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

• 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; Antarctic; The Antarctic; Antarc*
• 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

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.