Abstract
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.
Highlights
When the local temperature gradient is steeper than the one associated with an adiabat, small perturbations from the hydrostatic equilibrium amplify to the well-known Rayleigh-Taylor convective instability
The spectral resolution is limited to Nl = 2/3 Nθ
We have performed an extensive numerical modeling campaign of rapidly rotating convection in a spherical shell that exhibits a sandwiched stable stratified layer between two convective zones. Such a system is most suitable for Saturn, where the H/He demixing generates a compositional gradient around middepth and though suppresses thermal convection locally
Summary
When the local temperature gradient is steeper than the one associated with an adiabat, small perturbations from the hydrostatic equilibrium amplify to the well-known Rayleigh-Taylor convective instability. This leads to vigorous convection that very rapidly re-establishes bulk adiabatic gradients of density and temperature due to the inherent mixing and heat transport efficiency. Stable stratified regions, in which the heat flux is conductive or radiative, are widespread phenomena in stars and planets. Those regions are caused by either subadiabatic temperature or positive heavy element gradient. In the Earth’s liquid outer core, the outermost layer seems stratified caused by either a subadiabatic temperature gradient or a local enrichment of light elements
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
