Magnetohydrodynamic turbulence and the geodynamo

Abstract

Ideal magnetohydrodynamic (MHD) turbulence contains an intrinsic statistical mechanism called ‘broken ergodicity’ for producing an energetic, large-scale, quasi-stationary coherent structure. Since MHD turbulence occurs in the Earth’s liquid outer core, the implication is that the Earth’s dipole magnetic field may be due to MHD turbulence, per se. The purpose of this work is to examine how ideal MHD results apply to the real (i.e., dissipative) MHD turbulence found in the outer core. Prior theoretical and computational results will be briefly reviewed, after which new results will be presented. The significant effects caused by variations in the time-dependence of the forcing will be discussed. It will be also shown that dissipative MHD turbulence driven with isotropic forcing produces large-scale, coherent structures similar to those appearing in ideal MHD turbulence. A connection between spherical harmonic degree and turbulence wave number will be made, allowing for a qualitative comparison of numerical magnetic energy spectra with the International Geomagnetic Reference Field. In addition, a mechanism for explaining the dominance of the Earth’s axial dipole component over its azimuthal ones will also be described. These results indicate that MHD turbulence, per se, may underlie the geodynamo.