THE FLOW BEHIND RINGS - BLUFF-BODY WAKES WITHOUT END EFFECTS

Recent studies have demonstrated the strong influence of end effects o n low-Reynolds-number bluff body wakes, and a number of questions rema in concerning the intrinsic nature of three-dimensional phenomena in t wo-dimensional configurations. Some of them are answered by the presen t study which investigates the wake of bluff rings (i.e. bodies withou t ends) both experimentally and by application of the phenomenological Ginzburg-Landau model. The model turns out to be very accurate in des cribing qualitative and quantitative observations in a large Reynolds number interval. The experimental study of the periodic vortex sheddin g regime shows the existence of discrete shedding modes, in which the wake takes the form of parallel vortex rings or 'oblique' helical vort ices, 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 a ngle, 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-La ndau model identifies it as the Eckhaus modulational instability of th e spanwise structure of the near-wake formation region. It is independ ent 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 t he 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 highe r Reynolds numbers. The unusual shape of the Strouhal curve in this fl ow regime, including the discontinuity at the transition point, is qua litatively reproduced by the Ginzburg-Landau model. End effects in fin ite cylinder wakes are found to cause important changes in the transit ion behaviour also. they create a second Strouhal discontinuity, which is not observed in the present ring wake experiments.