Finite aspect ratio Taylor-Couette flow: Shil'nikov dynamics of 2-tori

Juan Lopez, Francisco Marques

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

The nonlinear dynamics of the flow in a short annular container driven by the rotation of the inner cylinder is studied using direct numerical simulations of the three-dimensional Navier-Stokes equations. The basic state is SO(2)×Z2 symmetric. For aspect ratios between 3.6 and 4.4, we have located three codimension-two bifurcations: a cusp, a double Hopf and a fold-Hopf bifurcation. All these local bifurcations are Z2-invariant. The breaking of Z2 symmetry involves very complex Shil'nikov-type dynamics, not directly connected to any of the three codimension-two bifurcations, but associated with five unstable limit cycles and a wealth of heteroclinic connections between them. Period-adding cascades, both direct and reverse, of 2-tori have been found. Narrow regions of chaotic dynamics are interspersed within these quasiperiodic solutions.

Original languageEnglish (US)
Pages (from-to)168-191
Number of pages24
JournalPhysica D: Nonlinear Phenomena
Volume211
Issue number1-2
DOIs
StatePublished - Nov 1 2005

Fingerprint

Taylor-Couette Flow
Couette flow
Aspect Ratio
Codimension
aspect ratio
Aspect ratio
Torus
Bifurcation
Heteroclinic Connection
Local Bifurcations
Quasi-periodic Solutions
Chaotic Dynamics
Cusp
Container
Limit Cycle
Hopf Bifurcation
Nonlinear Dynamics
Cascade
Reverse
Navier-Stokes Equations

Keywords

  • Homoclinic and heteroclinic bifurcations
  • Shil'nikov dynamics
  • Symmetry breaking
  • Taylor-Couette flow

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

Finite aspect ratio Taylor-Couette flow : Shil'nikov dynamics of 2-tori. / Lopez, Juan; Marques, Francisco.

In: Physica D: Nonlinear Phenomena, Vol. 211, No. 1-2, 01.11.2005, p. 168-191.

Research output: Contribution to journalArticle

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