Darrieus-landau and rayleigh-taylor instabilities in outwardly-propagating, accelerating flames

Expanding reaction fronts are central not only to many laboratory and industrial phenomena, they also constitute such cosmic phenomena as the thermonuclear combustion in supernovae. While in terrestrial conditions the effect of intrinsic flamefront instabilities is generally believed to be supplementary to, say, external turbulence and chamber dynamics, at the astrophysical scale the role of instabilities in the flame acceleration is presumably dominant. Moreover, while in terrestrial systems we focus mainly on the hydrodynamic, Darrieus-Landau (DL) instability, the Rayleigh-Taylor (RT; body-force) instability is a key issue for supernovae flames because of the enormous gravity. Within the 0^th-order approach, the DL instability is irrelevant to the perturbation wave numbers, hence leading to a globally-spherical structure of the flamefront. In contrast, however, the RT instability is favored at large scales. Consequently, if RT instability dominates over that of DL, the globally-spherical flamefront can be replaced by an "8"-like bubble rising outwardly. In the present work we develop a self-similar formulation describing a globally-spherical expanding flamefront corrugated due to the DL instability in a central gravitation filed. The associated scenario of the flame acceleration, the evolution of the upstream flow, and the locus of the deflagration-to-detonation transition (DDT) are determined. We also compare the effects of DL and RT instabilities, estimating whether a globally-spherical DL-corrugated flamefront is subsequently converted to a RT bubble. It is shown how the locus of such a conversion is coupled to various flame and flow parameters.