The turbulent dynamo as an instability in a noisy medium

Abstract

We study an example of instability in presence of a multiplicative noise, namely the spontaneous generation of a magnetic field in a turbulent medium. This so-called turbulent dynamo problem remains challenging, experimentally and theoretically. In this field, the prevailing theory is the Mean-Field Dynamo (Krause and Rädler, 1980) where the dynamo effect is monitored by the mean magnetic field (other possible choices would be the energy, flux,...). In recent years, it has been shown on stochastic oscillators that this type of approach could be misleading. In this paper, we develop a stochastic description of the turbulent dynamo effect which permits us to define unambiguously a threshold for the dynamo effect, namely by globally analyzing the probability density function of the magnetic field instead of a given moment.

6 pages

References in corpus (4)

• Particles and fields in fluid turbulence
• Numerical study of homogeneous dynamo based on experimental von Karman type flows
• Stability analysis of a noise-induced Hopf bifurcation
• A Solvable Model for Nonlinear Mean Field Dynamo

Cited by in corpus (12)

• Influence of turbulence on the dynamo threshold
• Low frequency noise controls on-off intermittency of bifurcating systems
• Subcritical dynamo bifurcation in the Taylor Green flow
• Fluctuation of magnetic induction in von Kármán swirling flows
• Parametric instability of the helical dynamo
• Homopolar oscillating-disc dynamo driven by parametric resonance
• Oscillating Ponomarenko dynamo in the highly conducting limit
• Global fluctuations in magnetohydrodynamic dynamos
• Stability of a nonlinear oscillator with random damping
• Robust estimate of dynamo thresholds in the von Kármán sodium experiment using the Extreme Value Theory
• Fully developed turbulent dynamo at low magnetic Prandtl numbers
• Characterization of turbulence in inhomogeneous anisotropic flows