A comparison of subgrid-scale models for large-eddy simulations of convection in the Earth's core

Abstract

Large-eddy simulations provide a strategy for modelling large-scale flow when the smallest scales are not resolved. The approach relies on spatial filtering to eliminate scales smaller than the grid spacing, but requires models for the influence of the subgrid scales. We investigate four subgrid-scale models in numerical calculations of magnetoconvection in the Earth's core. Three of the models are based on eddy diffusivities, while the fourth is the similarity model of Bardina et al. (1980). The predictions of the subgrid-scale models are tested using a direct numerical simulation (DNS), which resolves the smallest dissipative scales. In order to achieve the required resolution we restrict the calculations to a small volume of the core with periodic boundary conditions. The grid is a cube with 128 × 64 × 32 nodes, oriented so that the z-coordinate is aligned with the rotation axis and the y-coordinate is parallel to an imposed magnetic field. The direction of gravity may be oriented arbitrarily in the x-z plane and several representative cases are considered. Output from the DNS is filtered on to a coarser grid prior to evaluating the subgrid-scale models. The results are compared with estimates of the subgrid-scale heat and momentum fluxes calculated from the fully resolved solution. Substantial anisotropy in the subgrid-scale fluxes is caused by the influences of rotation and the imposed magnetic field. Models based on scalar eddy diffusivities are incapable of reproducing this anisotropy, whereas the similarity model gives a good match to the amplitude and spatial distribution of the subgrid-scale fluxes.