Global stability analysis of the steady and periodic cylinder wake
- Max-Planck-Inst fur Stromungsforschung, Gottingen (Germany)
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 less than 54. The onset of periodicity is confirmed to be a supercritical Hopf bifurcation which can be modeled by the Landau equations. The periodic solution is observed to be only neutrally stable for 54 less than Re less than 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.
- Sponsoring Organization:
- USDOE
- OSTI ID:
- 85460
- Journal Information:
- Journal of Fluid Mechanics, Journal Name: Journal of Fluid Mechanics Vol. 270; ISSN JFLSA7; ISSN 0022-1120
- Country of Publication:
- United States
- Language:
- English
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