Hidden Geometry of Ocean Flows

Mendoza, Carolina; Mancho, Ana M.

doi:10.1103/physrevlett.105.038501

Cited by 166 publications

(146 citation statements)

References 13 publications

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“…Another distinguishing characteristic of the MET is that the convergence to its asymptotic value is always monotone in time whereas in all the other quantifiers convergence to their asymptotic values is oscillatory (except the arc-length map [34,35] which is monotone yet unbounded). Hence we expect that the convergence of the MET will be faster and more regular.…”

Section: Discussionmentioning

confidence: 99%

“…Some of the Lagrangian characteristics present the resulting observable after a certain integration time, with no information regarding the intermediate time dynamics (e.g. the AD and RD fields depend only on the initial and final location of the particles), whereas some of the other Lagrangian characteristics use averaging or integration along the trajectories [3,17,26,[33][34][35]. These Lagrangian fields are commonly used to identify regions of small and enhanced stretching and, in particular, are used to identify the spatial position of dividing surfaces between different regions, the Lagrangian Coherent Structures (LCS) [2,26,27].…”

Section: Introductionmentioning

confidence: 99%

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New Lagrangian diagnostics for characterizing fluid flow mixing

et al. 2014

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A new kind of Lagrangian diagnostic family is proposed and a specific form of it is suggested for characterizing mixing: the maximal extent of a trajectory (MET). It enables the detection of coherent structures and their dynamics in two-(and potentially three-) dimensional unsteady flows in both bounded and open domains. Its computation is much easier than all other Lagrangian diagnostics known to us and provides new insights regarding the mixing properties on both short and long time scales and on both spatial plots and distribution diagrams. We demonstrate its applicability to two dimensional flows using two toy models and a data set of surface currents from the Mediterranean Sea.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

New Lagrangian diagnostics for characterizing fluid flow mixing

et al. 2014

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“…Other techniques include DHTs (Ide et al, 2002;Ju et al, 2003) and the direct calculation of manifolds as material surfaces (Mancho et al, 2003(Mancho et al, , 2004(Mancho et al, , 2006b, the geodesic theory of Lagrangian coherent structures (LCS) (Haller and Beron-Vera, 2012) and the variational theory of LCS (Farazmand and Haller, 2012), etc. Our choice in this work will be the use of the Lagrangian descriptor (LD) function M introduced by Madrid and Mancho (2009) and Mendoza and Mancho (2010). The function M has been applied in a variety of geophysical contexts.…”

Section: Lagrangian Descriptorsmentioning

confidence: 99%

A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex

García-Garrido¹,

Curbelo

Mechoso

et al. 2017

Nonlin. Processes Geophys.

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Abstract. In this work, we study the Lagrangian footprint of the planetary waves present in the Southern Hemisphere stratosphere during the exceptional sudden Stratospheric warming event that took place during September 2002. Our focus is on constructing a simple kinematic model that retains the fundamental mechanisms responsible for complex fluid parcel evolution, during the polar vortex breakdown and its previous stages. The construction of the kinematic model is guided by the Fourier decomposition of the geopotential field. The study of Lagrangian transport phenomena in the ERA-Interim reanalysis data highlights hyperbolic trajectories, and these trajectories are Lagrangian objects that are the kinematic mechanism for the observed filamentation phenomena. Our analysis shows that the breaking and splitting of the polar vortex is justified in our model by the sudden growth of a planetary wave and the decay of the axisymmetric flow.

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“…We have found that such POs can be obtained through a variational procedure based on Lagrangian descriptors (LDs). [36][37][38][39][40][41][42][43][44] The connection of the LD to the construction of POs is presented in Sec. II.…”

Section: Introductionmentioning

confidence: 99%

Variational principle for the determination of unstable periodic orbits and instanton trajectories at saddle points

2017

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The complexity of arbitray dynamical systems and chemical reactions, in particular, can often be resolved if only the appropriate periodic orbit-in the form of a limit cycle, dividing surface, instanton trajectories or some other related structure-can be uncovered. Determining such a periodic orbit, no matter how beguilingly simple it appears, is often very challenging. We present a method for the direct construction of unstable periodic orbits and instanton trajectories at saddle points by means of Lagrangian descriptors. Such structures result from the minimization of a scalarvalued phase space function without need for any additional constraints or knowledge. We illustrate the approach for two-degree of freedom systems at a rank-1 saddle point of the underlying potential energy surface by constructing both periodic orbits at energies above the saddle point as well as instanton trajectories below the saddle point energy.

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Hidden Geometry of Ocean Flows

Abstract: We introduce a new global Lagrangian descriptor that is applied to flows with general time dependence (altimetric datasets). It succeeds in detecting simultaneously, with great accuracy, invariant manifolds, hyperbolic and non-hyperbolic flow regions.

Cited by 166 publications

References 13 publications

New Lagrangian diagnostics for characterizing fluid flow mixing

New Lagrangian diagnostics for characterizing fluid flow mixing

A simple kinematic model for the Lagrangian description of relevant nonlinear processes in the stratospheric polar vortex

Variational principle for the determination of unstable periodic orbits and instanton trajectories at saddle points

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