Title

A Periodically Forced Flow Displaying Symmetry Breaking Via A Three-Tori Gluing Bifurcation And Two-Tori Resonances

Keywords

Gluing bifurcation; Naimark-Sacker bifurcation; Periodic forcing; Symmetry breaking; Taylor-Couette flow

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. © 2001 Elsevier Science B.V.

Publication Date

8-1-2001

Publication Title

Physica D: Nonlinear Phenomena

Volume

156

Issue

1-2

Number of Pages

81-97

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1016/S0167-2789(01)00261-5

Socpus ID

0035427180 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0035427180

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