Sub-grid scale model for convection-driven dynamos in a rotating plane layer

We develop a sub-grid scale (SGS) model for convection-driven dynamos, based on the nonlinear gradient model of Leonard [Leonard, A., 1974. Energy cascade in large-eddy simulations of turbulent fluid flows. Adv. Geophys. 18, 237–248]. The predictions of the SGS model are tested using snapshots from a direct numerical simulation (DNS). Good agreement is obtained throughout most of the fluid, but discrepancies occur near the boundaries. We also implement the SGS model in a large-eddy simulation (LES) to assess the temporal behavior of the SGS model. Both the DNS and LES have large time variation in the kinetic and magnetic energies, so comparisons are made using time averages. The time-averaged energies in the LES are slightly larger than those in the resolved DNS, but not as high as those obtained in an unresolved DNS with the same grid resolutions as the LES. The source of dissipation in the LES is revealed by examining the energy balances. The work done by the SGS Lorentz term and the magnetic energy generated by the SGS induction term are both negative, indicating that these SGS terms transfer energy from the resolved scales into the unresolved scales.