Deterministic Decomposition and Prediction of Irregular Ocean Waves
Authors: Zhang Jun , Wen Jiangang , Yang Jun , Prislin lgor 
Published: October 2008

Abstract
The Directional Hybrid Wave Model (DHWM) has been developed for the deterministic decomposition and prediction of irregular ocean waves. The Extended Maximum Likelihood Method (EMLM) is employed to determine the directional spreading of wave energy, and the initial phases of directional free-wave components are calculated by least-square fitting. The nonlinear effects are computed using a hybrid second-order wave-wave interaction model which is a combination of the conventional perturbation approach and the phase modulation approach, and are subtracted from the measurements. The free-wave components are obtained by iteratively decoupling the free-wave components and their nonlinear interactions. The DHWM can decompose a wave field defined by multiple fixed-point measurements into a set of directional free-wave components. Based on these derived free-wave components, the wave properties can be predicted in the vicinity of the measurements. The present method is verified numerically and applied to both laboratory and field measurements in various scenarios. Satisfactory agreement between the predictions based on the decomposed free-wave components and the corresponding measurements demonstrates that the DHWM is reliable and robust. It is expected that the DHWM will have a variety of applications to ocean science and engineering.

Introduction
Deterministic predictions, based on related measurements, of wave characteristics of directional sea waves are indispensable to many ocean and coastal science and engineering problems, such as wave groupness, maximum wave height and wave-structure interactions, etc. However, such a prediction tool has not been proposed in previous studies (Zhang et al. 1997). Ocean waves are usually the superpositions of many wave components of different frequencies, amplitudes and advancing in different directions, and the nonlinear interactions of these wave components. The basic wave components, known as free-wave (or linear) components, obey the dispersion relation. Due to the nonlinearity of surface waves, the interactions among these free-wave components result in bound-wave components which in general do not obey the dispersion relation. In the cases of steep waves, the free-wave components of frequencies near the spectral peak frequency are dominant but the amplitudes of boundwave components may be dominant or important with respect to the free-wave components of the same frequency in the frequency bands either far lower and higher than the peak frequency (Zhang et al. 1996a). It is known that the relationship between the amplitudes of the elevation and potential of a free-wave component is quite different from that of a bound-wave component. The existing linear wave theories either ignore bound-wave components or treat them in the same way as the free-wave components of the same frequency. Hence, wave characteristics predicted by using linear wave theory, e.g. wave kinematics based on measured wave elevation or wave elevation based on measured dynamic pressure, were found to be inaccurate (Torum & Gudmestad 1989; Spell et al. 1996; Zhang et al. 1996b). For accurate prediction, nonlinear wave effects have to be treated as what they are in the decomposition and superposition of a wave field. That is, the bound-wave components are decoupled from the measured wave characteristics before a wave field is decomposed into its free-wave components.