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Article de synthèse
Radiatively driven convection: diffusivity-free regimes of geophysical and astrophysical flows in the laboratory
[La convection engendrée par forçage radiatif, ou comment reproduire en laboratoire les régimes «  ultimes » des écoulements géo- et astrophysiques]
Comptes Rendus. Physique, Online first (2024), pp. 1-16.

Cet article traite du transport turbulent de chaleur engendré par convection thermique. Si la croyance dominante est que les propriétés de transport de l’écoulement turbulent sont asymptotiquement indépendantes des diffusivités moléculaires du fluide, ce régime dit « ultime » semble difficile à mettre en évidence dans les expériences traditionnelles de laboratoire (dispositif de Rayleigh–Bénard). Nous avons donc récemment développé un dispositif de convection par chauffage radiatif, dans lequel le fluide est chauffé en volume dans sa partie inférieure. Nous montrerons comment ce dispositif conduit naturellement à l’observation du régime ultime de convection thermique en laboratoire. Nous décrirons ensuite l’ajout d’une rotation globale à ce dispositif expérimental, ingrédient important des écoulements géophysiques et astrophysiques. Nous montrerons en particulier comment ce dispositif a permis la première observation expérimentale du régime ultime de convection en rotation rapide, dit régime de « turbulence géostrophique » .

We consider the turbulent heat transport induced by thermal convection. The widespread belief is that the transport properties of the turbulent flow should be independent of the tiny molecular diffusivities for asymptotically strong driving, but the associated “ultimate” scaling regime proves challenging to observe experimentally using standard convection cells (Rayleigh–Bénard geometry). We thus recently introduced an alternate experimental setup where convection is driven radiatively, with internal heating within the lower region of the body of fluid. This setup naturally leads to the ultimate regime of thermal convection. We then discuss how adding global rotation to the experimental setup has led to the first laboratory observation of the diffusivity-free regime of rapidly rotating turbulent convection, also known as the “geostrophic turbulence” scaling regime.

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DOI : 10.5802/crphys.207
Keywords: turbulent convection, geophysical and astrophysical fluid dynamics, rotating turbulence
Mots-clés : convection turbulente, dynamique des fluides géophysiques et astrophysiques, turbulence en rotation

Gabriel Hadjerci 1 ; Vincent Bouillaut 2 ; Benjamin Miquel 3 ; Sébastien Aumaître 1 ; Basile Gallet 1

1 Université Paris-Saclay, CNRS, CEA, Service de Physique de l’Etat Condensé, 91191 Gif-sur-Yvette, France
2 Onera Châtillon, 92320, Châtillon, France
3 Univ Lyon, CNRS, Ecole Centrale de Lyon, INSA Lyon, Université Claude Bernard Lyon 1, LMFA, UMR5509, 69130, Ecully, France
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {Radiatively driven convection: diffusivity-free regimes of geophysical and astrophysical flows in the laboratory},
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Gabriel Hadjerci; Vincent Bouillaut; Benjamin Miquel; Sébastien Aumaître; Basile Gallet. Radiatively driven convection: diffusivity-free regimes of geophysical and astrophysical flows in the laboratory. Comptes Rendus. Physique, Online first (2024), pp. 1-16. doi : 10.5802/crphys.207.

[1] D. J. Stevenson Turbulent thermal convection in the presence of rotation and a magnetic field: A heuristic theory, Geophys. Astrophys. Fluid Dyn., Volume 12 (1979) no. 1, pp. 139-169 | DOI | Zbl

[2] J. Marshall; F. Schott Open‐ocean convection: Observations, theory, and models, Rev. Geophys., Volume 37 (1999) no. 1, pp. 1-64 | DOI

[3] J. M. Aurnou; M. A. Calkins; J. S. Cheng et al. Rotating convective turbulence in Earth and planetary cores, Phys. Earth Planet. Inter., Volume 246 (2015), pp. 52-71 | DOI

[4] M. F. De Jong; L. De Steur Strong winter cooling over the Irminger Sea in winter 2014–2015, exceptional deep convection, and the emergence of anomalously low SST, Geophys. Res. Lett., Volume 43 (2016) no. 13, pp. 7106-7113 | DOI

[5] K. M. Soderlund Ocean dynamics of outer solar system satellites, Geophys. Res. Lett., Volume 46 (2019) no. 15, pp. 8700-8710 | DOI

[6] B. W. Hindman; N. A. Featherstone; K. Julien Morphological Classification of the Convective Regimes in Rotating Stars, Astrophys. J., Volume 898 (2020) no. 2, p. 120 | DOI

