Mean-field view on rotating magnetoconvection and a geodynamo model

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 derivatives of the mean magnetic field up to the first order are calculated with the fluid velocity taken from the direct numerical simulations by two different methods. While the first one does not use specific approximations, the second one is based on the first-order smoothing approximation. There is satisfying agreement of the results of 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 the simple 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. (c) 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.