Magnetic induction maps in a magnetized spherical Couette flow experiment

Henri-Claude Nataf

doi:10.1016/j.crhy.2012.12.002

Prix Paul Doistau–Emile Blutet 2011 de lʼAcadémie des sciences

Magnetic induction maps in a magnetized spherical Couette flow experiment
[Cartographie de lʼinduction magnétique dans un écoulement de Couette sphérique soumis à un champ magnétique]

Henri-Claude Nataf ¹

¹ ISTerre, Université de Grenoble 1, CNRS, 38041 Grenoble, France

Comptes Rendus. Physique, Volume 14 (2013) no. 2-3, pp. 248-267.

Résumé
Abstract

Lʼexpérience DTS consiste en un écoulement de Couette sphérique soumis à un champ magnétique dipolaire. Le fluide utilisé est du sodium liquide. Au cours dʼune série de campagnes de mesure, nous avons obtenu des données sur le champ de vitesse moyen axisymétrique, le champ magnétique moyen, et le potentiel électrique. Toutes ces quantités sont couplées à travers lʼéquation dʼinduction. En particulier, la rotation différentielle du fluide produit un fort effet ω qui induit un champ magnétique azimutal conséquent. Profitant de la géométrie sphérique de lʼexpérience, je développe les champs azimutaux et méridionaux en polynômes de Legendre et jʼobtiens les expressions qui relient toutes les mesures aux fonctions radiales du champ de vitesse pour chaque degré. Pour de petits nombres de Reynolds magnétiques Rm les relations sont linéaires et les équations azimutale et méridionale sont découplées. Je sélectionne un jeu de mesures pour une vitesse de rotation donnée de la sphère interne ( $Rm ≃ 9.4$ ) et jʼinverse simultanément les données de vitesse et magnétiques, reconstruisant ainsi à la fois les champs azimutaux et méridionaux dans la coquille fluide. Les résultats démontrent la bonne cohérence des mesures et indiquent que les fluctuations turbulentes non-axisymétriques ne contribuent pas de façon significative à lʼinduction magnétique axisymétrique.

The DTS experiment is a spherical Couette flow experiment with an imposed dipolar magnetic field. Liquid sodium is used as a working fluid. In a series of measurement campaigns, we have obtained data on the mean axisymmetric velocity, the mean induced magnetic field and electric potentials. All these quantities are coupled through the induction equation. In particular, a strong ω-effect is produced by differential rotation within the fluid shell, inducing a significant azimuthal magnetic field. Taking advantage of the simple spherical geometry of the experiment, I expand the azimuthal and meridional fields into Legendre polynomials and derive the expressions that relate all measurements to the radial functions of the velocity field for each harmonic degree. For small magnetic Reynolds numbers Rm the relations are linear, and the azimuthal and meridional equations decouple. Selecting a set of measurements for a given rotation frequency of the inner sphere ( $Rm ≃ 9.4$ ), I invert simultaneously the velocity and the magnetic data and thus reconstruct both the azimuthal and the meridional fields within the fluid shell. The results demonstrate the good internal consistency of the measurements, and indicate that turbulent non-axisymmetric fluctuations do not contribute significantly to the axisymmetric magnetic induction.

Reçu le : 2012-10-05
Accepté le : 2012-12-12
Publié le : 2013-01-10

DOI : 10.1016/j.crhy.2012.12.002

Keywords: Dynamo, Magnetohydrodynamics, Omega effect, Liquid sodium, DTS
Mot clés : Dynamo, Magnétohydrodynamique, Effet oméga, Sodium liquide, DTS

Affiliations des auteurs :

Henri-Claude Nataf ¹

¹ ISTerre, Université de Grenoble 1, CNRS, 38041 Grenoble, France

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Henri-Claude Nataf. Magnetic induction maps in a magnetized spherical Couette flow experiment. Comptes Rendus. Physique, Volume 14 (2013) no. 2-3, pp. 248-267. doi : 10.1016/j.crhy.2012.12.002. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/j.crhy.2012.12.002/

