This paper presents the results of an extensive experimental investigation of the in-line and transverse forces acting on smooth and rough circular cylinders placed in oscillatory flow at Reynolds numbers up to 700,000, Keulegan-Carpenter numbers up to 150, and relative roughnesses from 0.002 to 0.02. The drag and inertia coefficients have been determined through the use of the Fourier analysis and the least squares method. The transverse force (lift) has been analyzed in terms of its maximum, semi peak-to-peak, and root-mean-square values. In addition, the frequency of vortex shedding and the Strouhal number have been determined.

The results have shown that (a) for smooth cylinders, all of the coefficients cited above are functions of the Reynolds and Keulegan and Carpenter numbers, particularly for Reynolds numbers larger than about 20,000; (b) for rough cylinders, the force coefficients also depend on the relative roughness k/D and differ significantly from those corresponding to the smooth cylinder; and that (c) the use of the 'frequency parameter' D2/vT and the roughness Reynolds number Umk/v allow a new interpretation of the present as well as the previously obtained data and the establishment of model laws for oscillatory flow about cylinders at supercritical Reynolds numbers.


The design of structures for the marine environment requires the prediction of the forces generated by waves and currents. Much of the present knowledge has been obtained by means of model tests at Reynolds numbers generally two to three orders of magnitude smaller than prototype Reynolds numbers. These model tests have relied heavily on the so-called Morison formula for expressing the force as the sum of a drag and inertia force. The values of the drag and inertia coefficients to be used in the Morison equation became the subject of many experimental studies in the last twenty years. The correlation of these coefficients with the relative amplitude of the waves (or the Keulegan-Carpenter number) has been generally inconclusive. Furthermore, lift forces which are associated with vortex shedding have received relatively little attention. It thus became clear that much is to be gained by considering plane oscillatory flow about cylinders at high Reynolds numbers in order to isolate the influence of individual factors such as relative amplitude, Reynolds number, and the relative roughness on vortex shedding and resistance. It is with this realization that the present investigation was undertaken and the preliminary results obtained with smooth cylinders in a small U-shaped water tunnel operating at relatively low Reynolds numbers (2,500 to 25,000) have been previously reported [].

The present paper deals with in-line and transverse forces acting on smooth and artificially- roughened circular cylinders in harmonic flow at critical and supercritical Reynolds numbers.

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