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Transition phenomena in the wake of a square cylinder

Journal of Fluids and Structures
Publication Date
DOI: 10.1016/j.jfluidstructs.2006.08.012


Abstract The transition phenomena in the wake of a square cylinder were investigated. The existence of mode A and mode B instabilities in the wake of a square cylinder was demonstrated. The critical Reynolds numbers for the inception of these instability modes were identified through the determination of discontinuities in the St–Re curves, and were found to have mean values of 160 and 204 for the onset of mode A and B instabilities, respectively. The spectra and time traces of the wake streamwise velocity component were found to display three distinct patterns in laminar, mode A and mode B flow regimes. Streamwise vortices with different wavelength at various Reynolds numbers were observed through different measures. The symmetries and evolution of the secondary vortices were observed using laser-induced-fluorescent dye. It was found that, just like the case of a circular cylinder, the secondary vortices from the top and bottom rows were out-of-phase with each other in the mode A regime, but in-phase with each other in the mode B regime. From the flow visualization, it was qualitatively proven that there is stronger interaction between braid regions in the mode B regime. At the same time, analysis of PIV measurements quantitatively demonstrated the presence of the stronger cross flow in mode B regime when compared to the mode A regime. It suggests that the in-phase symmetry of the mode B instability is the result of strong interaction between the top and bottom vortex rows. It was also observed that although the vorticity of the secondary vortices in the mode A regime was smaller, its circulation was more than twice that of mode B instability. Compared to primary vortices, the circulations of both mode A and mode B vortices were much smaller, which indicates that the secondary vortices most likely originate from the primary vortices. The wavelengths of the streamwise vortices in the mode A and B regimes were measured using the auto-correlation method, and were found to be 5.1 (±0.1) D, 1.3 (±0.1) D, and 1.1 (±0.1) D at Re=183 (mode A), 228 and 377 (both mode B), respectively. From the present investigation, mode A instability was likely to be due to the joint-effects of the deformation of primary vortex cores and the stretching of vortex sheets in the braid region. On the other hand, mode B instability was thought to originate from the “imprinting” process.

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