The in-line and transverse forces acting on smooth and sand-roughened circular cylinders placed on a plane boundary (with no gap) in a sinusoidally oscillating flow in a U-shaped vertical water tunnel have been measured. The drag and inertia coefficients for the in-line force have been determined through the use of the Morison's equation and the Fourier analysis. The transverse force has been analyzed in terms of its maximum and minimum values, root-mean-square values, and the time it remains above a fraction of its maximum. The results have been presented as a function of the Keulegan-Carpenter number and the frequency parameter (available in full paper).
The design of unburied pipelines laid on or near the ocean bottom requires an understanding of the external fluid forces acting on them and an appreciation of the complexities stemming from all other environmental conditions.
Numerous studies have been conducted both in laboratory and in the field on the determination of the forces acting on submerged pipelines. l -10 In spite of these past efforts, however, there still remains much to be learned about the fluid forces acting on smooth and rough cylinders resting on a plane boundary. Recently Yomamot, Nath, and Slotta7 and Wright and Yamamoto 10 investigated the wave forces on cylinders near a plane boundary for small values of the Reynolds number and the Keulegan-Carpenter number. It is a well known fact that for small values of the period parameter the flow about the cylinder does not quite separate, the wake-dependent drag force is very small or negligible, and the in-line as well as the transverse forces are essentially from the wave temporal accelerator. Under such circumstances, the appropriate coefficients may be evaluated from the potential theory. The results of such a study show that7 when the cylinder touches the boundary a net force exists away from the wall. However, if even a very small gap exists between the cylinder and the wall, then a large net force exists toward the wall. The inertial forces alone do not usually give rise to the maximum load situation for small structures, such as pipelines located on or near bottom, and the separation effects become extremely important not only in the determination of the magnitude but also the direction of the forces.
Sarpkaya8,9 determined the drag, inertia, and lift coefficients for circular cylinders placed near a plane boundary in oscillatory flow at high Reynolds numbers and Keulegan-Carpenter numbers for various relative gaps of e/D. He has shown that the drag and inertia coefficients for the in-line force acting on a cylinder in the vicinity of a plane wall are increased by the presence of the wall. This increase is most evident in the range of e/D values smaller than about 0.5. Both coefficients depend on the Reynolds number, Keulegan-Carpenter number, and the relative gap. The effect of the boundary layer or the penetration depth of the viscous wave is small provided that the boundary" layer remains laminar.