## Abstract

This paper is a detailed report on a programme of direct numerical simulations of incompressible nonhehcal randomly forced magnetohydrodynamic (MHD) turbulence that are used to settle a long-standing issue in the turbulent dynamo theory and demonstrate that the fluctuation dynamo exists in the limit of large magnetic Reynolds number Rm ≫1 and small magnetic Prandtl number Pm ≪ 1. The dependence of the critical Rm_{c} for dynamo versus the hydrodynamic Reynolds number Re is obtained for 1 ≲ Re ≲ 6700. In the limit Pm ≪ 1, Rm_{c} is at most three times larger than for the previously well established dynamo at large and moderate Prandtl numbers: Rm_{c} ≲ 200 for Re ≳ 6000 compared to Rm_{c} ∼ 60 for Pm ≥ 1. The stability curve Rm_{c}(Re) (and, it is argued, the nature of the dynamo) is substantially different from the case of the simulations and liquid-metal experiments with a mean flow. It is not as yet possible to determine numerically whether the growth rate of the magnetic energy is ∝Rm^{1/2} in the limit Re ≫ Rm ≫ 1, as should be the case if the dynamo is driven by the inertial-range motions at the resistive scale, or tends to an Rm -independent value comparable to the turnover rate of the outer-scale motions. The magnetic-energy spectrum in the low-Pm regime is qualitatively different from the Pm ≥ 1 case and appears to develop a negative spectral slope, although current resolutions are insufficient to determine its asymptotic form. At Rm e (1, Rm_{c}), the magnetic fluctuations induced via the tangling by turbulence of a weak mean field are investigated and the possibility of a k^{-1} spectrum above the resistive scale is examined. At low Rm < 1, the induced fluctuations are well described by the quasistatic approximation; the k-^{11/3} spectrum is confirmed for the first time in direct numerical simulations. Applications of the results on turbulent induction to understanding the nonlocal energy transfer from the dynamo-generated magnetic field to smaller-scale magnetic fluctuations are discussed. The results reported here are of fundamental importance for understanding the genesis of small-scale magnetic fields in cosmic plasmas.

Original language | English (US) |
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Article number | 300 |

Journal | New Journal of Physics |

Volume | 9 |

DOIs | |

State | Published - Aug 31 2007 |

Externally published | Yes |

## All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)