HR: 1330h
AN: G22A-0303    [PDF]
TI: Sub-grid scale modeling for simulations of magnetoconvection in the Earth's core
AU: * Matsui, H
EM: matsui@geosci.uchicago.edu
AF: Department of the Geophysical Sciences, the University of Chicago, 5734 S Ellis Ave., Chicago, IL 60637 United States
AU: Buffett, B A
EM: buffett@geosci.uchicago.edu
AF: Department of the Geophysical Sciences, the University of Chicago, 5734 S Ellis Ave., Chicago, IL 60637 United States
AB: The fluid motion and the magnetic field in the Earth's outer core have small scale components which cannot be resolved in numerical simulations because of the small Ekman number and large Rayleigh number. Many geodynamo simulations have been performed with much larger viscosity or hyper diffusivity, but more realistic sub-grid scale (SGS) modeling is required. The influence of sub-grid scale motion and magnetic field are modeled in magneto-convection simulations using the nonlinear gradient model by Leonard (1994). We implement this method using a gaussian filter in a dynamo simulation code using the finite-element method. As a preliminary test, we investigated the contribution of SGS terms in each equation using the results of a magneto-convection simulation in a cubic domain. We consider a cubic domain with equal dimensions in three coordinate directions. The directions of gravity and rotation vectors are parallel to the $z$-axis, and a constant magnetic field is imposed in the $y$-direction. We investigate magnitudes of the sub-grid heat flux, momentum flux, Maxwell stress, and induction terms using the results of the direct simulation. We compared the ratio of running mean square of the SGS nonlinear terms to corresponding original terms. The results show that the ratio of the SGS momentum flux and that of the SGS heat flux are similar. However, the ratios of the SGS Maxwell stress term and induction term are approximately $10^{-5}$ times of the ratio of the SGS heat advection and inertia terms. The results suggest that the SGS modeling for the momentum and heat flux is more important than that of the Maxwell stress and the induction terms. We will investigate how these ratios change under the large Rayleigh number and small Ekman number cases.
DE: 1510 Dynamo theories
DE: 7843 Numerical simulation studies
SC: Geodesy [G]
MN: 2003 Fall Meeting