2016/04/30 by David Oettinger, George Haller · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Deformation (meteorology) #Dynamical system (definition) #Dynamical systems theory #Eigenvalues and eigenvectors #Flow (mathematics) #Invariant (physics) #Lagrangian #Lagrangian system #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Quasicrystal Structures and Properties #math.DS #nlin.CD #physics.flu-dyn
paper · pdf · doi:10.1063/1.4965026
openalex created_date 2016/06/24 · arxiv created 2016/08/24 · openalex publication_date 2016/10/01 · arxiv updated 2016/11/23 · openalex updated_date 2026/08/05
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.