Comptes Rendus
Article de synthèse
Seven decades of exploring planetary interiors with rotating convection experiments
[Sept décennies d’exploration des intérieurs de planètes par les expériences de convection en rotation]
Comptes Rendus. Physique, Online first (2024), pp. 1-55.

Les intérieurs de toutes les planètes du système solaire sont constitués de couches internes, dont la plupart sont fluides. Quand ces couches sont sujettes à un gradient de température ou de composition chimique super-adiabatiques, un écoulement convectif s’installe qui transporte chaleur et moment angulaire. De plus, les planètes tournent extrêment vite. Ainsi, le processus-clé qui sous-tend l’évolution des planètes est la convection en rotation. Alors que les intérieurs de planètes sont eloignés et impropres à l’observation directe, les expériences de laboratoire présentent des modèles cohérents à même de guider notre compréhension et de complémenter les simulations numériques. Si nous parvenons à comprendre la mécanique des fluides des modèles de laboratoire, nous finirons peut-être par comprendre l’original complètement. Cependant, reproduire expérimentalement une convection en rotation pertinente pour les intérieurs de planètes présente une gageure en soi, ne serait-ce qu’au niveau de la modélisation de la gravité centrale d’une planète et de son gradient de température parallèle. Trois classes d’expériences distinctes sont apparues pour relever ce défi. Une première approche consiste à utiliser une autre force centrale, telle que la force de Coulomb. L’inconvénient est que ces forces sont typiquement plus faibles que la gravité ambiante et nécessitent donc d’aller dans l’espace. Une autre méthode implique de faire tourner le dispositif suffisamment vite pour que la force centrifuge dépasse et même remplace la gravité terrestre. Cette technique imite les conditions des regions équatoriales et à faible latitude d’une planète. Finalement, utiliser la véritable gravité terrestre alignée avec l’axe de rotation nous renseigne sur les régions polaires et à haute latitude. Ces expériences ont été perfectionnées au cours de plus de sept décenies. Nous parcourons ici leur évolution, depuis les premières visualisations des motifs au départ de la convection, en passant par les expériences à gravité centrale conduites à bord d’engins spatiaux, l’avènement de la vélocimétrie à ultrasons dans le métaux liquides, jusqu’aux dernières cartographies de champs de vitesse par méthodes optiques dans des écoulements de magnoconvection en rotation dans de l’acide sulfurique à l’intérieur d’aimants à champs fort. Nous montrons comment des concepts expérimentaux innovants couplés aux techniques expérimentales émergentes ont poussé notre compréhension des intérieurs de planètes et nous ont aidé à en dépeindre une image toujours plus détaillée et plus réaliste, en particulier du cœur liquide de la Terre.

Compléments :
Des compléments sont fournis pour cet article dans le fichier séparé :

The interiors of all the planets in the solar system consist of layers, most of which are made out of fluids. When these layers are subject to superadiabatic temperature or compositional gradients, turbulent convection takes place that transports heat and momentum. In addition, planets are fast rotators. Thus, the key process that underpins planetary evolution, the existence of dynamo action or lack thereof, the observable flow patterns, and much more, is rotating convection. Because planetary interiors are remote and inaccessible to direct observation, experiments offer crucial, physically consistent models capable of guiding our understanding and complementing numerical simulations. If we can fully understand the fluid dynamics of the laboratory model, we may eventually fully understand the original. Experimentally reproducing rotating thermal convection relevant to planetary interiors comes with very specific challenges, in particular, modelling the central gravity field of a planet that is parallel to the temperature gradient. Three distinct classes of experiments have been developed to tackle this challenge. One approach consists of using an alternative central force field such as the electric one. This comes with the caveat that these forces are typically weaker than gravity and require going to space. Another method entails rotating the device fast enough so that the centrifugal force exceeds and effectively supersedes Earth’s gravity. This mimics the equatorial and lower latitude regions of a planet. Lastly, insight into the polar and higher latitude regions is gained by using the actual lab gravity aligned with the rotation axis. These experiments have been continuously refined during the past seven decades. Here, we review their evolution, from the early days of visualising the onset patterns of convection, over central force field experiments in spacecraft, ultrasound velocity measurements in liquid metals, to the latest optical velocity mapping of rotating magnetoconvection in sulphuric acid inside high-field magnets. We show how innovative experimental design coupled with emerging experimental techniques has advanced our understanding of planetary interiors and helped us paint a more realistic, detailed picture of them, including Earth’s liquid metal outer core.

Supplementary Materials:
Supplementary material for this article is supplied as a separate file:

Reçu le :
Révisé le :
Accepté le :
Première publication :
DOI : 10.5802/crphys.233
Keywords: Rotating convection, Experimental fluid mechanics, Measurement techniques, Planetary interiors, Turbulent convection
Mots-clés : Convection en rotation, Méchanique des fluides exprérimentale, Techniques de mesure, Intérieurs de planètes, Convection turbulente

Alban Pothérat 1 ; Susanne Horn 1

1 Centre for Fluid and Complex Systems, Coventry University, Mile Lane, CV1 2NL Coventry, UK
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
@article{CRPHYS_2024__25_S3_A23_0,
     author = {Alban Poth\'erat and Susanne Horn},
     title = {Seven decades of exploring planetary interiors with rotating convection experiments},
     journal = {Comptes Rendus. Physique},
     publisher = {Acad\'emie des sciences, Paris},
     year = {2024},
     doi = {10.5802/crphys.233},
     language = {en},
     note = {Online first},
}
TY  - JOUR
AU  - Alban Pothérat
AU  - Susanne Horn
TI  - Seven decades of exploring planetary interiors with rotating convection experiments
JO  - Comptes Rendus. Physique
PY  - 2024
PB  - Académie des sciences, Paris
N1  - Online first
DO  - 10.5802/crphys.233
LA  - en
ID  - CRPHYS_2024__25_S3_A23_0
ER  - 
%0 Journal Article
%A Alban Pothérat
%A Susanne Horn
%T Seven decades of exploring planetary interiors with rotating convection experiments
%J Comptes Rendus. Physique
%D 2024
%I Académie des sciences, Paris
%Z Online first
%R 10.5802/crphys.233
%G en
%F CRPHYS_2024__25_S3_A23_0
Alban Pothérat; Susanne Horn. Seven decades of exploring planetary interiors with rotating convection experiments. Comptes Rendus. Physique, Online first (2024), pp. 1-55. doi : 10.5802/crphys.233.

[1] R. D. Oldham The constitution of the interior of the Earth, as revealed by earthquakes, Quart. J. Geol. Soc., Volume 62 (1906) no. 1–4, pp. 456-475 | DOI

[2] I. Lehmann P’, Publications du Bureau central séismologique international. Série A: Travaux scientifiques, Volume 14 (1936), pp. 87-115

[3] M. I. Billen Modeling the dynamics of subducting slabs, Annu. Rev. Earth Planet. Sci., Volume 36 (2008) no. 1, pp. 325-356 | DOI

[4] T. M. Olugboji; J. Park Structures of the oceanic lithosphere-asthenosphere boundary: Mineral-physics modeling and seismological signatures, Geochem. Geophys. Geosyst., Volume 14 (2013) no. 4, pp. 880-901 | DOI

[5] S. Mukhopadhyay; R. Parai Noble gases: A record of Earth’s evolution and mantle dynamics, Annu. Rev. Earth Planet. Sci., Volume 47 (2019) no. 1, pp. 389-419 | DOI

[6] M. D. Long Constraints on subduction geodynamics from seismic anisotropy, Rev. Geophys., Volume 51 (2013) no. 1, pp. 76-112 | DOI

[7] L. Stixrude; C. Lithgow-Bertelloni Geophysics of chemical heterogeneity in the mantle, Annu. Rev. Earth Planet. Sci., Volume 40 (2012) no. 1, pp. 569-595 | DOI

[8] J. P. Brodholt Pressure-induced changes in the compression mechanism of aluminous perovskite in the Earth’s mantle, Nature, Volume 407 (2000) no. 6804, pp. 620-622 | DOI

[9] C. Normand; Y. Pomeau; M. G. Velarde Convective instability: a physicist’s approach, Rev. Mod. Phys., Volume 49 (1977) no. 3, pp. 581-624 | DOI

[10] R. Jeanloz; H.-R. Wenk Convection and anisotropy of the inner core, Geophys. Res. Lett., Volume 15 (1988) no. 1, pp. 72-75 | DOI | Zbl

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

[12] R. E. Ecke; O. Shishkina Turbulent rotating Rayleigh–Bénard convection, Annu. Rev. Fluid Mech., Volume 55 (2023), pp. 603-638 | DOI

