  We investigate the linear stability of a flat interface that separates a
liquid layer from a fully-developed turbulent gas flow. In this context,
linear-stability analysis involves the study of the dynamics of a
small-amplitude wave on the interface, and we develop a model that describes
wave-induced perturbation turbulent stresses (PTS). We demonstrate the effect
of the PTS on the stability properties of the system in two cases: for a
laminar thin film, and for deep-water waves. In the first case, we find that
the PTS have little effect on the growth rate of the waves, although they do
affect the structure of the perturbation velocities. In the second case, the
PTS enhance the maximum growth rate, although the overall shape of the
dispersion curve is unchanged. Again, the PTS modify the structure of the
velocity field, especially at longer wavelengths. Finally, we demonstrate a
kind of parameter tuning that enables the production of the thin-film (slow)
waves in a deep-water setting.
