[Cartographie de lʼinduction magnétique dans un écoulement de Couette sphérique soumis à un champ magnétique]
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 () 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 (), 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.
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Mot clés : Dynamo, Magnétohydrodynamique, Effet oméga, Sodium liquide, DTS
@article{CRPHYS_2013__14_2-3_248_0,
author = {Henri-Claude Nataf},
title = {Magnetic induction maps in a magnetized spherical {Couette} flow experiment},
journal = {Comptes Rendus. Physique},
pages = {248--267},
publisher = {Elsevier},
volume = {14},
number = {2-3},
year = {2013},
doi = {10.1016/j.crhy.2012.12.002},
language = {en},
}
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/
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