2012 BFY Abstract Detail Page
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Abstract Title: 
W27  Chaotic fluid mixing and Hamiltonian phase space 
Abstract: 
Very simple, twodimensional (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 juniorlevel 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 WindowsPC. 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 PoincarĂ© 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 largerscale 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: 
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Workshop Document (2): 
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Workshop Document (3): 
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Workshop Document (4): 
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Author/Organizer Information 
Primary Contact: 
Tom Solomon
Bucknell University

