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Volume 542, June 2012
Article Number A26
Number of page(s) 11
Section The Sun
Published online 30 May 2012

Online material

Appendix A:

Here, we describe the contributions of the mean-electromotive force that are involved in Eq. (1). The basic formulation is given in Pipin (2008, P08). In this paper we reformulate tensor , which represents the hydrodynamical part of the α-effect, by using Eq. (23) from P08 in the following form, (A.1)The contribution of magnetic helicity (a is a fluctuating vector magnetic field potential) to the α-effect is defined as , where (A.2)The turbulent pumping, γi,j, is also part of the mean electromotive force in Eq. (23) (P08). Here we rewrite it in a more traditional form (cf., e.g., ), (A.3)The effect of turbulent diffusivity, which is anisotropic because of the Coriolis force, is given by (A.4)Functions depend on the Coriolis number Ω ∗  = 2τcΩ0 and the typical convective turnover time in the mixing-length approximation, τc = /u′. They can be found in P08. The turbulent diffusivity is parametrized in the form, , where is the characteristic mixing-length turbulent diffusivity, u′ is the rms convective velocity, is the mixing length, Cη is a constant to control the intensity of turbulent mixing. The other quantities in Eqs. (A.1), (A.3), (A.4) are is the density stratification scale, is the scale of turbulent diffusivity, e = Ω/|Ω| is a unit vector along the axis of rotation. Equations (A.1), (A.3), (A.4) take into account the influence of the fluctuating small-scale magnetic fields, which can be present in the background turbulence and stem from the small-scale dynamo. In our paper, the parameter , which measures the ratio between the magnetic and kinetic energies of fluctuations in the background turbulence, is assumed to be equal to 1. This corresponds to the energy equipartition. The quenching function of the hydrodynamical part of α-effect is defined by (A.5)Note in the notation of P08 , and .

Below we give the functions of the Coriolis number defining the dependence of the turbulent transport generation and diffusivities on the angular velocity:

© ESO, 2012

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