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Preface

In a seminal paper published in 1984, Hassan Aref coined the term chaotic advection to denote the study of stochastic particle motion in a fluid due to deterministic processes. In the nonlinear dynamics formulation of the problem, phase space is physical space and solution trajectories are the paths fluid particles take through the fluid (see below). This close association of abstract phase space concepts and dynamics in real space was particularly appealing to me. I first heard about chaotic advection from J.T. Stuart during a visit to Imperial in the summer of 1984. It took me another two years before I saw the contribution I could make. During a visit to Mike Gaster's lab in Cambridge in the summer of 1986 I was shown the recently published paper by Chaiken, Chevray, Tabor and Tan [Proc. R. Soc. London Ser. A 408 (1986) 165] on the time-periodic forcing of a two-dimensional Stokes flow between eccentric rotating cylinders. The colour photographs of the experiment were absolutely beautiful! I saw this as an example of a forced 2D oscillator and saw immediately that one should be able to realize the case of chaotic streamlines in a steady three-dimensional flow simply by studying Taylor-vortex flow between eccentric rotating cylinders.

My original idea was to set up an experimental flow and demonstrate the expected effects, and this would stimulate my mathematical colleagues to either compute the flow numerically or investigate the asymptotic model derived by DiPrima and Stuart in the 1970s. It proved more difficult than I anticipated to get the experiment working, and at that time we had no experience at Warwick in computational fluid dynamics. The final option was to undertake the difficult task of putting together the DiPrima and Stuart velocity field and investigate its streamlines. A look at the DiPrima and Stuart papers will soon convince anyone that this was a major task. It was certainly beyond my own skills. Finally though Peter Ashwin decided to have a go, and the rest is ``history''. We submitted our first paper to the Journal of Fluid Mechanics in late 1993.

What amazed me then and still amazes me now is why the lack of attention on chaotic advection in laminar 3D Navier-Stokes flows! It is even more amazing when you consider that our work appeared 12 years after Wayne Arter's paper on chaotic streamlines in steady Rayleigh-Benard convection with square planform [Ar83]. I have no explanation for it other than to carry out particle path investigations as a function of Rayleigh or Reynolds number is difficult. You need some guiding principle. We believe we have such a guiding principle with the Eulerian diagnostics developed in Yannacopoulos et al [YMRK98].


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Next: Mixing in a laminar Up: Mixing with Chaos Previous: Mixing with Chaos
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UK Nonlinear News
4/29/1998