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Session MM - Chaos and Fractals.
MIXED session, Tuesday afternoon, November 23
Whidbey, Westin Seattle

[MM.003] Lagrangian chaos and resonance phenomena in Stokes flows

Dmitri Vainchtein (University of California Santa Barbara), Neishtadt Neishtadt (Space Research Institute, Moscow, Russia), Igor Mezic (University of California Santa Barbara)

We discuss the Lagrangian chaos in a Stokes flow between two counter-rotating coaxial cylinders with the angular velocities depending on the coordinate along the axis. The streamlines of the unperturbed system are closed and the flow is regular. However, if an additional weak flow parallel to the axis is applied, Lagrangian chaos develops. We show that this phenomenon is caused by quasi-random changes (jumps) in the adiabatic invariant of the flow, which occur when streamlines cross the resonance surface. We demonstrate that the accumulation of the jumps leads to the diffusion of adiabatic invariant. For multiple resonance crossings. We discuss the statistical properties of the jumps. We study the long-time mixing properties of the flow and compare our results with numerical simulations.

Part M of program listing