Physically motivated heat-conduction treatment in simulations of solar-like stars: effects on dynamo transitions

Viviani, M.; Käpylä, Maarit J.

doi:10.1051/0004-6361/202038603

Cited by 11 publications

(8 citation statements)

References 55 publications

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“…Several numerical studies have shown that the deep parts of density-stratified CZs are often weakly stably stratified (e.g., Chan & Gigas 1992;Tremblay et al 2015;Bekki et al 2017;Hotta 2017;Käpylä et al 2017). Such layers have also been found from semi-global and global simulations of rotating solar-like CZs (e.g., Karak et al 2018;Käpylä et al 2019;Viviani & Käpylä 2021) as well as from fully convective spheres (Käpylä 2021). We call this layer the Deardorff zone after Brandenburg (2016).…”

Section: Overshooting Below the Convection Zonementioning

confidence: 57%

Prandtl number dependence of stellar convection: Flow statistics and convective energy transport

Käpylä

2021

A&A

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Context. The ratio of kinematic viscosity to thermal diffusivity, the Prandtl number, is much smaller than unity in stellar convection zones. Aims. The main goal of this work is to study the statistics of convective flows and energy transport as functions of the Prandtl number. Methods. Three-dimensional numerical simulations of compressible non-rotating hydrodynamic convection in Cartesian geometry are used. The convection zone (CZ) is embedded between two stably stratified layers. The dominant contribution to the diffusion of entropy fluctuations comes in most cases from a subgrid-scale diffusivity whereas the mean radiative energy flux is mediated by a diffusive flux employing Kramers opacity law. Here, we study the statistics and transport properties of up- and downflows separately. Results. The volume-averaged rms velocity increases with decreasing Prandtl number. At the same time, the filling factor of downflows decreases and leads to, on average, stronger downflows at lower Prandtl numbers. This results in a strong dependence of convective overshooting on the Prandtl number. Velocity power spectra do not show marked changes as a function of Prandtl number except near the base of the convective layer where the dominance of vertical flows is more pronounced. At the highest Reynolds numbers, the velocity power spectra are more compatible with the Bolgiano-Obukhov k−11/5 than the Kolmogorov-Obukhov k−5/3 scaling. The horizontally averaged convected energy flux (F̅conv), which is the sum of the enthalpy (F̅enth) and kinetic energy fluxes (F̅kin), is independent of the Prandtl number within the CZ. However, the absolute values of F̅enth and F̅kin increase monotonically with decreasing Prandtl number. Furthermore, F̅enth and F̅kin have opposite signs for downflows and their sum F̅↓conv diminishes with Prandtl number. Thus, the upflows (downflows) are the dominant contribution to the convected flux at low (high) Prandtl numbers. These results are similar to those from Rayleigh-Benárd convection in the low Prandtl number regime where convection is vigorously turbulent but inefficient at transporting energy. Conclusions. The current results indicate a strong dependence of convective overshooting and energy flux on the Prandtl number. Numerical simulations of astrophysical convection often use a Prandtl number of unity because it is numerically convenient. The current results suggest that this can lead to misleading results and that the astrophysically relevant low Prandtl number regime is qualitatively different from the parameter regimes explored in typical contemporary simulations.

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Section: Overshooting Below the Convection Zonementioning

confidence: 57%

Prandtl number dependence of stellar convection: Flow statistics and convective energy transport

Käpylä

2021

A&A

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“…Käpylä et al 2017;Käpylä 2019Käpylä , 2021. Thus far these studies have mostly concentrated on non-rotating convection (see, however Käpylä et al 2019;Viviani & Käpylä 2021). Here rotation is included to study its impact on the formation and extent of stably stratified Deardorff layers where the convective flux runs counter to the entropy gradient.…”

Section: Introductionmentioning

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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“…Such layers have also been found from semi-global and global simulations of rotating solarlike CZs (e.g. Karak et al 2018;Käpylä et al 2019;Viviani & Käpylä 2021) as well as from fully convective spheres (Käpylä 2021). We call this layer the Deardorff zone after Brandenburg (2016).…”

Section: Overshooting Below the Convection Zonementioning

confidence: 63%

Prandtl number dependence of compressible convection: Flow statistics and convective energy transport

Käpylä

2021

Preprint

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Context. The ratio of kinematic viscosity to thermal diffusivity, the Prandtl number, is much smaller than unity in stellar convection zones. Aims. The main goal is to study the statistics of convective flows and energy transport as functions of the Prandtl number. Methods. Three-dimensional numerical simulations of compressible non-rotating hydrodynamic convection in Cartesian geometry are used. The convection zone (CZ) is embedded between two stably stratified layers. The dominant contribution to the diffusion of entropy fluctuations comes in most cases from a subgrid scale (SGS) diffusivity whereas the mean radiative energy flux is mediated by a diffusive flux employing Kramers opacity law. Statistics and transport properties of up-and downflows are studied separately.Results. The volume-averaged rms velocity increases with decreasing Prandtl number. At the same time the filling factor of downflows decreases and leads to, on average, stronger downflows at lower Prandtl numbers. This results in a strong dependence of convective overshooting on the Prandtl number. Velocity power spectra do not show marked changes as a function of Prandtl number except near the base of the convective layer where the dominance of vertical flows is more pronounced. At the highest Reynolds numbers the velocity power spectra are more compatible with the Bolgiano-Obukhov k −11/5 than the Kolmogorov-Obukhov k −5/3 scaling. The horizontally averaged convected energy flux (F conv), which is the sum of the enthalpy (F enth ) and kinetic energy fluxes (F kin ), is independent of the Prandtl number within the CZ. However, the absolute values of F enth and F kin increase monotonically with decreasing Prandtl number. Furthermore, F enth and F kin have opposite signs for downflows and their sum F ↓ conv diminishes with Prandtl number. Thus the upflows (downflows) are the dominant contribution to the convected flux at low (high) Prandtl number. These results are similar to those from Rayleigh-Benárd convection in the low Prandtl number regime where convection is vigorously turbulent but inefficient at transporting energy. Conclusions. The current results indicate a strong dependence of convective overshooting and energy flux on the Prandtl number. Numerical simulations of astrophysical convection often use Prandtl number of unity because it is numerically convenient. The current results suggest that this can lead to misleading results and that the astrophysically relevant low Prandtl number regime is qualitatively different from the parameters regimes explored in typical contemporary simulations.

show abstract

Physically motivated heat-conduction treatment in simulations of solar-like stars: effects on dynamo transitions

Cited by 11 publications

References 55 publications

Prandtl number dependence of stellar convection: Flow statistics and convective energy transport

Prandtl number dependence of stellar convection: Flow statistics and convective energy transport

Overshooting in simulations of compressible convection

Prandtl number dependence of compressible convection: Flow statistics and convective energy transport

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