[13] J. M. Aurnou; M. A. Calkins; J. S. Cheng; K. Julien; E. M. King; D. Nieves; K. M. Soderlund; S. Stellmach Rotating convective turbulence in Earth and planetary cores, Phys. Earth Planet. Inter., Volume 246 (2015), pp. 52-71 | DOI

[14] 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

[15] B. Willis The Mechanics of Appalachian Structure, US Government Printing Office, Washington, 1894

[16] H. Bénard Les tourbillons cellulaires dans une nappe liquide, Revue Gen. Sci. Pure Appl., Volume 11 (1900), pp. 1261-1271 | Zbl

[17] L. Rayleigh On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side, Lond. Edinb. Dubl. Philos. Mag. J. Sci., Volume 32 (1916) no. 192, pp. 529-546 | DOI | Zbl

[18] A. Oberbeck Ueber die Wärmeleitung der Flüssigkeiten bei Berücksichtigung der Strömungen infolge von Temperaturdifferenzen, Ann. Phys., Volume 243 (1879) no. 6, pp. 271-292 | DOI | Zbl

[19] J. V. Boussinesq Théorie analytique de la chaleur, 2, Gauthier-Villars, Paris, 1903

[20] D. D. Gray; A. Giorgini The validity of the Boussinesq approximation for liquids and gases, Int. J. Heat Mass Transfer, Volume 19 (1976) no. 5, pp. 545-551 | DOI | Zbl

[21] F. Marques; I. Mercader; O. Batiste; J. M. Lopez Centrifugal effects in rotating convection: axisymmetric states and three-dimensional instabilities, J. Fluid Mech., Volume 580 (2007), pp. 303-318 | DOI | Zbl

[22] S. Horn; J. M. Aurnou Regimes of Coriolis-centrifugal convection, Phys. Rev. Lett., Volume 120 (2018), 204502 | DOI

[23] S. Horn; J. M. Aurnou Tornado-like vortices in the quasi-cyclostrophic regime of Coriolis-centrifugal convection, J. Turbul., Volume 22 (2021) no. 4–5, pp. 297-324 | DOI | Zbl

[24] S. Horn; J. M. Aurnou Rotating convection with centrifugal buoyancy: Numerical predictions for laboratory experiments, Phys. Rev. Fluids, Volume 4 (2019) no. 7, 073501 | DOI

[25] F. H. Busse Thermal instabilities in rapidly rotating systems, J. Fluid Mech., Volume 44 (1970) no. 3, pp. 441-460 | DOI | Zbl

[26] F. H. Busse Is low Rayleigh number convection possible in the Earth’s core?, Geophys. Res. Lett., Volume 29 (2002) no. 7, p. 9-1–9-3 | DOI

[27] S. Chandrasekhar Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford University Press, Oxford, 1961

[28] W. Thomson LII. On the stability of steady and of periodic fluid motion, Lond. Edinb. Dubl. Philos. Mag. J. Sci., Volume 23 (1887) no. 144, pp. 459-464 | DOI

[29] J. Proudman On the motion of solids in a liquid possessing vorticity, Proc. R. Soc. Lond. A, Volume 92 (1916) no. 642, pp. 408-424 | DOI

[30] H. P. Greenspan The Theory of Rotating Fluids, Cambridge University Press, Cambridge, 1969

[31] T. Clune; E. Knobloch Pattern selection in rotating convection with experimental boundary conditions, Phys. Rev. E, Volume 47 (1993) no. 4, pp. 2536-2550 | DOI

[32] H. F. Goldstein; E. Knobloch; I. Mercader; M. Net Convection in a rotating cylinder. Part 1. Linear theory for moderate Prandtl numbers, J. Fluid Mech., Volume 248 (1993), pp. 583-604 | DOI | Zbl

[33] H. F. Goldstein; E. Knobloch; I. Mercader; M. Net Convection in a rotating cylinder. Part 2. Linear theory for low Prandtl numbers, J. Fluid Mech., Volume 262 (1994), pp. 293-324 | DOI

[34] S. Horn; P. J. Schmid Prograde, retrograde, and oscillatory modes in rotating Rayleigh–Bénard convection, J. Fluid Mech., Volume 831 (2017), pp. 182-211 | DOI | Zbl

[35] J. M. Aurnou; V. Bertin; A. M. Grannan; S. Horn; T. Vogt Rotating thermal convection in liquid gallium: multi-modal flow, absent steady columns, J. Fluid Mech., Volume 846 (2018), pp. 846-876 | DOI | Zbl

[36] T. Vogt; S. Horn; J. M. Aurnou Oscillatory thermal–inertial flows in liquid metal rotating convection, J. Fluid Mech., Volume 911 (2021), A5 | DOI | Zbl

[37] P. H. Roberts On the thermal instability of a rotating-fluid sphere containing heat sources, Philos. Trans. R. Soc. Lond. A Math. Phys. Sci., Volume 263 (1968) no. 1136, pp. 93-117 | Zbl

[38] A. Barik; S. A. Triana; M. Calkins; S. Stanley; J. Aurnou Onset of convection in rotating spherical shells: Variations with radius ratio, Earth Space Sci., Volume 10 (2023) no. 1, e2022EA002606 | DOI

[39] E. Dormy; A. M. Soward; C. A. Jones; D. Jault; P. Cardin The onset of thermal convection in rotating spherical shells, J. Fluid Mech., Volume 501 (2004), pp. 43-70 | DOI | Zbl

[40] R. E. Ecke; O. Shishkina Turbulent rotating Rayleigh–Bénard convection, Annu. Rev. Fluid Mech., Volume 55 (2023) no. 1, pp. 603-638 | DOI

[41] J. Brons; T. P. Thomas; A. Pothérat Transition between advection and propagation of inertial waves in rotating turbulence, J. Fluid Mech., Volume 886 (2020), A22 | DOI

[42] J. Brons; T. P. Thomas; A. Pothérat Mean flow anisotropy without waves in rotating turbulence, J. Fluid Mech., Volume 889 (2020), A37 | DOI | Zbl

[43] P. Billant Is the Taylor–Proudman theorem exact in unbounded domains? Case study of the three-dimensional stability of a vortex pair in a rapidly rotating fluid, J. Fluid Mech., Volume 920 (2021), R1 | DOI | Zbl

[44] F. S. Godeferd; F. Moisy Structure and dynamics of rotating turbulence: a review of recent experimental and numerical results, Appl. Mech. Rev., Volume 67 (2015) no. 3, 030802 | DOI

[45] L. Biferale Rotating turbulence, J. Turbul., Volume 22 (2021) no. 4–5, pp. 232-241 | DOI

[46] U. Harlander; M. V. Kurgansky; K. Speer; M. Vincze Baroclinic instability from an experimental perspective, C. R. Phys., Volume 25 (2024) no. S3, pp. 1-48 | DOI

[47] K. Aujogue; A. Pothérat; B. Sreenivasan; F. Debray Experimental study of the convection in a rotating tangent cylinder, J. Fluid Mech., Volume 843 (2018), pp. 355-381 | DOI

[48] R. Agrawal; M. Holdsworth; A. Pothérat Regimes of rotating convection in a tangent cylinder, Preprint, ArXiv, 2024 | arXiv

[49] T. Gastine; J. M. Aurnou Latitudinal regionalization of rotating spherical shell convection, J. Fluid Mech., Volume 954 (2023), R1 | DOI | Zbl

[50] F. H. Busse; C. R. Carrigan Laboratory simulation of thermal convection in rotating planets and stars, Science, Volume 191 (1976) no. 4222, pp. 81-83 | DOI

[51] J. Pedlosky Geophysical Fluid Dynamics, Springer Verlag, New York, Heidelberg, Berlin, 1987 | DOI

[52] B. W. Hindman; R. Jain Radial trapping of thermal Rossby waves within the convection zones of low-mass stars, Astrophys. J., Volume 932 (2022) no. 1, 68 | DOI

[53] R. Hide Free hydromagnetic oscillations of the earth’s core and the theory of the geomagnetic secular variation, Philos. Trans. R. Soc. Lond. A Math. Phys. Sci., Volume 259 (1966) no. 1107, pp. 615-650 | DOI

[54] F. H. Busse; C. R. Carrigan Convection induced by centrifugal buoyancy, J. Fluid Mech., Volume 62 (1974) no. 3, pp. 579-592 | DOI

[55] F. H. Busse; R. D. Simitev Convection in rotating spherical fluid shells, Preprint, ArXiv, 2009 | arXiv

[56] K. Aujogue; A. Pothérat; I. Bates; F. Debray; B. Sreenivasan Little Earth experiment: An instrument to model planetary cores, Rev. Sci. Instrum., Volume 87 (2016), 084502 | DOI

[57] V. W. Ekman On the influence of the earth’s rotation on ocean-currents, Arkiv for Matematik, Astronomi Och Fysik, Volume 2 (1905) no. 11, pp. 1-53 | Zbl

