  We examine the small-scale dynamics of black hole accretion disks in which
radiation pressure exceeds gas pressure. Local patches of disk are modeled by
numerically integrating the equations of radiation MHD in the flux-limited
diffusion approximation. The shearing-box approximation is used, and the
vertical component of gravity is neglected. Magneto-rotational instability
(MRI) leads to turbulence in which accretion stresses are due primarily to
magnetic torques. When radiation is locked to gas over the length and time
scales of fluctuations in the turbulence, the accretion stress, density
contrast, and dissipation differ little from those in the corresponding
calculations with radiation replaced by extra gas pressure. However, when
radiation diffuses each orbit a distance that is comparable to the RMS vertical
wavelength of the MRI, radiation pressure is less effective in resisting
squeezing. Large density fluctuations occur, and radiation damping of
compressive motions converts PdV work into photon energy. The accretion stress
in calculations having a net vertical magnetic field is found to be independent
of opacity over the range explored, and approximately proportional to the
square of the net field. In calculations with zero net magnetic flux, the
accretion stress depends on the portion of the total pressure that is effective
in resisting compression. The stress is lower when radiation diffuses rapidly
with respect to the gas. We show that radiation-supported Shakura-Sunyaev disks
accreting via internal magnetic stresses are likely in their interiors to have
radiation marginally coupled to turbulent gas motions.