Bibliographie
Cité par

[1] J. Larmor How could a Rotating Body such as the Sun become a Magnet?, Report of the British Association for the Advancement of Science, 87th Meeting, 1919, pp. 159-160

[2] W.M. Elsasser Induction effects in terrestrial magnetism part I, Theory Phys. Rev., Volume 69 (1946) no. 3–4, pp. 106-116

[3] E.N. Parker Hydromagnetic dynamo models, Astrophys. J., Volume 122 (1955), pp. 293-314

[4] A. Gailitis; O. Lielausis; E. Platacis; S. Dementʼev; A. Cifersons; G. Gerbeth; T. Gundrum; F. Stefani; M. Christen; G. Will Magnetic field saturation in the Riga dynamo experiment, Phys. Rev. Lett., Volume 86 (2001), pp. 3024-3027

[5] Agris Gailitis; Gunter Gerbeth; Thomas Gundrum; Olgerts Lielausis; Ernests Platacis; Frank Stefani History and results of the Riga dynamo experiments, C. R. Physique, Volume 9 (2008) no. 7, pp. 721-728

[6] R. Stieglitz; U. Müller Experimental demonstration of a homogeneous two-scale dynamo, Phys. Fluids, Volume 13 (2001), pp. 561-564

[7] Ulrich Mueller; Robert Stieglitz; Fritz H. Busse; Andreas Tilgner The Karlsruhe two-scale dynamo experiment, C. R. Physique, Volume 9 (2008) no. 7, pp. 729-740

[8] P. Frick; S. Denisov; S. Khripchenko; V. Noskov; D. Sokoloff; R. Stepanov A nonstationary dynamo experiment in a braked torus, Cargese, France, August 21–26, 2000 (P. Chossat; D. Ambruster; I. Oprea, eds.) (NATO Science Series, Series II: Mathematics, Physics and Chemistry), Volume vol. 26, NATO; CNRS; Natl. Sci. Fdn., Springer, Dordrecht, Netherlands (2001), pp. 1-8

[9] D.P. Lathrop; W.L. Shew; D.R. Sisan Laboratory experiments on the transition to MHD dynamos, Plasma Phys. Control. Fusion, Volume 43 (2001) no. 12A, p. A151-A160

[10] R. OʼConnell; R. Kendrick; M. Nornberg; E. Spence; A. Bayliss; C.B. Forest On the possibility of an homogeneous MHD dynamo in the laboratory, Cargese, France, August 21–26, 2000 (P. Chossat; D. Ambruster; I. Oprea, eds.) (NATO Science Series, Series II: Mathematics, Physics and Chemistry), Volume vol. 26, NATO; CNRS; Natl. Sci. Fdn. Springer, Dordrecht, Netherlands (2001), pp. 59-66

[11] P. Cardin; D. Brito; D. Jault; H.-C. Nataf; J.-P. Masson Towards a rapidly rotating liquid sodium dynamo experiment, Magnetohydrodynamics, Volume 38 (2002), pp. 177-189

[12] L. Marié; M. Bourgoin; F. Pétrélis; J. Roy; J. Burguete; A. Chiffaudel; F. Daviaud; S. Fauve; P. Odier; J.F. Pinton Water experiments related to the “Von Karman Sodium” dynamo project, 6th Experimental Chaos Conference, Potsdam, Germany, June 22–26, 2001 (S. Boccaletti; B.J. Gluckman; J. Kurths; L.M. Pecora; M.L. Spano, eds.) (AIP Conference Proceedings), Volume vol. 622, USN, Off Res., Amer. Inst. Physics, Melville, NY, USA (2002), pp. 453-461

[13] G. Verhille; N. Plihon; M. Bourgoin; P. Odier; J.-F. Pinton Laboratory dynamo experiments, Space Sci. Rev., Volume 152 (2010) no. 1–4, pp. 543-564

