The computation of finite-time Lyapunov exponents on unstructured meshes and for non-Euclidean manifolds
- 8 February 2010
- journal article
- conference paper
- Published by AIP Publishing in Chaos: An Interdisciplinary Journal of Nonlinear Science
- Vol. 20 (1) , 017505
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 Möbius 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.Keywords
This publication has 59 references indexed in Scilit:
- Detecting dynamical boundaries from kinematic data in biomechanicsChaos: An Interdisciplinary Journal of Nonlinear Science, 2010
- Top marine predators track Lagrangian coherent structuresProceedings of the National Academy of Sciences, 2009
- Evaluation of the threshold of stability for the human spineJournal of Biomechanics, 2009
- Lagrangian coherent structures in the planar elliptic restricted three-body problemCelestial Mechanics and Dynamical Astronomy, 2009
- Oceanic mesoscale eddies as revealed by Lagrangian coherent structuresGeophysical Research Letters, 2008
- Characterization of Coherent Structures in the Cardiovascular SystemAnnals of Biomedical Engineering, 2008
- PREFACEJournal of the Atmospheric Sciences, 2005
- Hyperbolic lines and the stratospheric polar vortexChaos: An Interdisciplinary Journal of Nonlinear Science, 2002
- Relation between Kinematic Boundaries, Stirring, and Barriers for the Antarctic Polar VortexJournal of the Atmospheric Sciences, 2002
- Finding finite-time invariant manifolds in two-dimensional velocity fieldsChaos: An Interdisciplinary Journal of Nonlinear Science, 2000