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Colloquium September 15

Date: Friday September 15

Time: 16:00 to 17:00

Place: 455 McBryde (Commons Room)

Speaker: Francois Lekien of Princeton

Title: Stretching, Separation and Coherent Structures in Time-Chaotic Flows

Abstract

Dye streaklines in fluid experiments, GPS drifters in the oceans, and the evolution of pollutants typically reveal complex bundles of Lagrangian trajectories. In autonomous and time-periodic dynamical systems, the stable and unstable manifolds of hyperbolic fixed points and periodic orbits can be used to understand the complexity of these trajectories. The invariant manifold divide regions of qualitatively different dynamics and govern transport between these regions.

Most real fluids and geophysical flows are, however, strongly aperiodic and do not have, in general, fixed points or periodic orbits. Nevertheless, their dynamics exhibit similar coherent structures that can be rendered by studying stretching and folding in the fluid. These structures indicate alleyways and barriers to transport and provide a geometric description of the mixing processes.

In this talk, I will describe fluid transport and separation in Monterey Bay. High-frequency radar stations provide current measurements in real-time for the bay and permit the computation of dynamical barriers and alleyways in this complex system. The coherent structures reveal the existence of optimal release windows in which contaminants can be efficiently advected away from the coast, reducing their negative impact on the marine environment. In addition, the alleyways can be used to optimize the deployment of drifters and the routes of underwater vehicles to maximize coverage of an area.

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