BOUNDS ON ENHANCED TURBULENT FLAME SPEEDS FOR COMBUSTION WITH FRACTALVELOCITY-FIELDS

Rigorous upper bounds are derived for large-scale turbulent flame spee ds in a prototypical model problem. This model problem consists of a r eaction-diffusion equation with KPP chemistry with random advection co nsisting of a turbulent unidirectional shear flow. When this velocity field is fractal with a Hurst exponent H with 0<H<1, the almost sure u pper bounds suggest that there is an accelerating large-scale turbulen t flame front with the enhanced anomalous propagation law y = C(H)t(1H) for large renormalized times. In contrast, a similar rigorous almos t sure upper bound for velocity fields with finite energy yields the t urbulent flame propagation law y = (C) over tilde(H)t within logarithm ic corrections. Furthermore, rigorous theorems are developed here whic h show that upper bounds for turbulent name speeds with fractal veloci ty fields are not self-averaging, i.e., bounds for the ensemble-averag ed turbulent flame speed can be extremely pessimistic and misleading w hen compared with the bounds for every realization.