Mean-field view on geodynamo models

M. Schrinner¹ - K.-H. Rädler² - D. Schmitt¹ - M. Rheinhardt² - U. Christensen¹

¹ Max Planck Institute for Solar System Research, Max-Planck-Straße 2, D-37191 Katlenburg-Lindau, Germany
² Astrophysical Institute Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany

Abstract
A comparison is made between direct numerical simulations of magnetohydrodynamic processes in a rotating spherical shell and their mean-field description. The mean fields are defined by azimuthal averaging. The coefficients that occur in the traditional representation of the mean electromotive force considering spatial derivatives of the mean magnetic field up to the first order are calculated by two different methods, with the fluid velocity taken from the direct numerical simulations. While the first method does not use intrinsic approximations, the second one is based on the first-order smoothing approximation. There is satisfying agreement of the results of the both methods for sufficiently slow fluid motions. For the investigated example of rotating magnetoconvection, the mean magnetic field derived from the direct numerical simulation is well reproduced on the mean-field level. For a quasi-steady geodynamo model a discrepancy occurs, which is probably a consequence of the neglect of higher-order derivatives of the mean magnetic field in the mean electromotive force. At higher excitations, geodynamo models of the same type show highly time-dependent fluid motions and magnetic fields. The coefficients determining the mean electromotive force fluctuate then considerably in space and time, but on the average their profiles resemble those of their counterparts in the quasi-steady case. Figs 8, Refs 12.