Williamson, C. H. K. (1989) Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers. Journal of Fluid Mechanics, 206 . pp. 579-627. ISSN 0022-1120. http://resolver.caltech.edu/CaltechAUTHORS:20120531-090309675
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Two fundamental characteristics of the low-Reynolds-number cylinder wake, which have involved considerable debate, are first the existence of discontinuities in the Strouhal-Reynolds number relationship, and secondly the phenomenon of oblique vortex shedding. The present paper shows that both of these characteristics of the wake are directly related to each other, and that both are influenced by the boundary conditions at the ends of the cylinder, even for spans of hundreds of diameters in length. It is found that a Strouhal discontinuity exists, which is not due to any of the previously proposed mechanisms, but instead is caused by a transition from one oblique shedding mode to another oblique mode. This transition is explained by a change from one mode where the central flow over the span matches the end boundary conditions to one where the central flow is unable to match the end conditions. In the latter case, quasi-periodic spectra of the velocity fluctuations appear; these are due to the presence of spanwise cells of different frequency. During periods when vortices in neighbouring cells move out of phase with each other, ‘vortex dislocations’ are observed, and are associated with rather complex vortex linking between the cells. However, by manipulating the end boundary conditions, parallel shedding can be induced, which then results in a completely continuous Strouhal curve. It is also universal in the sense that the oblique-shedding Strouhal data (S_θ) can be collapsed onto the parallel-shedding Strouhal curve (S_0) by the transformation, S_0 = S_θ/cosθ, where θ is the angle of oblique shedding. Close agreement between measurements in two distinctly different facilities confirms the continuous and universal nature of this Strouhal curve. It is believed that the case of parallel shedding represents truly two-dimensional shedding, and a comparison of Strouhal frequency data is made with several two-dimensional numerical simulations, yielding a large disparity which is not clearly understood. The oblique and parallel modes of vortex shedding are both intrinsic to the flow over a cylinder, and are simply solutions to different problems, because the boundary conditions are different in each case.
|Additional Information:||© 1989 Cambridge University Press. Received September 30 1988. Revised February 19 1989. Published Online April 26 2006. The author is particularly grateful to Anatol Roshko for valuable discussions, and to Garry L. Brown (Director of the Aeronautical Research Laboratories, Melbourne, Australia) for his suggestions and great enthusiasm during many of the wind tunnel experiments. Special thanks are due to Holger Eisenlohr (University of Göttingen) for our conversations regarding oblique shedding. The author is also grateful for discussions/help received from Paul Taylor (of Shell Research Ltd., Thornton, England), S. Schneider, M. Holcomb, I. Sugioka, D. Lisoski, J. Jacobs, and for the technical construction work of R. Paniagua. Lastly, the author is grateful to F. Raichlen for the use of a small towing tank (in 1985) which resulted in the visualization of figure 23. This work was supported by the Office of Naval Research Contract No. N00014-84-K-0618.|
|Official Citation:||Oblique and parallel modes of vortex shedding in the wake of a circular cylinder at low Reynolds numbers C. H. K. Williamson Journal of Fluid Mechanics, Volume 206, September 1989, pp 579 - 627 DOI: http://dx.doi.org/10.1017/S0022112089002429|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Ruth Sustaita|
|Deposited On:||31 May 2012 16:27|
|Last Modified:||26 Dec 2012 15:17|
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