Chaotic mixing in a bounded three-dimensional flow

G. O. Fountain, D. V. Khakhar, I. Mezic, J. M. Ottino*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

106 Scopus citations


Even though the first theoretical example of chaotic advection was a three-dimensional flow (Henon 1966), the number of theoretical studies addressing chaos and mixing in three-dimensional flows is small. One problem is that an experimentally tractable three-dimensional system that allows detailed experimental and computational investigation had not been available. A prototypical, bounded, three-dimensional, moderate-Reynolds-number flow is presented; this system lends itself to detailed experimental observation and allows high-precision computational inspection of geometrical and dynamical effects. The flow structure, captured by means of cuts with a laser sheet (experimental Poincare section), is visualized via continuously injected fluorescent dye streams, and reveals detailed chaotic structures and chains of high-period islands. Numerical experiments are performed and compared with particle image velocimetry (PIV) and flow visualization results. Predictions of existing theories for chaotic advection in three-dimensional volume-preserving flows are tested. The ratio of two frequencies of particle motion - the frequency of motion around the vertical axis and the frequency of recirculation in the plane containing the axis - is identified as the crucial parameter. Using this parameter, the number of islands in the chain can be predicted. The same parameter - using as a base-case the integrable motion - allows the identification of operating conditions where small perturbations lead to nearly complete mixing.

Original languageEnglish (US)
Pages (from-to)265-301
Number of pages37
JournalJournal of fluid Mechanics
StatePublished - 2000

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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