Idealized hydrodynamic simulations of turbulent oxygen-burning shell convection in 4π geometry

This work investigates the properties of convection in stars with particular emphasis on entrainment across the upper convective boundary (CB). Idealized simulations of turbulent convection in the O-burning shell of a massive star are performed in 4π geometry on 768³ and 1536³ grids, driven by a representative heating rate. A heating series is also performed on the 768³ grid. The 1536³ simulation exhibits an entrainment rate at the upper CB of 1.33 × 10^-6M_⊙ s^-1. The 768³ simulation with the same heating rate agrees within 17 per cent. The entrainment rate at the upper CB is found to scale linearly with the driving luminosity and with the cube of the shear velocity at the upper boundary, while the radial rms fluid velocity scales with the cube root of the driving luminosity, as expected. The mixing is analysed in a 1D diffusion framework, resulting in a simple model for CB mixing. The analysis confirms that limiting the MLT mixing length to the distance to the CB in 1D simulations better represents the spherically averaged radial velocity profiles from the 3D simulations and provide an improved determination of the reference diffusion coefficient D₀ for the exponential diffusion CB mixing model in 1D. From the 3D simulation data, we adopt as the CB the location of the maximum gradient in the horizontal velocity component which has 2σ spatial fluctuations of ≈0.17H_P. The exponentially decaying diffusion CB mixing model with f = 0.03 reproduces the spherically averaged 3D abundance profiles.