Deep Water Wave Interaction with a Bi-Directionally Oscillating Cylinder

Deep Water Wave Interaction with a Bi-Directionally Oscillating Cylinder. Deep water wave interaction with a vertical, elastically-mounted cylinder results in the patterns of quasi-two-dimensional flow structure shown in the image layout. The cylinder is suspended on a mini-jet-air-bearing and has a very low mass-damping ratio. The stiffness of the cylinder system is non-preferential in the circumferential direction, thereby allowing examination of bidirectional (two-dimensional) oscillations. The indicated images were acquired in a horizontal plane immediately beneath the free-surface of the wave, at a value of the Keulegan-Carpenter number KC = 0.53.

       
The first and second rows of images correspond to two different phases of the wave cycle, designated as   N = 7 and N = 9. The steady-state trajectory of the cylinder oscillation is an inclined elliptical pattern, as indicated in the schematic.  The instantaneous position of the cylinder is designated by the bold dot.  Patterns of positive (red) and negative (yellow) vorticity are indicated.  Considering, first of all, the layers of distributed vorticity A and B at N = 7, they rotate in a clockwise direction about the cylinder and take the form indicated in image N = 9.  Also shown are patterns of instantaneous streamline topology, along with instantaneous values of the vectors Vc representing the cylinder velocity, Uw indicating the wave velocity, and VR corresponding to the wave velocity relative to the cylinder.  At N = 7, a saddlepoint (apparent intersection of streamlines) exists at the upper right corner of the images and, furthermore, lines of separation and reattachment occur on the right side of the cylinder, in accord with the negative concentration of vorticity B.  At the later instant, N = 9, the aforementioned saddlepoint has rotated down and to the right and, furthermore, the patterns of separating and reattaching streamlines have moved in a clockwise direction about the cylinder.

As a complement to these patterns of vorticity and streamline topology, patterns of instantaneous streamwise velocity component u* and transverse velocity component v* are also provided. In these images, the color green denotes a positive, and blue indicates a negative component of velocity.