A second-order solution is derived for the diffraction of a nonlinear progressive wave in deep water, incident on a vertical, surface-piercing, circular cylinder. Particular attention is directed to the asymptotic condition on the second-order potential, and the second-order contributions to the fluctuating wave force on the cylinder. Linear diffraction theory, currently used for large cylinders, underestimates the maximum wave force. For waves of length greater than three cylinder diameters, the deficit is no more than about 14% for waves of maximum steepness. The percentage deficit is greater for the less important shorter waves. For slender cylinders, fifth-order inertial theory, as frequently used, is shown to adequately cover second-order diffraction effects in the limit.
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Hunt et al. (1981) studied this question.