On the evolution of thermonuclear flames on large scales

The thermonuclear explosion of a massive white dwarf in a Type la supernova explosion is characterized by vastly disparate spatial and temporal scales. The extreme dynamic range inherent to the problem prevents the use of direct numerical simulation and forces modelers to resort to subgrid models to describe physical processes taking place on unresolved scales. We consider the evolution of a model thermonuclear flame in a constant gravitational field on a periodic domain. The gravitational acceleration is aligned with the overall direction of the flame propagation, making the flame surface subject to the Rayleigh-Taylor instability. The flame evolution is followed through an extended initial transient phase well into the steady state regime. The properties of the evolution of flame surface are examined. We confirm the form of the governing equation of the evolution suggested by Khokhlov in 1995. The mechanism of vorticity production and the interaction between vortices and the flame surface are discussed. Previously observed periodic behavior of the flame evolution is reproduced and is found to be caused by the turnover of the largest eddies. The characteristic timescales are found to be similar to the turnover time of these eddies. Relations between flame surface creation and destruction processes and basic characteristics of the flow are discussed. We find that the flame surface creation strength is associated with the Rayleigh-Taylor timescale. Also, in fully developed turbulence, the flame surface destruction strength scales as 1/L³, where L is the turbulent driving scale. The results of our investigation provide support for Khokhlov's self-regulating model of turbulent thermonuclear flames. Based on these results, one can revise and extend the original model. The revision uses a local description of the flame surface enhancement and the evolution of the flame surface since the onset of turbulence, rendering it free from the assumption of an instantaneous steady state of turbulence. This new model can be applied to the initial transient phase of the flame evolution, where the self-regulation mechanism yet to be fully established. Details of this new model will be presented in a forthcoming paper.