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| Detecting barriers to, and facilitators of, transport is a fundamental problem in studying the behavior of Lagrangian trajectories in a fluid. A recent extension of two-dimensional results provides definitions, characterizations and computational methods to extract the most locally repelling, attracting and shearling material surfaces. Such surfaces characterize tracer patterns seen in nature and experiments. In particular, the theory provides an objective definition of a Lagrangian vortex boundary as an outermost member of a family of most shearing cylindrical material surfaces. The detection of such a 3D vortex boundary yields an accurate estimate on the volume the vortex transports. We compute such vortices in kinematic models and a use a global circulation model to detect coherent three-dimensional Agulhas rings in the South Atlantic. |
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