Nonlinear Scattering of Long Waves by a Vertical Cylinder

The dominant wave loads on large offshore platforms can be analyzed on the basis of linear potential theory. We denote the wave amplitude A, wavelength λ, and wavenumber K = 2π/λ. Typical amplitudes are a few meters, with periods in the range of 8–11 seconds corresponding to wavelengths of 100–200m. In these conditions it is reasonable to use a perturbation expansion based on the assumption K A = O(e), where e < < 1. The first-order solution is linear in e, and higher-order nonlinear effects are proportional to en where (n = 2,3,…). For platforms with vertical circular columns which intersect the free surface, the column radius a is the most important geometrical length scale. Typical values of a are on the order of 10 meters. The usual theoretical description applies to the ‘diffraction regime’ K a = O(1).