Topological fluid mechanics of the formation of the Kármán-vortex street

Matthias Heil, Jordan Rosso, Andrew L. Hazel, Morten Brøns

    Research output: Contribution to journalArticlepeer-review

    Abstract

    We explore the two-dimensional flow around a circular cylinder with the aim of elucidating the changes in the topology of the vorticity field that lead to the formation of the Kármán vortex street. Specifically, we analyse the formation and disappearance of extremal points of vorticity, which we consider to be feature points for vortices. The basic vortex creation mechanism is shown to be a topological cusp bifurcation in the vorticity field, where a saddle and an extremum of the vorticity are created simultaneously. We demonstrate that vortices are first created approximately 100 diameters downstream of the cylinder, at a Reynolds number, ReK, which is slightly larger than the critical Reynolds number, Recrit∼46, at which the flow becomes time periodic. For Re slightly above ReK, the newly created vortices disappear again a short distance further downstream. As is further increased, the points of creation and disappearance move rapidly upstream and downstream, respectively, and the Kármán vortex street persists over increasingly large streamwise distances.

    Original languageEnglish
    Pages (from-to)199-221
    Number of pages23
    JournalJournal of Fluid Mechanics
    Volume812
    Early online date22 Dec 2016
    DOIs
    Publication statusPublished - 10 Feb 2017

    Keywords

    • topological fluid dynamics
    • vortex shedding
    • vortex streets

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