Three-dimensional Floquet stability analysis of the wake of a circular cylinder
Results are reported from a highly accurate, global numerical stability analysis of the periodic wake of a circular cylinder for Reynolds numbers between 140 and 300. The analysis shows that the two-dimensional wake becomes (absolutely) linearly unstable to three-dimensional perturbations at a critical Reynolds number of 188.5±1.0. The critical spanwise wavelength is 3.96 ± 0.02 diameters and the critical Floquet mode corresponds to a 'Mode A' instability. At Reynolds number 259 the two-dimensional wake becomes linearly unstable to a second branch of modes with wavelength 0.822 diameters at onset. Stability spectra and corresponding neutral stability curves are presented for Reynolds numbers up to 300.
© 1996 Cambridge University Press. (Received 20 March 1995 and in revised form 16 April 1996) We wish to thank H. M. Blackburn, M. Gharib, A. Leonard, T. Leweke, D. Meiron, B. R. Noack, A. Roshko, L. S. Tuckerman, D. R. Williams, and C. H. K Williamson for their questions, comments, and suggestions which have added significantly to this paper. D. B. acknowledges the hospitality of the Center for Nonlinear Dynamics at the University of Texas at Austin where part of this work was conducted. He also thanks the Nuffield Foundation for their support and the NSF for their support though Grant No. DMS 92-06224. R. D. H. acknowledges financial support from the NSF through Grant No. CDA-9318145 and the ONR through Grant No. N000-94-1-0793. Computational resources for this work were provided by the University of Texas System Center for High Performance Computing and the JPL High Performance Computing and Communications program at the California Institute of Technology.