Chaotic Advection in Fluid Flows

Ying Cheng Lai, T. Tél

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

The advection of tracer particles in hydrodynamical flows represents one of the successful applications of chaos theory. The basic observation is that molecular diffusion is negligible on the typical time scale of the flow. As a result, in the absence of any diffusion-enhancing mechanism such as hydrodynamical turbulence, advection dominates. Indeed, the main physical mechanism for fluid stirring is advection, whose efficiency can be enhanced greatly by chaotic dynamics. The spreading of pollutants on large scales is also dominated by advection. Potential applications of chaotic advection range from laboratory investigations of fluid dynamics to the study of large-scale environmental flows. From the point of view of dynamical systems, an appealing feature of the passive advection problem is that its phase space coincides with the physical space of the fluid, rendering possible direct experimental observation and characterization of fractal structures associated with chaotic dynamics.

Original languageEnglish
Title of host publicationApplied Mathematical Sciences (Switzerland)
PublisherSpringer
Pages343-383
Number of pages41
DOIs
Publication statusPublished - Jan 1 2011

Publication series

NameApplied Mathematical Sciences (Switzerland)
Volume173
ISSN (Print)0066-5452
ISSN (Electronic)2196-968X

Keywords

  • Coherent Structure
  • Lyapunov Exponent
  • Open Flow
  • Stable Manifold
  • Unstable Manifold

ASJC Scopus subject areas

  • Applied Mathematics

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  • Cite this

    Lai, Y. C., & Tél, T. (2011). Chaotic Advection in Fluid Flows. In Applied Mathematical Sciences (Switzerland) (pp. 343-383). (Applied Mathematical Sciences (Switzerland); Vol. 173). Springer. https://doi.org/10.1007/978-1-4419-6987-3_10