Extended Subadiabatic Layer in Simulations of Overshooting Convection

Käpylä, Petri J.; Rheinhardt, M.; Brandenburg, Axel; Arlt, R.; Käpylä, Maarit J.; Lagg, A.; Olspert, N.; Warnecke, Jörn

doi:10.3847/2041-8213/aa83ab

Cited by 58 publications

(105 citation statements)

References 29 publications

(39 reference statements)

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“…First and foremost is that penetrative convection in the strict definition of the term (i.e. the extension of the convection zone substantially beyond the threshold for linear instability) had so far not been observed in fully turbulent 3D simulations (Brummell et al 2002;Käpylä et al 2017;Brun et al 2017), and this continues to be the case here. As reviewed in Section 1, the fact that penetration is seen in 2D at sufficiently low values of S (e.g.…”

Section: Comparison With Previous Numerical Experimentsmentioning

confidence: 66%

“…This difference between our simulations and theirs is probably due to two complementary effects. Käpylä et al (2017) ran fully compressible simulations which more realistically capture the asymmetry between weak warm upflows and strong cold downflows than our Boussinesq setup. This asymmetry promotes non-local heat transport by the plumes, allowing the strongest cold downflows to penetrate more coherently and more deeply into the RZ than they would otherwise before warming up.…”

Section: Thermal Mixing In the Rzmentioning

confidence: 99%

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Convective overshooting and penetration in a Boussinesq spherical shell

Korre

Garaud

Brummell

2019

Monthly Notices of the Royal Astronomical Society

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We study the dynamics associated with the extension of turbulent convective motions from a convection zone (CZ) into a stable region (RZ) that lies below the latter. For that purpose, we have run a series of three-dimensional direct numerical simulations solving the Navier-Stokes equations under the Boussinesq approximation in a spherical shell geometry. We observe that the overshooting of the turbulent motions into the stably stratified region depends on three different parameters: the relative stability of the RZ, the transition width between the two, and the intensity of the turbulence. In the cases studied, these motions manage to partially alter the thermal stratification and induce thermal mixing, but not so efficiently as to extend the nominal CZ further down into the stable region. We find that the kinetic energy below the convection zone can be modeled by a half-Gaussian profile whose amplitude and width can be predicted a priori for all of our simulations. We examine different dynamical lengthscales related to the depth of the extension of the motions into the RZ, and we find that they all scale remarkably well with a lengthscale that stems from a simple energetic argument. We discuss the implications of our findings for 1D stellar evolution calculations.

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Section: Comparison With Previous Numerical Experimentsmentioning

confidence: 66%

Section: Thermal Mixing In the Rzmentioning

confidence: 99%

Convective overshooting and penetration in a Boussinesq spherical shell

Korre

Garaud

Brummell

2019

Monthly Notices of the Royal Astronomical Society

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“…Finally the Deardorff zone (DZ) is characterised by a formally stable stratification with a positive vertical mean entropy gradient (∂ z s > 0) and F conv > 0; see, Tremblay et al (2015). In this layer, the convective energy transport is dominated by a nonlocal non-gradient contribution to the enthalpy flux introduced by Deardorff (1961Deardorff ( , 1966; see also Brandenburg (2016) and Käpylä et al (2017). Such layers have been reported by various authors from simulations (e.g.…”

Section: Definitions Of Convection Zone and Overshootingmentioning

confidence: 72%

“…Set S employs a static step profile of heat conductivity, K = K(z). These three sets correspond to Runs K, P, and S of Käpylä et al (2017). Additionally, Sets Kh and Sh are the otherwise the same as Sets K and S but lower viscosity and SGS entropy diffusion were used.…”

Section: Resultsmentioning

confidence: 99%

Overshooting in simulations of compressible convection

Käpylä

2019

A&A

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Context. Convective motions overshooting to regions that are formally convectively stable cause extended mixing. Aims. To determine the scaling of overshooting depth (dos) at the base of the convection zone as a function of imposed energy flux (Fn) and to estimate the extent of overshooting at the base of the solar convection zone. Methods. Three-dimensional Cartesian simulations of compressible non-rotating convection with unstable and stable layers are used. The simulations use either a fixed heat conduction profile or a temperature and density dependent formulation based on Kramers opacity law. The simulations cover a range of almost four orders of magnitude in the imposed flux. Results. A smooth heat conduction profile (either fixed or through Kramers opacity law) leads to a relatively shallow power law with dos ∝ F 0.08 n for low Fn. A fixed step-profile of the heat conductivity at the bottom of the convection zone leads to a somewhat steeper dependency with dos ∝ F 0.12 n in the same regime. Experiments with and without subgrid-scale entropy diffusion revealed a strong dependence on the effective Prandtl number which is likely to explain the steep power laws as a function of Fn reported in the literature. Furthermore, changing the heat conductivity artificially in the radiative and overshoot layers to speed up thermal saturation is shown to lead to substantial underestimation of overshooting depth. Conclusions. Extrapolating from the results obtained with smooth heat conductivity profiles, which are the most realistic of the setups considered, suggest that the overshooting depth for the solar energy flux is of the order of 20 per cent of the pressure scale height at the base of the convection zone which is two to four times higher than the estimates from helioseismology. The current simulations do not include rotation or magnetic fields which are known to reduce the convective overshooting.

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“…In Xiong's (1981) and Li & Yang's (2007) models, the typical value of the turbulent kinetic energy flux at the base of thick convective envelopes (for solar models or red-giant models) is of order L K,bc = −(10 −3 − 10 −2 )L total . In contrast, numerical simulations (e.g., Singh et al 1995;Tian et al 2009;Hotta et al 2014;Käpylä et al 2017) show significant turbulent kinetic energy in a convective envelope and the L K,bc /L total could be as significant as ∼ −40% (e.g., Singh et al 1995). However, the gradient type approximations adopted to model the thirdorder correlations in those statistical turbulent convection models could be invalid near the BCZ (Tian et al 2009).…”

Section: The Turbulent Kinetic Energy Fluxmentioning

confidence: 96%

Solar Models with Convective Overshoot, Solar-wind Mass Loss, and PMS Disk Accretion: Helioseismic Quantities, Li Depletion, and Neutrino Fluxes

Zhang

Christensen‐Dalsgaard

2019

ApJ

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Helioseismic observations have revealed many properties of the Sun: the depth and the helium abundance of the convection zone, the sound-speed and the density profiles in the solar interior. Those constraints have been used to judge the stellar evolution theory. With the old solar composition (e.g., GS98), the solar standard model is in reasonable agreement with the helioseismic constraints. However, a solar model with revised composition (e.g., AGSS09) with low abundance Z of heavy elements cannot be consistent with those constraints. This is the so-called "solar abundance problem", standing for more than ten years even with the recent upward revised Ne abundance. Many mechanisms have been proposed to mitigate the problem. However, there is still not a low-Z solar model satisfying all helioseismic constraints. In this paper, we report a possible solution to the solar abundance problem. With some extra physical processes that are not included in the standard model, solar models can be significantly improved. Our new solar models with convective overshoot, the solar wind, and an early mass accretion show consistency with helioseismic constraints, the solar Li abundance, and observations of solar neutrino fluxes.

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Extended Subadiabatic Layer in Simulations of Overshooting Convection

Cited by 58 publications

References 29 publications

Convective overshooting and penetration in a Boussinesq spherical shell

Convective overshooting and penetration in a Boussinesq spherical shell

Overshooting in simulations of compressible convection

Solar Models with Convective Overshoot, Solar-wind Mass Loss, and PMS Disk Accretion: Helioseismic Quantities, Li Depletion, and Neutrino Fluxes

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