The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds
Chaos 20, 017505.

Francois Lekien1, Shane D. Ross2
1Ecole Polytechnique, Universite Libre de Bruxelles
2Engineering Science and Mechanics, Virginia Tech


We generalize the concepts of Finite-Time Lyapunov Exponent (FTLE) and Lagrangian Coherent Structures (LCS) 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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