Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows

By Shawn C. Shadden, Francois Lekien, Jerrold E. Marsden. 2005

1,445 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/91363db33dd5997965fa4b43ad546d1a749af009

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

The onset of dynamic stall revisited (2012, background): “…forward and backward in time yielding positive and negative finite– time Lyapunov exponent (pFTLE and nFTLE) fields (see e. g. Haller 2002; Shadden et al 2005; Garth et al 2007, for a comprehensive discussion of the general properties and basic concepts involved in the computation of the…”
An analytic framework for identifying finite-time coherent sets in time-dependent dynamical systems (2012, background): “In non-periodic time-dependent settings, finite-time hyperbolic material lines and surfaces, and more generally Lagrangian coherent structures (LCSs) [26, 27, 44, 29] have been put forward as a geometric approach to identifying barriers to mixing.”
Comparison between Eulerian diagnostics and finite-size Lyapunov exponents computed from altimetry in the Algerian basin (2008, background): “…at transport properties from the analysis of particle170 trajectories (Pierrehumbert, 1991; Ridderinkhof and Zimmerman, 1992; Miller et al., 1997;171 Haller and Yuan, 2000; Coulliette and Wiggins, 2001; Koh and Legras, 2002; d’Ovidio et al.,172 2004; Shadden et al., 2005; Mancho et al., 2006).”
A variational theory of hyperbolic Lagrangian Coherent Structures (2010, methodology): “To quantify the degree of non-invariance of FTLE ridges, [4,5] present an elegant expression for the leading-order material flux through FTLE ridges.”
Almost-invariant sets and invariant manifolds — Connecting probabilistic and geometric descriptions of coherent structures in flows (2009, methodology): “This autonomous ODE has been constructed from a snapshot of the nonautonomous double-gyre system [11].”
A Lagrangian Particle Dynamics Approach for Crowd Flow Segmentation and Stability Analysis (2007, methodology): “After a time interval this perturbation becomes [ 10 ][1]:”
Frontiers of chaotic advection (2014, methodology): “Because this simplified computation, LCS were often approximated by ridges of Finite Time Lyapunov Exponent (FTLE) and Finite Size Lyapunov Exponent (FSLE) fields, which were assumed to exist near true LCS; see Haller and Sapsis (2011); Joseph and Legras (2002); Shadden et al. (2005).”
Transport of inertial particles by Lagrangian coherent structures: application to predator–prey interaction in jellyfish feeding (2009, methodology): “For a precise definition of a ridge line, refer to Shadden et al. (2005) .”
Oceanic mesoscale eddies as revealed by Lagrangian coherent structures (2008, methodology): “Unlike prior work [e.g., d’Ovidio et al., 2004; Shadden et al., 2005], LCSs are computed for the whole globe and compared with satellite-tracked drogue drifter trajectories in a selected region of the South Atlantic.”
Detection of Lagrangian coherent structures in three-dimensional turbulence (2007, neutral): “Quantitative criteria for defining ridges in two-dimensional DLE fields have been given by Shadden, Lekien & Marsden (2005) .”