Computational analysis of physical mechanisms at the onset of three-dimensionality in the wake of a square cylinder

Abstract

A high-order spectral element method is used to perform direct numerical simulations of flow past a square cylinder at the transition from the two-dimensional von Kármán vortex street in the wake of the cylinder to three-dimensionality. A Reynolds number range between 100 and 300 has been considered and good agreement with previous numerical and experimental results is obtained. At transition, the spanwise perturbation observed in the cylinder wake occurs before the onset of the streamwise vortex separation, while the former mechanism is commonly shown, in the literature, to originate from the latter by an instability of the cores or interactions of shed vortices in the vicinity of the cylinder. It is shown that the first three-dimensional unstable mode, the mode $A$, originates from an axial stretching of the upstream perturbed vorticity, existing on the braids, due to the strain field created by the spanwise vortices which evolve under a shear instability of the wake when viscous effects are small. On the other hand, the mode $B$ is observed to arise only after spanwise vortices are shed downstream of the cylinder.