Material barriers to diffusive and stochastic transport

Haller, George; Karrasch, Daniel; Kogelbauer, Florian

doi:10.1073/pnas.1720177115

Cited by 69 publications

(118 citation statements)

References 37 publications

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“…They are well documented in geophysics [33], classical fluid dynamics [23], plasma fusion [6], reactive flows [27] and molecular dynamics [32], yet no general theory for them has been available until recently. In [13], we have put forward such a theory for incompressible flows and weakly diffusing substances by defining and solving an extremum problem for material surfaces that block the diffusive transport of passive scalars more than neighboring surfaces do.…”

Section: Introductionmentioning

confidence: 99%

“…While valid in arbitrary dimension, the results in [13] rely explicitly on the assumption that the flow carrying the concentration field of interest is incompressible. Fluid flows arising in applications are indeed practically incompressible, but air flows are relatively easy to compress.…”

Section: Introductionmentioning

confidence: 99%

“…Fluid flows arising in applications are indeed practically incompressible, but air flows are relatively easy to compress. This precludes the application of [13] to atmospheric transport problems, such as the identification of temperature barriers surrounding the polar vortices (cf. [2,4,17,29]).…”

Section: Introductionmentioning

confidence: 99%

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Barriers to the Transport of Diffusive Scalars in Compressible Flows

Haller¹,

Karrasch²,

Kogelbauer³

2020

SIAM J. Appl. Dyn. Syst.

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Our recent work identifies material surfaces in incompressible flows that extremize the transport of an arbitrary, weakly diffusive scalar field relative to neighboring surfaces. Such barriers and enhancers of transport can be located directly from the deterministic component of the velocity field without diffusive or stochastic simulations. Here we extend these results to compressible flows and to diffusive concentration fields affected by sources or sinks, as well as by spontaneous decay. We construct diffusive transport extremizers with and without constraining them on a specific initial concentration distribution. For two-dimensional flows, we obtain explicit differential equations and a diagnostic scalar field that identify the most observable extremizers with pointwise uniform transport density. We illustrate our results by uncovering diffusion barriers and enhancers in analytic, numerical, and observational velocity fields.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Barriers to the Transport of Diffusive Scalars in Compressible Flows

Haller¹,

Karrasch²,

Kogelbauer³

2020

SIAM J. Appl. Dyn. Syst.

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“…These velocities are derived from satellite altimetry data. We choose a time window (starting November 26, 2016) for which a small spatial piece has been used repeatedly as a data set "benchmark" case in the literature; cf., for instance, [24,14], and earlier studies on slightly larger domains [23,29]. The domain studied in the first references is highlighted by a small white rectangle in Figs.…”

Section: Global Ocean Surface Flowmentioning

confidence: 94%

“…In this framework, material barriers to diffusive and stochastic transport have been defined in [24] as material surfaces which extremize diffusive transport over the finite observation time interval. There, it is shown that in two-dimensional flows, the diffusive transport through a one-dimensional material manifold Γ is given in leading order (with respect to diffusivity ε) by…”

Section: Mathematical Settingmentioning

confidence: 99%

Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains

Karrasch¹,

Schilling²

2020

The SMAI Journal of Computational Mathematics

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We describe a new method for computing coherent Lagrangian vortices in two-dimensional flows according to any of the following approaches: blackhole vortices [23], objective Eulerian Coherent Structures (OECSs) [37], material barriers to diffusive transport [24,25], and constrained diffusion barriers [25]. The method builds on ideas developed previously in [29], but our implementation alleviates a number of shortcomings and allows for the fully automated detection of such vortices on unprecedentedly challenging real-world flow problems, for which specific human interference is absolutely infeasible. Challenges include very large domains and/or parameter spaces. We demonstrate the efficacy of our method in dealing with such challenges on two test cases: first, a parameter study of a turbulent flow, and second, computing material barriers to diffusive transport in the global ocean.

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Do eddies connect the tropical Atlantic Ocean and the Gulf of Mexico?

Andrade-Canto¹,

Beron-Vera²

2022

Preprint

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Consistent with satellite-tracked trajectories of drogued drifters, but at odds with Eulerian assessment of satellite-altimetry measurements of sea-surface height, we show that North Brazil Currents Rings (NBCRs) are incapable of bypassing the Lesser Antilles as structures that coherently transport material. The nature of the inability of the de-facto oceanographic Eulerian, streamline-based eddy detection technique to produce a correct assessment is rooted in its lack of objectivity. We arrive at this conclusion by applying geodesic eddy detection on the altimetric dataset over nearly its entire extent. While we detect northwestward translating NBCRs that can be classified as coherent Lagrangian eddies, they typically experience strong filamentation and complete loss of coherence prior to reaching the Lesser Antilles. Moreover, the filamented material hardly penetrates into the Caribbean Sea, let alone the Gulf of Mexico, and not without substantively mixing with the ambient fluid east of the archipelago.

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Material barriers to diffusive and stochastic transport

Cited by 69 publications

References 37 publications

Barriers to the Transport of Diffusive Scalars in Compressible Flows

Barriers to the Transport of Diffusive Scalars in Compressible Flows

Fast and robust computation of coherent Lagrangian vortices on very large two-dimensional domains

Do eddies connect the tropical Atlantic Ocean and the Gulf of Mexico?

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