Transition waves and nonlinear interactions in the near wake of a circular cylinder

Transition waves and interactions between two kinds of instability—vortex shedding and transition wave in the near wake of a circular cylinder in the Reynolds number range 3 000–10 000 are studied by a domain decomposition hybrid numerical method. Based on high resolution power spectral analyses for velocity new results on the Reynolds-number dependence of the transition wave frequency, i.e.f _t /f_s∼Re^0.87 are obtained. The new predictions are in good agreement with the experimental results of Wei and Smith but different from Braza s prediction and some early experimental resultsf _t/f_s∼Re ^0.5 given by Blooret al. The multi-interactions between two kinds of vortex are clearly visualized numerically. The strong nonlinear interactions between the two independent frequencies (f _t,f _s ) leading to spectra broadening to form the couplingmf _s +nf _t are predicted and analyzed numerically, and the characteristics of the transition are described. Longitudinal variations of the transition wave and its coupling are reported. Detailed mechanism of the flow transition in the near wake before occurrence of the thedimensional evolution is provided. Project supported by the National Natural Science Foundation of China, the LNM of Institute of Mechanics, and partially by the National Basic Research Project.