Title

A periodically forced flow displaying symmetry breaking via a three-tori gluing bifurcation and two-tori resonances

Authors

Authors

F. Marques; J. M. Lopez;J. Shen

Comments

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Abbreviated Journal Title

Physica D

Keywords

periodic forcing; Taylor-Couette flow; symmetry breaking; gluing; bifurcation; Naimark-Sacker bifurcation; TAYLOR-COUETTE FLOW; ANOMALOUS MODES; CYLINDRICAL GEOMETRIES; INNER; CYLINDER; EQUATIONS; 2ND-ORDER; ENDWALL; SYSTEM; MOTION; FLUID; Mathematics, Applied; Physics, Multidisciplinary; Physics, Mathematical

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 Z(2) 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 Z(2) symmetry has been broken. However, this branch is not connected in a simple manner to the Z(2)-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. (C) 2001 Elsevier Science B.V. All rights reserved.

Journal Title

Physica D

Volume

156

Issue/Number

1-2

Publication Date

1-1-2001

Document Type

Article

Language

English

First Page

81

Last Page

97

WOS Identifier

WOS:000169908300005

ISSN

0167-2789

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