  We study the non-linear evolution of the acoustic 'Resonant Drag Instability'
(RDI) using numerical simulations. The acoustic RDI is excited in a dust-gas
mixture when dust grains stream through gas, interacting with sound waves to
cause a linear instability. We study this process in a periodic box by
accelerating neutral dust with an external driving force. The instability grows
as predicted by linear theory, eventually breaking into turbulence and
saturating. As in linear theory, the non-linear behavior is characterized by
three regimes - high, intermediate, and low wavenumbers - the boundary between
which is determined by the dust-gas coupling strength and the dust-to-gas mass
ratio. The high and intermediate wavenumber regimes behave similarly to one
another, with large dust-to-gas ratio fluctuations while the gas remains
largely incompressible. The saturated state is highly anisotropic: dust is
concentrated in filaments, jets, or plumes along the direction of acceleration,
with turbulent vortex-like structures rapidly forming and dissipating in the
perpendicular directions. The low-wavenumber regime exhibits large fluctuations
in gas and dust density, but the dust and gas remain more strongly coupled in
coherent 'fronts' perpendicular to the acceleration. These behaviors are
qualitatively different from those of dust 'passively' driven by external
hydrodynamic turbulence, with no back-reaction force from dust onto gas. The
virulent nature of these instabilities has interesting implications for
dust-driven winds in a variety of astrophysical systems, including around
cool-stars, in dusty torii around active-galactic-nuclei, and in and around
giant molecular clouds.
