves in a density stratified fluid in the weakly non-linear regime. The common feature to these studies is that they adopted the same strategy of injecting energy in weakly non-linear waves before increasing the forcing amplitude in order to trigger a transition to a wave turbulence regime. The motivation to these works is twofold. On the one hand, it has long been proposed that the dynamics of small oceanic scales is driven by a regime of weakly non-linear internal wave turbulence, without however a definitive confirmation so far. A better understanding of the weakly non-linear internal wave turbulence thus appears as an important lever for improving the parameterization of small oceanic scales in climate models. On the other hand, the identification of valid solutions to the theory of internal gravity wave turbulence is still an open problem, and the experimental observation of this regime is therefore of great interest to guide future theoretical developments. We conclude that two features should be improved in the experiments in order to access to a genuine weakly non-linear wave turbulence in the laboratory. First, one should mitigate the finite size effects and especially prevent the concentration of the energy in wave eigenmodes of the fluid domain. Second, one should implement a significant increase of the wavelength at which the energy is injected in order to access to larger Reynolds numbers and lower flow Froude numbers and build a turbulence with well developed power law spectra while remaining in the weakly non-linear regime.
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Mot clés : Ondes internes de gravité, Fluides stratifiés, Turbulence, Océans
Pierre-Philippe Cortet 1 ; Nicolas Lanchon 1
CC-BY 4.0
@article{CRPHYS_2024__25_S3_A2_0,
author = {Pierre-Philippe Cortet and Nicolas Lanchon},
title = {Turbulence of internal gravity waves in the laboratory},
journal = {Comptes Rendus. Physique},
publisher = {Acad\'emie des sciences, Paris},
year = {2024},
doi = {10.5802/crphys.192},
language = {en},
note = {Online first},
}
Pierre-Philippe Cortet; Nicolas Lanchon. Turbulence of internal gravity waves in the laboratory. Comptes Rendus. Physique, Online first (2024), pp. 1-20. doi : 10.5802/crphys.192.
[1] Internal gravity waves: From instabilities to turbulence, Annu. Rev. Fluid Mech., Volume 34 (2002), pp. 559-593 | DOI | Zbl
[2] Internal Gravity Waves, Cambridge University Press, 2010, 046603 | DOI
[3] Instabilities of internal wave beams, Annu. Rev. Fluid Mech., Volume 50 (2018), pp. 131-156 | DOI | Zbl
[4] Scale effects in internal wave attractors, Phys. Rev. Fluids, Volume 2 (2017), 114803 | DOI
[5] Linear and non linear regimes of an inertial wave attractor, Phys. Rev. Fluids, Volume 4 (2019), 034801 | DOI
[6] The Theory of Rotating Fluids, Cambridge University Press, 1968
[7] Waves in Fluids, Cambridge University Press, 1978
[8] Damping of quasi-two-dimensional internal wave attractors by rigid-wall friction, J. Fluid Mech., Volume 841 (2018), 034801, pp. 614-635 | DOI | Zbl
[9] On the amphidromic structure of inertial waves in a rectangular parallelepiped, Fluid Dyn. Res., Volume 33 (2003), 44001, p. 373 | DOI | Zbl
[10] Observation of inertia-gravity wave attractors in an axisymmetric enclosed basin, Phys. Rev. Fluids, Volume 8 (2023), 104802 | DOI
[11] Three-dimensionality of the triadic resonance instability of a plane inertial wave, Phys. Rev. Fluids, Volume 6 (2021), 074801, 014105 | DOI
