Large-eddy simulations of convection-driven dynamos using a dynamic scale-similarity model

Dynamo simulations require sub-grid scale (SGS) models for the momentum and heat flux, the Lorentz force, and the magnetic induction. Previous large eddy simulations (LES) using the scale similarity model have represented many aspects of the SGS motion. However, discrepancies are observed due to interchanging the order of filtering operation and spatial differentiation. In this study, we implement a correction term for this commutation error specifically for the scale-similarity model. Furthermore, we implement a dynamic scheme to evaluate time-dependent coefficients for the SGS models. We perform dynamo simulations in a rotating plane layer with different spatial resolutions, and compare results for the time dependence of the large-scale magnetic field. Simulations are performed at two different Rayleigh numbers, using constant values for the other dimensionless numbers (Ekman, Prandtl, and magnetic Prandtl numbers). Both cases show that the dynamic LES can accurately represent the large-scale magnetic field, whereas the dynamo failed in the direct simulations without the SGS terms at the same spatial resolutions. We conclude that the dynamic versions of the SGS and commutation error correction are essential for successful dynamos on coarser grids.