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A global stability analysis of the steady and periodic cylinder wake

Published online by Cambridge University Press:  26 April 2006

Bernd R. Noack  and
Helmut Eckelmann
Bernd R. Noack
Affiliation:
Max-Planck-Institut für Strömungsforschung, Bunsenstraße 10, D-37 073 Göttingen, Germany
Helmut Eckelmann
Affiliation:
Max-Planck-Institut für Strömungsforschung, Bunsenstraße 10, D-37 073 Göttingen, Germany
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Abstract

A global, three-dimensional stability analysis of the steady and the periodic cylinder wake is carried out employing a low-dimensional Galerkin method. The steady flow is found to be asymptotically stable with respect to all perturbations for Re < 54. The onset of periodicity is confirmed to be a supercritical Hopf bifurcation which can be modelled by the Landau equations. The periodic solution is observed to be only neutrally stable for 54 < Re < 170. While two-dimensional perturbations of the vortex street rapidly decay, three-dimensional perturbations with long spanwise wavelengths neither grow nor decay. The periodic solution becomes unstable at Re = 170 by a perturbation with the spanwise wavelength of 1.8 diameters. This instability is shown to be a supercritical Hopf bifurcation in the spanwise coordinate and leads to a three-dimensional periodic flow. Finally the transition scenario for higher Reynolds numbers is discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 270 , 10 July 1994 , pp. 297 - 330
Copyright
© 1994 Cambridge University Press

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