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A global stability analysis of the steady and periodic cylinder wake. (English) Zbl 0813.76025
Summary: A global, three-dimensional stability analysis of the steady and the periodic cylinder wake is carried out employing in 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.

MSC:
76E05 Parallel shear flows in hydrodynamic stability
76D25 Wakes and jets
76M25 Other numerical methods (fluid mechanics) (MSC2010)
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