Europhys. Lett.
Volume 75, Number 5, September 2006
Page(s) 750 - 756
Section Electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics
Published online 26 July 2006
Europhys. Lett., 75 (5), pp. 750-756 (2006)
DOI: 10.1209/epl/i2006-10168-7

Linear analysis of the cylinder wake mean flow

D. Barkley

Mathematics Institute, University of Warwick - Coventry, CV4 7AL, UK

received 27 March 2006; accepted in final form 7 July 2006
published online 26 July 2006

A highly accurate 2D linear stability analysis is performed on the mean flow of laminar vortex shedding from a circular cylinder for Reynolds numbers between 46 and 180. Consistent with past studies of mean profiles, the analysis shows that the eigenfrequency of the mean flow tracks almost exactly the Strouhal number of vortex shedding. The linear growth rate reveals that the wake mean flow is a marginally stable state over the whole range of Reynolds numbers for stable 2D vortex shedding. This is contrasted with 2D stability analysis about the unstable steady base flow. The relevance to nonlinear saturation and frequency selection are discussed.

47.20.Ft - Instability of shear flows (e.g., Kelvin-Helmholtz).
47.20.Ky - Nonlinearity, bifurcation, and symmetry breaking.

© EDP Sciences 2006