Magnetic reynolds number and model-z geodynamo

Abstract

The magnetic Reynolds number (MRN) is used in estimating the quantities appearing in the current theory of the nearly symmetric dynamo. In kinematic theory, all expansions can be developed in terms of the MRN, but this seems to be less advantageous in the case of hydromagnetic theory and in particular the model-Z. An attempt has been made to replace the role of the MRN in the nearly symmetric expansion by the amplitudes of the individual quantities, where the amplitudes of the non-axisymmetric quantities are considered to be small compared with those of the azimuthal quantities. The amplitude of the axially asymmetric velocities and the amplitude of Archimedean buoyancey play essential roles here.

The expansions of the theory are valid only when certain assumptions are made about the field amplitude, and the velocity and buoyancy forces, even though the amplitude of the resulting a-effect is unaffected. The a-effect can be altered only by rapid changes in the non-symmetric velocities in the generation region.