Convective overshooting and penetration in a Boussinesq spherical shell

TL;DR

This study uses 3D simulations to analyze how turbulent convection extends into stable regions in a spherical shell, revealing key parameters that influence overshooting and thermal mixing relevant for stellar models.

Contribution

It provides a quantitative model for turbulent overshoot extent and introduces a scaling law based on energetic arguments applicable to stellar evolution.

Findings

Overshooting depends on stability, transition width, and turbulence intensity.

Kinetic energy profile below CZ follows a half-Gaussian shape.

Dynamical lengthscales scale with a simple energetic lengthscale.

Abstract

We study the dynamics associated with the extension of turbulent convective motions from a convection zone (CZ) into a stable region (RZ) that lies below the latter. For that purpose, we have run a series of three-dimensional direct numerical simulations solving the Navier-Stokes equations under the Boussinesq approximation in a spherical shell geometry. We observe that the overshooting of the turbulent motions into the stably stratified region depends on three different parameters: the relative stability of the RZ, the transition width between the two, and the intensity of the turbulence. In the cases studied, these motions manage to partially alter the thermal stratification and induce thermal mixing, but not so efficiently as to extend the nominal CZ further down into the stable region. We find that the kinetic energy below the convection zone can be modeled by a half-Gaussian profile whose amplitude and width can be predicted a priori for all of our simulations. We examine different dynamical lengthscales related to the depth of the extension of the motions into the RZ, and we find that they all scale remarkably well with a lengthscale that stems from a simple energetic argument. We discuss the implications of our findings for 1D stellar evolution calculations.