## Abstract

Rigorous upper bounds are derived for large-scale turbulent flame speeds in a prototypical model problem. This model problem consists of a reaction-diffusion equation with KPP chemistry with random advection consisting of a turbulent unidirectional shear flow. When this velocity field is fractal with a Hurst exponent H with 0 < H < 1, the almost sure upper bounds suggest that there is an accelerating large-scale turbulent flame front with the enhanced anomalous propagation law y = C_{H}t^{1 + H} for large renormalized times. In contrast, a similar rigorous almost sure upper bound for velocity fields with finite energy yields the turbulent flame propagation law y = C̃_{H}t within logarithmic corrections. Furthermore, rigorous theorems are developed here which show that upper bounds for turbulent flame speeds with fractal velocity fields are not self-averaging, i.e., bounds for the ensemble-averaged turbulent flame speed can be extremely pessimistic and misleading when compared with the bounds for every realization.

Original language | English (US) |
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Pages (from-to) | 933-954 |

Number of pages | 22 |

Journal | Journal of Statistical Physics |

Volume | 83 |

Issue number | 5-6 |

DOIs | |

State | Published - Jun 1996 |

## Keywords

- Combustion
- Fractal fields
- Turbulence

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics