Overshooting in simulations of compressible convection. (arXiv:1812.07916v1 [astro-ph.SR])
<a href="http://arxiv.org/find/astro-ph/1/au:+Kapyla_P/0/1/0/all/0/1">Petri J. Käpylä</a> (Georg-August-Universität Göttingen, ReSoLVE Center of Excellence/Aalto)
Context: Convective motions overshooting to regions that are formally
convectively stable cause extended mixing. Aims: To determine the scaling of
overshooting depth ($d_{rm os}$) at the base of the convection zone as a
function of imposed energy flux ($mathscr{F}_{rm n}$) 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: Two distinct regimes were
found where the scaling properties of overshooting differ depending on the heat
conductivity profile. A smooth heat conduction profile (either fixed or through
Kramers opacity law) and surface cooling via a relaxation term leads to a
relatively shallow power law with $d_{rm os}propto mathscr{F}_{rm
n}^{0.08}$ for low $mathscr{F}_{rm n}$. A fixed step-profile of the heat
conductivity at the bottom of the convection zone leads to a somewhat steeper
dependency with $d_{rm os}propto mathscr{F}_{rm n}^{0.14}$ in the same
regime. Furthermore, changing the heat conductivity artificially in the
radiative and overshoot layers to speed up thermal saturation is shown to lead
to a 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 Sun is on the order of 10 per cent of the pressure
scale height at the base of the convection zone in broad agreement with
helioseismic constraints.
Context: Convective motions overshooting to regions that are formally
convectively stable cause extended mixing. Aims: To determine the scaling of
overshooting depth ($d_{rm os}$) at the base of the convection zone as a
function of imposed energy flux ($mathscr{F}_{rm n}$) 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: Two distinct regimes were
found where the scaling properties of overshooting differ depending on the heat
conductivity profile. A smooth heat conduction profile (either fixed or through
Kramers opacity law) and surface cooling via a relaxation term leads to a
relatively shallow power law with $d_{rm os}propto mathscr{F}_{rm
n}^{0.08}$ for low $mathscr{F}_{rm n}$. A fixed step-profile of the heat
conductivity at the bottom of the convection zone leads to a somewhat steeper
dependency with $d_{rm os}propto mathscr{F}_{rm n}^{0.14}$ in the same
regime. Furthermore, changing the heat conductivity artificially in the
radiative and overshoot layers to speed up thermal saturation is shown to lead
to a 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 Sun is on the order of 10 per cent of the pressure
scale height at the base of the convection zone in broad agreement with
helioseismic constraints.
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