Abstract
Context. The recently developed test-field method permits to compute dynamo coefficients from global, direct numerical simulations. The subsequent use of these parameters in mean-field models enables us to compare self-consistent dynamo models with their mean-field counterparts. So far, this has been done for a simulation of rotating magnetoconvection and a simple benchmark dynamo, which are both (quasi-)stationary. Aims. It is shown that chaotically time-dependent dynamos in a low Rossby number regime may be appropriately described by corresponding mean-field results. Also, it is pointed out under which conditions mean-field models do not match direct numerical simulations. Methods. We solve the equations of magnetohydrodynamics (MHD) in a rotating, spherical shell in the Boussinesq approximation. Based on this, we compute mean-field coefficients for several models with the help of the previously developed test-field method. The parameterization of the mean electromotive force by these coefficients is tested against direct numerical simulations. In addition, we use the determined dynamo coefficients in mean-field models and compare the outcome with azimuthally averaged fields from direct numerical simulations. Results. The azimuthally and time-averaged electromotive force in fast rotating dynamos is sufficiently well parameterized by the set of determined mean-field coefficients. In comparison to the previously considered (quasi-)stationary dynamo, the chaotic time-dependence leads to an improved scale separation and thus to a better agreement between direct numerical simulations and mean-field results.
Highlights
Mean-field electrodynamics provides a conceptual understanding of dynamo processes generating coherent, large-scale magnetic fields in planets, stars, and galaxies (Krause & Rädler 1980; Moffatt 1978)
The mean-field description of astationary dynamo has been affected by a poor scale-separation, from an insufficiently accurate parameterization of the electromotive force (Schrinner et al 2007)
We have demonstrated that the chaotically time-dependent dynamos considered here can provide improvements in both cases, if a combined azimuthal and time average is applied
Summary
Mean-field electrodynamics provides a conceptual understanding of dynamo processes generating coherent, large-scale magnetic fields in planets, stars, and galaxies (Krause & Rädler 1980; Moffatt 1978). It depends on a number of free parameters, that are only poorly known under astrophysically relevant conditions. We briefly summarize the essentials of mean-field theory to specify this point. Within a mean-field approach, the velocity and the magnetic field are usually divided into largescale mean fields, V, B, and residual parts, u, b, that vary on much shorter length or timescales,. The evolution of the mean field is governed by ∂B ∂t = ∇ ×
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