Scale dependence of alpha effect and turbulent diffusivity

¹ NORDITA, Roslagstullsbacken 23, 10691 Stockholm, Sweden e-mail: brandenb@nordita.org
² Astrophysical Institute Potsdam, An der Sternwarte 16, 14482 Potsdam, Germany
³ Max-Planck-Institut für Sonnensystemforschung, 37191 Katlenburg-Lindau, Germany

Received: 8 January 2008
Accepted: 8 February 2008

Abstract

Aims. We determine the alpha effect and turbulent magnetic diffusivity for mean magnetic fields with profiles of different length scales from simulations of isotropic turbulence. We then relate these results to nonlocal formulations in which alpha and the turbulent magnetic diffusivity correspond to integral kernels.

Methods. We solve evolution equations for magnetic fields that give the response to imposed test fields. These test fields correspond to mean fields with various wavenumbers. Both an imposed fully helical steady flow consisting of a pattern of screw-like motions (Roberts flow) and time-dependent, statistically steady isotropic turbulence are considered. In the latter case the evolution equations are solved simultaneously with the momentum and continuity equations. The corresponding results for the electromotive force are used to calculate alpha and magnetic diffusivity tensors.

Results. For both, the Roberts flow under the second-order correlation approximation and the isotropic turbulence alpha and turbulent magnetic diffusivity are greatest on large scales and these values diminish toward smaller scales. In both cases, the alpha effect and turbulent diffusion kernels are approximated by exponentials, corresponding to Lorentzian profiles in Fourier space. For isotropic turbulence, the turbulent diffusion kernel is half as wide as the alpha effect kernel. For the Roberts flow beyond the second-order correlation approximation, the turbulent diffusion kernel becomes negative on large scales.