[7] S. Bire; W. Kang; A. Ramadhan; J.-M. Campin; J. Marshall Exploring ocean circulation on icy moons heated below, J. Geophys. Res. Planets, Volume 127 (2022) no. 3, e2021JE007025 | DOI

[8] U. Frisch Turbulence: The Legacy of A.N. Kolmogorov, Cambridge University Press, 1995 | DOI

[9] B. Castaing; G. Gunaratne; F. Heslot et al. Scaling of hard thermal turbulence in Rayleigh–Bénard convection, J. Fluid Mech., Volume 204 (1989), p. 1-–30 | DOI

[10] S. Cioni; S. Ciliberto; J. Sommeria Strongly turbulent Rayleigh–-Bénard convection in mercury: comparison with results at moderate Prandtl number, J. Fluid Mech., Volume 335 (1997), pp. 111–-140 | DOI

[11] A. Naert; T. Segawa; M. Sano High-Reynolds-number thermal turbulence in mercury, Phys. Rev. E, Volume 56 (1997) no. 2, p. R1302-R1305 | DOI

[12] X. Chavanne; F. Chillà; B. Chabaud; B. Castaing; B. Hébral Turbulent Rayleigh-–Bénard convection in gaseous and liquid He, Phys. Fluids, Volume 13 (2001) no. 5, 1300 | DOI | Zbl

[13] P.-E. Roche; F. Gauthier; R. Kaiser; J. Salort On the triggering of the Ultimate Regime of convection, New J. Phys., Volume 12 (2010) no. 8, 085014 | DOI

[14] X. He; D. Funfschilling; H. Nobach; E. Bodenschatz; G. Ahlers Transition to the Ultimate State of Turbulent Rayleigh–Bénard Convection, Phys. Rev. Lett., Volume 108 (2012) no. 2, 024502 | DOI

[15] C. R. Doering Absence of Evidence for the Ultimate State of Turbulent Rayleigh–Bénard Convection, Phys. Rev. Lett., Volume 124 (2020) no. 22, 229401 | DOI

[16] M. Gibert; H. Pabiou; F. Chillà; B. Castaing High-Rayleigh-Number Convection in a Vertical Channel, Phys. Rev. Lett., Volume 96 (2006) no. 8, 084501 | DOI

[17] M. Gibert; H. Pabiou; J.-C. Tisserand; B. Gertjerenken; B. Castaing; F. Chillà Heat convection in a vertical channel: Plumes versus turbulent diffusion, Phys. Fluids, Volume 21 (2009) no. 3, 035109 | DOI | Zbl

[18] J.-C. Tisserand; M. Creyssels; M. Gibert; B. Castaing; F. Chillà Convection in a vertical channel, New J. Phys., Volume 12 (2010) no. 7, 075024 | DOI

[19] M. R. Cholemari; J. H. Arakeri Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe, J. Fluid Mech., Volume 621 (2009), pp. 69-102 | DOI | Zbl

[20] S. S. Pawar; J. H. Arakeri Two regimes of flux scaling in axially homogeneous turbulent convection in vertical tube, Phys. Rev. Fluids, Volume 1 (2016) no. 4, 042401 | DOI

[21] Y. Shen; P. Tong; K.-Q. Xia Turbulent Convection over Rough Surfaces, Phys. Rev. Lett., Volume 76 (1996) no. 6, pp. 908-911 | DOI

[22] S. Ciliberto; C. Laroche Random Roughness of Boundary Increases the Turbulent Convection Scaling Exponent, Phys. Rev. Lett., Volume 82 (1999) no. 20, pp. 3998-4001 | DOI

[23] Y.-B. Du; P. Tong Turbulent thermal convection in a cell with ordered rough boundaries, J. Fluid Mech., Volume 407 (2000), pp. 57-84 | DOI

[24] P.-E. Roche; B. Castaing; B. Chabaud; B. Hébral Observation of the 1/2 power law in Rayleigh–Bénard convection, Phys. Rev. E, Volume 63 (2001) no. 4, 045303 | DOI

[25] X.-L. Qiu; K.-Q. Xia; P. Tong Experimental study of velocity boundary layer near a rough conducting surface in turbulent natural convection, J. Turbul., Volume 6 (2005), N30 | DOI