[58] D. J. Acheson; R. Hide Hydromagnetics of rotating fluids, Rep. Progr. Phys., Volume 36 (1973) no. 2, pp. 159-221 | DOI

[59] A. Pothérat; J. Sommeria; R. Moreau An effective two-dimensional model for MHD flows with tranverse magnetic field, J. Fluid Mech., Volume 424 (2000), pp. 75-100 | DOI | Zbl

[60] P. A. Davidson; A. Pothérat A note on Bodewadt–Hartmann layers, Eur. J. Mech. B Fluids, Volume 21 (2002) no. 5, pp. 545-559 | DOI | Zbl

[61] K. Stewartson On almost rigid rotations, J. Fluid Mech., Volume 3 (1957) no. 1, pp. 17-26 | DOI | Zbl

[62] R. P. J. Kunnen; H. J. H. Clercx; G. J. F. Van Heijst The structure of sidewall boundary layers in confined rotating Rayleigh–Bénard convection, J. Fluid Mech., Volume 727 (2013), pp. 509-532 | DOI | Zbl

[63] F. Zhong; R. Ecke; V. Steinberg Asymmetric modes and the transition to vortex structures in rotating Rayleigh–Bénard convection, Phys. Rev. Lett., Volume 67 (1991) no. 18, pp. 2473-2476 | DOI

[64] F. Zhong; R. E. Ecke; V. Steinberg Rotating Rayleigh–Bénard convection: asymmetric modes and vortex states, J. Fluid Mech., Volume 249 (1993), pp. 135-159 | DOI

[65] J. Herrmann; F. H. Busse Asymptotic theory of wall-attached convection in a rotating fluid layer, J. Fluid Mech., Volume 255 (1993), pp. 183-194 | DOI | Zbl

[66] E. Y. Kuo; M. C. Cross Traveling-wave wall states in rotating Rayleigh–Bénard convection, Phys. Rev. E, Volume 47 (1993) no. 4, R2245 | DOI

[67] K. Zhang; X. Liao The onset of convection in rotating circular cylinders with experimental boundary conditions, J. Fluid Mech., Volume 622 (2009), pp. 63-73 | DOI | Zbl

[68] R. E. Ecke Rotating Rayleigh–Bénard convection: bits and pieces, Phys. D: Nonlinear Phenom., Volume 444 (2023), 133579 | DOI

[69] X. Zhang; D. PM. Van Gils; S. Horn et al. Boundary zonal flow in rotating turbulent Rayleigh–Bénard convection, Phys. Rev. Lett., Volume 124 (2020) no. 8, 084505 | DOI

[70] X. Zhang; R. E. Ecke; O. Shishkina Boundary zonal flows in rapidly rotating turbulent thermal convection, J. Fluid Mech., Volume 915 (2021), A62 | DOI | Zbl

[71] R. E. Ecke; X. Zhang; O. Shishkina Connecting wall modes and boundary zonal flows in rotating Rayleigh–Bénard convection, Phys. Rev. Fluids, Volume 7 (2022) no. 1, L011501 | DOI

[72] X. M. de Wit; W. J. Boot; M. Madonia; A. J. Aguirre Guzmán; R. P. Kunnen Robust wall modes and their interplay with bulk turbulence in confined rotating Rayleigh–Bénard convection, Phys. Rev. Fluids, Volume 8 (2023) no. 7, 073501 | DOI

[73] 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

[74] J. Aubert; D. Brito; H.-C. Nataf; P. Cardin; J.-P. Masson A systematic experimental study of rapidly rotating spherical convection in water and liquid gallium, Phys. Earth Planet. Inter., Volume 128 (2001) no. 1, pp. 51-74 | DOI

[75] F. D. Stacey Physics of the Earth, Brookfield Press, Brisbane, 1992

[76] F. Xu; G. Morard; N. Guignot et al. Thermal expansion of liquid Fe-S alloy at high pressure, Earth Planet. Sci. Lett., Volume 563 (2021), 116884 | DOI

[77] G. Morard; J. Siebert; D. Andrault; N. Guignot; G. Garbarino; F. Guyot; D. Antonangeli The Earth’s core composition from high pressure density measurements of liquid iron alloys, Earth Planet. Sci. Lett., Volume 373 (2013), pp. 169-178 | DOI

[78] L. E. González; D. J. González Structure and dynamics in liquid iron at high pressure and temperature. A first principles study, J. Geophys. Res.: Solid Earth, Volume 128 (2023) no. 2, e2022JB025119 | DOI

[79] M. Pozzo; C. Davies; D. Gubbins; D. Alfe Thermal and electrical conductivity of iron at Earths core conditions, Nature, Volume 485 (2012) no. 7398, pp. 355-358 | DOI

[80] G. Schubert; K. M. Soderlund Planetary magnetic fields: Observations and models, Phys. Earth Planet. Inter., Volume 187 (2011) no. 3, pp. 92-108 | DOI

[81] O. Andreev; Y. Kolesnikov; A. Thess Visualization of the Ludford column, J. Fluid Mech., Volume 721 (2013), pp. 438-453 | DOI | Zbl

[82] B. Moudjed; A. Pothérat; M. Holdsworth PIV mapping of pressure and velocity fields in the plane magnetohydrodynamic Couette flow, Exp. Fluids, Volume 61 (2020) no. 12, 255 | DOI

[83] A. Pothérat; K. Aujogue; F. Debray Magnetic Taylor–Proudman constraint explains flows into the Tangent cylinder, Phys. Rev. Lett., Volume 133 (2024) no. 18, 184101 | DOI

[84] J. E. Hart; J. Toomre; A. E. Deane et al. Laboratory experiments on planetary and stellar convection performed on Spacelab 3, Science, Volume 234 (1986) no. 4772, pp. 61-64 | DOI

[85] C. Egbers; W. Brasch; B. Sitte; J. Immohr; J.-R. Schmidt Estimates on diagnostic methods for investigations of thermal convection between spherical shells in space, Meas. Sci. Technol., Volume 10 (1999) no. 10, pp. 866-877 | DOI

[86] J. P. Koulakis; Y. Ofek; S. Pree; S. Putterman Thermal convection in a central force field mediated by sound, Phys. Rev. Lett., Volume 130 (2023) no. 3, 034002 | DOI

[87] S. Sahoo; B. Sreenivasan Convection in a rapidly rotating cylindrical annulus with laterally varying boundary heat flux, J. Fluid Mech., Volume 883 (2020), A1 | DOI | Zbl

[88] H. Jiang; X. Zhu; D. Wang; S. G. Huisman; C. Sun Supergravitational turbulent thermal convection, Sci. Adv., Volume 6 (2020) no. 40, eabb8676 | DOI

[89] J. A. Chamberlain; C. R. Carrigan An experimental investigation of convection in a rotating sphere subject to time varying thermal boundary conditions, Geophys. Astrophys. Fluid Dyn., Volume 35 (1986) no. 1–4, pp. 303-327 | DOI

[90] S. Cordero; F. H. Busse Experiments on convection in rotating hemispherical shells: Transition to a quasi-periodic state, Geophys. Res. Lett., Volume 19 (1992) no. 8, pp. 733-736 | DOI

[91] P. Cardin; P. Olson An experimental approach to thermochemical convection in the Earth’s core, Geophys. Res. Lett., Volume 19 (1992) no. 20, pp. 1995-1998 | DOI

[92] I. Sumita; P. Olson A laboratory model for convection in Earth’s core driven by a thermally heterogeneous mantle, Science, Volume 286 (1999) no. 5444, pp. 1547-1549 | DOI

[93] W. L. Shew; D. P. Lathrop Liquid sodium model of geophysical core convection, Phys. Earth Planet. Inter., Volume 153 (2005) no. 1–3, pp. 136-149 | DOI

[94] N. Gillet; D. Brito; D. Jault; H.-C. Nataf Experimental and numerical studies of magnetoconvection in a rapidly rotating spherical shell, J. Fluid Mech., Volume 580 (2007), pp. 123-143 | DOI

[95] D. Fultz; Y. Nakagawa; P. Frenzen An instance in thermal convection of Eddington’s “Overstability”, Phys. Rev., Volume 94 (1954) no. 6, pp. 1471-1472 | DOI

[96] J. Aurnou; S. Andreadis; L. Zhu; P. Olson Experiments on convection in Earths core tangent cylinder, Earth Planet. Sci. Lett., Volume 212 (2003) no. 1–2, pp. 119-134 | DOI

[97] K. Aujogue Little Earth experiment: a journey towards the Earth’s tangent cylinder, PhD thesis, Coventry University (2016)

