  The aim of this work is to identify and explain the necessary conditions
required for an energetic explosion of a Chandrasekhar-mass white dwarf. We
construct and analyze weakly compressible turbulence models with nuclear
burning effects for carbon/oxygen plasma at a density expected for
deflagration-to-detonation transition (DDT) to occur. We observe formation of
carbon deflagrations and transient carbon detonations at early times. As
turbulence becomes increasingly inhomogeneous, sustained carbon detonations are
initiated by the Zel'dovich reactivity gradient mechanism. The fuel is suitably
preconditioned by the action of compressive turbulent modes with wavelength
comparable to the size of resolved turbulent eddies; no acoustic wave is
involved in this process. Oxygen detonations are initiated either aided by
reactivity gradients or by collisions of carbon detonations. The observed
evolutionary timescales are found sufficiently short for the above process to
occur in the expanding, centrally ignited massive white dwarf. The
inhomogeneous conditions produced prior to DDT might be of consequence for the
chemical composition of the outer ejecta regions of SN Ia from the single
degenerate channel, and offer potential for validation of the proposed model.
