Analysis of freak wave measurements in the Sea of Japan

This paper presents an analysis of a set of available freak wave measurements gathered from several periods of continuous wave recordings made in the Sea of Japan during 1986–1990 by the Ship Research Institute of Japan. The analysis provides an ideal opportunity to catch a glimpse of the statistics of freak waves in the ocean. The results show that a well-defined freak wave may occur in the developed wind–wave condition: S(f)∝f⁻⁴, with single-peak directional spectra. The crest and trough amplitude distributions of the observed sea waves including freak waves are different from the Rayleigh distribution, although the wave height distribution tends to agree with the Rayleigh distribution. Freak waves can be readily identified from the wavelet spectrum where a strong energy density occurs in the spectrum, and is instantly surged and seemingly carried over to the high-frequency components at the instant the freak wave occurs.     

基于实测资料的畸形波概率及波浪要素分析

根据Kjeldsen对畸形波的定义：波高大于有效波高的2倍（H/H_1/3＞2）,基于实测波浪资料,统计分析了江苏射阳海域和广东南澳海域的畸形波个数和波浪要素。江苏射阳海域畸形波发生概率为0.005 7%,广东南澳海域畸形波发生概率为0.007%。用Rayleigh分布、双参数Weibull 分布和MER分布对实测数据得到的特征波高进行了拟合,研究了海域内畸形波发生的概率分布。拟合结果表明：MER分布更适合描述两个海域畸形波的发生概率,两个海域畸形波的发生概率均高于Rayleigh分布和Weibull分布。在测量数据期间,台风在海域过境可能增加畸形波的发生概率;同时两个海域的双峰谱占比为22.7%和5.8%,可能也是导致畸形波发生概率增加的原因之一。     

Effects of wave breaking on wave statistics for deep-water random wave train

The experimental studies of the breaking effects on wave statistics for deep-water random waves are presented. It is especially focused on the behavior of kurtosis of surface elevations due to wave breaking. Wave breaking suppresses the maximum limit of kurtosis of the surface elevation, although skewness depends on characteristic wave steepness. The mean instantaneous wave steepness of breaking waves defined using the zero-down-crossing method was much lower than expected from the Stokes waves.     

波高非线性概率分布高阶谱数值模型研究

由于波浪的调制不稳定以及非线性波-波相互作用等因素的存在,波浪的分布会偏离线性假设下瑞利分布的结果。通过使用高阶谱模型对不同初始条件下波浪数值模拟。对统计得到的波高与线性理论下的瑞利分布和考虑非线性下改进的埃奇沃思-瑞利（MER）分布和依据Gram-Charlier展开的分布（GC分布）进行对比。结果表明,深水条件下波浪传播过程中偏度值变化较小,而峰度值出现增长。在较小有效波高值的波况下波高分布符合瑞利分布,但随着有效波高值的增加,波浪的非线性增强,波高分布与考虑非线性影响下的GC和MER分布结果相符。宽谱下的波高分布偏离瑞利分布的程度小于窄谱的情况,波高分布更接近瑞利分布的结果。     

Wavelet transform based coherence analysis of freak wave and its impact

The present paper presents the results of a wavelet transform-based coherence analysis of freak wave and its impact. Wavelet transform has been used as a tool in analyzing signals in the time domain as well as in the frequency domain. The analysis was applied to laboratory-generated freak waves. The wavelet transform of the time history of the freak wave and its impact force revealed that a wide range of frequency components were contained in them. The coherence analysis was conducted on the wave and its impact force time histories. The coherence analysis revealed that some high-frequency components were highly correlated with the impact forces. The present study demonstrates that the wavelet transform can be an alternative tool in the analysis of strongly nonlinear freak wave and its impact.     

Wave crest and trough distributions in a broad-banded directional wave field

It is well established that the modulational instability enhances the probability of occurrence for extreme events in long crested wave fields. Recent studies, however, have shown that the coexistence of directional wave components can reduce the effects related to the modulational instability. Here, numerical simulations of the Euler equations are used to investigate whether the modulational instability may produce significant deviations from second-order statistical properties of surface gravity waves when short crestness (i.e., directionality) is accounted for. The case of a broad-banded directional wave field (i.e. wind sea) is investigated. The analysis is concentrated on the wave crest and trough distribution. For completeness a comparison with a unidirectional wave field is presented also. Results will show that the distributions based on second-order theory provide a good estimate for the simulated crest and trough height also at low probability levels.     

