Thin front propagation in steady and unsteady cellular flows

Cencini, Massimo; Torcini, Alessandro; Vergni, Davide; Vulpiani, Angelo

doi:10.1063/1.1541668

Cited by 54 publications

(110 citation statements)

References 43 publications

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“…After this, the front propagates periodically in space and time with an average speed v f , which is enhanced with respect to the propagation speed v 0 of the fluid at rest [31] (see Ref. [29] for some pictorial views).…”

Section: Front Speed In the Geometrical Optics Regimementioning

confidence: 99%

Front speed enhancement in cellular flows

Abel

Cencini

Vergni

et al. 2002

Chaos: An Interdisciplinary Journal of Nonlinear Science

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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

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Section: Front Speed In the Geometrical Optics Regimementioning

confidence: 99%

Front speed enhancement in cellular flows

Abel

Cencini

Vergni

et al. 2002

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…This flow is easily accessible to experimentalists for instance using magnetohydrodynamics techniques similar to Rayleigh-Bénard convection with a control over the flow [21,22,23]. As such, understanding its influence on the advection of passive or active quantities is considered a necessary first step in order to uncover the different mechanisms governing transport in general or reactiondiffusion processes such as front propagation in turbulent flows [34,35,36,37,38]. The stream function which models an experiment in a channel with slip boundary conditions writes:…”

Section: Introductionmentioning

confidence: 99%

Targeted mixing in an array of alternating vortices

et al. 2007

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Transport and mixing properties of passive particles advected by an array of vortices are investigated. Starting from the integrable case, it is shown that a special class of perturbations allows one to preserve separatrices which act as effective transport barriers, while triggering chaotic advection. In this setting, mixing within the two dynamical barriers is enhanced while long range transport is prevented. A numerical analysis of mixing properties depending on parameter values is performed; regions for which optimal mixing is achieved are proposed. Robustness of the targeted mixing properties regarding errors in the applied perturbation are considered, as well as slip/no-slip boundary conditions for the flow.

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“…The experimental flow differs from the model flow of refs. [15,17,21,22] in two respects: a) there are no-slip rather than free-slip boundary conditions at the bottom and sides of the annulus; and b) there is a weak, secondary, three-dimensional flow that slowly pumps fluid inward along the bottom and up through the vortex centers [23].…”

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confidence: 99%

“…Recently, reaction fronts have been investigated theoretically in this flow [8,9,17]. For the oscillatory regime, locking bands are predicted where the front propagates an integer number N of wavelengths in an integer number M of drive periods.…”

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Experimental studies of front propagation and mode-locking in an advection-reaction-diffusion system

Paoletti¹,

Solomon²

2005

Europhys. Lett.

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processes. The dynamics of these fronts are governed by the interplay between mixing in the system and the interaction between the different species. Several previous studies have examined this phenomenon in the reaction-diffusion limit in which fluid flows are not present and mixing is achieved solely via molecular diffusion [5]. But fluid systems typically are not stagnant; rather, flows in the system dramatically alter and enhance transport and mixing. Despite this fact, the more general advection-reaction-diffusion problem has only recently received attention [6][7][8][9], and there have been almost no experimental studies [10][11][12]. The importance of mixing is particularly significant in light of recent studies indicating that mixing can be chaotic, even for well-ordered, laminar fluid flows [13,14].In this letter, we present experimental studies of the propagation of chemical fronts in a cellular flow consisting of a chain of oscillating vortices [15,16]. In particular, we investigate the propagation velocities for the fronts. We compare the experimental results to a theory [17] that predicts locking of the fronts to the external forcing. Mode-locking of this nature has been found in a variety of physical systems [18,19]; this, however, is the first experimental evidence of mode-locking in an advection-reaction-diffusion system.

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Thin front propagation in steady and unsteady cellular flows

Cited by 54 publications

References 43 publications

Front speed enhancement in cellular flows

Front speed enhancement in cellular flows

Targeted mixing in an array of alternating vortices

Experimental studies of front propagation and mode-locking in an advection-reaction-diffusion system

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