二维随机波浪中畸形波的数值模拟

发布时间：2018-01-25 19:20

本文关键词： 畸形波非线性薛定谔方程 Benjamin-Feir不稳定性 Jonswap谱　出处：《大连理工大学》2014年硕士论文　论文类型：学位论文

【摘要】：畸形波是一种在没有预警的情况下突然发生,并迅速消失的灾害性事件。由于畸形波会给海洋建筑物和船只带来巨大威胁,畸形波受到人们越来越多的重视。以往的研究主要集中在畸形波的生成机制,而在工程中我们更加关心的是畸形波的发生概率和如何预报。本文采用四阶非线性薛定谔方程模拟了二维JONSWAP谱情况下畸形波的生成。为了探讨波浪参数对畸形波的影响,模拟实验分成了多组初始波浪参数不同的工况。首先分析了深水不稳定波列的演化过程。畸形波从形成到消失的演化过程即调制一反调制的过程：调制过程中,畸形波位置处能量发生汇聚,波高升高,其附近的波高减小；反调制过程中,畸形波位置处波幅减小,直至畸形波的特征消失,其他位置处波高增大。然后本文探讨了峰度、有效波高、偏度值和波浪谱的演化过程以及JONSWAP谱参数对它们的影响。结果表明：Benjamin-Feir指数(BFI)是判断波列不稳定调制是否发生的重要参数；峰度值的空间演化曲线和畸形波生成概率曲线趋势一致,峰度值可以预测畸形波生成概率的大小。在随机波浪场中,谱宽较窄和有效波高较小时,畸形波较容易发生。有效波高和偏度值在波浪传播过程中基本无变化,偏度的大小与初始波陡有关。波浪之间的非线性作用导致主频处的能量向高频和低频部分传递,因此在波浪传播过程中谱峰高度下降,频谱变宽。在讨论了前面一系列问题的基础上,我们分析了Benjamin-Feir不稳定性与深水畸形波的内在联系和畸形波的发生机制。畸形波的生成与波浪二阶非线性和束缚波关系很小,畸形波的生成主要是四波共振造成的,也就是Benjamin-Feir不稳定性。最后对模拟实验波高进行了统计分析。结果表明：对于BFI1.0的情况,模拟波高分布与瑞利分布基本一致；而对于BFI1.0的情况,由于发生了不稳定调制,瑞利分布只在演化初期与模拟波高分布相吻合,在其他位置处瑞利分布会低估大波发生的概率,畸形波发生概率比瑞利分布预测的大一个数量级以上。初始有效波高较小,谱峰升高因子较大时,波高分布与瑞利分布的差异较大。Forri stall分布和瑞利分布均不能很好的预测波峰分布。在非线性成长后,MER分布与模拟波高分布吻合较好,能够准确预报畸形波的发生概率。
[Abstract]:Freak wave is a sudden occurrence without warning, and rapidly disappearing disaster events. Because of the freak wave will bring a huge threat to the marine structures and ships, freak waves have attracted more and more attention. Previous studies focused on the generation mechanism of freak waves, and in the project we are more concerned about the occurrence probability and how to forecast the freak wave.
This paper uses four order nonlinear Schrodinger equation to simulate the two-dimensional JONSWAP spectrum under the freak wave generation. In order to investigate the influence of freak wave wave parameters, simulation experiment is divided into several groups of different parameters of the initial wave conditions. Firstly, analyzing the evolution of deepwater instability. The freak wave wave from the formation to the evolution of the process of disappearing a modulation counter modulation: modulation process, the position of the freak wave energy aggregation, wave height increased, in the vicinity of the wave height decreases; the anti modulation process, the position of the freak wave amplitude decreases, until the disappearance of freak wave characteristics, the other position of the wave height increases.
Then this paper discusses the effective wave height, kurtosis, skewness and evolution of the wave spectrum and JONSWAP spectrum parameters influence on them. The results showed that the Benjamin-Feir index (BFI) is an important parameter in evaluating whether modulation instability wave train; curve and abnormal wave generation probability curve consistent evolution of kurtosis value space, kurtosis can predict the probability of freak wave generation. In random wave field, narrow spectral width and wave height is small, the freak wave is easy to occur. The effective wave height and skewness in the wave propagation process basically no change, and the size of the initial wave steepness of the partial nonlinear interaction between waves. The frequency of lead energy transfer to high frequency and low frequency, therefore in the process of wave propagation in the peak height decreased, the spectrum becomes wider. Discusses a series of problems on the front, we analyzed Benjamin-Feir The relationship between instability and deep-water freak waves and the mechanism of freak waves occur. The generation of freak waves is very limited to the two order nonlinear and bound waves. The generation of freak waves is mainly caused by four wave resonance, that is, Benjamin-Feir instability.
At the end of the simulation wave were analyzed. The results show that: for BFI1.0, simulation of wave height distribution and Rayleigh distribution are basically the same; and in the case of BFI1.0, due to the instability of modulation, the Rayleigh distribution only in the early stage of evolution and Simulation of wave height distribution match in other locations will underestimate the probability distribution of Rayleigh wave the freak wave occurrence prediction biruili distribution probability of a large number of above. The initial effective wave height is smaller, peak elevation factor is higher, the difference with the Rayleigh distribution of wave height distribution of larger.Forri stall distribution and Rayleigh distribution is not a good predictor of peak distribution. In the non-linear growth, MER distribution and wave height the distribution agreement can accurately forecast the occurrence probability of freak wave.

【学位授予单位】：大连理工大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：P731.22

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