Intermittent turbulent dynamo at very low and high magnetic Prandtl numbers 

Eric Buchlin Submitted: 20111109 15:48
Context: Direct numerical simulations have shown that the dynamo is efficienteven at low Prandtl numbers, i.e., the critical magnetic Reynolds number Rm_cnecessary for the dynamo to be efficient becomes smaller than the hydrodynamicReynolds number Re when Re > infinity. Aims: We test the conjecture (Iskakovet al. 2007) that Rm_c actually tends to a finite value when Re > infinity,and we study the behavior of the dynamo growth factor gamma at very low andhigh magnetic Prandtl numbers. Methods: We use local and nonlocal shellmodelsof magnetohydrodynamic (MHD) turbulence with parameters covering a much widerrange of Reynolds numbers than direct numerical simulations, but ofastrophysical relevance. Results: We confirm that Rm_c tends to a finite valuewhen Re > infinity. The limit for Rm > infinity of the dynamo growth factorgamma in the kinematic regime behaves like Re^eta, and, similarly, thelimit for Re > infinity of gamma behaves like Rm^{eta'}, witheta=eta'=0.4. Conclusion: Comparison with a phenomenology based on anintermittent smallscale turbulent dynamo, together with the differencesbetween the growth rates in the different local and nonlocal models, indicate aweak contribution of nonlocal terms to the dynamo effect.
Authors: E. Buchlin
Projects: None

Publication Status: A&A Letters (published)
Last Modified: 20111110 10:58


