Experimental Investigation of Vortex-Induced Vibrations of a Flexibly Mounted Circular Cylinder in Combined Current and Wave Flows

This paper presents the experimental investigation of vortex-induced vibrations (VIV) of a flexibly mounted circular cylinder in combined current and wave flows. The same experimental setup has previously been used in our previous study (OMAE2020-18161) on VIV in regular waves. The system comprises a pendulum-type vertical cylinder mounted on two-dimensional springs with equal stiffness in in-line and cross-flow directions. The mass ratio of the system is close to 3, the aspect ratio of the tested cylinder based on its submerged length is close to 27, and the damping in still water is around 3.4%. Three current velocities are considered in this study, namely 0.21 m/s, 0.29 m/s and 0.37 m/s, in combination with the generated regular waves. The cylinder motion is recorded using targets and two Qualisys cameras, and the water elevation is measured utilizing a wave probe. The covered ranges of Keulegan-Carpenter number KC are [9.6–35.4], [12.8–40.9] and [16.3–47.8], and the corresponding ranges of reduced velocity Vr are [8–16.3], [10.6–18.4] and [14–20.5] for the cases with current velocity of 0.21 m/s, 0.29 m/s and 0.37 m/s, respectively. The cylinder response amplitudes, trajectories and vibration frequencies are extracted from the recorded motion signals. In all cases the cylinder oscillates primarily at the flow frequency in the in-line direction, and the in-line VIV component additionally appears for the intermediate (0.29 m/s) and high (0.37 m/s) current velocities. The cross-flow oscillation frequency is principally at two or three times the flow frequency in the low current case, similar to what is observed in pure regular waves. For higher current velocities, the cross-flow frequency tends to lock-in with the system natural frequency, as in the steady flow case. The inline and cross-flow cylinder response amplitudes of the combined current and regular wave flow cases are eventually compared with the amplitudes from the pure current and pure regular wave flow cases.

On the application of the Green‒Nagdi equations for the simulation of wave flows with undular bores

The basic conservation laws in the Green–Nagdi model of shallow-water theory are derived from the two-dimensional integral conservation laws of mass and the total momentum describing the plane-parallel flow in an ideal incompressible fluid above a horizontal bottom. This conclusion is based on the concept of a local hydrostatic approximation, which generalizes the concept of the long-wavelength approximation and is used for analyzing the applicability of the Green–Nagdi equations in modeling the wave flows with undular bores.