Bounds on enhanced turbulent flame speeds for combustion with fractal velocity fields

Andrew J. Majda, Panagiotis E. Souganidis

Research output: Contribution to journalArticlepeer-review


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 = CHt1 + 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 = C̃Ht 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 languageEnglish (US)
Pages (from-to)933-954
Number of pages22
JournalJournal of Statistical Physics
Issue number5-6
StatePublished - Jun 1996


  • Combustion
  • Fractal fields
  • Turbulence

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics


Dive into the research topics of 'Bounds on enhanced turbulent flame speeds for combustion with fractal velocity fields'. Together they form a unique fingerprint.

Cite this