Estimation of turbulent diffusivity with direct numerical simulation of stellar convection

Abstract

We investigate the value of horizontal turbulent diffusivity η by numerical calculation of thermal convection. In this study, we introduce a new method whereby the turbulent diffusivity is estimated by monitoring the time development of the passive scalar, which is initially distributed in a given Gaussian function with a spatial scale d 0. Our conclusions are as follows: (1) assuming the relation η = L c v rms/3, where v rms is the root-mean-square (rms) velocity, the characteristic length L c is restricted by the shortest one among the pressure (density) scale height and the region depth. (2) The value of turbulent diffusivity becomes greater with the larger initial distribution scale d 0. (3) The approximation of turbulent diffusion holds better when the ratio of the initial distribution scale d 0 to the characteristic length L c is larger. © 2012. The American Astronomical Society. All rights reserved..