EDP Sciences
Free access
Volume 495, Number 1, February III 2009
Page(s) 1 - 8
Section Astrophysical processes
DOI http://dx.doi.org/10.1051/0004-6361:200810359
Published online 11 December 2008
A&A 495, 1-8 (2009)
DOI: 10.1051/0004-6361:200810359

Alpha effect and diffusivity in helical turbulence with shear

D. Mitra1, P. J. Käpylä2, R. Tavakol1, and A. Brandenburg3

1  Astronomy unit, School of Mathematical Sciences, Queen Mary University of London, Mile End Road, London E1 4NS, UK
    e-mail: dhruba.mitra@gmail.com
2  Observatory, Tähtitorninmäki (PO Box 14), 00014 University of Helsinki, Finland
3  NORDITA, Roslagstullsbacken 23, 10691 Stockholm, Sweden

Received 10 June 2008 / Accepted 28 November 2008

Aims. We study the dependence of turbulent transport coefficients, such as the components of the $\alpha$ tensor $(\alpha_{ij})$ and the turbulent magnetic diffusivity tensor $(\eta_{ij})$, on shear and magnetic Reynolds number in the presence of helical forcing.
Methods. We use three-dimensional direct numerical simulations with periodic boundary conditions and measure the turbulent transport coefficients using the kinematic test field method. In all cases the magnetic Prandtl number is taken as unity.
Results. We find that with increasing shear the diagonal components of $\alpha_{ij}$ quench, whereas those of $\eta_{ij}$ increase. The antisymmetric parts of both tensors increase with increasing shear. We also propose a simple expression for the turbulent pumping velocity (or $\gamma$ effect). This pumping velocity is proportional to the kinetic helicity of the turbulence and the vorticity of the mean flow. For negative helicity, i.e. for a positive trace of $\alpha_{ij}$, it points in the direction of the mean vorticity, i.e. perpendicular to the plane of the shear flow. Our simulations support this expression for low shear and magnetic Reynolds number. The transport coefficients depend on the wavenumber of the mean flow in a Lorentzian fashion, just as for non-shearing turbulence.

Key words: magnetohydrodynamics (MHD) -- hydrodynamics -- turbulence -- magnetic fields

© ESO 2009