Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers

By A. Schekochihin, A. Iskakov, S. Cowley, James C. McWilliams, M. Proctor, T. Yousef. 2007

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This paper is a detailed report on a programme of direct numerical simulations of incompressible nonhelical 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 Rmc for dynamo versus the hydrodynamic Reynolds number Re is obtained for 1 ≲ Re ≲ 6700. In the limit Pm ≫ 1, Rmc is at most three times larger than for the previously well established dynamo at large and moderate Prandtl numbers: Rmc ≲ 200 for Re ≳ 6000 compared to Rmc ∼ 60 for . The stability curve Rmc(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 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 , 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.

Subfields: Astronomy and Astrophysics, Computational Mechanics, Molecular Biology

View Paper: https://www.semanticscholar.org/paper/524cd16227416fcbb991c5e5457ee00ca965f3d2

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In Astronomy and Astrophysics

  1. Matthias Rempel
  2. Paul Charbonneau
  3. Mark S. Miesch
  4. J. Toomre
  5. A. Brun
  6. M. Browning

In Computational Mechanics

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In Molecular Biology

  1. Matthias Rempel
  2. Paul Charbonneau
  3. Mark S. Miesch
  4. J. Toomre
  5. A. Brun
  6. M. Browning

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