Characteristic amplitudes in the solution of the anelastic geodynamo model

Abstract

Braginsky and Roberts [Geophys. Astrophys. Fluid Dyn. 79 (1995) 1] presented energy and entropy balance equations that are applicable to the 3D geodynamo model in the anelastic approximation by Glatzmaier and Roberts [Physica D 97 (1996) 81]. These slightly modified equations allow us to discuss the expected characteristic amplitudes in the solution of the model. We demonstrate that the entire energy balance of the dynamo does not play a role in obtaining the characteristic amplitudes of the solution. The amplitudes are primarily influenced by the flux of the light constituent and by the superadiabatic heat flux. Based on this we obtain the characteristic amplitudes of entropy, the light constituent and velocity which are in agreement with the solution presented by Glatzmaier and Roberts [Physica D 97 (1996) 81]. The characteristic amplitude of the magnetic field we obtain relates more to the axisymmetrical part of their solution. Our analysis also suggests suitable dimensionless units as a measure of individual quantities when solving the model.