Vortex decay in the Kármán eddy street

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In this paper, we analyze the effect of viscosity on the vorticity distribution and its rate of decay in the Kármán vortex street behind a circular cylinder. We used direct numerical simulation data, which we compare to well-known experimental measurements. By decomposing the incompressible velocity field in a frame of reference attached to the cylinder into its solenoidal and harmonic components, we identify the eddy structures associated with the formation, shedding, and rearrangement of the vortices into the Kármán street, and study their subsequent decay. This allows us to extend the conclusions of the partially viscous model by Hooker ["On the action of viscosity in increasing the spacing ratio of a vortex street," Proc. R. Soc. London, Ser. A154, 67 (1936)], who made several simplifying hypotheses: initial infinite-length filament-vortex wake, circular Lamb vortices of equal age at subsequent times, and no overlapping of the vortex cores. We show that the vortices have elliptical cores with an elliptical ratio that evolves downstream according to a systematic law. We also find that the vortex cores exhibit a Gaussian vorticity profile and a vorticity versus stream-function scatter plot clearly consistent with the Lamb-vortex model. The peak vorticity in the core decays downstream with a hyperbolic decay rate determined by the amount of circulation contained in the core at the early stages of the street, which is also consistent with Lamb's solution. © 2010 American Institute of Physics.

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Physics of Fluids