Chaotic Geodesics
arXiv:0711.4125 · doi:10.1142/9789812818805_0003
Abstract
When a shallow layer of inviscid fluid flows over a substrate, the fluid particle trajectories are, to leading order in the layer thickness, geodesics on the two-dimensional curved space of the substrate. Since the two-dimensional geodesic equation is a two degree-of-freedom autonomous Hamiltonian system, it can exhibit chaos, depending on the shape of the substrate. We find chaotic behaviour for a range of substrates.
arXiv comment13 pages, 27 figures. PDFLaTeX with RevTeX4-1 macros. Fixed some typos and updated references. Published in proceedings of the conference on "Chaos, Complexity, and Transport" (Le Pharo, Marseille, June 2007)