Hamiltonian maps and transport in structured fluids

Astronomy and Astrophysics – Astrophysics

Scientific paper

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Scientific paper

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 both the vortex and the perturbation.
Current address: Program in Atmospheric and Oceanic Sciences, Department of Astrophysical, Planetary, and Atmospheric Sciences, Campus Box 311, University of Colorado, Boulder, CO 80309, USA.

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