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Three-dimensional Floquet stability analysis of the wake of a circular cylinder

Published online by Cambridge University Press:  26 April 2006

Dwight Barkley
Affiliation:
Nonlinear Systems Laboratory, Mathematics Institute. University of Warwick, Coventry, CV4 7AL, UK
Ronald D. Henderson
Affiliation:
Aeronautics and Applied Mathematics, California Institute of Technology, Pasadena, CA 91125, USA

Abstract

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.

Type
Research Article
Copyright
© 1996 Cambridge University Press

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