Objective Eulerian Coherent Structures
Dynamical Systems
2016-06-22 v2 Mathematical Physics
math.MP
Fluid Dynamics
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.
Keywords
Cite
@article{arxiv.1512.02112,
title = {Objective Eulerian Coherent Structures},
author = {Mattia Serra and George Haller},
journal= {arXiv preprint arXiv:1512.02112},
year = {2016}
}