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

2010/02/08 by Francois Lekien, François Lekien, Shane D. Ross · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Geomagnetism and Paleomagnetism Studies #Quantum chaos and dynamical systems #Scientific Research and Discoveries

paper · pdf · doi:10.1063/1.3278516

openalex publication_date 2010/02/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02

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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