Topological Defects in Vortex Streets Behind Tapered Circular Cylinders at Low Reynolds Numbers

Abstract

Exploratory hot-wire measurements show that vortex shedding behind uniformly tapered cylinders with taper ratios in the range 32:1–13:1 is two-frequency quasiperiodic or chaotic, depending on the value of the local spanwise Reynolds number. For quasiperiodic shedding the modulation frequency of the vortex shedding is found to be equal to the frequency difference between equally spaced multiple-shedding-frequency spectral peaks. The relative energies, but not the frequencies, of these discrete peaks evolve in a continuous fashion with spanwise location, implying a long range spanwise correlation over most of the cylinder. Spanwise interactions are thus much stronger than in the cellular shedding observed by Gaster for mildly tapered cylinders, for which adjacent cells had their own individually different, but cellwise-constant shedding frequencies. Comparison with flow visualization pictures showed that chaotic regimes may be associated with topological defects in the vortex pattern.