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Objective Eulerian coherent structures.

Mattia Serra1, George Haller1

  • 1Institute for Mechanical Systems, ETH Zürich, Leonhardstrasse 21, 8092 Zurich, Switzerland.

Chaos (Woodbury, N.Y.)
|June 3, 2016
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Summary
This summary is machine-generated.

We introduce objective Eulerian Coherent Structures (OECSs) as the most influential material curves in dynamical systems. These structures accurately capture short-term trajectory deformation patterns in unsteady flow data.

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Area of Science:

  • Fluid dynamics
  • Dynamical systems theory
  • Scientific computing

Background:

  • Understanding material transport and deformation is crucial in fluid dynamics.
  • Existing Eulerian diagnostic tools may not fully capture instantaneous flow structures.
  • Objective Eulerian Coherent Structures (OECSs) offer a novel approach to identify influential material curves.

Purpose of the Study:

  • To define and derive objective Eulerian Coherent Structures (OECSs) for two-dimensional, non-autonomous dynamical systems.
  • To develop explicit differential equations for various types of OECSs.
  • To validate the efficacy of OECSs in analyzing real-world flow data.

Main Methods:

  • Formulating OECSs based on variational principles of averaged instantaneous material stretching and shearing rates.
  • Deriving differential equations governing hyperbolic, elliptic, and parabolic OECSs.
  • Applying the OECS framework to an unsteady ocean velocity dataset.

Main Results:

  • OECSs are defined as instantaneously most influential material curves.
  • Explicit differential equations for OECSs were successfully derived.
  • OECSs accurately identified short-term cores of trajectory deformation in oceanographic data.

Conclusions:

  • OECSs provide a robust and objective method for identifying key structures in unsteady flows.
  • The derived OECS framework offers improved insights compared to traditional Eulerian diagnostics.
  • This approach has significant implications for analyzing complex dynamical systems and fluid transport phenomena.