  [abridged] Radiation pressure on dust grains may be an important mechanism in
driving winds in a wide variety of astrophysical systems. However, the
efficiency of the coupling between the radiation field and the dusty gas is
poorly understood in environments characterized by high optical depths. We
present a series of idealized numerical experiments, performed with the
radiation-hydrodynamic code ORION, in which we study the dynamics of such winds
and quantify their properties. We find that, after wind acceleration begins,
radiation Rayleigh-Taylor instability forces the gas into a configuration that
reduces the rate of momentum transfer from the radiation field to the gas by a
factor ~ 10 - 100 compared to an estimate based on the optical depth at the
base of the atmosphere; instead, the rate of momentum transfer from a driving
radiation field of luminosity L to the gas is roughly L/c multiplied by one
plus half the optical depth evaluated using the photospheric temperature, which
is far smaller than the optical depth one would obtain using the interior
temperature. When we apply our results to conditions appropriate to ULIRGs and
star clusters, we find that the asymptotic wind momentum flux from such objects
should not significantly exceed that carried by the direct radiation field,
L/c. This result constrains the expected mass loss rates from systems that
exceed the Eddington limit to be of order the so-called "single-scattering"
limit, and not significantly higher. We present an approximate fitting formula
for the rate of momentum transfer from radiation to dusty gas through which it
passes, which is suitable for implementation in sub-grid models of galaxy
formation. Finally, we provide a first map of the column density distribution
of gas in a radiatively-driven wind as a function of velocity, and velocity
dispersion.
