Deterministic decomposition of deep water short-crested irregular gravity waves

Abstract

A method is developed for the deterministic decomposition of nonlinear short-crested irregular ocean waves accurate up to second order in wave steepness. Initially, an alternative maximum likelihood method is used to determine the directional spreading of wave energy. Then a least squares fitting scheme is used to calculate the initial phases of directional free-wave components. The effects of nonlinear wave-wave interactions among these free-wave components are calculated using a conventional second-order wave-wave interaction model and subtracted from the measurements. The final results are obtained through an iterative process of computing the free-wave components and their nonlinear interactions. Given an ocean wave field defined by multiple feed-point measurements, the method is capable of decomposing the wave field into a set of directional free-wave components. On the basis of the derived free-wave components, the wave characteristics of the wave field can be predicted in the vicinity of the measurements. The method has been applied to two sets of ocean wave pressure measurements which were collected from an array of sensors mounted on an offshore production platform near the California coast. Satisfactory agreement between the predictions based on the decomposed free-wave components and related measurements indicates the proposed method is reliable. It is expected that this method will have a variety of applications to ocean science and engineering.