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Drifting Speed of Lagrangian Fronts and Oil Spill Dispersal at the Ocean Surface. REMOTE SENSING 2021. [DOI: 10.3390/rs13224499] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Due to its dire impacts on marine life, public health, and socio-economic services, oil spills require an immediate response. Effective action starts with good knowledge of the ocean dynamics and circulation, from which Lagrangian methods derive key information on the dispersal pathways present in the contaminated region. However, precise assessments of the capacity of Lagrangian methods in real contamination cases remain rare and limited to large slicks spanning several hundreds of km. Here we address this knowledge gap and consider two medium-scale (tens of km wide) events of oil in contrasting conditions: an offshore case (East China Sea, 2018) and a recent near-coastal one (East Mediterranean, 2021). Our comparison between oil slicks and Lagrangian diagnostics derived from near-real-time velocity fields shows that the calculation of Lagrangian fronts is, in general, more robust to errors in the velocity fields and more informative on the dispersion pathways than the direct advection of a numerical tracer. The inclusion of the effect of wind is also found to be essential, being capable of suddenly breaking Lagrangian transport barriers. Finally, we show that a usually neglected Lagrangian quantity, the Lyapunov vector, can be exploited to predict the front drifting speed, and in turn, its future location over a few days, on the basis of near-real-time information alone. These results may be of special relevance in the context of next-generation altimetry missions that are expected to provide highly resolved and precise near-real-time velocity fields for both open ocean and coastal regions.
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2
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Abstract
The finite size Lyapunov exponent (FSLE) has been used extensively since the late 1990s to diagnose turbulent regimes from Lagrangian experiments and to detect Lagrangian coherent structures in geophysical flows and two-dimensional turbulence. Historically, the FSLE was defined in terms of its computational method rather than via a mathematical formulation, and the behavior of the FSLE in the turbulent inertial ranges is based primarily on scaling arguments. Here, we propose an exact definition of the FSLE based on conditional averaging of the finite amplitude growth rate (FAGR) of the particle pair separation. With this new definition, we show that the FSLE is a close proxy for the inverse structural time, a concept introduced a decade before the FSLE. The (in)dependence of the FSLE on initial conditions is also discussed, as well as the links between the FAGR and other relevant Lagrangian metrics, such as the finite time Lyapunov exponent and the second-order velocity structure function.
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Ehstand N, Donner RV, López C, Hernández-García E. Characteristic signatures of Northern Hemisphere blocking events in a Lagrangian flow network representation of the atmospheric circulation. CHAOS (WOODBURY, N.Y.) 2021; 31:093128. [PMID: 34598473 DOI: 10.1063/5.0057409] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/20/2021] [Accepted: 09/02/2021] [Indexed: 06/13/2023]
Abstract
In the past few decades, boreal summers have been characterized by an increasing number of extreme weather events in the Northern Hemisphere extratropics, including persistent heat waves, droughts and heavy rainfall events with significant social, economic, and environmental impacts. Many of these events have been associated with the presence of anomalous large-scale atmospheric circulation patterns, in particular, persistent blocking situations, i.e., nearly stationary spatial patterns of air pressure. To contribute to a better understanding of the emergence and dynamical properties of such situations, we construct complex networks representing the atmospheric circulation based on Lagrangian trajectory data of passive tracers advected within the atmospheric flow. For these Lagrangian flow networks, we study the spatial patterns of selected node properties prior to, during, and after different atmospheric blocking events in Northern Hemisphere summer. We highlight the specific network characteristics associated with the sequence of strong blocking episodes over Europe during summer 2010 as an illustrative example. Our results demonstrate the ability of the node degree, entropy, and harmonic closeness centrality based on outgoing links to trace important spatiotemporal characteristics of atmospheric blocking events. In particular, all three measures capture the effective separation of the stationary pressure cell forming the blocking high from the normal westerly flow and the deviation of the main atmospheric currents around it. Our results suggest the utility of further exploiting the Lagrangian flow network approach to atmospheric circulation in future targeted diagnostic and prognostic studies.
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Affiliation(s)
- Noémie Ehstand
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC) (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Reik V Donner
- Department of Water, Environment, Construction and Safety, Magdeburg-Stendal University of Applied Sciences, Breitscheidstraße 2, 39114 Magdeburg, Germany
| | - Cristóbal López
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC) (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
| | - Emilio Hernández-García
- Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC) (CSIC-UIB), Campus Universitat de les Illes Balears, E-07122 Palma de Mallorca, Spain
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4
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Alvarez A. Modeling the odor-landscape resulting from the pumping behavior of bivalve clams in the presence of predators. J Theor Biol 2018; 453:40-47. [PMID: 29782927 DOI: 10.1016/j.jtbi.2018.05.019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2017] [Revised: 04/19/2018] [Accepted: 05/17/2018] [Indexed: 10/16/2022]
Abstract
Motivated by experimental findings, a computational fluid dynamics (CFD) model was used to investigate whether the clam Mercenaria mercenaria may alter its cue downstream variability by an exhalant random pumping behavior. This behavior was hypothesized to occur in the presence of predator chemical signals in order to prevent successful tracking by the predator. Simulated downstream flow and mixing conditions derived from the random nature of the clam exhalant jet in a crossflow were analyzed by computing an intermittency factor, determining the field of finite-time Lyapunov exponents (FTLEs) and identifying the resulting Lagrangian coherent structures (LCSs). Numerical simulations illustrate that the effectiveness of a fluctuating exhalant jet to prevent downstream tracking by a crab, depends on the ratio of the exhalant jet to the crossflow. Specifically, the clam could effectively enhance the downstream dispersion to prevent tracking, but only in the range of parameters where LCSs are generated (jet-to-crossflow ratio ≥ 1). Then, the probability of detection is reduced with respect to the case of a less fluctuating exhalant jet.
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Affiliation(s)
- A Alvarez
- Department of Marine Ecology (MARE), Instituto Mediterraneo de Estudios Avanzados-IMEDEA (CSIC-UIB), C/ Miquel Marques 21, Esporlas 07190, Spain.
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Lehahn Y, d'Ovidio F, Koren I. A Satellite-Based Lagrangian View on Phytoplankton Dynamics. ANNUAL REVIEW OF MARINE SCIENCE 2018; 10:99-119. [PMID: 28961072 DOI: 10.1146/annurev-marine-121916-063204] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
The well-lit upper layer of the open ocean is a dynamical environment that hosts approximately half of global primary production. In the remote parts of this environment, distant from the coast and from the seabed, there is no obvious spatially fixed reference frame for describing the dynamics of the microscopic drifting organisms responsible for this immense production of organic matter-the phytoplankton. Thus, a natural perspective for studying phytoplankton dynamics is to follow the trajectories of water parcels in which the organisms are embedded. With the advent of satellite oceanography, this Lagrangian perspective has provided valuable information on different aspects of phytoplankton dynamics, including bloom initiation and termination, spatial distribution patterns, biodiversity, export of carbon to the deep ocean, and, more recently, bottom-up mechanisms that affect the distribution and behavior of higher-trophic-level organisms. Upcoming submesoscale-resolving satellite observations and swarms of autonomous platforms open the way to the integration of vertical dynamics into the Lagrangian view of phytoplankton dynamics.
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Affiliation(s)
- Yoav Lehahn
- Department of Marine Geosciences, University of Haifa, Haifa 3498838, Israel;
- Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 76100, Israel;
| | - Francesco d'Ovidio
- Sorbonne Université (UPMC Paris 6/CNRS/IRD/MNHN), LOCEAN-IPSL, 75005 Paris, France;
| | - Ilan Koren
- Department of Earth and Planetary Sciences, Weizmann Institute of Science, Rehovot 76100, Israel;
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6
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Garaboa-Paz D, Eiras-Barca J, Huhn F, Pérez-Muñuzuri V. Lagrangian coherent structures along atmospheric rivers. CHAOS (WOODBURY, N.Y.) 2015; 25:063105. [PMID: 26117099 DOI: 10.1063/1.4919768] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/04/2023]
Abstract
We show that filamentous Atmospheric Rivers (ARs) over the Northern Atlantic Ocean are closely linked to attracting Lagrangian Coherent Structures (LCSs) in the large scale wind field. The detected LCSs represent lines of attraction in the evolving flow with a significant impact on all passive tracers. Using Finite-Time Lyapunov Exponents, we extract LCSs from a two-dimensional flow derived from water vapor flux of atmospheric reanalysis data and compare them to the three-dimensional LCS obtained from the wind flow. We correlate the typical filamentous water vapor patterns of ARs with LCSs and find that LCSs bound the filaments on the back side. Passive advective transport of water vapor in the AR from tropical latitudes is potentially possible.
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Affiliation(s)
- Daniel Garaboa-Paz
- Group of Nonlinear Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Jorge Eiras-Barca
- Group of Nonlinear Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
| | - Florian Huhn
- Institute of Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zürich, Leonhardtstrasse 21, CH-8092 Zurich, Switzerland
| | - Vicente Pérez-Muñuzuri
- Group of Nonlinear Physics, University of Santiago de Compostela, 15782 Santiago de Compostela, Spain
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Hernández-Carrasco I, López C, Hernández-García E, Turiel A. Seasonal and regional characterization of horizontal stirring in the global ocean. ACTA ACUST UNITED AC 2012. [DOI: 10.1029/2012jc008222] [Citation(s) in RCA: 31] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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Abstract
The lack of reliable forecasts for the spread of oceanic and atmospheric contamination hinders the effective protection of the ecosystem, society, and the economy from the fallouts of environmental disasters. The consequences can be dire, as evidenced by the Deepwater Horizon oil spill in the Gulf of Mexico in 2010. We present a methodology to predict major short-term changes in environmental contamination patterns, such as oil spills in the ocean and ash clouds in the atmosphere. Our approach is based on new mathematical results on the objective (frame-independent) identification of key material surfaces that drive tracer mixing in unsteady, finite-time flow data. Some of these material surfaces, known as Lagrangian coherent structures (LCSs), turn out to admit highly attracting cores that lead to inevitable material instabilities even under future uncertainties or unexpected perturbations to the observed flow. These LCS cores have the potential to forecast imminent shape changes in the contamination pattern, even before the instability builds up and brings large masses of water or air into motion. Exploiting this potential, the LCS-core analysis developed here provides a model-independent forecasting scheme that relies only on already observed or validated flow velocities at the time the prediction is made. We use this methodology to obtain high-precision forecasts of two major instabilities that occurred in the shape of the Deepwater Horizon oil spill. This is achieved using simulated surface currents preceding the prediction times and assuming that the oil behaves as a passive tracer.
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de Moura APS. Reacting particles in open chaotic flows. PHYSICAL REVIEW LETTERS 2011; 107:274501. [PMID: 22243312 DOI: 10.1103/physrevlett.107.274501] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/10/2011] [Indexed: 05/31/2023]
Abstract
We study the collision probability p of particles advected by open flows with chaotic advection. We show that p scales with the particle size (or, alternatively, reaction distance) δ as a power law whose coefficient is determined by the fractal dimensions of the invariant sets defined by the advection dynamics. We also argue that this same scaling also holds for the reaction rate of active particles in the low-density regime. These analytical results are compared to numerical simulations, and they are found to agree very well.
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Affiliation(s)
- Alessandro P S de Moura
- Institute of Complex Systems and Mathematical Biology, University of Aberdeen, Aberdeen, United Kingdom
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10
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Tallapragada P, Ross SD, Schmale DG. Lagrangian coherent structures are associated with fluctuations in airborne microbial populations. CHAOS (WOODBURY, N.Y.) 2011; 21:033122. [PMID: 21974657 DOI: 10.1063/1.3624930] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/31/2023]
Abstract
Many microorganisms are advected in the lower atmosphere from one habitat to another with scales of motion being hundreds to thousands of kilometers. The concentration of these microbes in the lower atmosphere at a single geographic location can show rapid temporal changes. We used autonomous unmanned aerial vehicles equipped with microbe-sampling devices to collect fungi in the genus Fusarium 100 m above ground level at a single sampling location in Blacksburg, Virginia, USA. Some Fusarium species are important plant and animal pathogens, others saprophytes, and still others are producers of dangerous toxins. We correlated punctuated changes in the concentration of Fusarium to the movement of atmospheric transport barriers identified as finite-time Lyapunov exponent-based Lagrangian coherent structures (LCSs). An analysis of the finite-time Lyapunov exponent field for periods surrounding 73 individual flight collections of Fusarium showed a relationship between punctuated changes in concentrations of Fusarium and the passage times of LCSs, particularly repelling LCSs. This work has implications for understanding the atmospheric transport of invasive microbial species into previously unexposed regions and may contribute to information systems for pest management and disease control in the future.
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Affiliation(s)
- P Tallapragada
- Mechanical Engineering and Engineering Science, University of North Carolina at Charlotte, North Carolina 28223, USA
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11
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Santitissadeekorn N, Froyland G, Monahan A. Optimally coherent sets in geophysical flows: a transfer-operator approach to delimiting the stratospheric polar vortex. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2010; 82:056311. [PMID: 21230580 DOI: 10.1103/physreve.82.056311] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2010] [Revised: 08/08/2010] [Indexed: 05/30/2023]
Abstract
The "edge" of the Antarctic polar vortex is known to behave as a barrier to the meridional (poleward) transport of ozone during the austral winter. This chemical isolation of the polar vortex from the middle and low latitudes produces an ozone minimum in the vortex region, intensifying the ozone hole relative to that which would be produced by photochemical processes alone. Observational determination of the vortex edge remains an active field of research. In this paper, we obtain objective estimates of the structure of the polar vortex by introducing a technique based on transfer operators that aims to find regions with minimal external transport. Applying this technique to European Centre for Medium-Range Weather Forecasts (ECMWF) ERA-40 three-dimensional velocity data, we produce an improved three-dimensional estimate of the vortex location in the upper stratosphere where the vortex is most pronounced. This computational approach has wide potential application in detecting and analyzing mixing structures in a variety of atmospheric, oceanographic, and general fluid dynamical settings.
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Affiliation(s)
- Naratip Santitissadeekorn
- School of Mathematics and Statistics, The University of New South Wales, Sydney, New South Wales 2052, Australia
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12
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Lekien F, Ross SD. The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds. CHAOS (WOODBURY, N.Y.) 2010; 20:017505. [PMID: 20370295 DOI: 10.1063/1.3278516] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/29/2023]
Abstract
We generalize the concepts of finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structures to arbitrary Riemannian manifolds. The methods are illustrated for convection cells on cylinders and Mobius strips, as well as for the splitting of the Antarctic polar vortex in the spherical stratosphere and a related point vortex model. We modify the FTLE computational method and accommodate unstructured meshes of triangles and tetrahedra to fit manifolds of arbitrary shape, as well as to facilitate dynamic refinement of the FTLE mesh.
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Affiliation(s)
- Francois Lekien
- Ecole Polytechnique, Université Libre de Bruxelles, B-1050 Brussels, Belgium.
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13
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Green MA, Rowley CW, Smits AJ. Using hyperbolic Lagrangian coherent structures to investigate vortices in bioinspired fluid flows. CHAOS (WOODBURY, N.Y.) 2010; 20:017510. [PMID: 20370300 PMCID: PMC2814836 DOI: 10.1063/1.3270045] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/24/2023]
Abstract
We use direct Lyapunov exponents to identify Lagrangian coherent structures (LCSs) in a bioinspired fluid flow: the wakes of rigid pitching panels with a trapezoidal planform geometry chosen to model idealized fish caudal fins. When compared with commonly used Eulerian criteria, the Lagrangian method has previously exhibited the ability to define structure boundaries without relying on a preselected threshold. In addition, qualitative changes in the LCS have previously been shown to correspond to physical changes in the vortex structure. For this paper, digital particle image velocimetry experiments were performed to obtain the time-resolved velocity fields for Strouhal numbers of 0.17 and 0.27. A classic reverse von Karman vortex street pattern was observed along the midspan of the near wake at low Strouhal number, but at higher Strouhal number the complexity of the wake increased downstream of the trailing edge. The spanwise vortices spread transversely across the wake and lose coherence, and this event was shown to correspond to a qualitative change in the LCS at the same time and location.
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14
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Abstract
Meso- and submesoscales (fronts, eddies, filaments) in surface ocean flow have a crucial influence on marine ecosystems. Their dynamics partly control the foraging behavior and the displacement of marine top predators (tuna, birds, turtles, and cetaceans). In this work we focus on the role of submesoscale structures in the Mozambique Channel in the distribution of a marine predator, the Great Frigatebird. Using a newly developed dynamic concept, the finite-size Lyapunov exponent (FSLE), we identified Lagrangian coherent structures (LCSs) present in the surface flow in the channel over a 2-month observation period (August and September 2003). By comparing seabird satellite positions with LCS locations, we demonstrate that frigatebirds track precisely these structures in the Mozambique Channel, providing the first evidence that a top predator is able to track these FSLE ridges to locate food patches. After comparing bird positions during long and short trips and different parts of these trips, we propose several hypotheses to understand how frigatebirds can follow these LCSs. The birds might use visual and/or olfactory cues and/or atmospheric current changes over the structures to move along these biologic corridors. The birds being often associated with tuna schools around foraging areas, a thorough comprehension of their foraging behavior and movement during the breeding season is crucial not only to seabird ecology but also to an appropriate ecosystemic approach to fisheries in the channel.
