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

Abstract eng:
We analyse the topology of the vorticity field downstream of a circular cylinder to show that the Karman vortex street develops at a large but finite distance downstream of the cylinder, and only when the Reynolds number is increased beyond a value ReK which is slightly larger than the value Remit at which the steady base flow becomes unstable to time-dependent perturbations. In the region of validity of our analysis, that is, small values of e N (Re i Benny/2, only a finite number of vortices exist. Moving downstream after their creation in a topological cusp bifurcation, the vortices later disappear in a similar but reversed event. However, the number of vortices and the length of the domain where they exist grow rapidly with e.

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