Session L3: Dynamical Systems and Chaos II

3:35 PM–5:45 PM, Monday, November 21, 2011
Room: 303

Chair: Tom Solomon, Bucknell University

Abstract ID: BAPS.2011.DFD.L3.1

Abstract: L3.00001 : Burning invariant manifolds for propagating fronts in a chain of vortices

3:35 PM–3:48 PM

Preview Abstract MathJax On | Off   Abstract  


  Tom Solomon
    (Bucknell University)

  Mark Kingsbury
    (Bucknell University)

  John Mahoney
    (University of California at Merced)

  Kevin Mitchell
    (University of California at Merced)

We present experimental studies of the behavior of reaction fronts in a chain of alternating vortices. The flow is produced by a magnetohydrodynamic forcing technique, and the fronts are produced by the ferroin-catalyzed Belousov-Zhabotinsky chemical reaction. We introduce {\em burning invariant manifolds} (BIMs) which act as barriers to front propagation, similar to the role played by invariant manifolds as barriers to passive transport in two-dimensional flows. Unlike manifolds for passive transport, though, BIMs are one-sided barriers, passing either left- or right-going fronts but blocking the other. We show how the BIMs can be measured experimentally for both time-independent and time-periodic flows. The experimental results are compared to simulations based on a simplified numerical model of the flow.

To cite this abstract, use the following reference: