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Mixing in fully chaotic flows.

A Wonhas1, J C Vassilicos

  • 1Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, United Kingdom.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|January 7, 2003
PubMed
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Lyapunov exponents explain passive scalar mixing in chaotic flows. However, a different mechanism, driven by large-scale flow nonuniformities, can dominate during the final mixing stages, leading to slower scalar variance decay than predicted by Lyapunov exponents.

Area of Science:

  • Fluid Dynamics
  • Chaos Theory
  • Statistical Mechanics

Background:

  • Passive scalar mixing in chaotic flows is typically modeled using Lyapunov exponents, which quantify particle pair separation rates.
  • This approach effectively describes the initial stages of mixing where scalar variance decays rapidly.

Purpose of the Study:

  • To review and investigate the limitations of Lyapunov exponents in describing passive scalar mixing.
  • To identify and analyze an alternative mixing mechanism that becomes dominant in the final stages of mixing.

Main Methods:

  • A unified theoretical review of existing approaches.
  • Analysis of mixing dynamics in the incompressible and diffusive baker map, a model chaotic flow.
  • Investigation of the role of large-scale flow nonuniformities versus small-scale stretching properties.

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Main Results:

  • Lyapunov exponents accurately describe the initial stage of scalar variance decay.
  • A different mixing mechanism, governed by large-scale flow nonuniformities, can lead to slower scalar variance decay during the final mixing stage.
  • This alternative mechanism's influence becomes apparent when it results in a slower decay than predicted by Lyapunov exponents.

Conclusions:

  • Lyapunov exponents are not universally sufficient to describe passive scalar mixing in all stages of chaotic flows.
  • Large-scale flow nonuniformities represent a critical factor in the late stages of mixing.
  • The findings are expected to be applicable to a broad range of chaotic flow systems.