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Attracting and repelling Lagrangian coherent structures from a single computation
Mohammad Farazmand1, George Haller
1Department of Mathematics, ETH Zürich, 8092 Zürich, Switzerland.
Chaos (Woodbury, N.Y.)
|July 5, 2013
Summary
This study introduces a new method to simultaneously identify repelling and attracting hyperbolic Lagrangian Coherent Structures (LCSs) in dynamical systems. This resolves inconsistencies in previous approaches for aperiodic flows.
Area of Science:
- Fluid dynamics
- Dynamical systems theory
- Chaos theory
Background:
- Lagrangian Coherent Structures (LCSs) are key indicators of flow behavior.
- Hyperbolic LCSs represent regions of maximal repulsion or attraction.
- Current methods require separate forward and backward time integrations, leading to inconsistencies in aperiodic systems.
Purpose of the Study:
- To develop a unified method for identifying both repelling and attracting hyperbolic LCSs simultaneously.
- To resolve inconsistencies arising from the assumption of flow recurrence in temporally aperiodic systems.
Main Methods:
- Utilizing a single forward or backward data run.
- Computing LCSs as surfaces normal to the eigenvectors of the Cauchy-Green strain tensor.
Main Results:
- Demonstrated simultaneous computation of repelling and attracting hyperbolic LCSs.
- Established a consistent method applicable to both periodic and aperiodic dynamical systems.
Conclusions:
- The new method provides a unified and consistent approach to LCS analysis.
- This advancement enhances the understanding of mixing and transport in complex flows.
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