The deflagration-to-detonation transition (DDT) mechanism remains one of the major unsolved problems of theoretical and computational combustion. Astrophysicists have suspected for almost 40 years that it is also directly responsible for at least a subclass of white dwarf explosions powering Type Ia supernovae (SN Ia). Astrophysical observational evidence for the DDT is, however, only indirect, which hinders progress in understanding the SN Ia explosion mechanism. Despite this hindrance, extensive research has been conducted to identify the conditions in which the DDT mechanism might operate in SN Ia. Much of this research has focused on the interactions of deflagration fronts with turbulence generated by the flame itself. Other work has focused on turbulence in the white dwarf pre-existing prior to ignition and the influence that turbulent properties have on the detonability of white dwarf plasma, such as the compressibility and intensity of this turbulence. In our work, we aim 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 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.