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Abstract
Abstract. Spatial maps of the finite-time Lyapunov exponent (FTLE) have been used extensively to study LCS in two-dimensional dynamical systems, in particular with application to transport in unsteady fluid flows. We use the time-periodic double-gyre model to compare spatial fields of FTLE and the path-integrated Eulerian Okubo–Weiss parameter (OW). Both fields correlate strongly, and by solving the dynamics of the deformation gradient tensor, a theoretical relationship between both magnitudes has been obtained. While for long integration times more and more FTLE ridges appear that do not seem to coincide with the stable manifold, ridges in the field of path-integrated OW represent fewer additional structures.
Highlights
The importance of Lagrangian analysis to understanding complex transport problems in fluids has been established during the last decade
Spatial maps of the finite-time Lyapunov exponent (FTLE) have been used extensively to study Lagrangian coherent structures (LCS) in two-dimensional dynamical systems, in particular with application to transport in unsteady fluid flows
Lagrangian analysis is directly linked to the dynamical systems approach to transport that analyzes the phase space of the dynamical system driving the trajectories in a flow
Summary
The importance of Lagrangian analysis to understanding complex transport problems in fluids has been established during the last decade (see Griffa et al, 2007 and Neufeld and Hernández-García, 2009 and references therein for a review). Repelling (attracting) LCS for τ > 0 (τ < 0) are time-dependent generalizations of the stable (unstable) manifolds of hyperbolic fixed points of the system These structures govern the stretching and folding mechanisms that control flow mixing. The FTLE method is known to produce false positive ridges in high shear regions (Haller, 2002) that are not generated by hyperbolic structures. This encourages one to study other Lagrangian descriptors and compare them to the FTLE approach
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