Turbulent Convection in Stellar Interiors. Iii. Mean-Field Analysis and Stratification Effects

Abstract

We present three-dimensional implicit large eddy simulations of the turbulent convection in the envelope of a 5 M red giant star and in the oxygen-burning shell of a 23 M supernova progenitor. The numerical models are analyzed in the framework of one-dimensional Reynolds-Averaged Navier-Stokes equations. The effects of pressure fluctuations are more important in the red giant model, owing to larger stratification of the convective zone. We show how this impacts different terms in the mean-field equations. We clarify the driving sources of kinetic energy, and show that the rate of turbulent dissipation is comparable to the convective luminosity. Although our flows have low Mach numbers and are nearly adiabatic, our analysis is general and can be applied to photospheric convection as well. The robustness of our analysis of turbulent convection is supported by the insensitivity of the mean-field balances to linear mesh resolution. We find robust results for the turbulent convection zone and the stable layers in the oxygen-burning shell model, and robust results everywhere in the red giant model, but the mean fields are not well converged in the narrow boundary regions (which contain steep gradients) in the oxygen-burning shell model. This last result illustrates the importance of unresolved physics at the convective boundary, which governs the mixing there.

The Compactness of Presupernova Stellar Cores

“…It also leads to an increased growth of the helium convective core at the end of helium burning that affects not only the CO core mass, but the carbon mass fraction when carbon burning ignites. Simulations by Meakin and collaborators (e.g., Meakin & Arnett 2007;Viallet et al 2013) confirm that some type of mixing will always take place at convective boundaries defined by either the Ledoux or Schwarzschild criterion, although the exact formulation of this mixing remains uncertain.…”

Proper use of Schwarzschild Ledoux criteria in stellar evolution computations

“…It also applies to a shrinking convective core provided that the mass on top of the overshooting zone also decreases and does not itself become convectively unstable. These problems have been discussed theoretically, but there are still too few numerical simulations and situations studied with the moment theory to allow us to find a rule to specify the depth of the overshooting (undershooting) layers and the run of the temperature gradient (see, e.g., Kupka & Montgomery 2002;Kupka et al 2009;Montgomery & Kupka 2004;Zhang & Li 2012a,b;Zhang 2013and, for numerical simulations, Freytag 1996Freytag & Steffen 2004;Kochukhov et al 2007;Rogers et al 2006;Tian et al 2009;Viallet et al 2013).…”

Synergies between Asteroseismology and Three-dimensional Simulations of Stellar Turbulence

“…In parallel, two-and three-dimensional (2D/3D) implicit large eddy simulations of turbulent convection at different evolutionary phases (e.g., Bazàn & Arnett 1994;Nordlund & Stein 1995;Freytag et al 1996;Miesch 2005;Meakin & Arnett 2006, 2007bNordlund et al 2009;Viallet et al 2013;Arnett et al 2015; and many more) have shed light on the behavior of stellar convection, and in particular, on the interface between convective and radiative zones. This allows the development of non-local time-dependent convective theories that are consistent with the 3D simulations.…”