# The interaction between shear and fingering (thermohaline) convection

## TL;DR

This study investigates how shear flows influence thermohaline convection in stars, revealing that shear reduces mixing efficiency and proposing an analytical model to incorporate these effects into stellar evolution simulations.

## Contribution

It is the first to analyze the impact of shear on fingering convection using simulations and to extend existing models to include shear effects.

## Key findings

- Moderate shear decreases fingering convection efficiency.
- A simple analytical model explains the effect of shear on mixing.
- Turbulent viscosity correlates with compositional mixing.

## Abstract

Fingering convection is a turbulent mixing process that can occur in stellar radiative regions whenever the mean molecular weight increases with radius. In some cases, it can have a significant observable impact on stellar structure and evolution. The efficiency of mixing by fingering convection as a standalone process has been studied by Brown et al. (2013), but other processes such as rotation, magnetic fields and shear can affect it. In this paper, we present a first study of the effect of shear on fingering (thermohaline) convection in astrophysics. Using Direct Numerical Simulations we find that a moderate amount of shear (that is not intrinsically shear-unstable) always decreases the mixing efficiency of fingering convection, as a result of the tilt it imparts to the fingering structures. We propose a simple analytical extension of the Brown et al. (2013) model in the presence of shear that satisfactorily explains the numerically-derived turbulent compositional mixing coefficient for moderate shearing rates, and can trivially be implemented in stellar evolution codes. We also measure from the numerical simulations a turbulent viscosity, and find that the latter is strongly tied to the turbulent compositional mixing coefficient. Observational implications and caveats of the model are discussed.