[98] J. E. Hart; G. A. Glatzmaier; J. Toomre Space-laboratory and numerical simulations of thermal convection in a rotating hemispherical shell with radial gravity, J. Fluid Mech., Volume 173 (1986), pp. 519-544 | DOI

[99] J. E. Hart; D. Ohlsen; S. Kittelman; N. Borhani; F. Leslie; T. Miller The geophysical fluid flow cell experiment (1999) no. TP 209576 (Technical report)

[100] J. E. Hart Experiments on thermal convection in rotating spherical shells with radial gravity: The geophysical fluid flow cell, Third Microgravity Fluid Physics Conference, 1996

[101] C. Egbers; W. Beyer; A. Bonhage; R. Hollerbach; P. Beltrame The geoflow-experiment on ISS (part I): Experimental preparation and design of laboratory testing hardware, Adv. Space Res., Volume 32 (2003) no. 2, pp. 171-180 | DOI

[102] B. Futterer; C. Egbers; N. Dahley; S. Koch; L. Jehring First identification of sub-and supercritical convection patterns from “GeoFlow”, the geophysical flow simulation experiment integrated in Fluid Science Laboratory, Acta Astronaut., Volume 66 (2010) no. 1–2, pp. 193-200 | DOI

[103] B. Futterer; N. Dahley; S. Koch; N. Scurtu; C. Egbers From isoviscous convective experiment “GeoFlow I” to temperature-dependent viscosity in “GeoFlow II” – Fluid physics experiments on-board ISS for the capture of convection phenomena in Earth’s outer core and mantle, Acta Astronaut., Volume 71 (2012), pp. 11-19 | DOI

[104] B. Futterer; A. Krebs; A.-C. Plesa; F. Zaussinger; R. Hollerbach; D. Breuer; C. Egbers Sheet-like and plume-like thermal flow in a spherical convection experiment performed under microgravity, J. Fluid Mech., Volume 735 (2013), pp. 647-683 | DOI | Zbl

[105] F. Zaussinger; A. Krebs; V. Travnikov; C. Egbers Recognition and tracking of convective flow patterns using Wollaston shearing interferometry, Adv. Space Res., Volume 60 (2017) no. 6, pp. 1327-1344 | DOI

[106] F. Zaussinger; P. Haun; P. S. Szabo; V. Travnikov; M. Al Kawwas; C. Egbers Rotating spherical gap convection in the GeoFlow International Space Station (ISS) experiment, Phys. Rev Fluids, Volume 5 (2020) no. 6, 063502 | DOI

[107] D. Fultz; Y. Nakagawa Experiments on over-stable thermal convection in mercury, Proc. R. Soc. Lond. A. Math. Phys. Sci., Volume 231 (1955) no. 1185, pp. 211-225 | DOI

[108] Y. Nakagawa; P. Frenzen A theoretical and experimental study of cellular convection in rotating fluids, Tellus, Volume 7 (1955) no. 1, pp. 2-21 | DOI

[109] Y. Nakagawa Experiments on the instability of a layer of mercury heated from below and subject to the simultaneous action of a magnetic field and rotation, Proc. R. Soc. Lond. A. Math. Phys. Sci., Volume 242 (1957) no. 1228, pp. 81-88 | DOI

[110] Y. Nakagawa Experiments on the instability of a layer of mercury heated from below and subject to the simultaneous action of a magnetic field and rotation. II, Proc. R. Soc. Lond. A. Math. Phys. Sci., Volume 249 (1959) no. 1256, pp. 138-145 | DOI

[111] I. R. Goroff An experiment on heat transfer by over stable and ordinary convection, Proc. R. Soc. Lond. A. Math. Phys. Sci., Volume 254 (1960) no. 1279, pp. 537-541 | DOI

[112] E. L. Koschmieder On convection of a uniformly heated plane, Beitrage zur Physik der Atmosphäre, Volume 39 (1967), pp. 216-225

[113] H. T. Rossby A study of Bénard convection with and without rotation, J. Fluid Mech., Volume 36 (1969) no. 2, pp. 309-335 | DOI | Zbl

[114] P. G. J. Lucas; J. M. Pfotenhauer; R. J. Donnelly Stability and heat transfer of rotating cryogens. Part 1. Influence of rotation on the onset of convection in liquid 4He, J. Fluid Mech., Volume 129 (1983), pp. 251-264 | DOI

[115] J. M. Pfotenhauer; P. G. J. Lucas; R. J. Donnelly Stability and heat transfer of rotating cryogens. Part 2. Effects of rotation on heat-transfer properties of convection in liquid He, J. Fluid Mech., Volume 145 (1984), pp. 239-252 | DOI

[116] J. M. Pfotenhauer; J. J. Niemela; R. J. Donnelly Stability and heat transfer of rotating cryogens. Part 3. Effects of finite cylindrical geometry and rotation on the onset of convection, J. Fluid Mech., Volume 175 (1987), pp. 85-96 | DOI

[117] B. M. Boubnov; G. S. Golitsyn Experimental study of convective structures in rotating fluids, J. Fluid Mech., Volume 167 (1986), pp. 503-531 | DOI

[118] B. M. Boubnov; G. S. Golitsyn Temperature and velocity field regimes of convective motions in a rotating plane fluid layer, J. Fluid Mech., Volume 219 (1990), pp. 215-239 | DOI

[119] H. J. Fernando; R.-R. Chen; D. L. Boyer Effects of rotation on convective turbulence, J. Fluid Mech., Volume 228 (1991), pp. 513-547 | DOI

[120] Y. Liu; R. E. Ecke Heat transport scaling in turbulent Rayleigh–Bénard convection: effects of rotation and Prandtl number, Phys. Rev. Lett., Volume 79 (1997) no. 12, pp. 2257-2260 | DOI

[121] L. Ning; R. E. Ecke Rotating Rayleigh–Bénard convection: Aspect-ratio dependence of the initial bifurcations, Phys. Rev. E, Volume 47 (1993) no. 5, pp. 3326-3333 | DOI

[122] Y. Liu; R. E. Ecke Heat transport measurements in turbulent rotating Rayleigh–Bénard convection, Phys. Rev. E, Volume 80 (2009) no. 3, 036314 | DOI

[123] P. Vorobieff; R. E. Ecke Transient states during spin-up of a Rayleigh–Bénard cell, Phys. Fluids, Volume 10 (1998) no. 10, pp. 2525-2538 | DOI

[124] S. Sakai The horizontal scale of rotating convection in the geostrophic regime, J. Fluid Mech., Volume 333 (1997), pp. 85-95 | DOI

[125] J. M. Aurnou; P. L. Olson Experiments on Rayleigh–Bénard convection, magnetoconvection and rotating magnetoconvection in liquid gallium, J. Fluid Mech., Volume 430 (2001), pp. 283-307 | DOI

[126] 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

[127] J. S. Cheng; S. Stellmach; A. Ribeiro; A. Grannan; E. M. King; J. M. Aurnou Laboratory-numerical models of rapidly rotating convection in planetary cores, Geophys. J. Int., Volume 201 (2015) no. 1, pp. 1-17 | DOI

[128] E. M. King; J. M. Aurnou Turbulent convection in liquid metal with and without rotation, Proc. Natl. Acad. Sci. USA, Volume 110 (2013) no. 17, pp. 6688-6693 | DOI

[129] A. M. Grannan; J. S. Cheng; A. Aggarwal; E. K. Hawkins; Y. Xu; S. Horn; J. Sánchez-Álvarez; J. M. Aurnou Experimental pub crawl from Rayleigh–Bénard to magnetostrophic convection, J. Fluid Mech., Volume 939 (2022), R1 | DOI

[130] R. P. J. Kunnen; H. J. H. Clercx Breakdown of large-scale circulation in turbulent rotating convection, Europhys. Lett., Volume 84 (2008) no. 2, 24001 | DOI

[131] R. P. J. Kunnen; B. J. Geurts; H. J. H. Clercx Experimental and numerical investigation of turbulent convection in a rotating cylinder, J. Fluid Mech., Volume 642 (2010), pp. 445-476 | DOI

[132] H. Rajaei; P. Joshi; K. M. Alards; R. P. Kunnen; F. Toschi; H. J. Clercx Transitions in turbulent rotating convection: A Lagrangian perspective, Phys. Rev. E, Volume 93 (2016) no. 4, 043129 | DOI

[133] P. Joshi; H. Rajaei; R. P. Kunnen; H. J. Clercx Effect of particle injection on heat transfer in rotating Rayleigh–Bénard convection, Phys. Rev. Fluids, Volume 1 (2016) no. 8, 084301 | DOI

[134] H. Rajaei; R. P. Kunnen; H. J. Clercx Exploring the geostrophic regime of rapidly rotating convection with experiments, Phys. Fluids, Volume 29 (2017) no. 4, 45105 | DOI

