Lagrangian structures and the rate of strain in a partition of two-dimensional turbulence

By G. Haller. 2001

258 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Networks and Communications, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/7666dbc498dc5017a7e5561416070eaf8e74236b

How researchers see this paper

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

In Computational Mechanics

In Computer Networks and Communications

In Statistical and Nonlinear Physics

Citations in the corpus

Frontiers of chaotic advection (2014, background): “The former yields a foliation of nested invariant tori; the latter admits (local) disintegration of these tori into chaotic zones by a variety of resonance phenomena (Cartwright et al., 1994; Dombre et al., 1986; Feingold et al., 1988; Haller, 2001a).”
A variational theory of hyperbolic Lagrangian Coherent Structures (2010, background): “The concept of uniform finite-time hyperbolicity for individual trajectorieswas apparently first introduced in [12], then elaborated on in [13,1,22,2,3,14].”
Pollution release tied to invariant manifolds: A case study for the coast of Florida (2005, methodology): “Tidal oscillations influence the flow mostly in the direction orthogonal to the coastline for such a linear coast.”
Definition and properties of Lagrangian coherent structures from finite-time Lyapunov exponents in two-dimensional aperiodic flows (2005, background): “Once the final positions, x(t + T ; t, x0), of each particle are found, the spatial gradient of the flow map can be evaluated at each point in the initial grid by finite differencing with values at the neighboring grid points [13,23].”
Oceanic mesoscale eddies as revealed by Lagrangian coherent structures (2008, background): “e, frame-independent) eddy boundary definition [Haller, 2001; Green et al., 2007], and is exploited here to unambiguously reveal mesoscale oceanic eddies with a sea surface signature.”
Defining coherent vortices objectively from the vorticity (2015, methodology): “Ellipticity-time diagnostic Haller (2001) studies the finite-time stability of a fluid trajectory x(t; t0, x0) in a frame aligned with the eigenvectors of the rate-of-strain tensor D(x, t) along the trajectory.”
An objective definition of a vortex (2004, methodology): “Following the arguments given in Haller (2001c), we obtain that for some fixed constant a > 0, all solutions ξ (t) with ξ (t0) ∈ Es(t0) satisfy the decay estimate |ξ (t)| |ξ (t0)|e−a(t−t0) (C 9) for any t, t0 ∈ I .”
Relation between kinematic boundaries, stirring, and barriers for the Antarctic polar vortex (2002, methodology): “The FSLE method is probably only a first step and a simple diagnostic tool that should be supplemented by more sophisticated approaches such as that described in Malhotra and Wiggins (1999), Haller (2000), Haller and Yuan (2000), or Haller (2001).”
Distinguished hyperbolic trajectories in time-dependent fluid flows: analytical and computational approach for velocity fields defined as data sets (2002, background): “Haller and Poje (1998) observed that when the timedependence of the velocity field is “slow enough” with respect to the Lagrangian time-scale, the ISP stays near the hyperbolic trajectory.”
Lagrangian Coherent Structures (2015, background): “The first works connecting FTLE ridges to repelling LCSs through the above heuristic argument were by Haller (2001a, 2002).”