Time scales separation for dynamo action

Emmanuel Dormy^1,3 and David Gérard-Varet^2,3

¹MAG (Ecole Normale Supérieure / Institut de Physique du Globe de Paris),
Département de Physique, LRA,
Ecole Normale Supérieure - 24, rue Lhomond, 75231 Paris Cedex 05, France.
²Département de Mathématiques et Applications,
Ecole Normale Supérieure - 45, rue d'Ulm, 75230 Paris Cedex 05, France.
³C.N.R.S., France.

EPL (Europhysics Letters), 81 64002 (2008).

received 13 September 2007; accepted in final form 21 January 2008
published online 21 February 2008

47.65.-d Magnetohydrodynamics
47.65.Md Plasma dynamos
47.20.-k Flow instabilities

Abstract. The study of dynamo action in astrophysical objects classically involves two timescales: the slow diffusive one and the fast advective one. We investigate the possibility of field amplification on an intermediate timescale associated with time dependent modulations of the flow. We consider a simple steady configuration for which dynamo action is not realised. We study the effect of time dependent perturbations of the flow. We show that some vanishing low frequency perturbations can yield exponential growth of the magnetic field on the typical time scale of oscillation. The dynamo mechanism relies here on a parametric instability associated with transient amplification by shear flows. Consequences on natural dynamos are discussed.