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

TL;DR

This paper demonstrates that mean-field dynamo models, derived from direct numerical simulations using the test-field method, can effectively describe chaotically time-dependent dynamos in rotating spherical shells, with improved accuracy over stationary models.

Contribution

It shows how mean-field models can accurately represent chaotic dynamo behavior in low Rossby number regimes, extending previous work on stationary dynamos.

Findings

Mean-field coefficients accurately parameterize electromotive force in fast rotating dynamos.

Chaotic time-dependence improves scale separation and model agreement.

Mean-field models match direct simulations better for time-dependent dynamos.

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.