title: Global variational approach to elliptic transport barriers in three dimensions.
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.
authors.affiliation: Institute of Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zürich, Leonhardstrasse 21, 8092 Zürich, Switzerland.
authors.forename: David
authors.initials: D
authors.lastname: Oettinger
authors.affiliation: Institute of Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zürich, Leonhardstrasse 21, 8092 Zürich, Switzerland.
authors.forename: Daniel
authors.initials: D
authors.lastname: Blazevski
authors.affiliation: Institute of Mechanical Systems, Department of Mechanical and Process Engineering, ETH Zürich, Leonhardstrasse 21, 8092 Zürich, Switzerland.
authors.forename: George
authors.initials: G
authors.lastname: Haller