http://arxiv.org/abs/1812.07916
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.
P. Käpylä
Thu, 20 Dec 18
56/62
Comments: 11 pages, 11 figures, submitted to Astron. Astrophys
You must be logged in to post a comment.