The interaction of waves with structures in the ocean environment is a major source of unsteady loading and vibration of a variety of structural components including long cables, components of offshore platforms, risers, as well as a number of other related geometrical configurations. In recent decades, substantial efforts have been devoted to enhancing our understanding of this class of flow-structure interaction. In the present investigation, the focus is on wave interaction with a horizontal cylinder. Previous related studies may be categorized according to: a circular cylinder in oscillatory flow; a cylinder in orbital flow/orbital motion; and a cylinder beneath a nominally stationary free-surface. Summaries of these efforts are provided in the following.
A variety of theoretical, numerical and experimental investigations have addressed the case of unidirectional, oscillatory flow past a circular cylinder. Sarpkaya & Isaacson (1981) summarize early studies, extending over a range of Keulegan-Carpenter number Kc, where Kc = UmT/D = 2*pi*A/D, in which Um is the maximum velocity of the flow, T is the period of the wave motion, D is the cylinder diameter, and A is amplitude. Recent investigations include those of Singh (1979), Honji (1981), Bearman et. al. (1981), Sarpkaya & Isaacson (1981), Ikeda & Yamamoto (1981), Iwagaki et al. (1983), Williamson (1985), Sarpkaya (1986), Obasaju et. al. (1988), and Tatsuno & Bearman (1990). These investigations provide insight into, among other features, the vortex patterns that can arise over various ranges of Kc.
From a theoretical perspective, description of the relationship between point vortices and loading on a cylinder was formulated by Sarpkaya (1963, 1968, 1969). Using this type of approach, Maull & Milliner (1978) qualitatively related the movement of visualized vortices about the cylinder to variations of the measured forces. Ikeda & Yamamoto (1981) approximated the variation of the lift force by tracking vortices and estimating their circulation using particle streak-marker visualization. Lin & Rockwell (1996) employed quantitative images of the patterns of distributed vorticity generated by an oscillating cylinder, and the lift force was approximated using the Maull-Milliner (1978) approach whereby each vortex was represented as an equivalent point vortex of given circulation. In addition, the vorticity moment approach of Lighthill (1986) was employed to account for the distributed nature of the instantaneous patterns of vorticity. Noca et. al. (1997) extended this technique to account for vorticity outside the field of view of the near-wake of the cylinder. Unal et. al. (1997) and Noca (1997) invoked yet another class of approaches for evaluating the forces. These methods, which are based on instantaneous patterns of velocity obtained by quantitative imaging, involve momentum-based approaches that employ a control volume about the cylinder.
Numerical approaches to this class of flows include a variety of techniques. Discrete vortex approaches have been employed and are reviewed by Sarpkaya (1989) and Lin et. al. (1996). Finite-difference solutions of the Navier-Stokes equations were used by Baba & Miyata (1987), Wang & Dalton (1991), Justesen (1991) and Miyata & Lee (1990). Solution of the Navier-Stokes equations has also been approached by Anagnostopoulos et. al. using a finite-element analysis and by Sun & Dalton (1996) via a method of large eddy simulation.
Insight into the decomposition of forces on cylinders in small-amplitude oscillatory flows is provided by Bearman et al. (1985a). The total force was considered to be composed of three parts: inertia of the accelerating flow; effects of viscous boundary layers, and shedding of vortices. Since this investigation focused on low values of Kc, the dominant part of the force is the inviscid inertia force. Onset of vortex shedding from a circular cylinder and a substantial contribution to the force occurs at a value of Kc of the order of 5.
The rich variety of vortex patterns that are generated at larger values of flow (or cylinder) oscillation amplitude, i.e., Kc = 2*pi*A/D, are summarized, for example, by Sarpkaya & Isaacson (1981), Williamson (1985) and Obasaju et. al. (1988). The interrelationship between vortex patterns and the induced forces on the cylinder were addressed by Obasaju et. al. (1988) for values of Kc up to 55. Over this range, the patterns of vortex formation were classified as asymmetric, transverse, diagonal and quasi-steady, which, in turn, have important consequences for the forces on the cylinder. Lin and Rockwell (1997) employed a technique of high-image-density particle image velocimetry to determine the instantaneous patterns of vorticity and velocity about the cylinder at a value of Kc = 10. The physics of vortex formation were shown to involve a complex series of events, described by vorticity and streamline topology. Moreover, in presence of a free-surface, the nature of vortex formation was found to be a strong function of the degree of submergence of the cylinder. These features were related to signatures of instantaneous lift.