Initially generated pure mode A in the three-dimensional wake transition of a circular cylinder

The initially generated pure mode A, as a transitional stage, is investigated in the three-dimensional wake transition of a circular cylinder. Direct numerical simulations are carried out over a range of Reynolds numbers from 100 to 210. According to the different dynamic behaviors of hydrodynamic parameters and similar features in the spatiotemporal evolution of vorticity in the near wake, two stages are identified. The first, investigated here, is the initial generation of pure mode A at Reynolds numbers less than 195, while the second, already reported, is the full development of pure mode A at Reynolds numbers greater than 195. The relationship between the volume-RMS (root-mean-square) vorticity and Reynolds number indicates two critical Reynolds numbers, 145 and 195 (at most). The first critical Reynolds number denotes the initial appearance of three-dimensional instability. The second critical Reynolds number indicates the transition of pure mode A from the initially generated state to the fully developed state in the near wake. After the first critical Reynolds number, the evolution of the vorticity in the near wake and on the rear surface of the cylinder clearly shows that the appearance of pure mode A is a gradual process, rather than a sudden process accompanied by a jump in vortex shedding frequency. In particular, as the Reynolds number increases, the streamwise vorticity first appears on and near the cylinder surface, then in the shear layers, and finally in the shedding primary vortices, instead of appearing instantaneously in the shedding vortices after the instability of primary vortex cores.