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Related Experiment Videos

Pattern formation in weakly forced Taylor-Couette flow.

Zhenyu Li1, Roger E Khayat

  • 1Department of Mechanical and Materials Engineering, The University of Western Ontario, London, Ontario, Canada N6A 5B9.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 1, 2004
PubMed
Summary
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Spatially modulated cylinders in Taylor-Couette flow induce steady vortex formation even at low Taylor numbers. Vortex patterns synchronize with forcing or become quasiperiodic, with optimal forcing wave numbers matching critical values.

Area of Science:

  • Fluid dynamics
  • Nonlinear dynamics

Background:

  • Taylor-Couette flow is a fundamental system for studying fluid instabilities.
  • Understanding vortex formation and pattern selection is crucial in fluid mechanics.

Purpose of the Study:

  • To investigate the effect of spatially modulated cylinders on vortex formation in axisymmetric Taylor-Couette flow.
  • To analyze vortex pattern selection under periodic forcing and varying Taylor numbers.

Main Methods:

  • Regular perturbation expansion for small modulation amplitudes.
  • Analysis of flow fields at small to moderately large Taylor numbers (Ta).

Main Results:

  • Weak modulation leads to steady Taylor-vortex flow even at vanishingly small Ta.

Related Experiment Videos

  • Vortex periodicity matches forcing for commensurate modulations; quasiperiodic patterns emerge for incommensurate modulations.
  • Increasing counter-rotation speed alters vortex structure, leading to commensurate rows.

    • Conclusions:

    • Spatial modulation acts similarly to end plates, inducing imperfect bifurcation and steady vortex flow.
    • The study reveals a clear relationship between forcing characteristics and emergent vortex patterns.
    • Optimal forcing wave numbers consistently approach critical values from linear stability analysis.