Dynamo Onset as a First-Order Transition: Lessons from a Shell Model for Magnetohydrodynamics

Abstract

We carry out systematic and high-resolution studies of dynamo action in a shell model for magnetohydrodynamic (MHD) turbulence over wide ranges of the magnetic Prandtl number $P{r}_{\mathrm{M}}$ and the magnetic Reynolds number $R{e}_{\mathrm{M}}$. Our study suggests that it is natural to think of dynamo onset as a nonequilibrium, first-order phase transition between two different turbulent, but statistically steady, states. The ratio of the magnetic and kinetic energies is a convenient order parameter for this transition. By using this order parameter, we obtain the stability diagram (or nonequilibrium phase diagram) for dynamo formation in our MHD shell model in the $(P{r}_{\mathrm{M}}^{-1},R{e}_{\mathrm{M}})$ plane. The dynamo boundary, which separates dynamo and no-dynamo regions, appears to have a fractal character. We obtain hysteretic behavior of the order parameter across this boundary and suggestions of nucleation-type phenomena.

9 pages, 9 figures

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Cited by in corpus (9)

• Systematics of the magnetic-Prandtl-number dependence of homogeneous, isotropic magnetohydrodynamic turbulence
• Bistability and chaos in Taylor-Green dynamo
• Supercriticality to subcriticality in dynamo transitions
• Melting of a nonequilibrium vortex crystal in a fluid film with polymers : elastic versus fluid turbulence
• Study on the large scale dynamo transition
• Multiscaling in superfluid turbulence: A shell-model study
• Multiscaling in Hall-Magnetohydrodynamic Turbulence: Insights from a Shell Model
• Intermittent turbulent dynamo at very low and high magnetic Prandtl numbers
• Chaos and irreversibility of a flexible filament in periodically-driven Stokes flow