Predictions Of Unidirectional Irregular Wave Kinematics And Evolution
Authors: Ye Mao , Zhang Jun 
Published: October 2008

Abstract
A numerical scheme is developed based on the hybrid wave model for the prediction of the short-distance wave evolution and kinematics of irregular waves. The hybrid wave model considers the interaction between the components in a wave field up to the second order of wave steepness. The numerical results have been extensively compared with three sets of laboratory wave elevation and kinematic measurements as well as the related predictions by linear random wave theory and its "stretching" and "extrapolation" modifications. The excellent agreement between the results of the hybrid wave model and the measurements confirms that the hybrid wave model is more accurate and more reliable than the other three methods, especially for steep and broad-banded wave trains.

Introduction
Precise knowledge of ocean waves is crucial to the design of offshore structures that are both safe and economical. The determination of wave loads on slender-body offshore structures using the Morison's equation requires the prediction of the kinematics induced by waves in the ambient fluid. In computing the total wave loads on an offshore platform, it is also desirable to know the evolution of irregular waves over a short distance (from one platform legs to another). It is well known that linear random wave theory fails to predict irregular wave kinematics near the free surface, especially near the crests of steep waves. Considerable progress has been made in improving the accuracy of predicting irregular wave kinematics in the last three decades, yet there is still no generally acceptable method of proven accuracy for the kinematic prediction of irregular surface water wave1. For example, different methods of predicting wave kinematics, such as Wheeler stretching and linear extrapolation, may render a fifty to one hundred percent difference in the predicted responses of compliant tower structures2. Therefore, it is desirable to develop a numerical scheme which may accurately predict irregular wave evolution and kinematics up to the free surface given a fixed-point elevation measurement.
Different from most "stretching" methods that were developed based on semi-empirical and semi-theoretical modifications of linear wave theory, this numerical scheme is based on a new hybrid wave model which satisfies basic hydrodynamic principles. The hybrid wave model considers an irregular wave field consisting of numerous free-traveling wave components with different frequencies. Different from linear wave theory, it considers interactions among different wave components and includes the effects of these interaction on the resultant wave elevation and kinematics. The interactions among wave components can be classified as either "strong" or "weak" wave interactions. The effects of strong wave interactions are noticeable after a duration of about one peak wave period, while those of weak wave interactions may be substantial only after a duration of hundreds of peak wave periods3,4. For the prediction of short-distance evolution, weak wave interactions need not be considered. The interaction between two different wave components is probably the most important strong wave interaction relevant to the prediction of wave kinematics and short-distance evolution.