Linearization of the Wave Spectrum: A Comparison of Methods

Abstract

The relative contributions of free waves and bound waves to the formation of an extreme wave event remains a topic of interest in offshore engineering. A variety of methods have been proposed for identifying and removing the bound wave components. The method of “phase separation” or “phase manipulation” repeats simulations/experiments of a wave field with an offset in the initial phase of the wave components and relies upon summation of the resulting wave fields to isolate the bound harmonics, following from a Stokes expansion in steepness; the method has proven effective in isolating bound harmonics but requires that all cases be repeated. Alternatively, the bound harmonics can be removed using a three-dimensional fast Fourier transform (3D-FFT) of the wave field. However, the Fourier transform requires periodicity in the signal and assumes homogeneity in space and stationarity in time, producing spurious modes otherwise. We compare the phase separation and 3D-FFT approaches for a steep, focusing wave group in deep water using the numerical simulation tool, OceanWave3D, and discuss the effectiveness of both methods.