Horizontal Oscillations of a Cylinder beneath a Free-Surface

Horizontal oscillations of a cylinder beneath a free-surface. Horizontal oscillations of a cylinder simulate long-wave motion past a stationary cylinder. When a cylinder is well-submerged beneath the free-surface, corresponding to h/R = 10, represented by the top row of images, a vorticity layer of positive vorticity is shed from the upper surface. It exhibits a train of smaller-scale concentrations, which form a counterrotating system of vorticity with the negative concentration of vorticity shed from the previous cycle. Simultaneously, a pronounced layer of negative vorticity forms along the lower left surface of the cylinder. The corresponding velocity field suggests a large-scale counterrotating pair. When the cylinder is moved closer to the free-surface, corresponding to h/R = 1.9, the mode of vortex formation changes completely. An alternating vortex system tends to form from the cylinder; it is accompanied by a jet-like flow initially directed upward towards the free-surface, then deflected to the left at the surface. Finally, when the cylinder is very close to the free-surface at h/R = 1.2, the gap between the cylinder and the free-surface has zero width due to a local depression of the free-surface. A large-scale concentration of positive vorticity, shed during the previous cycle, moves clockwise along the lower surface of the cylinder. In the corresponding velocity plot, it is evident that a jet-like flow around the lower surface of the cylinder is associated with the large-scale concentration of vorticity. All of the foregoing classes of vortex formation contribute to pronounced, but distinctly different, spikes of the transverse force signature. h = distance from upper surface of cylinder to free-surface; R = cylinder radius; Keulegan-Carpenter number KC = 2 πA/D = 10.