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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 layersdoi:10.1086/423415 fatcat:y2p4ugc7yjgvhpucxvgucxpsdi