Nonlinear Scattering of Long Waves by a Vertical Cylinder

Abstract

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(ε), where ε < < 1. The first-order solution is linear in ε, and higher-order nonlinear effects are proportional to εⁿ 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).