[12] Nonlinear gravity-wave interactions in stratified turbulence, Theor. Comput. Fluid Dyn., Volume 28 (2014), p. 131-–145 | DOI | Zbl
[13] Geophysical Fluid Dynamics, Springer, 1987 | DOI
[14] Atmospheric and Oceanic Fluid Dynamics, Cambridge University Press, 2006, 114803 | DOI
[15] Vertical mixing, energy and the general circulation of the oceans, Annu. Rev. Fluid Mech., Volume 36 (2004), pp. 281-314 | DOI | Zbl
[16] et al. Climate Process Team on Internal Wave-Driven Ocean Mixing, Bull. Am. Meteorol. Soc., Volume 98 (2017), p. 2429-–2454 | DOI
[17] Parametrization schemes: Keys to Understanding Numerical Weather Prediction Models, Cambridge University Press, 2007, 043016 | DOI
[18] Finescale parameterizations of turbulent dissipation, J. Geophys. Res., Volume 119 (2014), pp. 1383-1419 | DOI
[19] Mixing efficiency in the ocean, Ann. Rev. Mar. Sci., Volume 10 (2018), pp. 443-473 | DOI | Zbl
[20] Interacting internal waves explain global patterns of interior ocean mixing (2023) (preprint, arXiv:2310.19980) | DOI
[21] Turbulence in Rotating, Stratified and Electrically Conducting Fluids, Cambridge University Press, 2013 | DOI
[22] Recent Progress in Stratified Turbulence, Ten Chapters in Turbulence (P. Davidson; Y. Kaneda; K. Sreenivasan, eds.), Cambridge University Press, Cambdrige, UK, 2012, 132, pp. 269-317 | DOI | Zbl
[23] Layering, Instabilities, and Mixing in Turbulent Stratified Flows, Annu. Rev. Fluid Mech., Volume 53 (2021), pp. 113-145 | DOI | Zbl
[24] Regimes of stratified turbulence at low Prandtl number (2023) (preprint, arXiv:2311.06424) | DOI
[25] Scaling analysis and simulation of strongly stratified turbulent flows, J. Fluid Mech., Volume 585 (2007), 204502, pp. 343-368 | DOI | Zbl
[26] Energy Spectra of Nonlocal Internal Gravity Wave Turbulence, Phys. Rev. Lett., Volume 131 (2023), 264001 | DOI
[27] Saturated-cascade similitude theory of gravity wave spectra, J. Geophys. Res., Volume 102 (1997), A129, pp. 29799-29817 | DOI
[28] Critical balance in magnetohydrodynamic, rotating and stratified turbulence: towards a universal scaling conjecture, J. Fluid Mech., Volume 677 (2011), pp. 134-153 | DOI | Zbl
[29] The energy cascade in a strongly stratified fluid, J. Fluid Mech., Volume 550 (2006), pp. 207-242 | DOI | Zbl
[30] Wave Turbulence, Springer, 2011 | DOI
[31] Physics of Wave Turbulence, Cambridge University Press, 2022 | DOI
[32] Oceanic internal-wave field: Theory of scale-invariant spectra, J. Phys. Oceanogr., Volume 40 (2010), p. 2605-–2623 | DOI
[33] The dynamic balance of internal waves, J. Phys. Oceanogr., Volume 11 (1981), pp. 970–-986 | DOI
[34] Toward regional characterizations of the oceanic internal wavefield, Rev. Geophys., Volume 49 (2011), RG4003 | DOI
[35] Kinetic equations and stationary energy spectra of weakly nonlinear internal gravity waves, Dyn. Atmos. Oceans, Volume 32 (2000), pp. 81-112 | DOI
[36] Hamiltonian Formalism and the Garrett–Munk Spectrum of Internal Waves in the Ocean, Phys. Rev. Lett., Volume 87 (2001), 168501 | DOI
[37] Energy Spectra of the Ocean’s Internal Wave Field: Theory and Observations, Phys. Rev. Lett., Volume 92 (2004), 128501 | DOI
[38] Downscale energy fluxes in scale-invariant oceanic internal wave turbulence, J. Fluid Mech., Volume 915 (2021), A129 | DOI | Zbl
[39] Kinetics of internal gravity waves beyond hydrostatic regime (2023) (preprint, arXiv:2311.14370) | DOI
[40] Stratified Turbulence: A Possible Interpretation of Some Geophysical Turbulence Measurements, J. Atmos. Sci. (2008)
