Secondary vortex street in the wake of a rectangular cylinder: Effects of Reynolds number, aspect ratio and free-stream perturbation

The transition from the primary (Kármán) and two-layered vortex streets to a secondary vortex street in the relatively far wake of a rectangular cylinder is examined through direct numerical simulations. The parameter space spans a range of the cross-sectional aspect ratios (AR; the ratio between the streamwise and transverse lengths) of the cylinder between 0.01 and 0.5, and a range of the Reynolds numbers (Re) between 50 and 200. Unlike some previous studies which attributed the formation of the secondary vortices to either hydrodynamic instability of the mean flow or vortex merging, the present study shows that both mechanisms exist. Over the (AR, Re) parameter space, the two formation mechanisms are mapped out. For relatively small Re and relatively large AR, the secondary vortices emerge at the streamwise locations downstream of the annihilation of the two-layered vortices, such that the secondary vortices cannot be formed from the merging of the two-layered vortices and are thus formed from the hydrodynamic instability of the two bare shear layers. In contrast, for relatively large Re and relatively small AR, the secondary vortices emerge at the streamwise locations where the two-layered vortices still exist, such that the secondary vortices are formed from the merging of the two-layered vortices. In addition, the influence of free-stream perturbation on the formation mechanism is examined. An increase in the perturbation amplitude may result in a decreased critical Re for the change in the formation mechanism. The general conclusions are expected to be applicable to other bluff-body flows.