FLAME MODELING IN SUPERNOVAE

We study thermonuclear, carbon-oxygen deflagration flames in supernovae. A flame-capturing technique is used to simulate a flame front advected by a hydrodynamical flow in a manner independent of zoning. The flame is resolved down to a spatial scale lambda(c), where it becomes stable with respect to the Rayleigh-Taylor instability. At scales >lambda(c) the flame shows a complex behavior. Large bubbles of hot, burned matter rise, kill smaller bubbles, and tend to dominate the flow. The flame folds, thin layers of cold fuel penetrate deep into products, and the flame becomes multiply connected. The geometrical complexity of the flame front and the instantaneous turbulent flame speed vary with time. A substantial acceleration of burning is found. Results indicate a relation between the average turbulent flame speed and intensity of turbulent motions, which is consistent with the theory of Karlovitz et al. (1951) for premixed flames in gases. We show how this relation can be used to estimate the maximum turbulent flame speeds in white dwarfs. The speed is compared with that required for deflagration and delayed detonation models of Type Ia supernovae.