Penetrative Cellular Convection in a Stratified Atmosphere

摘要

Penetrative convection has been investigated within a simple compressible model consisting of three layers of differing stratification prior to the onset of convection. The middle one is a convectively unstable polytrope bounded above and below by two stably stratified polytropes. Nonlinear anelastic modal equations are used ot describe these convective motions. Penetrative boundary conditions are imposed at the top and bottom of the computational domain. One- and two- mode steady solutions with hexagonal planforms have been studied for Rayleigh numbers up ot about 1000 times critical, and for a range of Prandtl numbers, horizontal wavenumbers and stratifications. These show that: 1) Penetration into the lower stable layer by downward-directed plumes is substantially larger in a stratified medium than in a Boussinesq fluid, and produces an extended region of adiabatic stratification. 2) Overshooting into the upper stable layer can be sharply diminished by a reversal of the buoyancy occurring in the upper part of the unstable zone if the stratification is strong enough. These effects are all related to large pressure perturbations that arise in such convective flows. The strong asymmetry between upward and downward penetration in compressible media has major implications for the mixing of sable regions above and below stellar convection zones. Keywords: Astrophysical fluid dynamics; Stellar structure; Convection zones; Reprints.