Turbulent magnetic dynamo excitation at low magnetic Prandtl number

Abstract

Planetary and stellar dynamos likely result from turbulent motions in magnetofluids with kinematic viscosities that are small compared to their magnetic diffusivities. Laboratory experiments are in progress to produce similar dynamos in liquid metals. This work reviews recent computations of thresholds in critical magnetic Reynolds number above which dynamo amplification can be expected for mechanically-forced turbulence (helical and non-helical, short wavelength and long wavelength) as a function of the magnetic Prandtl number $P_M$. New results for helical forcing are discussed, for which a dynamo is obtained at $P_M=5\times 10^{-3}$. The fact that the kinetic turbulent spectrum is much broader in wavenumber space than the magnetic spectrum leads to numerical difficulties which are bridged by a combination of overlapping direct numerical simulations and subgrid models of magnetohydrodynamic turbulence. Typically, the critical magnetic Reynolds number increases steeply as the magnetic Prandtl number decreases, and then reaches an asymptotic plateau at values of at most a few hundred. In the turbulent regime and for magnetic Reynolds numbers large enough, both small and large scale magnetic fields are excited. The interactions between different scales in the flow are also discussed.

arXiv comment8 pages, 8 figures, to appear in Physics of Plasmas

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Cited by in corpus (8)

• Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers
• The Turbulent Dynamo
• Dynamo Transition in Low-dimensional Models
• A Spherical Plasma Dynamo Experiment
• Inverse cascades and alpha-effect at low magnetic Prandtl number
• The Lagrangian-averaged model for magnetohydrodynamics turbulence and the absence of bottleneck
• Wave-driven dynamo action in spherical MHD systems
• Fully resolved array of simulations investigating the influence of the magnetic Prandtl number on magnetohydrodynamic turbulence