Shear mixing in stellar radiative zones - II. Robustness of numerical simulations

TL;DR

This study tests the robustness of Zahn's model for shear mixing in stellar radiative zones through numerical simulations, examining the effects of numerical setup and Reynolds number, and finds the model holds at high Reynolds numbers.

Contribution

It demonstrates the consistency of shear mixing simulations across different numerical codes and confirms the validity of Zahn's model at high turbulent Reynolds numbers.

Findings

Turbulent diffusion coefficient is consistent across different codes.

Diffusion coefficient becomes independent of domain size with sufficient turbulent structures.

An asymptotic regime is observed for Reynolds numbers above 10^3.

Abstract

Recent numerical simulations suggest that the model by Zahn (1992, A&A, 265, 115) for the turbulent mixing of chemical elements due to differential rotation in stellar radiative zones is valid. We investigate the robustness of this result with respect to the numerical configuration and Reynolds number of the flow. We compare results from simulations performed with two different numerical codes, including one that uses the shearing-box formalism. We also extensively study the dependence of the turbulent diffusion coefficient on the turbulent Reynolds number. The two numerical codes used in this study give consistent results. The turbulent diffusion coefficient is independent of the size of the numerical domain if at least three large turbulent structures fit in the box. Generally, the turbulent diffusion coefficient depends on the turbulent Reynolds number. However, our simulations suggest that an asymptotic regime is obtained when the turbulent Reynolds number is larger than $10^3$. Shear mixing in the regime of small P\'eclet numbers can be investigated numerically both with shearing-box simulations and simulations using explicit forcing. Our results suggest that Zahn's model is valid at large turbulent Reynolds numbers.