Intermittent turbulent dynamo at very low and high magnetic Prandtl numbers
Abstract
Context. Direct numerical simulations of plasmas have shown that the dynamo effect is efficient even at low Prandtl numbers, i.e., the critical magnetic Reynolds number Rm_{c} that is necessary for a dynamo to be efficient becomes smaller than the hydrodynamic Reynolds number Re when Re → ∞.
Aims: We test the conjecture that Rm_{c} tends to a finite value when Re → ∞, and we study the behavior of the dynamo growth factor γ at very low and high magnetic Prandtl numbers.
Methods: We use local and nonlocal shell models of magnetohydrodynamic (MHD) turbulence with parameters covering a much wider range of Reynolds numbers than direct numerical simulations, that is of astrophysical relevance.
Results: We confirm that Rm_{c} tends to a finite value when Re → ∞. As Rm → ∞, the limit to the dynamo growth factor γ in the kinematic regime follows Re^{β}, and, similarly, the limit for Re → ∞ of γ behaves like Rm^{β'}, with β ≈ β' ≈ 0.4.
Conclusions: Our comparison with a phenomenology based on an intermittent smallscale turbulent dynamo, together with the differences between the growth rates in the different local and nonlocal models, indicate that nonlocal terms contribute weakly to the dynamo effect.
Figures 5 and 6 are available in electronic form at http://www.aanda.org
 Publication:

Astronomy and Astrophysics
 Pub Date:
 October 2011
 DOI:
 10.1051/00046361/201117890
 arXiv:
 arXiv:1109.4442
 Bibcode:
 2011A&A...534L...9B
 Keywords:

 dynamo;
 magnetohydrodynamics (MHD);
 turbulence;
 Physics  Plasma Physics;
 Astrophysics  Solar and Stellar Astrophysics
 EPrint:
 5 pages, 6 figures