Hostname: page-component-cd9895bd7-hc48f Total loading time: 0 Render date: 2024-12-23T17:16:37.711Z Has data issue: false hasContentIssue false

Mode interactions in an enclosed swirling flow: a double Hopf bifurcation between azimuthal wavenumbers 0 and 2

Published online by Cambridge University Press:  15 April 2002

F. MARQUES
Affiliation:
Departament de Física Aplicada, Universitat Politècnica de Catalunya, Jordi Girona Salgado s/n, Mòdul B4 Campus Nord, 08034 Barcelona, Spain
J. M. LOPEZ
Affiliation:
Department of Mathematics, Arizona State University, Tempe, AZ 85287, USA
J. SHEN
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, FL 32816-1632, USA

Abstract

A double Hopf bifurcation has been found of the flow in a cylinder driven by the rotation of an endwall. A detailed analysis of the multiple solutions in a large region of parameter space, computed with an efficient and accurate three-dimensional Navier-Stokes solver, is presented. At the double Hopf point, an axisymmetric limit cycle and a rotating wave bifurcate simultaneously. The corresponding mode interaction generates an unstable two-torus modulated rotating wave solution and gives a wedge-shaped region in parameter space where the two periodic solutions are both stable. By exploring in detail the three-dimensional structure of the flow, we have identified the two mechanisms that compete in the neighbourhood of the double Hopf point. Both are associated with the jet that is formed when the Ekman layer on the rotating endwall is turned by the stationary sidewall.

Type
Research Article
Copyright
© 2002 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)