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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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:
Lagrangian coherent structures
Rayleigh-bénard convection
N-vortex prblem
Invariant manifolds
Polar vortex
2-dimensional maps
Chaotic advection
Aperiodic flows
Rotating sphere
Point vortices
Antarc*
Antarctic
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
id ftvirginiatec:oai:vtechworks.lib.vt.edu:10919/24401
record_format openpolar
spelling ftvirginiatec:oai:vtechworks.lib.vt.edu:10919/24401 2024-05-19T07:29:15+00:00 The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds Chaos Lekien, F. Ross, Shane D. Biomedical Engineering and Mechanics Virginia Tech 2010-03-01 application/pdf 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 en_US eng American Institute of Physics Lekien, Francois and Ross, Shane D., “The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds,” Chaos 20, 017505 (2010), DOI:http://dx.doi.org/10.1063/1.3278516 1054-1500 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 In Copyright http://rightsstatements.org/vocab/InC/1.0/ Lagrangian coherent structures Rayleigh-bénard convection N-vortex prblem Invariant manifolds Polar vortex 2-dimensional maps Chaotic advection Aperiodic flows Rotating sphere Point vortices Article - Refereed Text 2010 ftvirginiatec https://doi.org/10.1063/1.3278516 2024-04-24T00:54:38Z 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. Article in Journal/Newspaper Antarc* Antarctic VTechWorks (VirginiaTech) Chaos: An Interdisciplinary Journal of Nonlinear Science 20 1 017505
institution Open Polar
collection VTechWorks (VirginiaTech)
op_collection_id ftvirginiatec
language English
topic Lagrangian coherent structures
Rayleigh-bénard convection
N-vortex prblem
Invariant manifolds
Polar vortex
2-dimensional maps
Chaotic advection
Aperiodic flows
Rotating sphere
Point vortices
spellingShingle Lagrangian coherent structures
Rayleigh-bénard convection
N-vortex prblem
Invariant manifolds
Polar vortex
2-dimensional maps
Chaotic advection
Aperiodic flows
Rotating sphere
Point vortices
Lekien, F.
Ross, Shane D.
The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds
topic_facet Lagrangian coherent structures
Rayleigh-bénard convection
N-vortex prblem
Invariant manifolds
Polar vortex
2-dimensional maps
Chaotic advection
Aperiodic flows
Rotating sphere
Point vortices
description 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.
author2 Biomedical Engineering and Mechanics
Virginia Tech
format Article in Journal/Newspaper
author Lekien, F.
Ross, Shane D.
author_facet Lekien, F.
Ross, Shane D.
author_sort Lekien, F.
title The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds
title_short The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds
title_full The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds
title_fullStr The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds
title_full_unstemmed The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds
title_sort computation of finite-time lyapunov exponents on unstructured meshes and for non-euclidean manifolds
publisher American Institute of Physics
publishDate 2010
url 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
genre Antarc*
Antarctic
genre_facet Antarc*
Antarctic
op_relation Lekien, Francois and Ross, Shane D., “The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds,” Chaos 20, 017505 (2010), DOI:http://dx.doi.org/10.1063/1.3278516
1054-1500
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
op_rights In Copyright
http://rightsstatements.org/vocab/InC/1.0/
op_doi https://doi.org/10.1063/1.3278516
container_title Chaos: An Interdisciplinary Journal of Nonlinear Science
container_volume 20
container_issue 1
container_start_page 017505
_version_ 1799478307378429952

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