Letter to the Editor

Intermittent turbulent dynamo at very low and high magnetic Prandtl numbers^⋆

¹ CNRS, Institut d’Astrophysique Spatiale, UMR 8617, 91405 Orsay, France
e-mail: eric.buchlin@ias.u-psud.fr
² Univ Paris Sud, Institut d’Astrophysique Spatiale, UMR 8617, 91405 Orsay, France

Received: 16 August 2011
Accepted: 20 September 2011

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 small-scale 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.