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

[15] M. Berhanu; R. Monchaux; S. Fauve; N. Mordant; F. Pétrélis; A. Chiffaudel; F. Daviaud; B. Dubrulle; L. Marié; F. Ravelet; M. Bourgoin; P. Odier; J.-F. Pinton; R. Volk Magnetic field reversals in an experimental turbulent dynamo, Europhys. Lett., Volume 77 ( March 2007 ), p. 59001

[16] R. Monchaux; M. Berhanu; M. Bourgoin; M. Moulin; P. Odier; J.-F. Pinton; R. Volk; S. Fauve; N. Mordant; F. Pétrélis; A. Chiffaudel; F. Daviaud; B. Dubrulle; C. Gasquet; L. Marié; F. Ravelet Generation of a magnetic field by dynamo action in a turbulent flow of liquid sodium, Phys. Rev. Lett., Volume 98 (2007) no. 4, p. 044502

[17] Sebastien Aumaitre; Michael Berhanu; Mickael Bourgoin; Arnaud Chiffaudel; Francois Daviaud; Berengere Dubrulle; Stephan Fauve; Louis Marié; Romain Monchaux; Nicolas Mordant; Philippe Odier; Francois Pétrélis; Jean-Francois Pinton; Nicolas Plihon; Florent Ravelet; Romain Volk The VKS experiment: turbulent dynamical dynamos, C. R. Physique, Volume 9 (2008) no. 7, pp. 689-701

[18] E.J. Spence; M.D. Nornberg; C.M. Jacobson; R.D. Kendrick; C.B. Forest Observation of a turbulence-induced large scale magnetic field, Phys. Rev. Lett., Volume 96 (2006) no. 5, p. 055002

[19] M. Steenbeck; F. Krause; K.H. Rädler A calculation of the mean electromotive force in an electrically conducting fluid in turbulent motion, under the influence of Coriolis forces, Z. Naturforsch. A, Volume 21 (1966), pp. 369-376

[20] P. Charbonneau Dynamo models of the solar cycle, Living Rev. Sol. Phys., Volume 2 ( October 2, 2012 ) http://www.livingreviews.org/lrsp-2005-2

[21] Michel Rieutord The solar dynamo, C. R. Physique, Volume 9 (2008) no. 7, pp. 757-765

[22] C.F. Barenghi; C.A. Jones Nonlinear planetary dynamos in a rotating spherical shell. 1. Numerical methods, Geophys. Astrophys. Fluid Dyn., Volume 60 (1991) no. 1–4, pp. 211-243

[23] A. Brandenburg; D. Moss; G. Rüdiger; I. Tuominen Hydromagnetic alpha-omega-type dynamos with feedback from large-scale motions, Geophys. Astrophys. Fluid Dyn., Volume 61 (1991) no. 1–4, pp. 179-198

[24] E.J. Spence; M.D. Nornberg; R.A. Bayliss; R.D. Kendrick; C.B. Forest Fluctuation-driven magnetic fields in the Madison dynamo experiment, Phys. Plasmas, Volume 15 (2008) no. 5

[25] A. Brandenburg; P. Chatterjee; F. Del Sordo; A. Hubbard; P.J. Kapyla; M. Rheinhardt Turbulent transport in hydromagnetic flows, Phys. Scr., Volume T142 (2009)

[26] F. Pétrélis; M. Bourgoin; L. Marié; J. Burguete; A. Chiffaudel; F. Daviaud; S. Fauve; P. Odier; J.F. Pinton Nonlinear magnetic induction by helical motion in a liquid sodium turbulent flow, Phys. Rev. Lett., Volume 90 (2003) no. 17, p. 174501

[27] Kian Rahbarnia; Benjamin P. Brown; Mike M. Clark; Elliot J. Kaplan; Mark D. Nornberg; Alex M. Rasmus; Nicholas Zane Taylor; Cary B. Forest; Frank Jenko; Angelo Limone; Jean-Francois Pinton; Nicolas Plihon; Gautier Verhille Direct observation of the turbulent emf and transport of magnetic field in a liquid sodium experiment, Astrophys. J., Volume 759 (2012), pp. 80-85

