Alpha effect and turbulent diffusion from convection

Free access article

Issue		A&A Volume 500, Number 2, June III 2009


Page(s)		633 - 646
Section		Astrophysical processes
DOI		http://dx.doi.org/10.1051/0004-6361/200811498
Published online		29 April 2009

A&A 500, 633-646 (2009)
DOI: 10.1051/0004-6361/200811498

Alpha effect and turbulent diffusion from convection

P. J. Käpylä¹, M. J. Korpi¹, and A. Brandenburg²

¹ Observatory, Tähtitorninmäki, PO Box 14, 00014 University of Helsinki, Finland
e-mail: petri.kapyla@helsinki.fi
² NORDITA, AlbaNova University Center, Roslagstullsbacken 23, 10691 Stockholm, Sweden

Received 10 December 2008 / Accepted 18 March 2009

Abstract
Aims. We study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection.
Methods. We use the test field method, together with three-dimensional numerical simulations of turbulent convection with shear and rotation, to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. We employ one-dimensional mean-field models with the derived turbulent transport coefficients to examine whether they give results that are compatible with direct simulations.
Results. The results for the $\alpha$ -effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately $\cos \theta$ latitude profile for moderate rotation. Turbulent diffusivity, $\eta_{\rm t}$ , is proportional to the square of the turbulent vertical velocity in all cases. Whereas $\eta_{\rm t}$ decreases approximately inversely proportional to the wavenumber of the field, the $\alpha$ -effect and turbulent pumping show a more complex behaviour with partial or full sign changes and the magnitude staying roughly constant. In the presence of shear and no rotation, a weak $\alpha$ -effect is induced which does not seem to show any consistent trend as a function of shear rate. Provided that the shear is large enough, this small $\alpha$ -effect is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are, however, well below those in direct simulations, suggesting that an incoherent $\alpha$ -shear dynamo may also act in the simulations. If both rotation and shear are present, the $\alpha$ -effect is more pronounced. At the same time, the combination of the shear-current and ${\Omega}\times{ J}$ -effects is also stronger than in the case of shear alone, but subdominant to the $\alpha$ -shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.

Key words: magnetohydrodynamics (MHD) -- convection -- turbulence -- Sun: magnetic fields -- stars: magnetic fields

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