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-Väisäla" 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 (Δ) 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.