The present investigation examines several simplifications and hydrodynamic approximations commonly employed in wave force analyses. Alternatives and modifications are sought which improve the resolution of a general Morison approach. This is accomplished by considering two basic arrangements; a vertical cylinder and a horizontal cylinder in progressive waves. The physical differences between the flows are explored and the results are compared to previous planar harmonic flow measurements. It was found that modifications to the usual Morison approach are required to adequately account for the orbital motions of the fluid and to account for the orientation of the orbits with respect to the cylinder axis. The consequences of this finding are discussed for inclined cylinders in waves and for cylinders in short-crested seas. The axial variations of the wave force on vertical cylinders are also examined in order to establish error bounds for the common practice of assuming constant values of Cm and CD over the entire span. Lastly, the methods of computing force transfer coefficients from a force record are examined and sources of error are identified and briefly discussed.


In the face of rising construction costs, the increased importance of dynamic loadings, and in view of the more hostile sites under consideration, the accuracy of wave force computations becomes a critical question. The least well understood wave loading regime, hence the one with the least accurate descriptions, is the regime wherein both drag and inertia forces are important. The basis for most wave force computations in this regime is the usual Morison equation. In the past the Morison approach has been tailored with some success to particular applications. However attempts to generalize the approach have not been successful and consequently large uncertainties accompany each new application. The discrepancies between prediction and observation can be as large as 50 to 100 percent.

For the most part these inaccuracies stem from a poor understanding of the unsteady vortex flows which occur in this regime and from several simplifications inherent in the usual Morison approach. In lieu of a complete hydrodynamic description of the various possible vortex flows, an unlikely accomplishment in the near future, an improved approach to wave force prediction appears to be one that can account for the major differences between vortex flows. This paper outlines such an approach and at the same time identifies uncertainties that can arise from differences in the methods of calculation.


The basis for many unsteady wave force calculations is the so-called Morison equation which may be written as

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for a unit length of the cylinder. Here CD and Cm are the usual force transfer coefficients, U is a characteristic maximum velocity, K = U T/D is the Keu1egan-Carpenter number, T is the wave period, and u is the velocity. A dot denotes a time derivative. The equation has its origins in the work of Stokes and, strictly speaking, pertains only to the component of force that is in line with a one dimensional unsteady flow.

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