SUPERNOVAE DEFLAGRATIONS IN 3 DIMENSIONS

Three-dimensional turbulent burning in supernovae is studied numerically on scales > lambda(c), where burning becomes unstable with respect to the Rayleigh-Taylor instability. The results are compared with the corresponding two-dimensional results. The behavior of the flame in three and two dimensions is qualitatively different. The tendency of large-scale motions to dominate the flow, and small-scale motions to decay, is an artifact of two-dimensional simulations. In three dimensions, the surface of the flame is more complicated, with many small-scale features present. This is consistent with the difference in the direction of the energy cascade in two- and three-dimensional turbulence. In three dimensions, the turbulence increases the flame speed more effectively. We argue that in three dimensions the energy cascade, which is directed from big to small scales, will excite an additional turbulence on scales < lambda(c) and will influence the flame speed on these scales.