Global dynamo models from direct numerical simulations and their mean-field counterparts

MAG (ENS/IPGP), LRA, Ecole Normale Supérieure, 24 rue Lhomond, 75252 Paris Cedex 05, France
e-mail: martin@schrinner.eu

Received: 3 February 2011
Accepted: 24 June 2011

Abstract

Context. The test-field method permits us 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. This has been done to date 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 can be appropriately described by corresponding mean-field results. We also identify conditions under which mean-field models disagree with 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 rapidly 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 closer agreement between direct numerical simulations and mean-field results.