Penetrative convection within the anelastic approximation

We present a method for studying penetrative convection within the anelastic approximation. This method is then applied to two- dimensional numerical simulations of a convective region bounded below by a stable ( radiative) region. Descending plumes penetrate into the stable layer, exciting gravity waves with a spectrum of frequencies limited by the Brunt-Vaisala'' frequency. The depth of penetration depends sensitively on the stiffness'' of the boundary between the unstable and stable layers ( quantified by S) and on the vigor of convection. We find scaling relations between the penetrative depth ( Delta) and S, spanning 3 orders of magnitude in S. The reference state in these models is allowed to evolve; the convective region tends toward adiabaticity, and for low values of S, the stable region can be altered considerably ( an extended superadiabatic region is developed). For high values of S, the stable region is left essentially unchanged.