[41] Stratified turbulence generated by internal gravity waves, J. Fluid Mech., Volume 546 (2006), pp. 313-339 | DOI | Zbl
[42] Stably stratified turbulence in the presence of largescale forcing, Phys. Rev. E, Volume 92 (2015), 013003, 041703 | DOI
[43] Self-similarity of strongly stratified inviscid flows, Phys. Fluids, Volume 13 (2001), pp. 1645–-1651 | DOI | Zbl
[44] Dynamics of turbulence strongly influenced by buoyancy, Phys. Fluids, Volume 15 (2003), 264001, p. 2047-–2059 | DOI | Zbl
[45] Experimental evidence for a new instability of a vertical columnar vortex pair in a strongly stratified fluid, J. Fluid Mech., Volume 418 (2000), pp. 167-188 | DOI | Zbl
[46] Theoretical analysis of the zigzag instability of a vertical columnar vortex pair in a strongly stratified fluid, J. Fluid Mech., Volume 419 (2000), pp. 29-63 | DOI | Zbl
[47] Stratified turbulence forced with columnar dipoles: numerical study, J. Fluid Mech., Volume 769 (2015), pp. 403-443 | DOI | Zbl
[48] Vertical spectra of stratified turbulence at large horizontal scales, Phys. Rev. Fluids, Volume 2 (2017), 104802, 054802 | DOI
[49] A climatology of atmospheric wavenumber spectra of wind and temperature observed by commercial aircraft, J. Atmos. Sci., Volume 42 (1985), 128501, pp. 950-960 | DOI
[50] Saturation and the ‘Universal’ spectrum for vertical profiles of horizontal scalar winds in the atmosphere, J. Geophys. Res., Volume 91 (1986), pp. 2742-2748 | DOI
[51] Equatorial mesoscale wind and temperature fluctuations in the lower atmosphere, J. Geophys. Res., Volume 106 (2001), pp. 1523-1532 | DOI
[52] Weak turbulence of the internal waves in the ocean, Izv. Acad. Sci. USSR Atmos. Oceanic Phys., Volume 13 (1977), 168501, pp. 187-193
[53] Internal waves in the ocean, Annu. Rev. Fluid Mech., Volume 11 (1979), pp. 339-369 | DOI
[54] Space-Time Scales of Internal Waves, Geophys. Fluid Dyn., Volume 2 (1972), pp. 225-264 | DOI
[55] Space-Time Scales of Internal Waves: A Progress report, J. Geophys. Res., Volume 80 (1975), 104802, pp. 291-297 | DOI | Zbl
[56] Experiments in Surface Gravity-Capillary Wave Turbulence, Annu. Rev. Fluid Mech., Volume 54 (2022), pp. 1-25 | DOI | Zbl
[57] Quantitative Experimental Observation of Weak Inertial-Wave Turbulence, Phys. Rev. Lett., Volume 125 (2020), 254502 | DOI
[58] Resonant Interaction of Oceanic Internal Waves, J. Geophys. Res., Volume 82 (1977), pp. 1397-1412 | DOI
[59] Excitation of internal waves and stratified turbulence by parametric instability, Dyn. Atmos. Oceans, Volume 23 (1996), pp. 335-343 | DOI
[60] Excitation and breaking of internal gravity waves by parametric instability, J. Fluid Mech., Volume 374 (1998), pp. 117-144 | DOI | Zbl
[61] Nonlinear Fate of Internal Wave Attractors, Phys. Rev. Lett., Volume 110 (2013), 234501, 074801 | DOI
[62] Energy cascade in internal-wave attractors, Eur. Phys. Lett., Volume 113 (2016), 44001 | DOI
[63] Internal wave attractors examined using laboratory experiments and 3D numerical simulations, J. Fluid Mech., Volume 793 (2016), pp. 109-131 | DOI
[64] Internal wave attractors: Different scenarios of instability, J. Fluid Mech., Volume 811 (2017), pp. 544-568 | DOI | Zbl
[65] Parametric instability and wave turbulence driven by tidal excitation of internal waves, J. Fluid Mech., Volume 840 (2018), pp. 498-529 | DOI | Zbl
[66] Succession of Resonances to Achieve Internal Wave Turbulence, Phys. Rev. Lett., Volume 124 (2020), 204502 | DOI