[135] J. Q. Zhong; R. J. Stevens; H. J. Clercx; R. Verzicco; D. Lohse; G. Ahlers Prandtl-, Rayleigh-, and Rossby-number dependence of heat transport in turbulent rotating Rayleigh–Bénard convection, Phys. Rev. Lett., Volume 102 (2009) no. 4, 044502 | DOI

[136] S. Weiss; R. Stevens; J.-Q. Zhong; H. J. Clercx; D. Lohse; G. Ahlers Finite-size effects lead to supercritical bifurcations in turbulent rotating Rayleigh–Bénard convection, Phys. Rev. Lett., Volume 105 (2010) no. 22, 224501 | DOI

[137] S. Weiss; G. Ahlers Heat transport by turbulent rotating Rayleigh–Bénard convection and its dependence on the aspect ratio, J. Fluid Mech., Volume 684 (2011), pp. 407-426 | DOI

[138] J. J. Niemela; S. Babuin; K. R. Sreenivasan Turbulent rotating convection at high Rayleigh and Taylor numbers, J. Fluid Mech., Volume 649 (2010), pp. 509-522 | DOI

[139] R. E. Ecke; J. J. Niemela Heat transport in the geostrophic regime of rotating Rayleigh–Bénard convection, Phys. Rev. Lett., Volume 113 (2014) no. 11, 114301 | DOI

[140] M. Wedi; D. P. Van Gils; E. Bodenschatz; S. Weiss Rotating turbulent thermal convection at very large Rayleigh numbers, J. Fluid Mech., Volume 912 (2021), A30 | DOI

[141] J. S. Cheng; J. M. Aurnou; K. Julien; R. P. Kunnen A heuristic framework for next-generation models of geostrophic convective turbulence, Geophys. Astrophys. Fluid Dyn., Volume 112 (2018) no. 4, pp. 277-300 | DOI

[142] J. S. Cheng; M. Madonia; A. J. Aguirre Guzmán; R. P. Kunnen Laboratory exploration of heat transfer regimes in rapidly rotating turbulent convection, Phys. Rev. Fluids, Volume 5 (2020) no. 11, 113501 | DOI

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

[144] J. A. Abbate; J. M. Aurnou Rotating convective turbulence in moderate to high Prandtl number fluids, Geophys. Astrophys. Fluid Dyn., Volume 117 (2023) no. 6, pp. 1-40 | DOI

[145] S.-S. Ding; K. L. Chong; J.-Q. Shi; G.-Y. Ding; H.-Y. Lu; K.-Q. Xia; J.-Q. Zhong Inverse centrifugal effect induced by collective motion of vortices in rotating thermal convection, Nat. Commun., Volume 12 (2021) no. 1, 5585 | DOI

[146] H.-Y. Lu; G.-Y. Ding; J.-Q. Shi et al. Heat-transport scaling and transition in geostrophic rotating convection with varying aspect ratio, Phys. Rev. Fluids, Volume 6 (2021) no. 7, L071501 | DOI

[147] J.-Q. Shi; H.-Y. Lu; S.-S. Ding; J.-Q. Zhong Fine vortex structure and flow transition to the geostrophic regime in rotating Rayleigh–Bénard convection, Phys. Rev. Fluids, Volume 5 (2020) no. 1, 011501 | DOI

[148] Y.-B. Hu; Y.-C. Xie; K.-Q. Xia On the centrifugal effect in turbulent rotating thermal convection: onset and heat transport, J. Fluid Mech., Volume 938 (2022), R1 | DOI

[149] F. H. Busse; L. L. Hood Differential rotation driven by convection in a rapidly rotating annulus, Geophys. Astrophys. Fluid Dyn., Volume 21 (1982) no. 1–2, pp. 59-74 | DOI | Zbl

[150] M. A. Azouni; E. W. Bolton; F. H. Busse Convection driven by centrifugal bouyancy in a rotating annulus, Geophys. Astrophys. Fluid Dyn., Volume 34 (1986) no. 1–4, pp. 301-317 | DOI

[151] C. R. Carrigan; F. H. Busse An experimental and theoretical investigation of the onset of convection in rotating spherical shells, J. Fluid Mech., Volume 126 (1983), pp. 287-305 | DOI | Zbl

[152] S. Cordero Experiments on convection in a rotating hemispherical shell: transition to chaos, Geophys. Res. Lett., Volume 20 (1993) no. 23, pp. 2587-2590 | DOI

[153] P. Cardin; P. Olson Chaotic thermal convection in a rapidly rotating spherical shell: consequences for flow in the outer core, Phys. Earth Planet. Inter., Volume 82 (1994) no. 3–4, pp. 235-259 | DOI

[154] M. Jaletzky; F. H. Busse New patterns of centrifugally driven thermal convection, Proc. Natl. Acad. Sci. USA, Volume 97 (2000) no. 10, pp. 5060-5064 | DOI

[155] M. Westerburg; F. H. Busse Centrifugally driven convection in the rotating cylindrical annulus with modulated boundaries, Nonlinear Process. Geophys., Volume 10 (2003) no. 3, pp. 275-280 | DOI

[156] I. Sumita; P. Olson Laboratory experiments on high Rayleigh number thermal convection in a rapidly rotating hemispherical shell, Phys. Earth Planet. Inter., Volume 117 (2000) no. 1, pp. 153-170 | DOI

[157] I. Sumita; P. Olson Rotating thermal convection experiments in a hemispherical shell with heterogeneous boundary heat flux: Implications for the Earth’s core, J. Geophys. Res.: Solid Earth, Volume 107 (2002) no. B8, ETG-5 | DOI

[158] I. Sumita; P. Olson Experiments on highly supercritical thermal convection in a rapidly rotating hemispherical shell, J. Fluid Mech., Volume 492 (2003), pp. 271-287 | DOI | Zbl

[159] N. Gillet; D. Brito; D. Jault; H. C. Nataf Experimental and numerical studies of convection in a rapidly rotating spherical shell, J. Fluid Mech., Volume 580 (2007), pp. 83-121 | DOI | Zbl

[160] S. S. Sahoo; B. Sreenivasan Response of Earth’s magnetic field to large lower mantle heterogeneity, Earth Planet. Sci. Lett., Volume 549 (2020), 116507 | DOI

[161] H. Jiang; D. Wang; S. Liu; C. Sun Experimental evidence for the existence of the ultimate regime in rapidly rotating turbulent thermal convection, Phys. Rev. Lett., Volume 129 (2022) no. 20, 204502 | DOI

[162] E. K. Hawkins; J. S. Cheng; J. A. Abbate; T. Pilegard; S. Stellmach; K. Julien; J. M. Aurnou Laboratory models of planetary core-style convective turbulence, Fluids, Volume 8 (2023) no. 4, 106 | DOI | Zbl

[163] C. K. Hill; U. S. N. Aeronautics; S. Administration; G. C. M. S. F. Center Spacelab Mission 3 Experiment Descriptions, NASA Technical Memorandum, National Aeronautics and Space Administration, Scientific and Technical Information Branch, 1982

[164] D. E. Smylie Thermal convection in dielectric liquids and modelling in geophysical fluid dynamics, Earth Planet. Sci. Lett., Volume 1 (1966) no. 5, pp. 339-340 | DOI

[165] B. Chandra; D. E. Smylie A laboratory model of thermal convection under a central force field, Geophys. Fluid Dyn., Volume 3 (1972) no. 3, pp. 211-224 | DOI

[166] T. Gastine; J. Wicht; J. M. Aurnou Turbulent Rayleigh–Bénard convection in spherical shells, J. Fluid Mech., Volume 778 (2015), pp. 721-764 | DOI | Zbl

[167] N. A. Featherstone; B. W. Hindman The emergence of solar supergranulation as a natural consequence of rotationally constrained interior convection, Astrophys. J. Lett., Volume 830 (2016) no. 1, L15 | DOI

[168] S. Horn; O. Shishkina; C. Wagner On non-Oberbeck–Boussinesq effects in three-dimensional Rayleigh–Bénard convection in glycerol, J. Fluid Mech., Volume 724 (2013), pp. 175-202 | DOI | Zbl

[169] 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

[170] R. J. A. M. Stevens; H. J. H. Clercx; D. Lohse Optimal Prandtl number for heat transfer in rotating Rayleigh–Bénard convection, New J. Phys., Volume 12 (2010) no. 7, 075005 | DOI

[171] S. Horn; O. Shishkina Rotating non-Oberbeck–Boussinesq Rayleigh–Bénard convection in water, Phys. Fluids, Volume 26 (2014) no. 5, 055111 | DOI

[172] S. Horn; O. Shishkina Toroidal and poloidal energy in rotating Rayleigh–Bénard convection, J. Fluid Mech., Volume 762 (2015), pp. 232-255 | DOI

