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Bifurcations in the wake of a thick circular disk. (English) Zbl 1191.76045
Summary: Using DNS, we investigate the dynamics in the wake of a circular disk of aspect ratio \(\chi = d/w = 3\) (where \(d\) is the diameter and \(w\) the thickness) embedded in a uniform flow of magnitude \(U _{0}\) perpendicular to its symmetry axis. As the Reynolds number \(Re = U _{0} d/\nu \) is increased, the flow is shown to experience an original series of bifurcations leading to chaos. The range \(Re {\in} [150, 218]\) is analysed in detail. In this range, five different non-axisymmetric regimes are successively encountered, including states similar to those previously identified in the flow past a sphere or an infinitely thin disk, as well as a new regime characterised by the presence of two distinct frequencies. A theoretical model based on the theory of mode interaction with symmetries, previously introduced to explain the bifurcations in the flow past a sphere or an infinitely thin disk [D. Fabre et al., Phys. Fluids 20, No. 5, Paper No. 051702, 4 p. (2008; Zbl 1182.76238)], is shown to explain correctly all these results. Higher values of the Reynolds number, up to 270, are also considered. Results indicate that the flow encounters at least four additional bifurcations before reaching a chaotic state.

MSC:
76D25 Wakes and jets
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