Three-dimensional Combustion in Type Ia Supernovae

Turbulent combustion is three-dimensional. Turbulence in a Type Ia supernova is driven on large scales by the buoyancy of burning products. The turbulent cascade penetrates down to very small scales, and makes the rate of deflagration independent of the microphysics. The competition between the turbulent cascade and the freeze-out of turbulent motions due to stellar expansion determines the largest scale participating in the cascade. This sets the bulk rate of a deflagration in a supernova. The freeze-out limits the bulk rate of deflagration to a value that makes a powerful explosion impossible. Two-dimensional simulations cannot capture these essential elements of turbulent combustion, even in principle. A powerful delayed detonation explosion can take place if the burning makes a transition to a detonation. A deflagration to detonation transition (DDT) can occur in a layer of mixed cold fuel and hot burning products created either inside an active turbulent burning region by a high intensity of turbulence, or by mixing cold fuel with ashes of a dead deflagration front during the global pulsation of a star, or by both.