[67] Generation of weakly nonlinear turbulence of internal gravity waves in the Coriolis facility, Phys. Rev. Fluids, Volume 5 (2020), 073801, 104802 | DOI
[68] Experimental observations of internal wave turbulence transition in a stratified fluid, Phys. Rev. Fluids, Volume 7 (2022), 094802 | DOI
[69] From Internal Waves to Turbulence in a Stably Stratified Fluid, Phys. Rev. Lett., Volume 131 (2023), 264101 | DOI
[70] Internal wave turbulence in a stratified fluid with and without eigenmodes of the experimental domain, Phys. Rev. Fluids, Volume 8 (2023), 054802 | DOI
[71] Energy dissipation and vortex structure in freely decaying, stratified grid turbulence, Dyn. Atmos. Oceans, Volume 23 (1996), pp. 155-169 | DOI
[72] Decaying grid turbulence in a strongly stratified fluid, J. Fluid Mech., Volume 522 (2005), RG4003, pp. 1-33 | DOI | Zbl
[73] The decay of turbulence in thermally stratified flow, J. Fluid Mech., Volume 210 (1990), pp. 57-112 | DOI
[74] The evolution of grid-generated turbulence under conditions of stable thermal stratification, J. Fluid Mech., Volume 215 (1990), eadh2899, pp. 601-638 | DOI
[75] On the layers produced by rapidly oscillating a vertical grid in a uniformly stratified fluid, J. Fluid Mech., Volume 124 (1982), pp. 391-409 | DOI
[76] Experimental study of stratified turbulence forced with columnar dipoles, Phys. Fluids, Volume 26 (2014), 046603 | DOI
[77] Density gradient techniques, Chem. Rev., Volume 63 (1963), 013003, p. 257-–268 | DOI
[78] General density gradients in general domains: the ‘two-tank’ method revisited, Exp. Fluids, Volume 32 (2002), 264101, pp. 434-440 | DOI
[79] Refractive index matching in largescale stratified experiments, Exp. Fluids, Volume 31 (2001), 094802, pp. 119–-126 | DOI
[80] Mixing by internal waves quantified using combined PIV/PLIF technique, Exp. Fluids, Volume 57 (2016), 132 | DOI
[81] Disentangling inertial waves from eddy turbulence in a forced rotating-turbulence experiment, Phys. Rev. E, Volume 91 (2015), 043016 | DOI
[82] Internal gravity waves: parametric instability and deep ocean mixing, C. R. Mécanique, Volume 335 (2007), 073801, pp. 665-678 | DOI
[83] The Dynamics of the Upper Ocean, Cambridge University Press, 1966, 234501
[84] Near-critical reflection of internal waves, J. Fluid Mech., Volume 390 (1999), pp. 271-295 | DOI | Zbl
[85] Geometric focusing of internal waves, J. Fluid Mech., Volume 300 (1995), pp. 1-41 | DOI | Zbl
[86] Observation of an internal wave attractor in a confined stably stratified fluid, Nature, Volume 388 (1997), pp. 557–-561 | DOI | Zbl
[87] Numerical simulation of a two-dimensional internal wave attractor, J. Fluid Mech., Volume 614 (2008), pp. 1-14 | DOI
[88] Observations on the wavenumber spectrum and evolution of an internal wave attractor, J. Fluid Mech., Volume 598 (2008), pp. 373-382 | DOI | Zbl
[89] Experimental parametric subharmonic instability in stratified fluids, Phys. Fluids, Volume 24 (2012), 041703 | DOI
[90] Attracteurs d’ondes internes de gravité : des résonances en cascade : une approche expérimentale des régimes linéaire et non linéaire, Ph. D. Thesis, Université de Lyon, Lyon, France (2019)
[91] Experimental evidence of a triadic resonance of plane inertial waves in a rotating fluid, Phys. Fluids, Volume 24 (2012), 014105 | DOI
[92] Direct visualization of the quantum vortex lattice structure, oscillations, and destabilization in rotating He, Sci. adv., Volume 9 (2023), eadh2899 | DOI
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