[173] T. Gastine; J. Wicht; J. Aubert Scaling regimes in spherical shell rotating convection, J. Fluid Mech., Volume 808 (2016), pp. 690-732 | DOI

[174] N. A. Featherstone; E. H. Anders; K. C. Augustson et al. The puzzling structure of solar convection: Window into the dynamo, Heliophysics 2024 Decadal Whitepapers, Volume 55, 2023 no. 3 https://api.semanticscholar.org/CorpusID:258686768 (accessed 25 February 2025)

[175] M. Luna; F. Moreno-Insertis; E. Priest Are tornado-like magnetic structures able to support solar prominence plasma?, Astrophys. J. Lett., Volume 808 (2015) no. 1, L23 | DOI

[176] S. Horn; J. M. Aurnou Rotating convection with centrifugal buoyancy: Numerical predictions for laboratory experiments, Phys. Rev. Fluids, Volume 4 (2019) no. 7, 073501 | DOI

[177] H. Kuniyoshi; M. Shoda; H. Iijima; T. Yokoyama Magnetic tornado properties: A substantial contribution to the solar coronal heating via efficient energy transfer, Astrophys. J., Volume 949 (2023) no. 1, 8 | DOI

[178] K. Tziotziou; E. Scullion; S. Shelyag et al. Vortex motions in the solar atmosphere: Definitions, theory, observations, and modelling, Space Sci. Rev., Volume 219 (2023) no. 1, 1 | DOI

[179] R. E. Rosensweig; J. Browaeys; J.-C. Bacri; A. Zebib; R. Perzynski Laboratory study of spherical convection in simulated central gravity, Phys. Rev. Lett., Volume 83 (1999) no. 23, pp. 4904-4907 | DOI

[180] W.-G. Früh Using magnetic fluids to simulate convection in a central force field in the laboratory, Nonlinear Process. Geophys., Volume 12 (2005) no. 6, pp. 877-889 | DOI

[181] J. P. Koulakis; S. Pree; A. L. Thornton; S. Putterman Trapping of plasma enabled by pycnoclinic acoustic force, Phys. Rev. E, Volume 98 (2018) no. 4, 043103 | DOI

[182] J. P. Koulakis; S. Putterman Convective instability in a stratified ideal gas containing an acoustic field, J. Fluid Mech., Volume 915 (2021), A25 | DOI

[183] M. Schnaubelt; F. H. Busse Convection in a rotating cylindrical annulus part 3. Vacillating and spatially modulated flows, J. Fluid Mech., Volume 245 (1992), pp. 155-173 | DOI | Zbl

[184] F. H. Busse; A. C. Or Convection in a rotating cylindrical annulus: thermal Rossby waves, J. Fluid Mech., Volume 166 (1986), pp. 173-187 | DOI | Zbl

[185] F. H. Busse Asymptotic theory of convection in a rotating, cylindrical annulus, J. Fluid Mech., Volume 173 (1986), pp. 545-556 | DOI | Zbl

[186] A. C. Or; F. H. Busse Convection in a rotating cylindrical annulus. Part 2. Transitions to asymmetric and vacillating flow, J. Fluid Mech., Volume 174 (1987), pp. 313-326 | DOI | Zbl

[187] J. Tao Thermal convection in a rotating cylindrical annulus and its mean zonal flows, J. Fluid Mech., Volume 552 (2006), pp. 73-82 | DOI | Zbl

[188] M. Auer; F. H. Busse; R. M. Clever Three-dimensional convection driven by centrifugal buoyancy, J. Fluid Mech., Volume 301 (1995), pp. 371-382 | DOI | Zbl

[189] F. H. Busse; F. Finocchi The onset of thermal convection in a rotating cylindrical annulus in the presence of a magnetic field, Phys. Earth Planet. Inter., Volume 80 (1993) no. 1–2, pp. 13-23 | DOI

[190] E. Kurt; W. Pesch; F. H. Busse Pattern formation in the rotating cylindrical annulus with an azimuthal magnetic field at low Prandtl numbers, J. Vib. Control, Volume 13 (2007) no. 9–10, pp. 1321-1330 | DOI | Zbl

[191] F. H. Busse A model of the geodynamo, Geophys. J. Int., Volume 42 (1975) no. 2, pp. 437-459 | Zbl

[192] F. H. Busse Convection driven zonal flows and vortices in the major planets, Chaos: Interdiscip. J. Nonlinear Sci., Volume 4 (1994) no. 2, pp. 123-134 | DOI

[193] F. H. Busse; G. Hartung; M. Jaletzky; G. Sommermann Experiments on thermal convection in rotating systems motivated by planetary problems, Dyn. Atmos. Oceans, Volume 27 (1997) no. 1–4, pp. 161-174 | DOI

[194] F. H. Busse Convective flows in rapidly rotating spheres and their dynamo action, Phys. Fluids, Volume 14 (2002) no. 4, pp. 1301-1314 | DOI

[195] A. P. Bassom; A. M. Soward Localised rotating convection induced by topography, Physica D, Volume 97 (1996) no. 1–3, pp. 29-44 | DOI

[196] J. S. Oishi; K. J. Burns; J. B. Marston; S. M. Tobias Direct statistical simulation of the Busse annulus, J. Fluid Mech., Volume 949 (2022), R1 | DOI

[197] R. J. Teed; C. A. Jones; R. Hollerbach On the necessary conditions for bursts of convection within the rapidly rotating cylindrical annulus, Phys. Fluids, Volume 24 (2012) no. 6, 066604 | DOI | Zbl

[198] J. Wicht; M. French; S. Stellmach; N. Nettelmann; T. Gastine; L. Duarte; R. Redmer Modeling the interior dynamics of gas planets, Magnetic Fields in the Solar System: Planets, Moons and Solar Wind Interactions, Volume 448, Springer International Publishing, Cham, 2018, pp. 7-81 | DOI

[199] M. A. Calkins; K. Julien; P. Marti Three-dimensional quasi-geostrophic convection in the rotating cylindrical annulus with steeply sloping endwalls, J. Fluid Mech., Volume 732 (2013), pp. 214-244 | DOI | Zbl

[200] D. J. Baker A technique for the precise measurement of small fluid velocities, J. Fluid Mech., Volume 26 (1966) no. 3, pp. 573-575 | DOI

[201] P. Olson Laboratory experiments on the dynamics of the core, Phys. Earth Planet. Inter., Volume 187 (2011) no. 3–4, pp. 139-156 | DOI

[202] P. Olson Experimental dynamos and the dynamics of planetary cores, Annu. Rev. Earth Planet. Sci., Volume 41 (2013), pp. 153-181 | DOI

[203] P. Cardin; P. Olson 8.13 - Experiments on core dynamics, Treatise on Geophysics (G. Schubert, ed.), Elsevier, Amsterdam, Boston, Heidelberg, London, New York, Oxford, Paris, San Diego, San Francisco, Singapore, Sydney, Tokyo, 2015, pp. 317-339 | DOI

[204] G. Hulot; J.-L. Le Mouë; D. Jault The flow at the core-mantle boundary symmetry properties, J. Geomagn. Geoelec., Volume 42 (1990) no. 7, pp. 857-874 | DOI

[205] D. Gubbins; J. Bloxham Morphology of the geomagnetic field and implications for the geodynamo, Nature, Volume 325 (1987) no. 6104, pp. 509-511 | DOI

[206] J. Bloxham; D. Gubbins; A. Jackson Geomagnetic secular variation, Philos. Trans. R. Soc. Lond. A Math. Phys. Sci., Volume 329 (1989) no. 1606, pp. 415-502

[207] D. Brito; H.-C. Nataf; P. Cardin; J. Aubert; J.-P. Masson Ultrasonic doppler velocimetry in liquid gallium, Exp. Fluids, Volume 31 (2001) no. 6, pp. 653-663 | DOI

[208] N. T. Baker; A. Pothérat; L. Davoust; F. Debray Controlling the dimensionality of MHD turbulence at low Rm, Exp. Fluids, Volume 58 (2017) no. 7, 79 | DOI

[209] Signal Processing 2D/3D Ultrasonic velocimetry https://signal-processing.com/udv-md/ (accessed 25 February 2025)

[210] P. B. Rhines Waves and turbulence on a beta-plane, J. Fluid Mech., Volume 69 (1975) no. 3, pp. 417-443 | DOI | Zbl

[211] T. L. Lonner; A. Aggarwal; J. M. Aurnou Planetary core-style rotating convective flows in paraboloidal laboratory experiments, J. Geophys. Res.: Planets, Volume 127 (2022) no. 10, e2022JE007356 | DOI

[212] P. Read; Y. Afanasyev; J. Aurnou; D. Lemasquerier Eddy-driven zonal jet flows in the laboratory, C. R. Phys., Volume 25 (2024) no. S3, pp. 1-51 | DOI

