Instability of the homopolar disk-dynamo in presence of white noise

Nicolas Leprovost (1) , Bérengère Dubrulle (2) , Franck Plunian (3)

1 LPS - Laboratoire de Physique Statistique de l'ENS
2 SPEC - UMR3680 - Service de physique de l'état condensé
3 LEGI - Laboratoire des Écoulements Géophysiques et Industriels [Grenoble]

We study a modified Bullard dynamo and show that this system is equivalent to a non-linear oscillator subject to a multiplicative noise. The stability analysis of this oscillator is performed. Two bifurcations are identified, first, towards an łqłq intermittent\rq\rq state, where the absorbing (non-dynamo) state is no more stable but the most probable value of the amplitude of the oscillator is still zero, and, secondly, towards a łqłq turbulent\rq\rq (dynamo) state, where it is possible to define unambiguously a (non-zero) most probable value, around which the amplitude of the oscillator fluctuates. The bifurcation diagram of this system exhibits three regions, which are analytically characterized.

Domaines: Sciences de la Terre

Nicolas Leprovost, Bérengère Dubrulle, Franck Plunian. Instability of the homopolar disk-dynamo in presence of white noise. Magnetohydrodynamics c/c of Magnitnaia Gidrodinamika, 2006, 42 (2-3), pp.131 à 142. ⟨insu-00354244⟩