Robust estimate of dynamo thresholds in the von Kármán sodium experiment using the extreme value theory

Davide Faranda (1) , Mickaël Bourgoin (2, 3) , Sophie Miralles (2) , Philippe Odier (2) , Jean-François Pinton (2) , Nicolas Plihon (2) , François Daviaud (1) , Bérengère Dubrulle (1)

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

We apply a new threshold detection method based on the extreme value theory (EVT) to the von Kármán sodium (VKS) experiment data. The VKS experiment is a successful attempt to get a dynamo magnetic field in a laboratory liquidmetal experiment. We first show that the dynamo threshold is associated with a change of the probability density function of the extreme values of the magnetic field. This method does not require the measurement of response functions from applied external perturbations and thus provides a simple threshold estimate. We apply our method to different configurations in the VKS experiment, showing that it yields a robust indication of the dynamo threshold as well as evidence of hysteretic behaviors. Moreover, for the experimental configurations in which a dynamo transition is not observed, the method provides a way to extrapolate an interval of possible threshold values.

Domaines: Mécanique des fluides [physics.class-ph]

Davide Faranda, Mickaël Bourgoin, Sophie Miralles, Philippe Odier, Jean-François Pinton, et al.. Robust estimate of dynamo thresholds in the von Kármán sodium experiment using the extreme value theory. New Journal of Physics, 2014, 16, pp.083001. ⟨10.1088/1367-2630/16/8/083001⟩. ⟨hal-01079009⟩