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Overshooting of turbulent motions from convective regions into adjacentstably stratified zones plays a significant role in stellar interior dynamicsas this process may lead to mixing of chemical species, and contribute to thetransport of angular momentum and magnetic fields. We present a series of fullynon-linear, three-dimensional (3D) anelastic simulations of overshootingconvection in a spherical shell which are focused on the dependence of theovershooting dynamics on the density stratification and the rotation, both keyingredients in stars which however have not been studied systematicallytogether via global simulations. We demonstrate that the overshoot lengthscaleis not simply a monotonic function of the density stratification in theconvective region but instead, it depends on the ratio of the densitystratifications in the two zones. Additionally, we find that the overshootlengthscale decreases with decreasing Rossby number Ro and scales asRo$^{0.23}$ while it also depends on latitude with higher Rossby cases leadingto a weaker latitudinal variation. We examine the mean flows arising due torotation and find that they extend beyond the base of the convection zone intothe stable region. Our findings may provide a better understanding of thedynamical interaction between stellar convective and radiative regions, andmotivate future studies particularly related to the solar tachocline and theimplications of its overlapping with the overshoot region.

On the dynamics of overshooting convection in spherical shells: Effect of density stratification and rotation