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Updated: Mar 23, 2026

Three-dimensional Particle Tracking Velocimetry for Turbulence Applications: Case of a Jet Flow
Published on: February 27, 2016
Global variational approach to elliptic transport barriers in three dimensions
David Oettinger1, Daniel Blazevski1, George Haller1
1Institute of Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zürich, Leonhardstrasse 21, 8092 Zürich, Switzerland.
Abstract:
We introduce an approach to identify elliptic transport barriers in three-dimensional, time-aperiodic flows. Obtained as Lagrangian Coherent Structures (LCSs), the barriers are tubular non-filamenting surfaces that form and bound coherent material vortices. This extends a previous theory of elliptic LCSs as uniformly stretching material surfaces from two-dimensional to three-dimensional flows. Specifically, we obtain explicit expressions for the normals of pointwise (near-) uniformly stretching material surfaces over a finite time interval. We use this approach to visualize elliptic LCSs in steady and time-aperiodic ABC-type flows.
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