Testing turbulent convection theory in solar models - I. Structure of the solar convection zone

Abstract

Turbulent convection models (TCMs) based on hydrodynamic moment equations are compared with the classical mixing‐length theory (MLT) in solar models. The aim is to test the effects of some physical processes on the structure of the solar convection zone, such as the dissipation, diffusion and anisotropy of turbulence that have been ignored in the MLT. Free parameters introduced by the TCMs are also tested in order to find appropriate values for astrophysical applications. It is found that the TCMs usually give larger convective heat fluxes than the MLT does, and the heat transport efficiency is sensitively related to the dissipation parameters used in the TCMs. As a result of calibrating to the present solar values, our solar models usually have rather smaller values of the mixing length to local pressure scaleheight ratio than the standard solar model. The turbulent diffusion is found to have important effects on the structure of the solar convection zone. It leads to significantly lowered and expanded profiles for the Reynolds correlations, and a larger temperature gradient in the central part of the superadiabatic convection region but a smaller one near the boundaries of the convection zone. It is interesting to note that, due to a careful treatment of turbulence developing towards isotropic state, our non‐local TCM results in radially dominated motion in the central part and horizontally dominated motion near the boundaries of the convection zone, just as what has been observed in many 3D numerical simulations. Our solar models with the TCMs give small but meaningful differences in the temperature and sound speed profiles compared with the standard solar model using the MLT.

Matter Mixing in Aspherical Core-collapse Supernovae: Three-dimensional Simulations with Single-star and Binary Merger Progenitor Models for SN 1987A

“…Overshooting is the penetration of elements over a convective zone into a dynamically stable region, which may be the most uncertain process in the context of the MLT and it has intensively studied in several aspects (e.g., Rogers et al 2006;Claret 2007;Deng & Xiong 2008;Zhang 2013;Montalbán et al 2013;Viallet et al 2015). For both the semiconvection and overshooting, nonlocality is essential and self-consistent non-local convection theories beyond the local MLT have been proposed (Xiong 1977;Grossman et al 1993;Xiong et al 1997;Canuto & Dubovikov 1998;Deng et al 2006;Li & Yang 2007;Zhang 2016), which has partly been motivated by the implications from multi-dimensional hydrodynamical simulations mentioned below. In general the time scale of the stellar evolution is determined by the nuclear burning which is much longer than the dynamical time scale of the turbulent motion of fluids in a convective layer and the crossing time of sound waves.…”

Chemical element transport in stellar evolution models

“…There are very sophisticated non-local Reynolds stress models that describe not only convection, but also (see below) semiconvection and overshooting [32][33][34][35][36][37]. They introduce a large number of equations to be coupled to the stellar structure equations and several free parameters to be calibrated observationally, and are generally not included in current stellar evolution modelling.…”

Upward Overshooting in Turbulent Compressible Convection. I. Effects of the Relative Stability Parameter, the Prandtl Number, and the Péclet Number

“…Beyond the mixing length theory (MLT), considerable progress has been made on the development of turbulent theories on time-dependent nonlocal Reynolds stress models (RSMs) (Xiong 1978(Xiong , 1989Xiong et al 1997;Kuhfuß 1986;Canuto 1992Canuto , 1993Canuto & Dubovikov 1998;Canuto et al 2001;Li & Yang 2007;Li 2012Li , 2017. In RSM, overshooting can be naturally considered as the nonlocal effect of turbulent convection.…”