Chaotic Geodesics

Details Chaotic Geodesics Chaotic Geodesics

2007-11-26

arxiv.org/abs/0711.4125v1

Nonlinear Sciences

Chaotic Dynamics

13 pages, 27 figures. PDFLaTeX with RevTeX4 macros. To appear in proceedings of the conference on "Chaos, Complexity, and Tran

Scientific paper

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.

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