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Transition to turbulence in a shear flow.

B Eckhardt1, A Mersmann

  • 1Fachbereich Physik, Philipps Universität Marburg, D-35032 Marburg, Germany.

Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|April 24, 2002
PubMed
Summary

We analyzed a 19-dimensional model of parallel shear flow. Findings suggest a universal transition scenario in fluid dynamics, with fractal dependencies observed in flow perturbations.

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Area of Science:

  • Fluid dynamics
  • Nonlinear dynamics
  • Computational physics

Background:

  • Parallel shear flows are fundamental in fluid dynamics.
  • Understanding flow stability and transitions is crucial for various applications.
  • Previous studies on shear flows like plane Couette flow provide context.

Purpose of the Study:

  • To analyze the properties of a 19-dimensional Galerkin approximation of parallel shear flow.
  • To investigate the stability of laminar flow and the occurrence of stationary flows.
  • To characterize the behavior of finite amplitude perturbations.

Main Methods:

  • Galerkin approximation with a 19-dimensional model.
  • Analysis of flow stability across different Reynolds numbers (Re).
  • Investigation of stationary flow bifurcations and perturbation lifetimes.

Main Results:

  • The sinusoidal laminar flow is stable for all Reynolds numbers (Re).
  • For large Re, unstable stationary flows emerge.
  • Perturbation lifetimes exhibit a fractal dependence on amplitude and Reynolds number.

Conclusions:

  • The observed transition scenario in parallel shear flow may be universal.
  • Findings align with observations in plane Couette flow.
  • The study provides insights into complex flow behavior and stability.

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