This paper deals with wave forces on a single cylinder. The wave forces are simulated in a laboratory by oscillating a cylinder sinusoidally in water otherwise at rest. This effort is a parametric study relating a force coefficient to such variables as instantaneous Reynolds number, period parameter, and d//VT. The force is not decomposed into drag and inertia components, but is represented as a continuous function of the previously mentioned parameters. The idea is to determine how the acceleration affects the force. Considerable deviation from a Reynolds-number only dependence is noted for low Reynolds numbers. The steady-flow drag coefficient value is asymptotically obtained for large Reynolds numbers.
This paper reports the results of an experimental study with an oscillating cylinder immersed vertically in a water tank. The resistance of the fluid to the motion of the cylinder is recorded and the force coefficient reported as a function of appropriate nondimensional parameters. This study pertains to the problem of wave forces on an offshore platform. This study is made in an attempt to obtain an understanding of an engineering problem in which a parametric study is beneficial and could not be obtained in a field study.
Designers of offshore platforms typically use what is known as the Morison force equation to calculate the wave forces on surface-piercing platform legs and on submerged portions of the structure. The Morison equation [1] considers the force to be the linear sum of an inertia force (proportional to acceleration) and a drag force (proportional to velocity squared). The drag is defined in terms of the standard drag-coefficient relationship. The inertia force is described in terms of the inertial coefficient which is related to the hydrodynamica1 added-mass coefficient. The Morison wave-force equation is
The problems of an oscillating cylinder in a fluid otherwise at rest and an oscillating fluid past a stationary cylinder are kinematically the same [3] when viewed from appropriate reference frames. The kinematics are of sufficient interest to be reviewed at this point. As the cylinder moves from, say, left to right, symmetric vortices will form behind the cylinder if the amplitude to diameter ratio is greater than about 0.5. If the amplitude-to-diameter ratio is greater than about 3 [4], the vortices will develop a nonsymmetric behavior. For amplitude to diameter ratios greater than about 6, the wake vortices begin to be shed in an alternating, periodic fashion similar to the steady-flow shedding of-(Karman) vortices. Continuing the analogy to steady flow, it may be said that a boundary layer has developed on the cylinder by the time the initial wake vortices are being shed.
As the cylinder begins to move back to the left, the original wake vortices are then in the upstream flow of the cylinder. The upstream pressure is affected by the presence of the original wake vortices. If the original vortices were not symmetrically spaced, their effect on the upstream pressure would be to cause a force transverse to the direction of motion.
