The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds

We generalize the concepts of finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structures to arbitrary Riemannian manifolds. The methods are illustrated for convection cells on cylinders and Moumlbius strips, as well as for the splitting of the Antarctic polar vortex in the spherical str...

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Bibliographic Details
Published in:Chaos: An Interdisciplinary Journal of Nonlinear Science
Main Authors: Lekien, F., Ross, Shane D.
Other Authors: Biomedical Engineering and Mechanics, Virginia Tech
Format: Article in Journal/Newspaper
Language:English
Published: American Institute of Physics 2010
Subjects:
Online Access:http://hdl.handle.net/10919/24401
http://scitation.aip.org/content/aip/journal/chaos/20/1/10.1063/1.3278516
https://doi.org/10.1063/1.3278516
Description
Summary:We generalize the concepts of finite-time Lyapunov exponent (FTLE) and Lagrangian coherent structures to arbitrary Riemannian manifolds. The methods are illustrated for convection cells on cylinders and Moumlbius strips, as well as for the splitting of the Antarctic polar vortex in the spherical stratosphere and a related point vortex model. We modify the FTLE computational method and accommodate unstructured meshes of triangles and tetrahedra to fit manifolds of arbitrary shape, as well as to facilitate dynamic refinement of the FTLE mesh.