In the event that orbital, as opposed to unidirectional, flow interacts with the cylinder, or equivalently, orbital versus unidirectional motion of the cylinder occurs in quiescent fluid, the processes of vortex formation and the associated loading are expected to be altered accordingly. Due to the orbital particle trajectories inherent to a wave, the velocity vectors of the water particles rotate, in contrast to the horizontally-directed velocities of a unidirectional, oscillatory flow. This distinction was emphasized by Ramberg & Niedzwecki (1979), who addressed the differences of the inertia Cm and drag Cd coefficients of Morison’s equation for planar oscillatory flow versus orbital flow.
Chaplin (1981a) calculated the limiting case of irrotational flow around a horizontal cylinder under long-crested waves, using Milne-Thompson's circle theorem. The presence of the cylinder was found to significantly distort the wave flow. Fully accounting for viscous effects, Borthwick (1986) performed a finite-difference solution of the Navier-Stokes equations for the case of flow due to orbital motion of a cylinder. Further numerical studies involving orbital wave motion past a circular cylinder were performed by Miyata & Lee (1990) and Chaplin (1992, 1993). These studies show the substantial influence of viscous effects and, at sufficiently high values of Kc, the possibility of vortex formation, which significantly influences the flow patterns and the corresponding forces on cylinders in wave-induced flows.
Corresponding experimental investigations have focused primarily on measurement of the loading on a cylinder. The forces on bodies in orbital motion were measured by Holmes & Chaplin (1978), Chaplin (1981b), Sarpkaya (1984), Grass et. al. (1985), Borthwick (1987), and Chaplin (1988). Williamson et. al. (1998) characterized the fluid loading and vortex dynamics for a cylinder moving in elliptic orbits. It was found that as the ellipticity of the orbit increases, there is a significant reduction in the drag force. Moreover, for circular orbits, the mean radial force is directed inwards relative to the orbit, due to the background circulation set up by repeated orbital cycles for the case of orbital wave motion past a stationary cylinder. For the case of wave motion past a stationary cylinder, Chaplin (1984) determined the forces on the cylinder for relatively low Kc < 3. For Kc < 2, the inertial force provides the dominant contribution to the loading. For Kc > 2, nonlinear contributions to the loading were found to be substantial. Forces on horizontal cylinders under periodic and random waves, at Keulegan-Carpenter numbers up to 20, were measured by Bearman et al. (1985b). The force coefficients were found to be similar for regular and random waves. In random waves, the vortex shedding is triggered when Kc exceeds a value of 7.