Hamiltonian Maps and Transport in Structured Fluids
Abstract
Structures such as waves, jets, and vortices have a dramatic impact on the transport properties of a flow. Passive tracer transport in incompressible two-dimensional flows is described by Hamiltonian dynamics, and, for idealized structures, the system is typically integrable. When such structures are perturbed, chaotic trajectories can result which can significantly change the transport properties. It is proposed that the transport due to the chaotic regions can be efficiently calculated using Hamiltonian mappings designed specifically for the structure of interest. As an example a new map is constructed, appropriate for studying transport by propagating isolated vortices. It is found that a perturbed vortex will trap fluid parcels for varying lengths of time, and that the distribution of such trapping times has slopes which are independent of the amplitudes of both the vortex and the perturbation.
Keywords
Cite
@article{arxiv.chao-dyn/9311006,
title = {Hamiltonian Maps and Transport in Structured Fluids},
author = {Jeffrey B. Weiss},
journal= {arXiv preprint arXiv:chao-dyn/9311006},
year = {2009}
}
Comments
14 pages, Plain TeX, 6 Postscript figures to be published in Physica D, Proceedings of the NATO and EGS Workshop on Chaotic Advection, Tracer Dynamics, and Turbulent Dispersion, Sereno Di Gavi, Italy, May 1993