A comparison between the near wake behind a cantilevered square cylinder and a periodic array of staggered vortex ring pairs*

A comparative analysis is presented between the evolution of half-loop shedding patterns, identified in the wake of a cantilevered square cylinder, and that of a periodic street of staggered, titled vortex ring pairs. The near-wake of the cylinder with a height-to-width ratio h/d = 4, protruding a thin laminar boundary layer of thickness δ/d = 0.21, is investigated experimentally using time-resolved stereoscopic particle image velocimetry at a Reynolds number (Re) of 10600, based on the obstacle diameter. This wake region is characterized with half-loop shedding patterns, which connect successive Kármán vortices. As a simplified model of the half-loop patterns, the evolution of a periodic street of staggered, opposite-signed vortex ring pairs is simulated at a circulation-based Re of 5000. Expressed in terms of the ring radius R, the vortex rings are initialized with streamwise and spanwise distances of R and 0.4R, respectively. Further, the rings on either side of the symmetry plane are tilted with equal but opposite angles of π/6 radians. We discuss the qualitative similarity between the evolution of the model flow and the experimental measurements in terms of the global vorticity field. More importantly, we point out key differences between experiments and model due to the effect of the incoming boundary layer over the ground plate.