Bruce Buffett $^{a}$ and Gary Glatzmaier $^{b}$
$^{a}$ Department of Earth and Ocean Sciences, University of British Columbia, Canada $^{b}$ Department of Earth Sciences and Institute of Geophysics and Planetary Physics, University of California, Santa Cruz, CA, USA
No computer model of the geodynamo has been able to afford the spatial resolution needed to simulate the turbulent spectrum in the Earth's liquid core, which spans at least seven orders of magnitude in length scale. All geodynamo models have employed greatly enhanced eddy diffusivities, which are both homogeneous and isotropic, to stabilize the low resolution numerical solutions and crudely account for the transport and mixing by the unresolved (subgrid-scale) turbulence. An alternative approach relies on better approximations for the nonlinear cascade of energy to and from the subgrid-scales, so that much smaller eddy diffusivities can be used in the numerical models. We present preliminary results of such an approach. The similarity method uses the time dependent structure of the large, resolved scales to estimate the structure and effects of the unresolved scales. Predictions for the effects of the unresolved turbulence on the resolved flow and field are inhomogeneous, anisotropic and time dependent. Results from 3D Cartesian and 3D spherical simulations are presented.