Estimation of turbulent diffusivity with direct numerical simulation of stellar convection

TL;DR

This paper introduces a new numerical method to estimate horizontal turbulent diffusivity in stellar convection by tracking passive scalar evolution, revealing dependencies on initial distribution scale and characteristic length.

Contribution

A novel approach to measure turbulent diffusivity using passive scalar evolution in numerical stellar convection simulations.

Findings

Turbulent diffusivity increases with larger initial scalar distribution scale.

The characteristic length is limited by the smaller of the pressure scale height and region depth.

Turbulent diffusion approximation improves with larger initial distribution scale relative to characteristic length.

Abstract

We investigate the value of horizontal turbulent diffusivity {\eta} by numerical calculation of thermal convection. In this study, we introduce a new method whereby the turbulent diffusivity is estimated by monitoring the time devel- opment of the passive scalar, which is initially distributed in a given Gaussian function with a spatial scale d0. Our conclusions are as follows: (1) Assuming the relation {\eta} = Lcvrms/3 where vrms is the RMS velocity, the characteristic length Lc 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 d0. (3) The approximation of turbulent diffusion holds better when the ratio of the initial distribution scale d0 to the characteristic length Lc is larger.