Formation mechanism of a secondary vortex street in a cylinder wake

Abstract

This study identifies and explains the formation mechanisms (FMs) of the secondary vortex street in the far wake of a circular cylinder. Direct numerical simulation and transient growth analysis are performed for a Reynolds number (Re) in the range of 100–200. Unlike most of the earlier studies, which have attributed the formation of the secondary vortices to either the hydrodynamic instability of the mean flow (FM1) or a merging of the two-layered vortices (FM2), the present study demonstrates that both FM1 and FM2 are at play. Specifically, FM1 is observed for Re = 150–160, whereas FM2 is observed for Re = 200. Interestingly, both FM1 and FM2 exist (in an alternate manner) for Re = 170 and 180. The underlying physical mechanism controlling the manifestation of either FM1 or FM2 is explored. In short, secondary vortices that emerge after and before the annihilation of the two-layered vortices are formed from FM1 and FM2, respectively. The variation in the streamwise locations for the emergence of the secondary vortices with Re is quantified and physically explained. Fundamentally, the emergence of the secondary vortices through either FM1 or FM2 is induced by the convective instability of the shear layers in the intermediate wake, which is further induced by an obvious increase in the shear rate of the shear layers as the wake gradually transitions from a primary vortex street to a two-layered vortex street. The general conclusions drawn from a circular cylinder are expected to be applicable to other bluff bodies.