Objective Eulerian Coherent Structures

2015/12/09 by Mattia Serra, George Haller · 1 citation
Mathematics · Physics and Astronomy · #math.DS #math-ph #math.MP #physics.flu-dyn

paper · pdf · doi:10.1063/1.4951720

arxiv created 2015/12/09 · arxiv updated 2016/06/22

Abstract

We define objective Eulerian Coherent Structures (OECSs) in two-dimensional, non-autonomous dynamical systems as instantaneously most influential material curves. Specifically, OECSs are stationary curves of the averaged instantaneous material stretching-rate or material shearing-rate functionals. From these objective (frame-invariant) variational principles, we obtain explicit differential equations for hyperbolic, elliptic and parabolic OECSs. As illustration, we compute OECSs in an unsteady ocean velocity data set. In comparison to structures suggested by other common Eulerian diagnostic tools, we find OECSs to be the correct short-term cores of observed trajectory deformation patterns.

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