The flow behind rings: bluff body wakes without end effects

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Abstract
Recent studies have demonstrated the strong influence of end effects on low-Reynoldsnumber bluff body wakes, and a number of questions remain concerning the intrinsic nature of three-dimensional phenomena in two-dimensional configurations. Some of them are answered by the present study which investigates the wake of bluff rings (i.e. bodies without ends) both experimentally and by application of the phenomenological Ginzburg–Landau model. The model turns out to be very accurate in describing qualitative and quantitative observations in a large Reynolds number interval. The experimental study of the periodic vortex shedding regime shows the existence of discrete shedding modes, in which the wake takes the form of parallel vortex rings or ‘oblique’ helical vortices, depending on initial conditions. The Strouhal number is found to decrease with growing body curvature, and a global expression for the Strouhal–Reynolds number relation, including curvature and shedding angle, is proposed, which is consistent with previous straight cylinder results. A secondary instability of the helical modes at low Reynolds numbers is discovered, and a detailed comparison with the Ginzburg–Landau model identifies it as the Eckhaus modulational instability of the spanwise structure of the near-wake formation region. It is independent of curvature and its clear observation in straight cylinder wakes is inhibited by end effects.The dynamical model is extended to higher Reynolds numbers by introducing variable parameters. In this way the instability of periodic vortex shedding which marks the beginning of the transition range is characterized as the Benjamin–Feir instability of the coupled oscillation of the near wake. It is independent of the shear layer transition to turbulence, which is known to occur at higher Reynolds numbers. The unusual shape of the Strouhal curve in this flow regime, including the discontinuity at the transition point, is qualitatively reproduced by the Ginzburg–Landau model. End effects in finite cylinder wakes are found to cause important changes in the transition behaviour also: they create a second Strouhal discontinuity, which is not observed in the present ring wake experiments.