Interaction of a deep-water wave with a vertical cylinder: effect of self-excited vibrations on quantitative flow patterns

Abstract

Interaction of a deep-water wave with a cylinder gives rise to ordered patterns of the flow structure, which are quantitatively characterized using a technique of high-image-density particle image velocimetry. When the cylinder is stationary, the patterns of instantaneous flow structure take on increasingly complex forms for increasing Keulegan--Carpenter number KC. These patterns involve stacking of small-scale vorticity concentrations, as well as large-scale vortex shedding. The time-averaged consequence of these patterns involves, at sufficiently high KC, an array of vorticity concentrations about the cylinder.When the lightly damped cylinder is allowed to undergo bidirectional oscillations, the trajectories can be classified according to ranges of KC. At low values of KC, the trajectory is elliptical, and further increases of KC allow, first of all, both elliptical and in-line trajectories as possibilities, followed by predominantly in-line and figure-of-eight oscillations at the largest value of KC.Representations of the quantitative flow structure, in relation to the instantaneous cylinder position on its oscillation trajectory, show basic classes of patterns. When the trajectory is elliptical, layers of vorticity rotate about the cylinder surface, in accordance with rotation of the relative velocity vector of the wave motion with respect to the oscillating cylinder. Simultaneously, the patterns of streamline topology take the form of large-scale bubbles, which also rotate about the cylinder. When the cylinder trajectory is predominantly in-line with the wave motion, generic classes of vortex formation and shedding can be identified; they include sweeping of previously shed vorticity concentrations past the cylinder to the opposite side. Certain of these patterns are directly analogous to those from the stationary cylinder.