Anisotropic diffusion and shear instabilities

TL;DR

This paper investigates how anisotropic turbulence in stratified stellar interiors influences shear instabilities, showing that horizontal turbulence weakens the stabilizing effects of molecular weight gradients and enhances vertical mixing.

Contribution

It provides a new analysis of shear instability thresholds considering anisotropic turbulence and estimates the resulting vertical turbulent diffusivity in stellar radiative zones.

Findings

Anisotropic turbulence reduces the critical shear needed for instability.

Horizontal turbulence weakens the stabilizing $ abla \mu$-gradient.

Derived estimates for vertical turbulent diffusivity.

Abstract

We examine the role of anisotropic turbulence on the shear instabilities in a stratified flow. Such turbulence is expected to occur in the radiative interiors of stars, due to their differential rotation and their strong stratification, and the turbulent transport associated with it will be much stronger in the horizontal than in the vertical direction. It will thus weaken the restoring force which is caused by the gradient of mean molecular weight ($\mu$). We find that the critical shear which is able to overcome the $\mu$-gradient is substantially reduced by this anisotropic turbulence, and we derive an estimate for the resulting turbulent diffusivity in the vertical direction.