Stellar evolution models with overshooting based on 3-equation non-local theories

Abstract

Context. Mixing by convective overshooting has long been suggested to play an important role in the amount of hydrogen available for nuclear burning in convective cores of stars. The best way to model this effect is still debated. Aims. We suggest an improved model for the computation of the dissipation rate of turbulent kinetic energy which can be used in non-local models of stellar convection and can readily be implemented and self-consistently used in 1D stellar evolution calculations. Methods. We review the physics underlying various models to compute the dissipation rate of turbulent kinetic energy, ϵ, in local models of convection in stellar astrophysics and particularly in non-local ones. The different contributions to the dissipation rate and their dependence on local stratification and on non-local transport are analysed and a new method to account for at least some of these physical mechanisms is suggested. Results. We show how the new approach influences predictions of stellar models of intermediate-mass main-sequence stars and how these changes differ from other modifications of the non-local convection model that focus on the ratio of horizontal to vertical (turbulent) kinetic energy. Conclusions. The new model is shown to allow for a physically more complete description of convective overshooting and mixing in massive stars. Dissipation by buoyancy waves is found to be a key ingredient which has to be accounted for in non-local models of turbulent convection.

Modelling Time-dependent Convective Penetration in 1D Stellar Evolution

“…Recently, work by Kupka et al (2022) and Ahlborn et al (2022) have successfully implemented two versions of a model for turbulent convection (Kuhfuss 1986) in a 1D stellar evolution code. This model successfully accounts for the nonlocal behavior of convective parcels, and predicts nonzero convective velocities and adiabatic mixing above the Schwarzschild boundary (Ahlborn et al 2022).…”

Asteroseismic Investigation on KIC 10526294 to Probe Convective Core Overshoot Mixing

“…This exponentially decreasing behavior of the diffusion coefficient is based on numerical simulations (e.g., Freytag et al 1982;Kupka et al 2018) that show exponentially decreasing mean vertical convective velocity in the overshoot region, and stellar turbulent convection models (e.g., Xiong 1989;Xiong & Deng 2002;Zhang & Li 2012b;Li 2017;Xiong 2021) that show exponentially decreasing turbulent kinetic energy and turbulent dissipation. The stellar turbulent convection models are based on hydrodynamic equations, focusing on the turbulent variables (e.g., turbulent kinetic energy, heat flux, temperature variance, turbulent dissipation, and chemical abundance flux) in statistical equilibrium with some closure models of diffusion and dissipation (Xiong 1985(Xiong , 1989Canuto 1993Canuto , 1997Canuto & Dubovikov 1998;Kupka 1999;Xiong & Deng 2002;Li 2007;Li 2012;Zhang & Li 2012b;Zhang 2013;Li 2017;Xiong 2021;Ahlborn et al 2022;Kupka et al 2022). The turbulent convection models are more reasonable and in better agreement than the classical overshoot models when compared with numerical simulations (e.g., Singh et al 1995;Kupka 1999;Brummell et al 2002;Kupka & Muthsam 2017).…”

Effects of particle concentration and size on the dissipation rate and turbulent kinetic energy of oil

“…Jiang et al [ 9 ] argued that turbulence dissipation is largely locally homogeneous, but not locally isotropic or axisymmetric, even after the annihilation of the main vortex. Kupka et al [ 10 ] proposed an improved calculation model for the turbulent flow energy (TKE) dissipation rate, analysed the different contributions of dissipation rates and their dependence on local stratification and non‐local transport, and proposed a new method to explain at least some of these physical mechanisms. Chen et al [ 11 ] proposed a new loss assessment model, which quantifies the total loss by averaging the loss of flow viscosity and the loss of turbulent flow on the basis of a detailed analysis of the average flow energy and the TKE budget.…”