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15
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Lekien F, Coulliette C. Chaotic stirring in quasi-turbulent flows. PHILOSOPHICAL TRANSACTIONS. SERIES A, MATHEMATICAL, PHYSICAL, AND ENGINEERING SCIENCES 2007; 365:3061-84. [PMID: 17872361 DOI: 10.1098/rsta.2007.0020] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/17/2023]
Abstract
Transport in laminar flows is governed by chaotic stirring and striation in long thin filaments. In turbulent flows, isotropic mixing dominates and tracers behave like stochastic variables. In this paper, we investigate the quasi-turbulent, intermediate regime where both chaotic stirring and turbulent mixing coexist. In these flows, the most common in nature, aperiodic Lagrangian coherent structures (LCSs) delineate particle transport and chaotic stirring. We review the recent developments in LCS theory and apply these techniques to measured surface currents in Monterey Bay, California. In the bay, LCSs can be used to optimize the release of drifting buoys or to minimize the impact of a coastal pollution source.
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16
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Lehahn Y, d'Ovidio F, Lévy M, Heifetz E. Stirring of the northeast Atlantic spring bloom: A Lagrangian analysis based on multisatellite data. ACTA ACUST UNITED AC 2007. [DOI: 10.1029/2006jc003927] [Citation(s) in RCA: 142] [Impact Index Per Article: 8.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
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17
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Vilela RD, de Moura APS, Grebogi C. Finite-size effects on open chaotic advection. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 73:026302. [PMID: 16605449 DOI: 10.1103/physreve.73.026302] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2005] [Indexed: 05/08/2023]
Abstract
We study the effects of finite-sizeness on small, neutrally buoyant, spherical particles advected by open chaotic flows. We show that, when observed in the configuration or physical space, the advected finite-size particles disperse about the unstable manifold of the chaotic saddle that governs the passive advection. Using a discrete-time system for the dynamics, we obtain an expression predicting the dispersion of the finite-size particles in terms of their Stokes parameter at the onset of the finite-size induced dispersion. We test our theory in a system derived from a flow and find remarkable agreement between our expression and the numerically measured dispersion.
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Affiliation(s)
- Rafael D Vilela
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970, São Paulo, São Paulo, Brazil
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18
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de Moura APS, Grebogi C. Reactions in flows with nonhyperbolic dynamics. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:036216. [PMID: 15524621 DOI: 10.1103/physreve.70.036216] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/09/2003] [Revised: 05/27/2004] [Indexed: 05/24/2023]
Abstract
We study the reaction dynamics of active particles that are advected passively by 2D incompressible open flows, whose motion is nonhyperbolic. This nonhyperbolicity is associated with the presence of persistent vortices near the wake, wherein fluid is trapped. We show that the fractal equilibrium distribution of the reactants is described by an effective dimension d(eff) , which is a finite resolution approximation to the fractal dimension. Furthermore, d(eff) depends on the resolution epsilon and on the reaction rate 1/tau . As tau is increased, the equilibrium distribution goes through a series of transitions where the effective dimension increases abruptly. These transitions are determined by the complex structure of Cantori surrounding the Kolmogorov-Arnold-Moser (KAM) islands.
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Affiliation(s)
- Alessandro P S de Moura
- Instituto de Física, Universidade de São Paulo, Caixa Postal 66318, 05315-970, São Paulo, SP, Brazil.
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19
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Haller G, Iacono R. Stretching, alignment, and shear in slowly varying velocity fields. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2003; 68:056304. [PMID: 14682881 DOI: 10.1103/physreve.68.056304] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/15/2003] [Indexed: 05/24/2023]
Abstract
We derive criteria that locate intense material stretching and shear in two-dimensional flows with slow time dependence. Our derivation makes use of the near integrability of the equation of variations along trajectories of the slowly varying flow. The criteria yield two diagnostic scalar fields for use in real-time Lagrangian predictions in geophysical flows.
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Affiliation(s)
- G Haller
- Department of Mechanical Engineering, MIT, Cambridge, Massachusetts 02139, USA
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