Mode competition of rotating waves in reflection-symmetric Taylor-Couette flow

J. Abshagen, Juan Lopez, F. Marques, G. Pfister

Research output: Contribution to journalArticle

24 Scopus citations

Abstract

We report on the results of a combined experimental and numerical study on mode interactions of rotating waves in Taylor-Couette flow. Our work shows that rotating waves which originate at a Hopf bifurcation from the steady axisymmetric Taylor vortex flow interact with this axisymmetric flow in a codimension-two fold-Hopf bifurcation. This interaction gives rise to an (unstable) low-frequency modulated wave via a subcritical Neimark-Sacker bifurcation from the rotating wave. At higher Reynolds numbers, a complicated mode interation between stable modulated waves originating at a different Neimark-Sacker bifurcation and a pair of symmetrically related rotating waves that originate at a cyclic pitchfork bifurcation is found to organize complex Z2-symmetry breaking of rotating waves via global bifurcations. In addition to symmetry breaking of rotating waves via a (local) cyclic pitchfork bifurcation, we found symmetry breaking of modulated waves via a saddle-node-infinite-period (SNIP) global bifurcation. Tracing these local and global bifurcation curves in Reynolds number/aspect ratio parameter space toward their apparant merging point, unexpected complexity arises in the bifurcation structure involving non-symmetric two-tori undergoing saddle-loop homoclinic bifurcations. The close agreement between the numerics and the experiment is indicative of the robustness of the observed complex dynamics.

Original languageEnglish (US)
Pages (from-to)269-299
Number of pages31
Journaljournal of fluid mechanics
Volume540
DOIs
StatePublished - Oct 10 2005

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ASJC Scopus subject areas

  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering

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