Laboratory measurements of the total in line forces on a fixed vertical 2-in. diameter cyl1nder in deep-water regular and random waves are given and compared with predictions from the Morison equation. Results show, for regular waves which heights ranging from 2 to 22 in. and frequencies ranging from 0.4 to 0.9 Hz that the Monson equation, with Stokes wave theory and constant drag and inertia coefficients of 1.2 and 1.8, respectively, provides good agreement with the measured maximum wave forces. The force variation over the entire wave cycle is also well represented. The linearized Morison equation, with linear wave theory and the same coefficients likewise provides close agreement with the measured and wave forces for irregular random waves having approximate Bretschneider spectra and significant wave heights from 5 to 14 in. The success of the constant-coefficient approximation is attributed to a decreased dependence of the coefficients on dimensionless flow parameters as a result of the circular particle motions and large kinematic gradients of the deep-water waves.


The in-line force exerted on a fixed vertical cylinder by water surface waves is if mail or interest in offshore structural engineering. It is customarily calculated using the well-known Morison equation1 which expresses the force per unit length at any section of the cylinder as the sum of drag and inert a components. These components are dependent, respectively, on the wave induced water velocity and acceleration in the vicinity of the section through empirical drag and inertia coefficients. The basic division of the equation into drag and inertia components is generally recognized as a good engineering approximation to a complex physical problem. However, the appropriate values if the drag and inertia coefficients to be used in the equation have been a subject of continuing discussion since the equation was first proposed more than 30 years ago.

In engineering applications, the coefficients are usually assumed constant, with the value of the drag coefficient chosen in the range 0.6 to 1 and that of the inertia coefficient chosen in the range 1.5 to 2. General dimensional reasoning shows however, that the coefficients are not necessarily constant and may vary with dimensionless flow numbers characterizing the periodic (the Keulegan-Carpenter number) and viscous (the Reynolds number) motion. Such dependence was, in fact first shown by Keulegan and Carpenter for a limited range of the dimensionless flow parameters and later by Sarpkaya3 for a much larger range.

In Keulegan and Carpenters' work, the drag and inertia coefficients were investigated using fixed horizontal cylinders in standing waves. In contrast, Sarpkaya's work has dealt with cylinders in one-dimensional oscillatory flow.

The question of the applicability of the extensive coefficient data of Sarpkaya to wave induced water motion has naturally received some attention in the last few years, but with conflicting conclusions.

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