Alpha effect and turbulent diffusion from convection

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 α-effect as a function of rotation rate are consistent with earlier numerical studies, i.e. increasing magnitude as rotation increases and approximately latitude profile for moderate rotation. Turbulent diffusivity, , is proportional to the square of the turbulent vertical velocity in all cases. Whereas decreases approximately inversely proportional to the wavenumber of the field, the α-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 α-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 α-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 α-shear dynamo may also act in the simulations. If both rotation and shear are present, the α-effect is more pronounced. At the same time, the combination of the shear-current and -effects is also stronger than in the case of shear alone, but subdominant to the α-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.