Nonlinear wave loads on a slender vertical cylinder

The diffraction of water waves by a vertical circular cylinder is considered in the regime where the wave amplitude A and cylinder radius a are of the same order, and both are small compared to the wavelength. The wave slope is small, and a conventional linear analysis applies in the outer domain far from the cylinder. Significant nonlinear effects exist in the complementary inner domain close to the cylinder, associated with the free-surface boundary condition. Using inner coordinates scaled with respect to a , it is shown that the leading-order nonlinear contribution to the velocity potential includes terms proportional to both A 2 a and A 3 . The wave load which acts on the cylinder near the free surface includes second- and third-harmonic components which are proportional respectively to A 2 a 2 and A 3 a . In a conventional perturbation analysis, where A [Lt ] a , these components would be ordered in magnitude corresponding to the different powers of A , but here they are of the same order. The second- and third-order components of the total force are of comparable magnitude for practical values of the wave slope.