Based on a domain decomposition hybrid numerical method and high resolution spectral analyses for velocity components at 12 various field points new results on the transition features behind a circular cylinder at Re=3000, 5000, and 9500 are presented. The frequency· Reynolds number dependence of the transition wave is predicted and behaves like ƒt/ƒs ∼ Re0.87. Which agrees well with experimental results of Wei & Smith, but differs from Braza's prediction and the experimental results of Bloor and Kourta et al. Nonlinear interaction of two kinds of vortices leading to the generation of new predominant frequencies of the type (m1/n1) ƒs ±(m2/n2) ƒt is shown clearly. Longitudinal variation of the transition wave and the coupling behind the cylinder is given. The present results provide detailed mechanism on the transition of near wake flow before the three-dimensional evolution occurs.
It has been established that in the near wake of a circular cylinder with the Reynolds number (Re) 2000–16000 the transition wave phenomena occur and become significant for Re greater than 2000. All previous experimental results suggested that the transition process is mainly governed by the interaction between the Strohual vortices in the wake and the small eddies in mixing layer and characterized by spectral broadening. The two instabilities corresponding to the vortex shedding and the transition wave are reputed to be initially two· dimensional and then be· come three-dimensional. Details on the matter have been pro· vided and shown in experimental studies of Bloor (1964), Wei & Smith (1986), Kourta et al. (1988), among others. However, the basic features concerning the Reynolds number dependence of the nondimensional transition wave frequency obtained by previous experiments were not coincided each other, particularly, Bloor provided a 0.5 power law Reynolds number dependence i.e. ƒt/ƒs ∼ Re0.5, which was also suggested by Kourta et al. later.