[213] D. P. Lathrop; C. B. Forest Magnetic dynamos in the lab, Phys. Today, Volume 64 (2011) no. 7, pp. 40-45 | DOI

[214] A. Tilgner Towards experimental fluid dynamos, Phys. Earth Planet. Inter., Volume 117 (2000) no. 1–4, pp. 171-177 | DOI

[215] P. H. Roberts; E. M. King On the genesis of the Earth’s magnetism, Rep. Prog. Phys., Volume 76 (2013) no. 9, 096801 | DOI

[216] S. Horn; J. M. Aurnou The Elbert range of magnetostrophic convection. I. Linear theory, Proc. R. Soc. A, Volume 478 (2022) no. 2264, 20220313 | DOI

[217] D. R. Fearn Thermal and magnetic instabilities in a rapidly rotating fluid sphere, Geophys. Astrophys. Fluid Dyn., Volume 14 (1979) no. 1, pp. 103-126 | DOI | Zbl

[218] A. M. Soward Convection driven dynamos, Phys. Earth Planet. Inter., Volume 20 (1979) no. 2–4, pp. 134-151 | DOI

[219] I. A. Eltayeb Hydromagnetic convection in a rapidly rotating fluid layer, Proc. R. Soc. Lond. A Math. Phys. Sci., Volume 326 (1972) no. 1565, pp. 229-254 | Zbl

[220] I. A. Eltayeb Overstable hydromagnetic convection in a rotating fluid layer, J. Fluid Mech., Volume 71 (1975) no. 01, pp. 161-179 | DOI | Zbl

[221] K. Aujogue; A. Pothérat; B. Sreenivasan The onset of plane rotating magnetoconvection at low Ekman number, Phys. Fluids, Volume 27 (2015) no. 10, 106602 | DOI | Zbl

[222] D. Gubbins; M. Richards Coupling of the core dynamo and mantle: thermal or topographic?, Geophys. Res. Lett., Volume 13 (1986) no. 13, pp. 1521-1524 | DOI

[223] J. Bloxham; D. Gubbins Thermal core–mantle interactions, Nature, Volume 325 (1987) no. 6104, pp. 511-513 | DOI

[224] C. L. Johnson; C. G. Constable Persistently anomalous Pacific geomagnetic fields, Geophys. Res. Lett., Volume 25 (1998) no. 7, pp. 1011-1014 | DOI

[225] G. A. Glatzmaier; R. S. Coe; L. Hongre; P. H. Roberts The role of the Earth’s mantle in controlling the frequency of geomagnetic reversals, Nature, Volume 401 (1999) no. 6756, pp. 885-890 | DOI

[226] C. Kutzner; U. R. Christensen Simulated geomagnetic reversals and preferred virtual geomagnetic pole paths, Geophys. J. Int., Volume 157 (2004) no. 3, pp. 1105-1118 | DOI

[227] J. Wicht; A. Tilgner Theory and modeling of planetary dynamos, Planetary Magnetism, Springer, New York, 2010, pp. 501-542 | DOI

[228] P. Olson; H. Amit Magnetic reversal frequency scaling in dynamos with thermochemical convection, Phys. Earth Planet. Inter., Volume 229 (2014), pp. 122-133 | DOI

[229] J. Wicht; D. G. Meduri A Gaussian model for simulated geomagnetic field reversals, Phys. Earth Planet. Inter., Volume 259 (2016), pp. 45-60 | DOI

[230] F. Terra-Nova; H. Amit Regionally-triggered geomagnetic reversals, Sci. Rep., Volume 14 (2024) no. 1, 9639 | DOI

[231] J. A. Tarduno; M. K. Watkeys; T. N. Huffman; R. D. Cottrell; E. G. Blackman; A. Wendt; C. A. Scribner; C. L. Wagner Antiquity of the South Atlantic Anomaly and evidence for top-down control on the geodynamo, Nat. Commun., Volume 6 (2015) no. 1, 7865 | DOI

[232] R. Boehler High-pressure experiments and the phase diagram of lower mantle and core materials, Rev. Geophys., Volume 38 (2000) no. 2, pp. 221-245 | DOI

[233] J. C. Castle; K. C. Creager; J. P. Winchester; R. D. van der Hilst Shear wave speeds at the base of the mantle, J. Geophys. Res.: Solid Earth, Volume 105 (2000) no. B9, pp. 21543-21557 | DOI

[234] E. J. Garnero Heterogeneity of the lowermost mantle, Annu. Rev. Earth Planet. Sci., Volume 28 (2000) no. 1, pp. 509-537 | DOI

[235] R. D. van der Hilst; H. Kárason Compositional heterogeneity in the bottom 1000 kilometers of Earth’s mantle: Toward a hybrid convection model, Science, Volume 283 (1999) no. 5409, pp. 1885-1888 | DOI

[236] N. Schaeffer; D. Jault; H.-C. Nataf; A. Fournier Turbulent geodynamo simulations: a leap towards Earths core, Geophys. J. Int., Volume 211 (2017) no. 1, pp. 1-29 | DOI

[237] S. Horn; J. M. Aurnou The Elbert range of magnetostrophic convection. II. Comparing linear theory to nonlinear low-Rm simulations, Proc. R. Soc. A (2025) (in press) | DOI

[238] E. M. King; J. M. Aurnou Magnetostrophic balance as the optimal state for turbulent magnetoconvection, Proc. Natl. Acad. Sci. USA, Volume 112 (2015) no. 4, pp. 990-994 | DOI

[239] S. Chandrasekhar Thermal convection, Daedalus, Volume 86 (1957) no. 4, pp. 323-339

[240] M. Wedi; V. M. Moturi; D. Funfschilling; S. Weiss Experimental evidence for the boundary zonal flow in rotating Rayleigh–Bénard convection, J. Fluid Mech., Volume 939 (2022), A14 | DOI

[241] O. Shishkina Tenacious wall states in thermal convection in rapidly rotating containers, J. Fluid Mech., Volume 898 (2020), F1 | DOI

[242] B. Favier; E. Knobloch Robust wall states in rapidly rotating Rayleigh–Bénard convection, J. Fluid Mech., Volume 895 (2020), R1 | DOI

[243] C. C. Finlay; N. Gillet; J. Aubert; P. W. Livermore; D. Jault Gyres, jets and waves in the Earths core, Nat. Rev. Earth Environ., Volume 4 (2023), pp. 377-392 | DOI

[244] G. Hulot; C. Eymin; B. Langlais; M. Mandea; N. Olsen Small-scale structure of the geodynamo inferred from Oersted and Magsat satellite data, Nature, Volume 416 (2002) no. 6881, pp. 620-623 | DOI

[245] P. Pugnat; R. Barbier; C. Berriaud et al. 43+T grenoble hybrid magnet: From final assembly to commissioning of the superconducting outsert, IEEE Trans. Appl. Supercond., Volume 32 (2022) no. 6, pp. 1-7 | DOI

[246] P. H. Roberts Introduction to Magnetohydrodynamics, Longmans, London, 1967

[247] D. Schmitt; T. Alboussière; D. Brito; P. Cardin; G. D.; D. Jault; H.-C. Nataf Rotating spherical Couette flow in a dipolar magnetic field: Experimental study of magneto-inertial waves, J. Fluid Mech., Volume 604 (2008), pp. 175-197 | DOI

[248] S. Lalloz; L. Davoust; F. Debray; A. Pothérat Alfvén waves at low Magnetic Reynolds number: transitions between diffusion, dispersive Alfvén waves and nonlinear propagation, J. Fluid Mech., Volume 1003 (2025), A19 | DOI

[249] N. Gillet; D. Jault; E. Canet; A. Fournier Fast torsional waves and strong magnetic field within the Earths core, Nature, Volume 465 (2010), pp. 74-77 | DOI

[250] N. Gillet; F. Gerick; D. Jault; T. Schwaiger; J. Aubert; M. Istas Satellite magnetic data reveal interannual waves in Earth’s core, Proc. Natl. Acad. Sci. USA, Volume 119 (2022) no. 13, e2115258119 | DOI

[251] H. Cao; R. K. Yadav; J. M. Aurnou Geomagnetic polar minima do not arise from steady meridional circulation, Proc. Natl. Acad. Sci. USA, Volume 115 (2018) no. 44, pp. 11186-11191 | DOI

[252] R. K. Yadav; T. Gastine; U. R. Christensen; L. D. Duarte; A. Reiners Effect of shear and magnetic field on the heat-transfer efficiency of convection in rotating spherical shells, Geophys. J. Int., Volume 204 (2016) no. 2, pp. 1120-1133 | DOI

