Determining the self-rotation number following a Naimark-Sacker bifurcation in the periodically forced Taylor-Couette flow

Juan Lopez, F. Marques

Research output: Contribution to journalArticle

3 Scopus citations

Abstract

Systems which admit waves via Hopf bifurcations and even systems that do not undergo a Hopf bifurcation but which support weakly damped waves may, when parametrically excited, respond quasiperiodically. The bifurcations are from a limit cycle (the time-periodic basic flow) to a torus, i.e. Naimark-Sacker bifurcations. Floquet analysis detects such bifurcations, but does not unambiguously determine the second frequency following such a bifurcation. Here we present a technique to unambiguously determine the frequencies of such quasiperiodic flows using only results from Floquet theory and the un queness of the self-rotation number (the generalization of the rotation number for continuous systems). The robustness of the technique is illustrated in a parametrically excited Taylor-Couette flow, even in cases where the bifurcating solutions are subject to catastrophic jumps in their spatial/temporal structure.

Original languageEnglish (US)
Pages (from-to)61-74
Number of pages14
JournalZeitschrift fur Angewandte Mathematik und Physik
Volume51
Issue number1
DOIs
StatePublished - Jan 2000

Keywords

  • Floquet theory
  • Parametric excitation
  • Quasiperiodic flow
  • Self-rotation number
  • Taylor-Couette flow

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)
  • Applied Mathematics

Fingerprint Dive into the research topics of 'Determining the self-rotation number following a Naimark-Sacker bifurcation in the periodically forced Taylor-Couette flow'. Together they form a unique fingerprint.

  • Cite this