Virginia TechLekien, F.Ross, Shane D.2013-12-042013-12-042010-03-01Lekien, 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/10.1063/1.32785161054-1500http://hdl.handle.net/10919/24401We 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.application/pdfen-USIn CopyrightLagrangian coherent structuresRayleigh-bénard convectionN-vortex prblemInvariant manifoldsPolar vortex2-dimensional mapsChaotic advectionAperiodic flowsRotating spherePoint vorticesArticle - Refereedhttp://scitation.aip.org/content/aip/journal/chaos/20/1/10.1063/1.3278516https://doi.org/10.1063/1.3278516