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Flame instabilities play a dominant role in accelerating the burning front toa large fraction of the speed of sound in a Type Ia supernova. We present athree-dimensional numerical simulation of a Rayleigh-Taylor unstable carbonflame, following its evolution through the transition to turbulence. A low Machnumber hydrodynamics method is used, freeing us from the harsh timesteprestrictions imposed by sound waves. We fully resolve the thermal structure ofthe flame and its reaction zone, eliminating the need for a flame model. Asingle density is considered, $1.5\times 10^7 \gcc$, and half carbon\slash halfoxygen fuel--conditions under which the flame propagated in the flamelet regimein our related two-dimensional study. We compare to a correspondingtwo-dimensional simulation, and show that while fire-polishing keeps the smallfeatures suppressed in two dimensions, turbulence wrinkles the flame on farsmaller scales in the three-dimensional case, suggesting that the transition tothe distributed burning regime occurs at higher densities in three dimensions.Detailed turbulence diagnostics are provided. We show that the turbulencefollows a Kolmogorov spectrum and is highly anisotropic on the large scales,with a much larger integral scale in the direction of gravity. Furthermore, wedemonstrate that it becomes more isotropic as it cascades down to small scales.Based on the turbulent statistics and the flame properties of our simulation,we compute the Gibson scale. We show the progress of the turbulent flamethrough a classic combustion regime diagram, indicating that the flame justenters the distributed burning regime near the end of our simulation.Comment: accepted to ApJ some figures degraded to conserve spac

Three‐dimensional Numerical Simulations of Rayleigh‐Taylor Unstable Flames in Type Ia Supernovae