A weakly non-gaussian model of wave height distribution for random wave train

The wave height distribution with Edgeworth’s form of a cumulative expansion of probability density function (PDF) of surface elevation are investigated. The results show that a non-Gaussian model of wave height distribution reasonably agrees with experimental data. It is discussed that the fourth order moment (kurtosis) of water surface elevation corresponds to the first order nonlinear correction of wave heights and is related with wave grouping.     

Effects of high-order nonlinear interactions on unidirectional wave trains

Numerical simulations of gravity waves with high-order nonlinearities in two-dimensional domain are performed by using the pseudo spectral method. High-order nonlinearities more than third order excite apparently chaotic evolutions of the Fourier energy in deep water random waves. The high-order nonlinearities increase kurtosis, wave height distribution and H_max/H_1/3 in deep water and decrease these wave statistics in shallow water. Moreover, they can generate a single extreme high wave with an outstanding crest height in deep water. High-order nonlinearities (more than third order) can be regarded as one cause of freak waves in deep water.     

Probability distributions for maximum wave and crest heights

The paper discusses short- and long-term probability models of ocean waves. The Gaussian theory is reviewed, and nonlinear short-term probability distributions are derived from a narrow band second-order model. The nonlinearity has different impact on different measurement techniques, and this is further demonstrated for wave data from the WAVEMOD Crete measurement campaign and laser data from the North Sea. Finally, we give some examples on how the short-term statistics may be used to estimate the probability distributions for the maximum waves during individual storms as well as in a wave climate described by long-term distributions.     

A probability distribution for depth-limited extreme wave heights in a sea state

A model for the depth-limited distribution of the highest wave in a sea state is presented. The distribution for the extreme wave height is based on a probability density function (pdf) for depth-limited wave height distribution for individual waves [Méndez, F.J., Losada, I.J., Medina, R. 2004. Transformation model of wave height distribution. Coastal Eng, Vol. 50, 97:115.] and considers the correlation between consecutive waves. The model is validated using field data showing a good representation of the extreme wave heights in the surf zone. Some important statistical wave heights are parameterized obtaining useful expressions that can be used in further calculations.     

Statistics of nonlinear wave crests and groups

Groups of large nonlinear waves with sharper higher crests can pose hazards to ships, induce harbor resonance and cause wave-overtopping of fixed and floating structures. Past interest in wave groups has mostly been focused on the statistics and modeling of linear wave groups. Studies on nonlinear wave groups are surprisingly few, and address deep water waves only. Here, statistics of nonlinear wave crests and wave-crest groups in deep and transitional water depths are considered, using an appropriate second-order representation for crest heights and the continuous wave-envelope approach. In particular, theoretical expressions describing the statistics of nonlinear wave crests and their groups are posed in the form of a simple second-order transformation of well-known results on linear waves. Predictions from the transformation so posed compare well with nonlinear wave data gathered in the North Sea, and demonstrate that nonlinearities do affect the statistics of large wave crests and their groups significantly.     

Observations of freak waves in random wave field in 2D experimental wave flume

Long time series of wave field are experimentally simulated by JONSWAP spectra with random phases in a 2D wave flume. Statistic properties of wave surface, such as significant wave height, skewness and kurtosis, are analyzed, and the freak wave occurrence probability and its relations with Benjamin-Feir index （BFI） are also investigated. The results show that the skewness and the kurtosis are significantly dependent on the wave steepness, and the kurtosis increases along the flume when BFI is large. The freak waves are observed in random wave groups. They occur more frequently than expected, especially for the wave groups with large BFI.     

Analysis of the Voyager storm

We analyse the wind and wave conditions present in the Mediterranean Sea at the time and location when the cruise ship Voyager was reportedly hit by one or more big waves and suffered substantial damage. The analysis is done using wind and wave modelling supported by satellite and buoy wind and wave data. Granted the hindcast of the storm, we also analyse the local conditions for the possibility of freak waves.     

