Scale dependence of alpha effect and turbulent diffusivity

TL;DR

This study investigates how the alpha effect and turbulent magnetic diffusivity depend on the scale of mean magnetic fields using simulations of isotropic turbulence and Roberts flow, revealing scale-dependent behaviors and kernel profiles.

Contribution

It provides a detailed analysis of the scale dependence of alpha and turbulent diffusivity, including their kernel shapes and differences between flow types, extending understanding beyond the second-order correlation approximation.

Findings

Alpha and turbulent diffusivity decrease at smaller scales.

Both kernels are well approximated by exponentials, Lorentzian in Fourier space.

Turbulent diffusion kernel is narrower than alpha kernel in isotropic turbulence.

Abstract

Aims: To determine alpha effect and turbulent magnetic diffusivity for mean magnetic fields with profiles of different length scale from simulations of isotropic turbulence, and to relate these results to nonlocal formulations in which alpha and the turbulent magnetic diffusivity correspond to integral kernels. Methods: A set of evolution equations for magnetic fields is solved which gives the response to imposed test fields, that is, mean magnetic 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 aforementioned 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 isotropic turbulence alpha and turbulent magnetic diffusivity are largest at large scales and these values diminish toward smaller scales. In both cases the alpha effect and turbulent diffusion kernels are well 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 at large scales.