  A Type Ia supernova explosion likely begins as a nuclear runaway near the
center of a carbon-oxygen white dwarf. The outward propagating flame is
unstable to the Landau-Darrieus, Rayleigh-Taylor, and Kelvin-Helmholtz
instabilities, which serve to accelerate it to a large fraction of the speed of
sound. We investigate the Rayleigh-Taylor unstable flame at the transition from
the flamelet regime to the distributed-burning regime, around densities of
$10^7$ g/cc, through detailed, fully resolved simulations. A low Mach number,
adaptive mesh hydrodynamics code is used to achieve the necessary resolution
and long time scales. As the density is varied, we see a fundamental change in
the character of the burning--at the low end of the density range the
Rayleigh-Taylor instability dominates the burning, whereas at the high end the
burning suppresses the instability. In all cases, significant acceleration of
the flame is observed, limited only by the size of the domain we are able to
study. We discuss the implications of these results on the potential for a
deflagration to detonation transition.
