  Celestial objects host interfaces between convective and stable stratified
interior regions. The interaction between both, e.g., the transfer of heat,
mass, or angular momentum depends on whether and how flows penetrate into the
stable layer. Powered from the unstable, convective regions, radial flows can
pierce into the stable region depending on their inertia (overshooting). In
rapidly rotating systems, the dynamics are strongly influenced by the Coriolis
force and radial flows penetrate in stratified regions due to the geostrophic
invariance of columnar convection even in the limit of vanishing inertia.
Within this study, we numerically investigate both mechanisms and hence explore
the nature of penetrative convection in rapidly rotating spherical shells. The
study covers a broad range of system parameters, such as the strength of the
stratification relative to the Coriolis force or the inertia. Guided by the
application to Saturn, we model a sandwiched stable stratified layer (SSL)
surrounded by two convective zones. A comprehensive analysis of the damping
behavior of convective flows at the edges of the SSL showed that the mean
penetration depth is controlled by the ratio of stratified and unstratified
buoyancy gradients and is hence independent of rotation. A scaling law is
derived and suggests that the penetration depth decreases with the square root
of the ratio of unstabilizing and stabilizing entropy gradients. The influence
of the Coriolis force, however, is evident by a modulation of the penetration
depth along latitude, since convective columns are elongated vertically and
hence pierce predominantly into the SSL around mid-latitudes and outside the
tangent cylinder. Our result also show that the penetration depth decreases
linearly with the flow length scale (low pass filter), confirming predictions
from the linear theory of rotating partially stratified convection.
