Galerkin analysis of kinematic dynamos in the von Karman geometry

Type Article
Date 2006-01
Language English
Author(s) Marie Louis1, 4, Normand C2, Daviaud F3
Affiliation(s) 1 : Service de Physique de l’Etat Condensé, DSM/DRECAM/SPEC, CNRS/SPM URA 2464, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France and Laboratoire de Physique des Océans, Université de Bretagne Occidentale, BP 809, 29285 Brest, France
2 : Service de Physique Théorique, CEA/DSM/SPhT, CNRS/SPM URA 2306, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France
3 : Service de Physique de l’Etat Condensé, DSM/DRECAM/SPEC, CNRS/SPM URA 2464, CEA/Saclay, 91191 Gif-sur-Yvette Cedex, France
Source Physics Of Fluids (1070-6631) (Amer Inst Physics), 2006-01 , Vol. 18 , N. 1 , P. 017102
DOI 10.1063/1.2158267
WOS© Times Cited 31
Abstract We investigate dynamo action by solving the kinematic dynamo problem for velocity fields of the von Karman type between two coaxial counter-rotating propellers in a cylinder. A Galerkin method is implemented that takes advantage of the symmetries of the flow and their subsequent influence on the nature of the magnetic field at the dynamo threshold. Distinct modes of instability have been identified that differ by their spatial and temporal behaviors. Our calculations give the result that a stationary and antisymmetric mode prevails at the dynamo threshold. We then present a quantitative analysis of the results based on the parametric study of four interaction coefficients obtained by reduction of our initially large eigenvalue problem. We propose these coefficients to measure the relative importance of the different mechanisms at play in the von Karman kinematic dynamo.
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