Fluid forcing, wake modes, and transitions for a cylinder undergoing controlled oscillations

Abstract In this study, we make extensive measurements of the fluid forces on a cylinder that is controlled to oscillate transverse to a free stream at Re = 4000 . These measurements are used to create very high resolution contour plots (considerably higher than in any previous study) of the magnitude of fluid forcing, and its phase relative to the cylinder motion (as well as other fluid forcing quantities) in the plane of normalized amplitude and wavelength. Previous contours of force have been assumed to be continuous in the amplitude–wavelength plane, despite the fact that jumps in the fluid forcing and vortex formation modes were known to occur in other studies, including free vibration. In this investigation, we find clear discontinuities in the force contours, and we are thus able to identify boundaries separating different fluid forcing regimes. These appear remarkably similar to boundaries separating different vortex shedding modes in the regime map of Williamson and Roshko [1988. Vortex formation in the wake of an oscillating cylinder. Journal of Fluids and Structures 2, 355–381]. Measurements of vorticity fields confirm the modes of vortex formation in each regime; we find the 2S, 2P, and P + S modes, as well as a regime where the vortex formation is not synchronized with the cylinder oscillation. A new characteristic, which is only observable with very high-resolution data, is the existence of a region where two vortex formation regimes overlap. In the overlap region, we identify a distinct mode of vortex formation where two pairs of vortices are shed per cycle of oscillation (similar to the 2P mode) but the secondary vortex is much weaker, which we have termed ‘ 2 P OVERLAP ’, or simply the ‘ 2 P O ’ mode. The wake can switch intermittently between the 2P and 2 P O modes, even as the cylinder is oscillating with constant amplitude and frequency. The highest amplitude yielding positive fluid excitation lies inside the overlap region, therefore a study of the vortex dynamics in this region is essential to understanding the behavior of a free vibration system at peak amplitude response.