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Traveling waves in pipe flow.

Holger Faisst1, Bruno Eckhardt

  • 1Fachbereich Physik, Philipps Universität Marburg, D-35032 Marburg, Germany. Holger.Faisst@physik.uni-marburg.de

Physical Review Letters
|December 20, 2003
PubMed
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Researchers identified three-dimensional traveling waves in pipe flow, characterized by vortices and streaks, originating at low Reynolds numbers. These unstable states form a chaotic saddle, explaining intermittent turbulence and sensitivity to initial conditions.

Area of Science:

  • Fluid dynamics
  • Nonlinear dynamics
  • Turbulence theory

Background:

  • Pipe flow is a fundamental system in fluid dynamics.
  • Understanding the transition to turbulence is a long-standing challenge.
  • Intermittency and sensitivity to initial conditions are key features of turbulent flows.

Purpose of the Study:

  • To identify and characterize three-dimensional traveling wave solutions in pipe flow.
  • To investigate the origin and stability of these wave solutions.
  • To explain the mechanisms behind intermittent turbulence and sensitive dependence on initial conditions.

Main Methods:

  • Numerical identification of traveling wave solutions.
  • Analysis of saddle-node bifurcations.
  • Investigation of flow stability and dynamical systems theory.

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Main Results:

  • A family of three-dimensional traveling waves was identified in pipe flow.
  • These waves are dominated by downstream vortices and streaks.
  • They emerge from saddle-node bifurcations at Reynolds numbers as low as 1250.
  • All identified states were found to be immediately unstable.

Conclusions:

  • The traveling waves provide a structural skeleton for the formation of a chaotic saddle.
  • This chaotic saddle mechanism explains the intermittent transition to turbulence.
  • It also accounts for the sensitive dependence on initial conditions observed in pipe shear flow.