Characterization of subgrid-scale terms in a numerical geodynamo simulation

Subgrid scale (SGS) models are required to account for effects of the unresolved flow and magnetic field in geodynamo simulations. Four nonlinear terms in the dynamo problem give rise to four SGS terms (SGS momentum and heat flux, SGS Lorentz force, and induction term). We make direct estimates of the SGS terms using snapshots of a fully resolved solution. After separating the resolved solution into large and small scales, the influence of the small scales on the large scales is directly calculated. Next, we filter the resolved solutions on to a coarser grid to eliminate the small scales and model the SGS terms using a dynamic scale similarity model. Finally, we apply an eddy diffusion model as an alternative representation of the SGS terms. The results show that the SGS terms obtained by the dynamic scale similarity method are in good agreement with the SGS terms from the direct estimation, while the turbulence diffusion model does not accurately represent the SGS terms. We also evaluate energy fluxes due to the SGS terms to investigate energy transfer between large and unresolved scales. The results suggests that the SGS Lorentz force transfers energy from large scale to unresolved scale across most of the fluid shell. However, Reynolds stress transfers the kinetic energy from unresolved scale to the resolved scale in the region of convection columns, where the magnetic field is primarily generated.