Objective Eulerian Coherent Structures

TL;DR

This paper introduces objective Eulerian Coherent Structures (OECSs) as frame-invariant, instantaneous material curves in 2D non-autonomous systems, providing explicit equations and demonstrating their effectiveness in ocean data analysis.

Contribution

It defines OECSs based on variational principles, derives explicit differential equations for different types, and validates their utility in identifying short-term deformation structures in ocean flows.

Findings

OECSs are frame-invariant and objectively identify influential material curves.

OECSs outperform traditional Eulerian diagnostics in capturing short-term deformation cores.

Application to ocean data demonstrates OECSs' effectiveness in real-world flow analysis.

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.