# Large-Eddy Simulations of Convection in the Earth's Core

Friday, March 22, 2002 - 9:10am - 10:10am

Keller 3-180

Bruce Buffett (University of British Columbia)

Large-eddy simulations (LES) provide a strategy for dealing with flows in which the smallest scales cannot be resolved in numerical calculations. The approach is based on spatial filtering to eliminate the scales that are smaller than the grid spacing. The influence of the subgrid scales must be modeled and several schemes have been proposed, including the Smagorinsky, the multiscale and the similarity methods. We apply each of these methods to the problem of convection in the Earth's core and test the predictions using a direct numerical simulation (DNS) on a finer grid. In order to resolve the smallest dissipative scales in the DNS we are forced to consider only a small volume of the core and assume periodic boundary conditions. The grid in the DNS calculation is a cube with 128x64x32 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 32^3 grid for the purpose of testing the LES models. Estimates of the subgrid heat and momentum flux are calculated explicitly using the solution on the finer grid. The results reveal a high degree of anisotropy due to the influences of rotation and the large-scale magnetic field. Comparisons with LES models on the coarser grid are poor when the model is based on a scalar diffusivity or viscosity; this includes the eddy viscosity, Smagorinsky and multiscale models. These (scalar) models are incapable of reproducing the strong anisotropy in the subgrid fluxes. The similarity method is much more succesful in reproducing the anisotropy of the subgrid fluxes. Spatial correlations between the similarity model and the exact subgrid fluxes in the three coordinate directions are typically in excess of 0.8. We incorporate the similarity model into our simulation to extend these calculations to larger scales and discus the implementation.