Stellar winds in H II regions – I. Unstable waves in ionized shells

In this paper we investigate in some detail the nature of acoustic disturbances in an ionized shell which is held under pressure by a shocked stellar wind, and surrounds a hot star such as an OB star or the nucleus of a planetary nebula. We find that for a large range of wavenumbers such waves can grow to finite amplitude in a time that is of the order of the sound crossing time for the HII layer, and therefore short compared with the dynamical time-scale of the nebula as a whole. An important consequence is that mixing will then occur between the hot shocked gas from the stellar wind and the cooler gas in the HII region.