Distinguished material surfaces and coherent structures in three-dimensional fluid flows

By G. Haller. 2001

890 citations recorded by the source corpus.

Subfields: Computational Mechanics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/36c2496415b1a487f6aed4eeb403b9056c0c4ad1

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In Computational Mechanics

In Statistical and Nonlinear Physics

Citations in the corpus

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 .”
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.”
The onset of dynamic stall revisited (2012, methodology): “3 tified and analysed utilising a combination of an Eulerian vortex centre allocation procedure (Michard et al 1997), a Lagrangian approach based on the Lyapunov exponent (Haller 2001), and a proper orthogonal decomposition (POD) of the velocity field (Sirovich 1987).”
A Lagrangian Particle Dynamics Approach for Crowd Flow Segmentation and Stability Analysis (2007, methodology): “Now, in order to locate these flow segments, we propose a flow segmentation framework which makes use of recent advances in the areas of nonlinear dynamical systems [2], fluid dynamics [4][ 6 ], and turbulence theory [1][11].”
Lagrangian Coherent Structures (2015, background): “The first works connecting FTLE ridges to repelling LCSs through the above heuristic argument were by Haller (2001a, 2002).”
Lagrangian coherent structures in n-dimensional systems (2007, methodology): “Using FTLE is, however, not necessary and ridges can be computed from other measures of hyperbolicity, such as hyperbolicity time Haller 2000, 2001 , finite strain Jones and Winkler 2002 , or finite-size Lyapunov exponents FSLE Koh and Legras 2002 ; Joseph and Legras 2002 .”
Almost-invariant sets and invariant manifolds — Connecting probabilistic and geometric descriptions of coherent structures in flows (2009, methodology): “[8]) the flow is non-integrable and the system exhibits non-trivial invariant sets which are enclosed by two-dimensional invariant manifolds.”
A variational theory of hyperbolic Lagrangian Coherent Structures (2010, background): “In [2,3], we suggested that at time t0, a repelling LCS over [t0, t] should appear as a local maximizing curve, or ridge, of the Finite-Time Lyapunov Exponent (FTLE) field computed over initial conditions at t0.”
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).”