Brownian fluctuations of flame fronts with small random advection

Christopher Henderson, Panagiotis E. Souganidis

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We study the effect of small random advection in two models in turbulent combustion. Assuming that the velocity field decorrelates sufficiently fast, we (i) identify the order of the fluctuations of the front with respect to the size of the advection; and (ii) characterize them by the solution of a Hamilton-Jacobi equation forced by white noise. In the simplest case, the result yields, for both models, a front with Brownian fluctuations of the same scale as the size of the advection. That the fluctuations are the same for both models is somewhat surprising, in view of known differences between the two models.

Original languageEnglish (US)
Pages (from-to)1375-1406
Number of pages32
JournalMathematical Models and Methods in Applied Sciences
Volume30
Issue number7
DOIs
StatePublished - Jun 30 2020

Keywords

  • Fisher-KPP equation
  • Front propagation
  • G-equation
  • Hamilton-Jacobi equations
  • stochastic advection

ASJC Scopus subject areas

  • Modeling and Simulation
  • Applied Mathematics

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