[28] P. Frick; V. Noskov; S. Denisov; R. Stepanov Direct measurement of effective magnetic diffusivity in turbulent flow of liquid sodium, Phys. Rev. Lett., Volume 105 ( October 27, 2010 ) no. 18, p. 184502

[29] Vitaliy Noskov; Sergey Denisov; Rodion Stepanov; Peter Frick Turbulent viscosity and turbulent magnetic diffusivity in a decaying spin-down flow of liquid sodium, Phys. Rev. E, Part 2, Volume 85 (2012) no. 1, p. 016303

[30] F. Ravelet; B. Dubrulle; F. Daviaud; P.-A. Ratie Kinematic alpha tensors and dynamo mechanisms in a von Karman Swirling flow, Phys. Rev. Lett., Volume 109 (2012) no. 2, p. 024503

[31] H.-C. Nataf; T. Alboussière; D. Brito; P. Cardin; N. Gagnière; D. Jault; J.-P. Masson; D. Schmitt Experimental study of super-rotation in a magnetostrophic spherical Couette flow, Geophys. Astrophys. Fluid Dyn., Volume 100 (2006), pp. 281-298

[32] H.-C. Nataf; T. Alboussière; D. Brito; P. Cardin; N. Gagnière; D. Jault; D. Schmitt Rapidly rotating spherical Couette flow in a dipolar magnetic field: an experimental study of the mean axisymmetric flow, Phys. Earth Planet. Inter., Volume 170 (2008), pp. 60-72

[33] D. Brito; T. Alboussière; P. Cardin; N. Gagnière; D. Jault; P. La Rizza; J.P. Masson; H.C. Nataf; D. Schmitt Zonal shear and super-rotation in a magnetized spherical Couette-flow experiment, Phys. Rev. E, Part 2, Volume 83 ( June 15, 2011 ) no. 6, p. 066310

[34] D. Schmitt; T. Alboussière; D. Brito; P. Cardin; N. Gagnière; 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

[35] D. Schmitt; P. Cardin; P. La Rizza; H.-C. Nataf Magneto-Coriolis waves in a spherical Couette flow experiment, Eur. J. Mech. B, Fluids, Volume 37 (2013), pp. 10-22 | DOI

[36] Henri-Claude Nataf; Nadege Gagniere On the peculiar nature of turbulence in planetary dynamos, C. R. Physique, Volume 9 (2008) no. 7, pp. 702-710

[37] A. Figueroa, N. Schaeffer, H.-C. Nataf, D. Schmitt, Modes and instabilities in magnetized spherical Couette flow, J. Fluid Mech. (2012), in press. | DOI

[38] D. Brito; H.-C. Nataf; P. Cardin; J. Aubert; J.-P. Masson Ultrasonic Doppler velocimetry in liquid gallium, Exp. Fluids, Volume 31 (2001), pp. 653-663

[39] P.H. Roberts Treatise on Geophysics, Core Dynamics, vol. 8, Elsevier B.V., 2007 (pp. 67–105, Chapter 8.03)

[40] D.R. Fearn; P.H. Roberts; A.M. Soward Convection, stability and the dynamo, Pitman Research Notes in Mathematics Series, Longman Scientific and Technical, 1988, pp. 60-324

[41] A. Tarantola; B. Valette Generalized non-linear inverse problems solved using the least-squares criterion, Rev. Geophys., Volume 20 (1982) no. 2, pp. 219-232

[42] V.C.A. Ferraro The non-uniform rotation of the sun and its magnetic field, Mon. Not. R. Astron. Soc., Volume 97 (1937), pp. 458-472

[43] A. Pouquet; U. Frisch; J. Léorat Strong MHD helical turbulence and nonlinear dynamo effect, J. Fluid Mech., Volume 77 (1976), pp. 321-354

[44] Francois Pétrélis; Stephan Fauve Inhibition of the dynamo effect by phase fluctuations, Europhys. Lett., Volume 76 (2006), pp. 602-608

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