  We present a statistical model which shows the influence of turbulence on a
thermonuclear flame propagating in C+O white dwarf matter. Based on a Monte
Carlo description of turbulence, it provides a method for investigating the
physics in the so-called distributed burning regime. Using this method we
perform numerical simulations of turbulent flames and show that in this
particular regime the flamelet model for the turbulent flame velocity loses its
validity. In fact, at high turbulent intensities burning in the distributed
regime can lead to a deceleration of the turbulent flame and thus induces a
competing process to turbulent effects that cause a higher flame speed. It is
also shown that in dense C+O matter turbulent heat transport is described
adequately by the Peclet number, Pe, rather than by the Reynolds number, which
means that flame propagation is decoupled from small-scale turbulence. Finally,
at the onset of our results we argue that the available turbulent energy in an
exploding C+O white dwarf is probably too low in order to make a deflagration
to detonation transition possible.
