Year: 2016
Type: article
Abstract: Lagrangian coherent structures (LCSs) are material surfaces that shape the finite-time tracer patterns in flows with arbitrary time dependence. Depending on their deformation properties, elliptic and hyperbolic LCSs have been identified from different variational principles, solving different equations. Here we observe that, in three dimensions, initial positions of all variational LCSs are invariant manifolds of the same autonomous dynamical system, generated by the intermediate eigenvector field, ξ2(x0), of the Cauchy-Green strain tensor. This ξ2-system allows for the detection of LCSs in any unsteady flow by classical methods, such as Poincaré maps, developed for autonomous dynamical systems. As examples, we consider both steady and time-aperiodic flows, and use their dual ξ2-system to uncover both hyperbolic and elliptic LCSs from a single computation.
DOI: 10.1063/1.4965026
Authors: David Oettinger, George Haller
Institutions: ETH Zurich, Institute of Mechanical Systems
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2337713663