1 Laboratoire de Physique Statistique de l'Ecole Normale Supérieure,
CNRS UMR 8550,
24 Rue Lhomond, 75231 Paris Cedex 05, France
2 MAG (IPGP/ENS), CNRS UMR 7154, LRA,
Ecole Normale Supérieure, 24 Rue Lhomond, 75231 Paris Cedex 05, France
Received 17 March 2010; accepted in final form 20 May 2010
published online 17 June 2010
91.25.Cw Origins and models of the magnetic field; dynamo theories
47.65.-d Magnetohydrodynamics and electrohydrodynamics
Abstract - We show that the modes involved in the dynamics of reversals of the magnetic field generated by the flow of an electrically conducting fluid in a spherical domain, strongly depend on the magnetic Prandtl number Pm, i.e., the ratio between viscous and magnetic diffusivities. For Pm~1, the axial dipolar field reverses in the presence of a strong equatorial dipolar component, whereas for Pm<0.5, field reversals mostly involve axisymmetric modes, axial magnetic dipole and quadrupole coupled through a broken symmetry of the flow. Using symmetry arguments, we write a dynamical system for these three modes that qualitatively reproduces the main features of the reversals observed in direct simulations for small Pm.