2012 BFY Abstract Detail Page

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Abstract Title: W27 - Chaotic fluid mixing and Hamiltonian phase space
Abstract: Very simple, two-dimensional (2D) fluids flows can exhibit mixing which is chaotic, in the sense that nearby tracers in the flow separate exponentially in time. Furthermore, the equations that describe tracer motion in a 2D flow are equivalent to Hamilton's equations of classical physics; consequently, the real space motion of a tracer in a 2D flow is equivalent to a phase space trajectory of a Hamiltonian system. For these reasons, simple experiments with 2D mixing are ideal for illustrating both the concepts of chaotic dynamics and also for developing an intuition for the value of using a phase space description of dynamical and kinematic processes.

In this workshop, we will discuss junior-level experiments that can be used to explore these topics, using two fluid flows: (a) a "blinking vortex flow" which can be set up in a simple petrie dish with some minimal electronics; and (b) an oscillating vortex chain flow which has become a paradigm in the scientific literature for chaotic mixing. The experiments are imaged from above with a CCD camera and analyzed on a Windows-PC. Individual tracers moving in the flow can be tracked in time; the resulting trajectories can be analyzed to show sensitive dependence on initial conditions and to assemble Poincaré sections that reveal the ordered/chaotic structure of the phase space. The mixing of dye in these systems illustrates the importance of chaotic stretching on larger-scale mixing processes. All of the experimental results can be compared with simple numerical simulations that students can perform. These flow systems are also ideal for independent research projects involving undergraduate students. In fact, in the past 15 years, we have published 17 papers -- 16 with undergrads -- on results from these systems, 4 of which are in Physical Review Letters and one in Nature.
Abstract Type: Workshop

Workshop Documents

Workshop Document: Download the Workshop Document
Workshop Document (2): Download the Workshop Document (2)
Workshop Document (3): Download the Workshop Document (3)
Workshop Document (4): Download the Workshop Document (4)

Author/Organizer Information

Primary Contact: Tom Solomon
Bucknell University