Semiconvection: theory

Abstract

A model is developed for the transport of heat and solute in a system of double-diffusive layers under astrophysical conditions (where viscosity and solute diffusivity are low compared with the thermal diffusivity). The process of formation of the layers is not part of the model but, as observed in geophysical and laboratory settings, is assumed to be faster than the life time of the semiconvective zone. The thickness of the layers is a free parameter of the model. When the energy flux of the star is specified, the effective semiconvective diffusivities are only weakly dependent on this parameter. An estimate is given of the evolution of layer thickness with time in a semiconvective zone. The model predicts that the density ratio has a maximum for which a stationary layered state can exist, R ρ < ∼ Le −1/2 . Comparison of the model predictions with a grid of numerical simulations is presented in a companion paper.

A New Model for Mixing by Double-Diffusive Convection (Semi-Convection). Iii. Thermal and Compositional Transport Through Non-Layered Oddc

“…More than being merely a qualitative difference, the different character of the layers in each context leads to significant quantitative differences in thermal and compositional transport. In particular, Wood et al (2013) found that contrary to Equation (28) proposed by Stevenson (1982) and used by Spruit (1992Spruit ( , 2013, g -tot 1 is not proportional to t 1 2 in systems where layers form spontaneously. Second, the non-layered ODDC regime is never observed in geophysical experiments, which is not surprising as (1) the range of parameters for which it could theoretically be observed is tiny, and (2) most experiments are initialized with layers in the first place.…”

“…Later, Shirtcliffe (1973) conducted similar laboratory experiments of double-diffusive convection where the diffusive quantities were sugar and salt dissolved in water. Linden & Shirtcliffe (1978) then used Shirtcliffe's results to develop the prescription for the relationship between the thermal and compositional fluxes that Stevenson (1982) later applied to the astrophysical case (see Equation (28)) and which is also at the heart of the models presented by Spruit (1992Spruit ( , 2013. Given that geophysical and astrophysical double-diffusive convection are governed by the same basic equations, and without the help of numerical simulations at low Pr, it was natural for Stevenson (1982) and Spruit (1992) to extrapolate from the results of geophysical experiments to draw conclusions about astrophysical systems.…”

The Compactness of Presupernova Stellar Cores

“…In our survey α SC was taken to be 0.1 as a "midpoint" between these two extremes, which is also well within the range used in literature (e.g., Yoon et al 2006). We also note that the work to eliminate or greatly constrain this parameter is underway (Wood et al 2013;Spruit 2013). Overshoot mixing in MESA is accomplished either by fully mixing the zones flagged as overshooting ("step" overshooting) or by applying an exponential cutoff to the diffusion coefficient calculated for convection in zones that are unstable by the Ledoux or Schwarzschild criterion.…”

Semi-convective layer formation

“…The layered convective regime is embedded between the fully convective regime, R ρ 1, and the very stable conductive regime, R ρ,max 10. The existence of this upper stability limit R ρ,max is known from, e.g., Stevenson [14] and in the astrophysical context from Spruit [13].…”