Coherent Lagrangian vortices: the black holes of turbulence

Haller, George; Beron-Vera, F. J.

doi:10.1017/jfm.2013.391

Cited by 195 publications

(326 citation statements)

References 13 publications

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“…These structures are referred to as Lagrangian coherent structures (LCS). 36,[40][41][42] The properties of the right Cauchy-Green (CG) strain tensor field are the basis for the definition of these structures. Geometric approaches have recently been comprehensively reviewed, 39,61 and here, we give a sufficiently detailed synopsis for 2D flows to provide the interested reader with an overview of the key concepts, and provide references for details on 3D flows.…”

Section: Geometric Coherent Structuresmentioning

confidence: 99%

“…32,41,79 Examples such as these are a driving force behind the development of novel Lagrangian mathematical methods that can identify persistent coherent transport features within even highly unsteady flows, and furthermore can assess the role that such structures play in the overall flow transport. There is the exciting potential that such methods may also yield new predictive capabilities and enable new Lagrangianbased control strategies.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Geometric Coherent Structuresmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Lagrangian based methods for coherent structure detection

Allshouse

Peacock

2015

Chaos: An Interdisciplinary Journal of Nonlinear Science

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“…In general, an eddy is considered a coherent structure characterized by water rotating around a common centre (Chelton et al, 2011;Faghmous et al, 2013) and a structure that retains all its initial mass as it propagates (Haller and Beron-Vera, 2013). Because this study focuses mainly on the splitting strategy, the choice of parameters is not of concern, and we simply use SLA as an example.…”

Section: Mononuclear Eddy Identificationmentioning

confidence: 99%

“…In this study, an eddy is split based on the fact that the negative gradient vector of the SLA points toward the eddy centre of an ideal circular-shaped eddy (Li et al, 2014) and the fact that the vortex is similar to a funnel (Haller and Beron-Vera, 2013). Because oceanic cyclonic eddies are similar to basins in the map of the SLA data, the natural divisions of the basins are the watersheds between them.…”

Section: Eddy Splitting Strategymentioning

confidence: 99%

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Technical Note: Watershed strategy for oceanic mesoscale eddy splitting

Sun

2015

Ocean Sci.

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Abstract. To identify oceanic mononuclear mesoscale eddies, a threshold-free splitting method was developed based on the watershed. Because oceanic eddies are similar to plateaus and basins in the map of the sea level anomaly (SLA) data, the natural divisions of the basins are the watersheds between them. The splitting algorithm is based on identifying these watersheds by finding the path of steepest descent. Compared to previous splitting methods, the proposed splitting algorithm has some advantages. First, there are no artificial parameters. Second, the algorithm is robust; the splitting strategy is independent of the algorithm and procedure and automatically guarantees that the split mononuclear eddies are simply connected pixel sets. Third, the new method is very fast, and the time complexity is O(N ), where N is the number of multinuclear eddy pixels; each pixel is scanned only once for splitting, regardless of how many extremes there are. Fourth, the algorithm is independent of parameters; the strategy can potentially be applied to any possible physical parameters (e.g. SLA, geostrophic potential vorticity, Okubo-Weiss parameter). Besides, the present strategy can also be applied to automatic identification of troughs and ridges from weather charts. Because this general method can be applied to a variety of eddy parameter fields, we denoted it the Universal Splitting Technology for Circulations (USTC) method.

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Coherent water transport across the South Atlantic

Wang

Olascoaga

Beron-Vera

2015

Geophysical Research Letters

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The role of mesoscale eddies in transporting Agulhas leakage is investigated using a recent technique from nonlinear dynamical systems theory applied on geostrophic currents inferred from the over two decade long satellite altimetry record. Eddies are found to acquire material coherence away from the Agulhas retroflection, near the Walvis Ridge in the South Atlantic. Yearly, one to four coherent material eddies are detected with diameters ranging from 40 to 280 km. A total of 23 eddy cores of about 50 km in diameter and with at least 30% of their contents traceable into the Indian Ocean were found to travel across the subtropical gyre with minor filamentation. Only one eddy core was found to pour its contents on the North Brazil Current. While the ability of eddies to carry Agulhas leakage northwestward across the South Atlantic is supported by our analysis, this is more restricted than suggested by earlier ring transport assessments.

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Coherent Lagrangian vortices: the black holes of turbulence

Cited by 195 publications

References 13 publications

Lagrangian based methods for coherent structure detection

Lagrangian based methods for coherent structure detection

Technical Note: Watershed strategy for oceanic mesoscale eddy splitting

Coherent water transport across the South Atlantic

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