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

Vincent Prat, Jérôme Guilet, Maxime Viallet, Ewald Müller

Published 2015-12-14Version 1

Recent numerical simulations suggest that Zahn's model 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 using 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 numbers is larger than $10^3$. Shear mixing in the small-P\'eclet-number regime can be investigated numerically both with shearing-box simulations and simulations using explicit forcing. Our results suggest that Zahn's theory is valid at large turbulent Reynolds numbers.