Abstract
The dynamics due to a periodic forcing (harmonic axial oscillations) in a Taylor-Couette apparatus of finite length is examined numerically in an axisymmetric subspace. The forcing delays the onset of centrifugal instability and introduces a Z2 symmetry that involves both space and time. This paper examines the influence of this symmetry on the subsequent bifurcations and route to chaos in a one-dimensional path through parameter space as the centrifugal instability is enhanced. We have observed a well-known route to chaos via frequency locking and torus break-up on a two-tori branch once the Z2 symmetry has been broken. However, this branch is not connected in a simple manner to the Z2-invariant primary branch. An intermediate branch of three-tori solutions, exhibiting heteroclinic and homoclinic bifurcations, provides the connection. On this three-tori branch, a new gluing bifurcation of three-tori is seen to play a central role in the symmetry breaking process.
Original language | English (US) |
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Pages (from-to) | 81-97 |
Number of pages | 17 |
Journal | Physica D: Nonlinear Phenomena |
Volume | 156 |
Issue number | 1-2 |
DOIs | |
State | Published - Aug 1 2001 |
Keywords
- Gluing bifurcation
- Naimark-Sacker bifurcation
- Periodic forcing
- Symmetry breaking
- Taylor-Couette flow
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics