Investigation of roles of subgrid scale (SGS) terms in dynamo simulations in a rotating spherical shell

Flow and magnetic fields in the Earth's outer core are expected to have a vast range of length scale from the size of the outer core to the thickness of the boundary layers. Limited spatial resolution in geodynamo simulations prohibits solutions with the full range of scales. Consequently, subgrid scale (SGS) models are required to account for the effects of the unresolved fields on the large scale solution. Each nonlinear term in the geodynamo problem requires a SGS model; this includes the SGS heat flux, Reynolds stress, SGS Maxwell stress, and SGS magnetic induction. We choose the dynamic scale-similarity model for the SGS model. The amplitudes of the SGS terms are adjusted using model coefficients, which are evaluated automatically using the fields in the numerical simulation. Reliable estimates for the model coefficients are obtained by averaging over the azimuthal direction, in which the characteristics of the fields are dynamically similar. Hence, the model coefficient is a function of radius and colatitude. We perform large-eddy simulations (LES) of a dynamo in a rotating spherical shell using the present dynamic SGS model, and evaluate the work of the Reynolds stress, SGS Maxwell stress, and energy flux of the SGS magnetic induction term. Our results show that the amplitudes of the energy flux for the three SGS terms are roughly similar to each other. A positive (upscale) energy flux is obtained for the modeled Reynolds stress in a cylindrical region outside of the tangential cylinder. A similar upscale energy transfer is observed in resolved convection calculations due to tilting of convection columns. Elsewhere in the core a negative (downscale) energy flux is obtained for the Reynolds stress. The net effect of the Reynolds stress is a small transfer of energy from the resolved scales into the unresolved scales. We compare the results of the LES with the results a resolved simulation on a finer grid. The average kinetic energy in the LES is similar to that in the resolved DNS, but deviations are found in the magnetic energy. Much of this discrepancy is due to the SGS heat flux. Removing the SGS heat flux improves the magnetic energy without substantially altering the kinetic energy. We discuss the origin of this interesting behavior and possible resolutions.