Phase-Focusing Model of Freak Wave Based on Boussinesq Equation

Abstract

Freak wave is a kind of instantaneous disastrous wave with large wave height, which has great destructive effect on the navigation of ships at sea. Based on the Boussinesq equation, a phase-focusing model for focusing simulation of freak wave is established, and the numerical generation of freak wave is realized. Through the calculation results, the evolution process and the non-linear characteristic parameters of freak wave are analyzed and discussed. The following conclusions are drawn: phase-focusing model based on Boussinesq equation can generate freak wave when the phase angle distribution is smaller than  6 . 1 . The change of phase angle distribution has less influence on skewness and more influence on kurtosis. Introduction As a special kind of disastrous wave, freak wave, because of its sudden occurrence and harmfulness to the safety of naval vessel activities, urgently needs us to improve our understanding of this threatening wave in order to protect the environment for human survival, predict the occurrence of such natural disasters and reduce the losses caused by it. Therefore, freak wave has become a hot topic in wave theory and application. At present, the research on the mechanism of freak wave formation is mostly carried out through the angle of energy focus. Kharif and Pelinovsky[1] summarized the generating mechanism of freak waves, believing that the generation of freak waves may be caused by one or more of the following factors: wave superposition, wave-current interaction, topographic change, wind action, Benjamin-Feir instability and so on. In order to studying the mechanism and influencing factors of freak wave, it is an effective way to reproduce the freak wave events in the laboratory. It is the most effective way to study freak wave in laboratory by focusing wave energy. Among them, the most commonly used method is the phase velocity method. According to the linear wave theory, the waves of different periods and amplitudes are combined in the form of linear superposition, and the initial phase of each component wave is artificially modulated to reach the maximum peak at the given position and time, so that the linear superposition of each component wave can produce large waves. In order to overcome the disadvantage that the wavefront in the focusing position is still before and after the wave is focused, and the probability of extreme wave is very low, Kriebel[2] and others divide the energy spectrum into two parts: background spectrum and singular spectrum. The background spectrum is used to generate random wave field, simulate the real sea surface, and use singular spectrum. The results show that only 15% or 20% of the total energy can be used to generate the extreme wave, that is, only a small part of the wave component can generate the extreme wave. Huang[3] used a model to obtain the time series of wave surface containing abnormal waves by manual intervention of the random initial phase of the composed waves, but the simulation efficiency was low. Pei[4] developed the two-wave train combination model to three-wave train superposition, which improved the efficiency of abnormal wave simulation. Based on this method, the measured freak wave was reconstructed, and the feasibility of this simulation method was demonstrated. Liu [5] simulated the generation of freak wave in three-dimensional wave field based on the above combined focusing model. Zhao[6] carried out an experimental study of abnormal waves in a two-dimensional wave flume. The effects of dimensionless water depth, wave steepness, spectral peak elevation factor and spectral peak period on the statistical characteristics of random wave and the appearance of International Conference on Modeling, Analysis, Simulation Technologies and Applications (MASTA 2019) Copyright © 2019, the Authors. Published by Atlantis Press. This is an open access article under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/). Advances in Intelligent Systems Research, volume 168