[26] J.-C. Tisserand; M. Creyssels; Y. Gasteuil; H. Pabiou; M. Gibert; B. Castaing; F. Chillà Comparison between rough and smooth plates within the same Rayleigh–-Bénard cell, Phys. Fluids, Volume 23 (2011) no. 1, 015105 | DOI

[27] E. Rusaouën; O. Liot; B. Castaing; J. Salort; F. Chillà Thermal transfer in Rayleigh-–Bénard cell with smooth or rough boundaries, J. Fluid Mech., Volume 837 (2018), pp. 443-460 | DOI

[28] S. Lepot; S. Aumaître; B. Gallet Radiative heating achieves the ultimate regime of thermal convection, Proc. Natl. Acad. Sci. USA, Volume 115 (2018) no. 36, pp. 8937-8941 | DOI | Zbl

[29] V. Bouillaut; S. Lepot; S. Aumaître; B. Gallet Transition to the ultimate regime in a radiatively driven convection experiment, J. Fluid Mech., Volume 861 (2019), R5 | DOI | Zbl

[30] V. Bouillaut; B. Miquel; K. Julien; S. Aumaître; B. Gallet Experimental observation of the geostrophic turbulence regime of rapidly rotating convection, Proc. Natl. Acad. Sci. USA, Volume 118 (2021) no. 44, e2105015118 | DOI

[31] E. A. Spiegel; G. Veronis On the Boussinesq approximation for a compressible fluid, Astrophys. J., Volume 131 (1960), pp. 442-447

[32] Louis N. Howard Heat transport by turbulent convection, J. Fluid Mech., Volume 17 (1963) no. 3, pp. 405-432 | DOI | Zbl

[33] Edward A. Spiegel A Generalization of the Mixing-Length Theory of Turbulent Convection., Astrophys. J., Volume 138 (1963), pp. 216-225 | DOI | Zbl

[34] E. A. Spiegel Convection in Stars I. Basic Boussinesq Convection, Annu. Rev. Astron. Astrophys., Volume 9 (1971) no. 1, pp. 323-352 | DOI

[35] R. H. Kraichnan Turbulent Thermal Convection at Arbitrary Prandtl Number, Phys. Fluids, Volume 5 (1962) no. 11, pp. 1374-1389 | DOI | Zbl

[36] Y.-C. Xie; K.-Q. Xia Turbulent thermal convection over rough plates with varying roughness geometries, J. Fluid Mech., Volume 825 (2017), pp. 573-599 | DOI

[37] X. Zhu; R. J. A. M. Stevens; R. Verzicco; D. Lohse Roughness-facilitated local 1/2 scaling does not imply the onset of the ultimate regime of thermal convection, Phys. Rev. Lett., Volume 119 (2017) no. 15, 154501 | DOI

[38] S. Toppaladoddi; A. J. Wells; C. R. Doering; J. S. Wettlaufer Thermal convection over fractal surfaces, J. Fluid Mech., Volume 907 (2021), A12 | DOI

[39] B. Miquel Coral: a parallel spectral solver for fluid dynamics and partial differential equations, J. Open Source Softw., Volume 6 (2021) no. 65, 2978 | DOI

[40] S. Kazemi; R. Ostilla-Mónico; D. Goluskin Transition between boundary-limited scaling and mixing-length scaling of turbulent transport in internally heated convection, Phys. Rev. Lett., Volume 129 (2022) no. 2, 024501 | DOI

[41] B. Miquel; V. Bouillaut; S. Aumaître; B. Gallet On the role of the Prandtl number in convection driven by heat sources and sinks, J. Fluid Mech., Volume 900 (2020), R1 | DOI | Zbl

[42] W. V. R. Malkus The heat transport and spectrum of thermal turbulence, Proc. R. Soc. Lond., Ser. A, Volume 225 (1954) no. 1161, pp. 196-212 | DOI | Zbl

[43] C. R. Doering; P. Constantin Variational bounds on energy dissipation in incompressible flows. III. Convection, Phys. Rev. E, Volume 53 (1996) no. 6, pp. 5957-5981 | DOI

[44] F. H. Busse On Howard’s upper bound for heat transport by turbulent convection, J. Fluid Mech., Volume 37 (1969), pp. 457-477 | DOI

[45] B. Miquel; S. Lepot; V. Bouillaut; B. Gallet Convection driven by internal heat sources and sinks: Heat transport beyond the mixing-length or ‘ultimate’ scaling regime, Phys. Rev. Fluids, Volume 4 (2019) no. 12, 121501 | DOI

