This paper presents a review of wave force predictions for rough and smooth cylinders. The Morison equation and some basic results for the drag and inertia coefficients in laboratory and ocean tests are reviewed. New results for rough cylinders at large Reynolds number are also presented.
The correct values of the drag' and inertia coefficients to use in conjunction with Morison's equation for prediction of the design loading of offshore structures have been a topic of considerable interest and discussion for at least three decades. Many experiments have been conducted both in the ocean and in laboratory wave channels but with limited success. Test results have frequently shown rather extreme scatter, leaving the designer in the unfortunate position of possibly grossly over designing the structure or using coefficients which are less than the range of reported values. At the present time the state of knowledge remains incomplete although considerable progress has been made, particularly in the last decade.
In this paper an attempt is made to review the Morison equation and discuss the results of various experiments regarding the coefficients of drag and inertia in relation to wave force calculations. particular emphasis is placed on recent results obtained from basic experiments in oscillatory, rectilinear flow past smooth and rough cylinders and the correlation of these results with results from ocean test platforms.
The so-called Morison's equation was apparently introduced by Morison et al.1 in 1950 as a semi-intuitive expression for predicting the force exerted on a body in a viscous fluid under unsteady flow conditions. Since that time the general validity of the expression and, particularly, the validity in relation to wave-induced loads on circular cylinders has been questioned. Nonetheless, during the three decade interim since 1950 a more appropriate formula has not been found.
Some insight into the appropriateness of Morison's equation can be gained through a dimensional analysis. For the sake of simplicity consider the force exerted on a circular cylinder placed in a simple rectilinear, harmonically oscillating flow. The instantaneous force is denoted by F and the cylinder is characterized by its diameter and roughness height, d and k, respectively. The pertinent fluid properties are its density, p, and kinematic viscosity, v. If the fluid motion is sinusoidal it may be completely characterized by the amplitude, a, and period, T. Thus, the instantaneous force per unit length of cylinder can be expressed as
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