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Related Experiment Videos

Standing waves in flow between finite counterrotating cylinders.

J Langenberg1, G Pfister, J Abshagen

  • 1Institute of Experimental and Applied Physics, University of Kiel, 24098 Kiel, Germany.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 20, 2003
PubMed
Summary

Standing waves emerge from a supercritical Hopf bifurcation in counterrotating Taylor-Couette flow, exhibiting distinct symmetries (SW0 and SW(pi)) based on aspect ratio. These findings align with theoretical predictions for spiral vortex flow.

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Area of Science:

  • Fluid Dynamics
  • Nonlinear Dynamics
  • Pattern Formation

Background:

  • Counterrotating Taylor-Couette flow is a canonical system for studying fluid instabilities.
  • Hopf bifurcations are critical for understanding pattern formation and transitions in dynamical systems.
  • Previous theoretical work predicted spiral vortex flow but experimental verification of bifurcation structures was needed.

Purpose of the Study:

  • To experimentally investigate standing wave formation in counterrotating Taylor-Couette flow.
  • To characterize the different types of standing waves and their symmetries.
  • To elucidate the bifurcation pathways leading to spiral vortex flow.

Main Methods:

  • Experimental realization of counterrotating Taylor-Couette flow.

Related Experiment Videos

  • Observation and analysis of flow patterns, identifying standing wave modes (SW0, SW(pi)).
  • Systematic variation of control parameters, particularly the aspect ratio, to map bifurcation structures.

    • Main Results:

    • Experimental evidence for standing waves as the primary instability via supercritical Hopf bifurcation.
    • Identification of two distinct standing wave modes (SW0, SW(pi)) with azimuthal wave number m=1, differing in symmetry.
    • Observation of a cusp bifurcation organizing the transition between SW0 and SW(pi), with spiral vortex flow arising from a secondary bifurcation.

    Conclusions:

    • The study experimentally validates theoretical predictions for Hopf bifurcation to spiral vortex flow in finite systems.
    • The observed bifurcation structure, including standing wave modes and their transitions, provides a comprehensive understanding of pattern formation.
    • The distinct symmetries of SW0 and SW(pi) offer insights into symmetry breaking in fluid dynamics.