PENETRATION BELOW A CONVECTIVE ZONE

Two-dimensional numerical simulations are used to investigate how full y compressible nonlinear convection penetrates into a stably stratifie d zone beneath a stellar convection zone. Estimates are obtained of th e extent of penetration as the relative stability S of the stable to t he unstable zone is varied over a broad range. The model deals with a perfect gas possessing a constant dynamic viscosity. The computational domain is divided into regions of initially stable and unstable polyt ropic stratification by varying the thermal conductivity with depth. E ffects of compressibility are accentuated by considering cases where t he mean density ratio across the unstable zone is initially 6, and as much as 114 across the entire domain. The dynamics is dominated by dow nward-directed plumes which can extend far into the stable material an d which can lead to the excitation of a broad spectrum of internal gra vity waves in the lower stable zone. The convection is highly time dep endent, with the close coupling between the lateral swaying of the plu mes and the internal gravity waves they generate serving to modulate t he strength of the convection. The depth of penetration Delta, determi ned by the position where the time-averaged kinetic flux has its first zero in the stable layer, is controlled by a balance between the kine tic energy carried into the stable layer by the plumes and the buoyanc y braking they experience there. A passive scalar is introduced into t he unstable layer to evaluate the transport of chemical species downwa rd. Such a tracer is effectively mixed within a few convective overtur ning times down to a depth of Delta within the stable layer. Analytica l estimates based on simple scaling laws are used to interpret the var iation of Delta with S, showing that it first involves an interval of adiabatic penetration if the local Peclet number of the convection exc eeds unity, followed by a further thermal adjustment layer, the depths of each interval scaling in turn as S-1 and S--1/4, These estimates a re in accord with the penetration results from the simulations.