Numerical study of nonlinear freak wave impact underneath a fixed horizontal deck in 2-D space

Freak waves are extreme and unexpected surface waves with huge wave heights that may lead to severe damage to ships and offshore structures. However, few researches have been conducted to investigate the impact underneath fixed horizontal decks caused by freak waves. To study these phenomena, a 2-D numerical wave tank is built in which nonlinear freak waves based on the Peregrine breather solution are generated. As a validation, a regular-wave-induced underneath impact is simulated and compared to the existing experimental measurements. Then the nonlinear freak-wave-induced impact is investigate with different values of deck clearance above the mean free surface. In addition, a comparative simulation of a “large” regular wave based on the 2nd-order Stokes wave theory with the same crest height and wave length of the nonlinear freak wave is carried out to reveal the unique features of the nonlinear freak-wave-induced impact. By applying a fluid–structure interaction (FSI) algorithm in which the bottom deck and front side wall are simplified as Euler beams in 2-D and discretized by the finite element method (FEM), the hydroelastic effects are considered during the impact event. The vertical force acting underneath the bottom deck, the transversal force acting on the front side wall, the structural displacements of the elastic deck and wall are analyzed and discussed respectively, from which meaningful conclusions are drawn.     

波高与风速联合概率分布研究

基于copula函数论述了两变量的联合概率分布方法.此方法的主要优点是边缘分布可由不同的分布函数构成,变量间可具相关性.以粤东汕尾海域极值波高与相应风速为研究实例,经分析获得以下结果:(1)优选的极值波高和风速可分别由P-Ⅲ型和GEV 分布表示:(2)拟合优度检验指标表明二者的最优连接函数为Archimedean co...     

湄洲湾波高和波周期的统计分布

本文探讨了福建湄洲湾海区的波高和波周期的一元分布和二元联合分布,并给出了该海区波浪的各种统计特征值,提出了波高和波周期的经验分布模式。     

Evolution of wave shape over a low-crested structure

This paper investigates the evolution of wave shape over a low-crested structure (LCS) using a 2-D RANS-VOF model. The model predictions of surface elevation and wave skewness and asymmetry are in good agreement with the recent measurements collected in a small scale wave channel at the University of Cantabria (UCA). The empirical formulae relating wave skewness and asymmetry to local Ursell number by Peng et al. (2009) have been extended to include the effect of wave reflection and the ramp in front of LCS and a wider range of Ursell number in the present study. In the presence of LCS, wave skewness decreases slightly above the seaward slope, then increases rapidly up to a maximum value above the structure crest, and decreases drastically above the leeward slope. Wave asymmetry decreases sharply above the seaward slope to a negative minimum value at the structure crest, and then increases rapidly to a positive value above the leeward slope. Our bispectral analysis indicates that sum interactions increase skewness and decrease asymmetry while difference interactions have opposite effects and that the former dominate above the seaward slope and on the structure crest but the latter dominate above the leeward slope of LCS. The observed wave shape evolution over a LCS can be attributed to the changes in the interplay of sum and difference interactions. We found that incident wave height and wave period, relative structure freeboard, structure crest width and structure porosity are the controlling factors for wave shape evolution over LCS. This study provides new insights on the role of wave skewness and asymmetry in the breakwaters stability and sediment transport around the structure and on the beaches behind it.     

Effect of sampling rate on wave height statistics

This paper examines the effects of digital processing, and therefore discretisation or sampling, of sea surface elevations that are, in reality, continuous. Using random linear wave theory, probability distributions for the measured (as opposed to actual) wave amplitudes and heights have been obtained which are conditional on the sampling rate. It is shown that with low sampling rates there are significant departures from the usual Rayleigh distribution. Rates of 1 Hz or less may lead to significant underestimation of the probability of very large waves. An analysis of full-scale measurements obtained from a platform in the North Sea supports these results.     

The difference between the joint probability distributions of apparent wave heights and periods and individual wave heights and periods

The joint distribution of wave heights and periods of individual waves is usually approximated by the joint distribution of apparent wave heights and periods. However there is difference between them. This difference is addressed and the theoretical joint distributions of apparent wave heights and periods due to Longuet-Higgins and Sun are modified to give more reasonable representations of the joint distribution of wave heights and periods of individual waves. The modification has overcome an inherent drawback of these joint PDFs that the mean wave period is infinite. A comparison is made between the modified formulae and the field data of Goda, which shows that the new formulae consist with the measurement better than their original counterparts.