  We study the linear growth and nonlinear saturation of the "acoustic Resonant
Drag Instability" (RDI) when the dust grains, which drive the instability, have
a wide, continuous spectrum of different sizes. This physics is generally
applicable to dusty winds driven by radiation pressure, such as occurs around
red-giant stars, star-forming regions, or active galactic nuclei. Depending on
the physical size of the grains compared to the wavelength of the radiation
field that drives the wind, two qualitatively different regimes emerge. In the
case of grains that are larger than the radiation's wavelength -- termed the
constant-drift regime -- the grain's equilibrium drift velocity through the gas
is approximately independent of grain size, leading to strong correlations
between differently sized grains that persist well into the saturated nonlinear
turbulence. For grains that are smaller than the radiation's wavelength --
termed the non-constant-drift regime -- the linear instability grows more
slowly than the single-grain-size RDI and only the larger grains exhibit
RDI-like behavior in the saturated state. A detailed study of grain clumping
and grain-grain collisions shows that outflows in the constant-drift regime may
be effective sites for grain growth through collisions, with large collision
rates but low collision velocities.