[253] A. J. Aguirre Guzmán; M. Madonia; J. S. Cheng; R. Ostilla-Mónico; H. J. H. Clercx; R. P. J. Kunnen Force balance in rapidly rotating Rayleigh–Bénard convection, J. Fluid Mech., Volume 928 (2021), A16 | DOI

[254] B. Favier; L. J. Silvers; M. R. Proctor Inverse cascade and symmetry breaking in rapidly rotating Boussinesq convection, Phys. Fluids, Volume 26 (2014) no. 9, 096605 | DOI

[255] C. Guervilly; D. W. Hughes; C. A. Jones Large-scale vortices in rapidly rotating Rayleigh–Bénard convection, J. Fluid Mech., Volume 758 (2014), pp. 407-435 | DOI

[256] S. Stellmach; M. Lischper; K. Julien; G. Vasil; J. S. Cheng; A. Ribeiro; E. M. King; J. M. Aurnou Approaching the asymptotic regime of rapidly rotating convection: boundary layers versus interior dynamics, Phys. Rev. Lett., Volume 113 (2014) no. 25, 254501 | DOI

[257] J. Aubert State and evolution of the geodynamo from numerical models reaching the physical conditions of Earths core, Geophys. J. Int., Volume 235 (2023) no. 1, pp. 468-487 | DOI

[258] D. J. Stevenson Cosmochemistry and structure of the giant planets and their satellites, Icarus, Volume 62 (1985) no. 1, pp. 4-15 | DOI

[259] H. C. Urey The Planets, Their Origin and Development, Yale Universith Press, New Haven, 1952

[260] 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

[261] E. K. Shea; B. P. Weiss; W. S. Cassata; D. L. Shuster; S. M. Tikoo; J. Gattacceca; T. L. Grove; M. D. Fuller A long-lived lunar core dynamo, Science, Volume 335 (2012) no. 6067, pp. 453-456 | DOI

[262] C. Stys; M. Dumberry A past lunar dynamo thermally driven by the precession of its inner core, J. Geophys. Res.: Planets, Volume 125 (2020) no. 7, e2020JE006396 | DOI

[263] U. R. Christensen Iron snow dynamo models for Ganymede, Icarus, Volume 247 (2015), pp. 248-259 | DOI

[264] R. Stieglitz; U. Müller Experimental demonstration of a homogeneous two-scale dynamo, Phys. Fluids, Volume 13 (2001) no. 3, pp. 561-564 | DOI

[265] A. Gailitis; O. Lielausis; S. Dement’ev et al. Detection of a flow induced magnetic field eigenmode in the Riga dynamo facility, Phys. Rev. Lett., Volume 84 (2000) no. 19, pp. 4365-4368 | DOI

[266] R. Monchaux; M. Berhanu; M. Bourgoin et al. Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium, Phys. Rev. Lett., Volume 98 (2007) no. 4, 044502 | DOI

[267] M. Berhanu; R. Monchaux; S. Fauve et al. Magnetic field reversals in an experimental turbulent dynamo, Europhys. Lett., Volume 77 (2007) no. 5, 59001 | DOI

[268] F. Stefani; A. Gailitis; G. Gerbeth; A. Giesecke; T. Gundrum; G. Rüdiger; M. Seilmayer; T. Vogt The DRESDYN project: liquid metal experiments on dynamo action and magnetorotational instability, Geophys. Astrophys. Fluid Dyn., Volume 113 (2019) no. 1–2, pp. 51-70 | DOI

[269] F. Stefani; S. Anders; S. Eckert et al. The DRESDYN precession experiment, C. R. Phys., Volume 25 (2024) no. S3, pp. 1-19 | DOI

[270] F. Pétrélis Experimental dynamos: from models to applications to the geodynamo, C. R. Phys., Volume 25 (2024) no. S3, pp. 1-17 | DOI

[271] T. Schwaiger; T. Gastine; J. Aubert Force balance in numerical geodynamo simulations: a systematic study, Geophys. J. Int., Volume 219 (2019), p. S101-S114 | DOI

[272] J. Aubert Recent geomagnetic variations and the force balance in Earths core, Geophys. J. Int., Volume 221 (2020) no. 1, pp. 378-393 | DOI

[273] E. Dormy Strong-field spherical dynamos, J. Fluid Mech., Volume 789 (2016), pp. 500-513 | DOI

[274] P. H. Roberts; K. Zhang Thermal generation of Alfvén waves in oscillatory magnetoconvection, J. Fluid Mech., Volume 420 (2000), pp. 201-223 | DOI | Zbl

[275] A. Alemany; R. Moreau; P. Sulem; U. Frisch Influence of an external magnetic field on homogeneous MHD turbulence, J. Méc., Volume 18 (1979) no. 2, pp. 277-313

[276] K. Messadek; R. Moreau An experimental investigation of MHD quasi-two-dimensional turbulent shear flows, J. Fluid Mech., Volume 456 (2002), pp. 137-159 | DOI | Zbl

[277] T. Alboussière; V. Uspenski; R. Moreau Quasi-2D MHD turbulent shear layers, Exp. Therm. Fluid Sci., Volume 20 (1999) no. 20, pp. 19-24 | DOI

[278] S. Eckert; G. Gerbeth; W. Witke; H. Langenbrunner MHD turbulence measurements in a sodium channel exposed to a transverse magnetic field, Int. J. Heat Fluid Flow, Volume 22 (2001) no. 3, pp. 358-364 | DOI

[279] A. Pothérat; R. Klein Why, how and when MHD turbulence at low Rm becomes three-dimensional, J. Fluid Mech., Volume 761 (2014), pp. 168-205 | DOI | Zbl

[280] A. Pothérat; R. Klein Do magnetic fields enhance turbulence at low magnetic Reynolds number?, Phys. Rev. Fluids, Volume 2 (2017) no. 6, 063702 | DOI

[281] N. Baker; A. Pothérat; L. Davoust; F. Debray Inverse and direct energy cascades in three-dimensional magnetohydrodynamic turbulence at low magnetic Reynolds number, Phys. Rev. Lett., Volume 120 (2018), 224502 | DOI

[282] L. Davoust; M. D. Cowley; R. Moreau; R. Bolcato Buoyancy-driven convection with a uniform magnetic field. Part 2. Experimental investigation, J. Fluid Mech., Volume 400 (1999), pp. 59-90 | DOI | Zbl

[283] T. Vogt; W. Ishimi; T. Yanagisawa; Y. Tasaka; A. Sakuraba; S. Eckert Transition between quasi-two-dimensional and three-dimensional Rayleigh–Bénard convection in a horizontal magnetic field, Phys. Rev. Fluids, Volume 3 (2018) no. 1, 013503 | DOI

[284] O. Andreev; A. Thess; C. Haberstroh Visualization of magnetoconvection, Phys. Fluids, Volume 15 (2003) no. 12, pp. 3886-3889 | DOI | Zbl

[285] A. Alferenok; A. Pothérat; U. Lüdtke Optimal magnet configuration for Lorentz Force Velocimetry in low conductivity fluids, Meas. Sci. Technol., Volume 24 (2013) no. 6, 065303 | DOI

[286] R. Hide An experimental study of thermal convection in a rotating liquid, Philos. Trans. R. Soc. Lond. A Math. Phys. Sci., Volume 250 (1958) no. 983, pp. 441-478 | DOI

[287] T. Alboussière; R. Deguen; M. Melzani Melting-induced stratification above the Earths inner core due to convective translation, Nature (London), Volume 466 (2010), pp. 744-747 | DOI

[288] J. Leconte; G. Chabrier A new vision of giant planet interiors: Impact of double diffusive convection, Astron. Astrophys., Volume 540 (2012), A20 | DOI

[289] T. Gastine; J. Wicht Stable stratification promotes multiple zonal jets in a turbulent Jovian dynamo model, Icarus, Volume 368 (2021), 114514 | DOI

[290] K. M. Moore; A. Barik; S. Stanley et al. Dynamo simulations of Jupiter’s magnetic field: The role of stable stratification and a dilute core, J. Geophys. Res.: Planets, Volume 127 (2022) no. 11, e2022JE007479 | DOI

[291] J. R. Fuentes; B. W. Hindman; A. E. Fraser; E. H. Anders Evolution of semiconvective staircases in rotating flows: Consequences for fuzzy cores in giant planets, Astrophys. J. Lett., Volume 975 (2024) no. 1, L1 | DOI

[292] S. Horn Oscillatory thermal-inertial layer formation in the outer molecular region of gas giants, 2024 (In preperation)

[293] B. A. Buffett; C. T. Seagle Stratification of the top of the core due to chemical interactions with the mantle, J. Geophys. Res.: Solid Earth, Volume 115 (2010) no. B4, B04407 | DOI

Cité par Sources :

Commentaires - Politique