Bistability in inhomogeneity—Effects of flow coherent structures on the fate of a bistable reaction

Tang, Wen; Dhumuntarao, Aditya

doi:10.1063/1.4923250

Cited by 3 publications

(4 citation statements)

References 15 publications

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“…The correlation changes with advection speed. For small values of Re, reacted regions lie primarily along vortex edges and in narrow filaments where stretching is strongest, consistent with simulations showing that stretching enhances reaction [1,37,38] [31].…”

supporting

confidence: 86%

“…In simulations of the double-gyre flow, a two-dimensional prescribed model, the reaction rate was observed to be enhanced in regions of strong stretching [37]. When two competing autocatalytic species were simulated in double-gyre flow, it was observed that the one initiated in a region of stronger stretching almost always dominated long term [38]. Similarly, in simulations of competing species in sine flow, another two-dimensional prescribed model, it was observed that local FTLEs accurately predict long-term concentrations [1].…”

mentioning

confidence: 97%

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Optimal Stretching in Advection-Reaction-Diffusion Systems

Nevins

Kelley

2016

Phys. Rev. Lett.

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We investigate growth of the excitable Belousov-Zhabotinsky reaction in chaotic, time-varying flows. In slow flows, reacted regions tend to lie near vortex edges, whereas fast flows restrict reacted regions to vortex cores. We show that reacted regions travel toward vortex centers faster as flow speed increases, but nonreactive scalars do not. For either slow or fast flows, reaction is promoted by the same optimal range of the local advective stretching, but stronger stretching causes reaction blowout and can hinder reaction from spreading. We hypothesize that optimal stretching and blowout occur in many advection-diffusion-reaction systems, perhaps creating ecological niches for phytoplankton in the ocean.

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supporting

confidence: 86%

mentioning

confidence: 97%

Optimal Stretching in Advection-Reaction-Diffusion Systems

Nevins

Kelley

2016

Phys. Rev. Lett.

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“…By calculating the FTLE field for an ensemble of runs and comparing the results to the asymptotic states of chemical reactions, it has been shown that there is a strong correlation between regions of high FTLE and dynamically different reaction fates. 71,72 Studies of chemical reaction systems have also been focusing on the identification of burning invariant manifolds, which are one-way barriers in the advection reaction systems that inhibit a chemical reaction. 49,55 Moving forward, there are several major avenues to be explored.…”

Section: Discussionmentioning

confidence: 99%

Lagrangian based methods for coherent structure detection

Allshouse

Peacock

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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There has been a proliferation in the development of Lagrangian analytical methods for detecting coherent structures in fluid flow transport, yielding a variety of qualitatively different approaches. We present a review of four approaches and demonstrate the utility of these methods via their application to the same sample analytic model, the canonical double-gyre flow, highlighting the pros and cons of each approach. Two of the methods, the geometric and probabilistic approaches, are well established and require velocity field data over the time interval of interest to identify particularly important material lines and surfaces, and influential regions, respectively. The other two approaches, implementing tools from cluster and braid theory, seek coherent structures based on limited trajectory data, attempting to partition the flow transport into distinct regions. All four of these approaches share the common trait that they are objective methods, meaning that their results do not depend on the frame of reference used. For each method, we also present a number of example applications ranging from blood flow and chemical reactions to ocean and atmospheric flows. The transport of material by advection in fluid systems is a process of vital and ubiquitous importance, underlying scenarios as diverse as pollutant distribution and searchand-rescue operations in the ocean to blood flow in the human body. The rapidly advancing field of Lagrangian based methods for studying flow transport has demonstrated an effective ability to find robust and significant transport features that underly the organization of flow transport in complex, unsteady flow fields. In this review, we present an overview of four of the leading Lagrangian approaches, each with their own strengths and challenges. Details of each method are presented along with an example application to the same model system, the double-gyre flow. Furthermore, we highlight a number of exciting applications and future directions to bring Lagrangian based analysis closer to implementation in real-time, real-world decision making strategies.

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“…43 Similarly, if two reactions compete, the one that is triggered where FTLEs are smaller is eventually overwhelmed. 2,44 Earlier experiments showed that the overall reaction rate increased when the average FTLE value increased. 45 However, recent evidence 1 suggests that strong stretching may inhibit the growth of reacted regions.…”

Section: Introductionmentioning

confidence: 99%

Optimal stretching in the reacting wake of a bluff body

Wang

Tithof

Nevins

et al. 2017

Chaos: An Interdisciplinary Journal of Nonlinear Science

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We experimentally study spreading of the Belousov-Zhabotinsky reaction behind a bluff body in a laminar flow. Locations of reacted regions (i.e., regions with high product concentration) correlate with a moderate range of Lagrangian stretching and that range is close to the range of optimal stretching previously observed in topologically different flows [T. D. Nevins and D. H. Kelley, Phys. Rev. Lett. 117, 164502 (2016)]. The previous work found optimal stretching in a closed, vortex dominated flow, but this article uses an open flow and only a small area of appreciable vorticity. We hypothesize that optimal stretching is common in advection-reaction-diffusion systems with an excitation threshold, including excitable and bistable systems, and that the optimal range depends on reaction chemistry and not on flow shape or characteristic speed. Our results may also give insight into plankton blooms behind islands in ocean currents.

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Bistability in inhomogeneity—Effects of flow coherent structures on the fate of a bistable reaction

Cited by 3 publications

References 15 publications

Optimal Stretching in Advection-Reaction-Diffusion Systems

Optimal Stretching in Advection-Reaction-Diffusion Systems

Lagrangian based methods for coherent structure detection

Optimal stretching in the reacting wake of a bluff body

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