[46] V. Bouillaut; B. Flesselles; B. Miquel; S. Aumaître; B. Gallet Velocity-informed upper bounds on the convective heat transport induced by internal heat sources and sinks, Philos. Trans. R. Soc. Lond., Ser. A, Volume 380 (2022) no. 2225, 20210034 | DOI

[47] B. Song; G. Fantuzzi; I. Tobasco Bounds on heat transfer by incompressible flows between balanced sources and sinks, Phys. D: Nonlinear Phenom., Volume 444 (2023), 133591 | DOI | Zbl

[48] E. M King; S. Stellmach; J. Noir; U. Hansen; J. M. Aurnou Boundary layer control of rotating convection systems, Nature, Volume 457 (2009) no. 7227, pp. 301-304 | DOI

[49] R. P. J. Kunnen The geostrophic regime of rapidly rotating turbulent convection, J. Turbul., Volume 22 (2021) no. 4-5, pp. 267-296 | DOI

[50] L. Terrien; B. Favier; E. Knobloch Suppression of wall modes in rapidly rotating Rayleigh–Bénard convection by narrow horizontal fins, Phys. Rev. Lett., Volume 130 (2023) no. 17, 174002 | DOI

[51] E. M. King; S. Stellmach; J. M. Aurnou Heat transfer by rapidly rotating Rayleigh–-Bénard convection, J. Fluid Mech., Volume 691 (2012), pp. 568-582 | DOI

[52] P. Joshi; H. Rajaei; R. P. J. Kunnen; H. J. H. Clercx Heat transfer in rotating Rayleigh–Bénard convection with rough plates, J. Fluid Mech., Volume 830 (2017), p. R3 | DOI

[53] V. K. Tripathi; P. Joshi Regimes in rotating Rayleigh– Bénard convection over rough boundaries, J. Fluid Mech., Volume 982 (2024), A15 | DOI

[54] F. Toselli; S. Musacchio; G. Boffetta Effects of rotation on the bulk turbulent convection, J. Fluid Mech., Volume 881 (2019), pp. 648-659 | DOI

[55] C. Liu; M. Sharma; K. Julien; E. Knobloch Fixed-flux Rayleigh–-Bénard convection in doubly periodic domains: generation of large-scale shear, J. Fluid Mech., Volume 979 (2024), A19 | DOI | Zbl

[56] K. Julien; E. Knobloch; J. Werne A New Class of Equations for Rotationally Constrained Flows, Theor. Comput. Fluid Dyn., Volume 11 (1998) no. 3-4, pp. 251-261 | DOI | Zbl

[57] K. Julien; E. Knobloch; R. Milliff; J. Werne Generalized quasi-geostrophy for spatially anisotropic rotationally constrained flows, J. Fluid Mech., Volume 555 (2006), pp. 233–-274 | DOI | Zbl

[58] K. Julien; E. Knobloch; A. M. Rubio; G. M. Vasil Heat Transport in Low-Rossby-Number Rayleigh–Bénard Convection, Phys. Rev. Lett., Volume 109 (2012) no. 25, 254503 | DOI

[59] K. Julien; A. M. Rubio; I. Grooms; E. Knobloch Statistical and physical balances in low Rossby number Rayleigh-–Bénard convection, Geophys. Astrophys. Fluid Dyn., Volume 106 (2012) no. 4-5, pp. 392-428 | DOI | Zbl

[60] A. J. Barker; A. M. Dempsey; Y. Lithwick Theory and simulations of rotating convection, Astrophys. J., Volume 791 (2014) no. 1, 13 | DOI

[61] S. Stellmach; M. Lischper; K. Julien et al. Approaching the asymptotic regime of rapidly rotating convection: boundary layers versus interior dynamics, Phys. Rev. Lett., Volume 113 (2014) no. 25, 254501 | DOI

[62] J. Song; O. Shishkina; X. Zhu Scaling regimes in rapidly rotating thermal convection at extreme Rayleigh numbers, J. Fluid Mech., Volume 984 (2024), A45 | DOI

[63] G. Hadjerci; V. Bouillaut; B. Miquel; B. Gallet Rapidly rotating radiatively driven convection: experimental and numerical validation of the ‘geostrophic turbulence’ scaling predictions, J. Fluid Mech., Volume 998 (2024), A9 | DOI

[64] J. M. Aurnou; S. Horn; K. Julien Connections between nonrotating, slowly rotating, and rapidly rotating turbulent convection transport scalings, Phys. Rev. Res., Volume 2 (2020) no. 4, 043115 | DOI

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