Journal of Fluid Mechanics


The evolution of a subharmonic mode in a vortex street

G. J. SHEARD a1c1, M. C. THOMPSON a1, K. HOURIGAN a1 and T. LEWEKE a2
a1 Fluids Laboratory for Aeronautical and Industrial Research (FLAIR), Department of Mechanical Engineering, Monash University, Melbourne, Victoria 3800, Australia
a2 Institut de Recherche sur les Phénomènes Hors Équilibre (IRPHÉ), UMR 6594 CNRS/Universités Aix-Marseille I & II, 12 avenue Général Leclerc, F-13003 Marseille, France

Article author query
sheard gj   [Google Scholar] 
thompson mc   [Google Scholar] 
hourigan k   [Google Scholar] 
leweke t   [Google Scholar] 


The development of a subharmonic three-dimensional instability mode in a vortex street is investigated both numerically and experimentally. The flow past a ring is considered as a test case, as a previous stability analysis has predicted that for a range of aspect ratios, the first-occurring instability of the vortex street is subharmonic. For the flow past a circular cylinder, the development of three-dimensional flow in the vortex street is known to lead to turbulent flow through the development of spatio-temporal chaos, whereas subharmonic instabilities have been shown to cause a route to chaos through the development of a period-doubling cascade. The three-dimensional vortex street in the flow past a ring is analysed to determine if a subharmonic instability can alter the route to turbulence for a vortex street.

A linear stability analysis and non-axisymmetric computations are employed to compute the flow past a ring with an aspect ratio ${\sc ar}\,{=}\,5$, and comparisons with experimental dye visualizations are included to verify the existence of a subharmonic mode in the wake. Computations at higher Reynolds numbers confirm that the subharmonic instability does not initiate a period-doubling cascade in the wake.

(Received February 11 2004)
(Revised November 9 2004)

c1 Author to whom correspondence should be addressed: