# Dependence of Convective Boundary Mixing on Boundary Properties and Turbulence Strength

## TL;DR

This study uses 3D hydrodynamical simulations to explore how convective boundary mixing in stellar evolution depends on boundary properties and turbulence, supporting the entrainment law's applicability in modeling.

## Contribution

It provides a controlled analysis of convective boundary mixing dependence on boundary properties and turbulence strength using 3D simulations and mean field analysis.

## Key findings

- Entrainment inversely proportional to bulk Richardson number.
- Vertical RMS velocity scales with driving luminosity.
- Boundary positions estimated via composition profiles.

## Abstract

Convective boundary mixing is one of the major uncertainties in stellar evolution. In order to study its dependence on boundary properties and turbulence strength in a controlled way, we computed a series of 3D hydrodynamical simulations of stellar convection during carbon burning with a varying boosting factor of the driving luminosity. Our 3D implicit large eddy simulations were computed with the PROMPI code. We performed a mean field analysis of the simulations within the Reynolds-averaged Navier-Stokes framework. Both the vertical RMS velocity within the convective region and the bulk Richardson number of the boundaries are found to scale with the driving luminosity as expected from theory. The positions of the convective boundaries were estimated through the composition profiles across them, and the strength of convective boundary mixing was determined by analysing the boundaries within the framework of the entrainment law. We find that the entrainment is approximately inversely proportional to the bulk Richardson number. Although the entrainment law does not encompass all the processes occurring at boundaries, our results support the use of the entrainment law to describe convective boundary mixing in 1D models, at least for the advanced phases. The next steps and challenges ahead are also discussed.