Brownian fluctuations of flame fronts with small random advection

TL;DR

This paper investigates how small random advection influences flame front fluctuations in turbulent combustion, revealing that fluctuations behave like Brownian motion and are similar across different models.

Contribution

It identifies the fluctuation scale and characterizes them via a stochastic Hamilton-Jacobi equation, highlighting a surprising universality in fluctuation behavior.

Findings

Fluctuations are of the same scale as the advection size.

Fluctuations are characterized by a stochastic Hamilton-Jacobi equation.

Both models exhibit similar Brownian fluctuations despite differences.

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.