  [abridged] The pressure exerted by the radiation of young stars may be an
important feedback mechanism in forming star clusters and the disks of
starburst galaxies. However, there is great uncertainty in how efficiently
radiation couples to matter in these high optical depth environments. In
particular, it is unclear what levels of turbulence the radiation can produce,
and whether the infrared radiation trapped by the dust opacity can give rise to
heavily mass-loaded winds. In this paper we report a series of two-dimensional
flux-limited diffusion radiation-hydrodynamics calculations performed with the
code ORION in which we drive strong radiation fluxes through columns of dusty
matter confined by gravity. We consider both systems where the radiation flux
is sub-Eddington throughout the gas column, and where it is super-Eddington at
the midplane but sub-Eddington in the atmosphere. In the latter, we find that
the radiation-matter interaction gives rise to radiation-driven Rayleigh-Taylor
instability, which drives supersonic turbulence at a level sufficient to fully
explain the turbulence seen in Galactic protocluster gas clouds, and to make a
non-trivial contribution to the turbulence observed in starburst galaxy disks.
However, the instability also produces a channel structure in which the
radiation-matter interaction is reduced because the radiation field is not
fully trapped. For astrophysical parameters relevant to forming star clusters
and starburst galaxies, we find that this effect reduces the net momentum
deposition rate in the dusty gas by a factor of ~2-6 compared to simple
analytic estimates, and that in steady state the Eddington ratio reaches unity
and there are no strong winds. We provide an approximation formula, appropriate
for implementation in analytic models and non-radiative simulations, for the
force exerted by the infrared radiation field in this regime.
