Chaotic Geodesics
Chaotic Dynamics
2015-02-06 v2
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.
Keywords
Cite
@article{arxiv.0711.4125,
title = {Chaotic Geodesics},
author = {Jean-Luc Thiffeault and Khalid Kamhawi},
journal= {arXiv preprint arXiv:0711.4125},
year = {2015}
}
Comments
13 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)