Evolution of vorticity regions of Kármán-vortex-street type

Abstract

The evolution of uniform or non-uniform circular vorticity regions (of radius R) of Kármán-vortex-street type (with a distance h between the two rows, and a spacing d of the regions of the same sign) is examined numerically and analytically. The domain in the (, ) plane for which the vorticity regions merge to nearly parallel vorticity layers and the domain for which they continue to be localized are obtained using the discrete vortex method. Here = h/R and = d/R. Most of this localized behavior is qualitatively explained by the theory in which each neighboring vorticity region is replaced by a point vortex. Moreover, the increase in / from a small value due to an external transverse flow causes the transition to the nearly parallel vorticity layers if initial value is small. It is suggested that h/d just before the breakdown of the Kármán vortex street in experiments is larger than 0.365.