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 nonhelical, short wavelength and long wavelength) as a function of the magnetic Prandtl number PM. New results for helical forcing are discussed, for which a dynamo is obtained at PM=5×10−3. The fact that the kinetic turbulent spectrum is much broader in wave-number space than the magnetic spectrum leads to numerical difficulties that 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.