HR: 0800h
AN: GP11D-0849    [Abstracts]
TI: Dynamic Sub-grid Scale model for MHD simulations in a rotating plane layer
AU: * Matsui, H
EM: matsui@geosci.uchicago.edu
AF: Dept. 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: Dept. of the Geophysical Sciences, the University of Chicago, 5734 S Ellis Ave., Chicago, IL 60637 United States
AB: The Sub-grid scale modeling is required for the geodynamo simulations because 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. We have previously modeled the influence of sub-grid scale motion for the momentum and heat flux, the Lorentz force, and the induction term using the nonlinear gradient model by Leonard (1974), which is a form of the scale similarity model. The result suggests that the nonlinear gradient model can represent basic characteristics of the effects of the sub-grid scale motion, but some discrepancies are observed around the boundaries. In the present study, we implement a dynamic version of the nonlinear gradient model, where the model coefficients are allowed to evolve according to the procedure introduced by Germano (1992). We also allow the model coefficients to vary as a function of the vertical position to investigate effects of the boundary on the SGS terms. In the present study, we evaluate the model coefficients using a snapshot of a MHD simulation in a rotating plane layer model with the periodic boundary in the horizontal direction. The dynamic model predicts large variations in the model coefficients around the boundaries, while the coefficients in the interior are relatively constant. This result suggests that the amplitude the SGS terms are changed by the presence of boundaries. Furthermore, the coefficient for the SGS induction term is smaller than the other coefficients. This result suggests that the dynamic SGS induction term is smaller, which is consistent with the previous simulations because the magnetic energy was over-damped by the SGS induction term when the model coefficients were all set to 1. References: Leonard, A., Energy cascade in large-eddy simulations of turbulent fluid flows, Advances in geophysics, 18, 237--248, 1974. Germano, M., Turbulence: the filtering approach, Journal of Fluid Mechanics, 238, 325--336, 1992.
DE: 7843 Numerical simulation studies
DE: 7863 Turbulence
DE: 1510 Dynamo theories
SC: Geomagnetism and Paleomagnetism [GP]
MN: 2004 AGU Fall Meeting