Front speed enhancement in cellular flows

Abstract

The problem of front propagation in a stirred medium is addressed in the case of cellular flows in three different regimes: slow reaction, fast reaction and geometrical optics limit. It is well known that a consequence of stirring is the enhancement of front speed with respect to the non-stirred case. By means of numerical simulations and theoretical arguments we describe the behavior of front speed as a function of the stirring intensity, $U$. For slow reaction, the front propagates with a speed proportional to $U^{1/4}$, conversely for fast reaction the front speed is proportional to $U^{3/4}$. In the geometrical optics limit, the front speed asymptotically behaves as $U/\ln U$.Comment: 10 RevTeX pages, 10 included eps figure

Quenching of reaction by cellular flows

“…The same scaling may be obtained from the formal predictions V A ∼ A 1/4 for the front speed V A in a cellular flow [1,2,3,32] -this implies that the front width is of the order A 1/4 . Hence one might expect that initial data with the support less than the front width L 0 < A 1/4 to be quenched.…”

“…where the values of all functions are taken at a point (X h t , X θ t ), while B (1) and B (2) t are independent one-dimensional Brownian motions. Clearly,…”

“…The first effect is related to the behavior of front-like solutions, and has been extensively studied recently: traveling fronts have been shown to exist in various flows [5,6,7,33,34,35,36], and flows have been shown to speed-up the front propagation due to the improved mixing [3,4,9,20,37], see [4,36] for recent reviews of the mathematical results in the area. This problem has also attracted a significant attention in the physical literature, we mention [1,2,3,17,18,19,22,23] among the recent papers and refer to [30] as a general reference. The present paper addresses the second phenomenon mentioned above: the possibility of flame extinction by a flow.…”

Periodic homogenization of the inviscid G-equation for incompressible flows

“…We conclude that there exists a subsequence {λ (2) m } m≥1 of {λ (1) m } m≥1 such that λ The lemma follows after we repeat this procedure l times. If not, owing to Lemma 2.3, then there exists another subsequence λ…”

Finite Element Computation of KPP Front Speeds in 3D Cellular and ABC Flows

“…A fundamental problem is to analyze and compute large scale front speeds in complex flows. Much progress has been made in recent years for the Kolmogorov-Petrovsky-Piskunov (KPP) reactive fronts in the large amplitude regime of steady periodic incompressible flows [1,3,30,35,46]. An extensively studied example is the two dimensional cellular flow consisting of periodic array of vortices.…”