The relation between local criteria for hydrodynamic instabilities and stellar stability is reconsidered. This leads to a discussion of the classical problem of stellar pulsation with a special emphasis on the pressure modes of high order spherical harmonics. It is shown that within the frame of the geometrical approximation, acoustic rays exist which are trapped inside any specified slab of a stellar envelope. The pressure modes associated with such rays are conjectured to give rise to small scale instabilities whenever a region exists in an envelope where any local criterium indicates pulsational instability. The model is expected to support and somewhat extend the recent developments concerning the role of pressure non-radial modes on the dynamics of the solar atmosphere and the heating of external layers.

Preliminary report available from Observatoire de Nice.