Transition to the secondary vortex street in the wake of a circular cylinder

Instabilities and flow characteristics in the far wake of a circular cylinder are examined through direct numerical simulations. The transitions to the two-layered and secondary vortex streets are quantified by a new method based on the time-averaged transverse velocity field. Two processes for the transition to the secondary vortex street are observed: (i) the merging of two same-sign vortices over a range of low Reynolds numbers ($Re$) between 200 and 300, and (ii) the pairing of two opposite-sign vortices, followed by the merging of the paired vortices into subsequent vortices, over a range of $Re$ between 400 and 1000. Single vortices may be generated between the merging cycles due to mismatch of the vortices. The irregular merging process results in flow irregularity and an additional frequency signal $f_{2}$ (in addition to the primary vortex shedding frequency $f_{1}$) in the two-layered and secondary vortex streets. In particular, a gradual energy transfer from $f_{1}$ to $f_{2}$ with distance downstream is observed in the two-layered vortex street prior to the merging. The frequency spectra of $f_{2}$ are broad-band for $Re=200$–300 but become increasingly sharp-peaked with increasing $Re$ because the vortex merging process becomes increasingly regular. The ratio of the sharp-peaked frequencies $f_{2}$ and $f_{1}$ is equal to the ratio of the numbers of vortices observed after and before the merging. The general conclusions drawn from a circular cylinder are expected to be applicable to other bluff bodies.