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Nonlinear dynamics and pattern formation in turbulent wake transition

Henderson, Ronald D. (1997) Nonlinear dynamics and pattern formation in turbulent wake transition. Journal of Fluid Mechanics, 352 . pp. 65-112. ISSN 0022-1120.

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Results are reported on direct numerical simulations of transition from two-dimensional to three-dimensional states due to secondary instability in the wake of a circular cylinder. These calculations quantify the nonlinear response of the system to three-dimensional perturbations near threshold for the two separate linear instabilities of the wake: mode A and mode B. The objectives are to classify the nonlinear form of the bifurcation to mode A and mode B and to identify the conditions under which the wake evolves to periodic, quasi-periodic, or chaotic states with respect to changes in spanwise dimension and Reynolds number. The onset of mode A is shown to occur through a subcritical bifurcation that causes a reduction in the primary oscillation frequency of the wake at saturation. In contrast, the onset of mode B occurs through a supercritical bifurcation with no frequency shift near threshold. Simulations of the three-dimensional wake for fixed Reynolds number and increasing spanwise dimension show that large systems evolve to a state of spatiotemporal chaos, and suggest that three-dimensionality in the wake leads to irregular states and fast transition to turbulence at Reynolds numbers just beyond the onset of the secondary instability. A key feature of these ‘turbulent’ states is the competition between self-excited, three-dimensional instability modes (global modes) in the mode A wavenumber band. These instability modes produce irregular spatiotemporal patterns and large-scale ‘spot-like’ disturbances in the wake during the breakdown of the regular mode A pattern. Simulations at higher Reynolds number show that long-wavelength interactions modulate fluctuating forces and cause variations in phase along the span of the cylinder that reduce the fluctuating amplitude of lift and drag. Results of both two-dimensional and three-dimensional simulations are presented for a range of Reynolds number from about 10 up to 1000.

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Additional Information:"Reprinted with the permission of Cambridge University Press." (Received October 1 1996); (Revised July 17 1997) This work would not have been possible without the assistance of Dwight Barkley at the University of Warwick -- his help is greatly appreciated! The author would also like to acknowledge several inspiring discussions with Michael Cross at Caltech, as well as questions and critical feedback from a number of other people: H. Blackburn, M. Gharib, A. Leonard, D. Hill, D. Meiron, A. Roshko, C. H. K. Williamson, S. Balachandar, H.-Q. Zhang, P. Monkewitz and the referees. Financial support was provided by the NSF through Grant No. CDA-9318145 and the ONR through Grant No. N000-94-1-0793. Computational resources were provided by the Center for Advanced Computing Research and the JPL High Performance Computing and Communications program at the California Institute of Technology.
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Deposited On:28 Jul 2006
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