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Lekien F, Ross SD. The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds. Chaos. 2010;20(1):017505doi: 10.1063/1.3278516.
Lekien, F., & Ross, S. D. (2010). The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds. Chaos (Woodbury, N.Y.), 20(1), 017505. https://doi.org/10.1063/1.3278516
Lekien, Francois, and Ross, Shane D. "The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds." Chaos (Woodbury, N.Y.) vol. 20,1 (2010): 017505. doi: https://doi.org/10.1063/1.3278516
Lekien F, Ross SD. The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds. Chaos. 2010 Mar;20(1):017505. doi: 10.1063/1.3278516. PMID: 20370295.
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Chaos. 2010 Mar;20(1):017505. doi: 10.1063/1.3278516.

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

Chaos (Woodbury, N.Y.)

Francois Lekien, Shane D Ross

Affiliations

  1. Ecole Polytechnique, Université Libre de Bruxelles, B-1050 Brussels, Belgium. [email protected]

PMID: 20370295 DOI: 10.1063/1.3278516

Abstract

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 Mobius 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.

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