Title

Mode Interactions In An Enclosed Swirling Flow: A Double Hopf Bifurcation Between Azimuthal Wavenumbers 0 And 2

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.

Publication Date

3-25-2002

Publication Title

Journal of Fluid Mechanics

Volume

455

Number of Pages

263-281

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1017/S0022112001007285

Socpus ID

0037171419 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0037171419

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