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Comptes Rendus Physique
Volume 9, n° 7
pages 683-688 (septembre 2008)
Doi : 10.1016/j.crhy.2008.07.001
Simple models and time scales in the dynamo effect
Modèles simples et échelles de temps dans lʼeffet dynamo
 

Philippe Nozières
Institut Laue-Langevin, BP 156, 38042 Grenoble cedex 9, France 

Abstract

The dynamo effect has been studied for 50 years, starting from the simple homopolar dynamo of Bullard. Numerical calculations on simple models, such as the crossed dynamos of Rikitake, display large oscillations and brutal reversals. The present Note puts emphasis on time scales. One scale  , purely electromagnetic, describes inductive decay (the frequency at which the skin depth is the size of the system), the other   is magnetohydrodynamic, controlling the exchanges of kinetic and magnetic energies. Usually  : a clear separation of time scales makes the physics much more transparent. We show why sharp reversals must be expected, starting either from the slow or from the fast time scale. Such a comparison clarifies the issue. To cite this article: P. Nozières, C. R. Physique 9 (2008).

The full text of this article is available in PDF format.
Résumé

Lʼeffet dynamo est une histoire vieille de 50 ans, qui commence avec la dynamo unipolaire de Bullard. Lʼétude numérique de modèles simples, par exemple les deux dynamos croisées de Rikitake, met en évidence des renversements brutaux et de grandes oscillations. La présente note met lʼaccent sur les échelles de temps. Lʼune dʼelles,  , décrit lʼamortissement inductif des courants (cʼest la fréquence à laquelle lʼépaisseur de peau est la taille du système). Lʼautre   est magnétohydrodynamique, contrôlant les échanges dʼénergies cinétique et magnétique. En général   : une séparation claire des deux échelles de temps rend alors la physique beaucoup plus transparente. Nous montrons que les renversements brutaux sont prévisibles, et nous décrivons les aspects qualitatifs du problème en partant soit de lʼéchelle lente, soit de lʼéchelle rapide. La comparaison est instructive. Pour citer cet article : P. Nozières, C. R. Physique 9 (2008).

The full text of this article is available in PDF format.

Keywords : Dynamo, Magnetohydrodynamics, Turbulence

Mots-clés : Dynamo, Magnétohydrodynamique, Turbulence




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