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Published on: July 19, 2016
Attracting Lagrangian coherent structures on Riemannian manifolds
1ETH Zürich, Institute for Mechanical Systems, Leonhardstrasse 21, 8092 Zürich, Switzerland.
Repelling and attracting Lagrangian Coherent Structures (LCSs) are typically identified using forward and backward finite-time Lyapunov exponent (FTLE) fields, respectively. This study reveals that attracting LCSs also appear as forward FTLE ridges in 2D incompressible flows, requiring new characterization methods.
Area of Science:
- Fluid Dynamics
- Dynamical Systems Theory
- Chaos Theory
Background:
- Lagrangian Coherent Structures (LCSs) are fundamental to understanding fluid transport and mixing.
- Traditionally, repelling LCSs are linked to forward finite-time Lyapunov exponent (FTLE) ridges, and attracting LCSs to backward FTLE ridges.
- This conventional identification faces challenges in accurately characterizing attracting LCSs solely through forward FTLE analysis in certain flow types.
Purpose of the Study:
- To investigate the appearance of attracting LCSs as ridges in the forward FTLE field for 2D incompressible flows.
- To develop methods for characterizing attracting LCSs using only forward finite-time Lyapunov analysis.
- To extend existing FTLE theory by analyzing the full Lyapunov spectrum and stretch directions.
Main Methods:
- Utilized the singular value decomposition (SVD) of the linearized flow map to analyze FTLE fields.
- Extended recent findings on the relationship between forward and backward maximal and minimal FTLEs.
- Applied geometrical insights from SVD to develop characterizations for attracting LCSs in forward time.
Main Results:
- Demonstrated that attracting LCSs can indeed appear as ridges in the forward FTLE field in 2D incompressible flows.
- Provided novel characterizations for attracting LCSs based on forward FTLE analysis, leveraging SVD.
- Successfully applied these characterizations to the specific case of an attracting FTLE ridge in an incompressible saddle flow.
Conclusions:
- The conventional separation of repelling and attracting LCS identification based on forward/backward FTLEs is insufficient for 2D incompressible flows.
- Forward FTLE analysis, when enhanced with SVD-based insights, can effectively characterize attracting LCSs.
- This work offers a more comprehensive understanding of LCSs and their identification in fluid dynamics.
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