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.     

未破碎变浅随机海浪的波高统计分布

利用青岛海洋大学海洋实验室现代化的大型水槽,设计进行了多种海浪强度下,由深水传入近岸不同坡度水底上的变浅随机海浪的模型实验。依据实验资料统计分析结果表明：对近岸变浅随机海浪而言,其波高分布不再符合Ｒａｙｌｅｉｇｈ分布,与Глуховский的经验分布也有差异,它不仅与参量Ｈ＊＝Ｈ／ｄ有关,且与表征深水海浪的波形特征量Ｈ０／Ｔ２０有关,并获得其经验关系,为实验应用变浅随机海浪的波高统计分布提供了可能。     

近岸浅水波的计算

采用理论推导与实验资料验证相结合的方法对近岸浅水波衰减计算进行研究。研究表明,波浪与浅水区运动传播衰减是各种能耗共同作用的结果,为此总结了分子粘性能耗、湍流能耗、底部渗透能耗、底部摩擦能耗、软尾海底弹性能耗等,由建立波能流平衡方程出发进行理论推导,得出各种能耗影响下波浪衰减的计算公式,并将该理论公式与作者1980年波浪水相试验资料比较,两者基本吻合,可适用干线性及非线性各种波能耗情况的计算。     

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.     

Occurrence probability of a freak wave in a nonlinear wave field

The Edgeworth’s form of a cumulative expansion of the probability density function (PDF) of surface elevation expands the maximum wave height distribution to predict the occurrence probability of freak waves. This study investigated the enhancement of the occurrence probability of freak waves due to the fourth order moment of surface elevation, kurtosis, change and found that the nonlinear effects on the occurrence probability of a freak wave linearly depends on kurtosis for a small number of waves N=250. The statistical theory was compared with field data, and freak waves sometimes appear when not expected by the Rayleigh theory, but they were predicted by the proposed theory.     

Virtual wave gauges based upon stereo imaging for measuring surface wave characteristics

A virtual wave gauge (VWG) technique based on stereo imaging is developed to remotely measure water wave height, period, and direction. VWG minimizes computational costs by directly tracking the elevation of the water surface at selected points of interest using a Eulerian based dynamic searching algorithm. Results show that the VWG technique developed in this paper dramatically improves efficiency by two orders of magnitude compared to the traditional Lagrangian–Eulerian based point cloud method of stereo image processing. VWG is tested against traditional wave wire gauges to within 98% accuracy for significant wave height. Furthermore, the flexibility of the VWG is demonstrated in two field applications. First in an offshore breaking wave case, an array of VWGs is used to efficiently measure wave directionality. Second to investigate the reflection coefficient of a rock-mounted structure interacting with nearshore waves, linear and spatial VWG arrays are designed and implemented based on a priori information of the wave field from a preliminary VWG measurement. Overall, we demonstrate that the flexible and computational efficient VWG technique has the potential to make real-time remote stereo imaging wave measurements a reality.     

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.     

Calibration and modification of energy dissipation models for irregular wave breaking

This study is undertaken to recalibrate eight existing energy dissipation models and find out the suitable models, which can be used to compute H_rms for a wide range of experimental conditions. The examination shows that the coefficients in the existing models are not the optimal values for a wide range of experimental conditions. Using the new calibrated coefficients, all existing models can be used for computing H_rms and the model of Battjes, J.A., Stive, M.J.F. [1985. Calibration and verification of a dissipation model for random breaking waves. Journal of Geophysical Research 90 (C5), 9159–9167] gives the best predictions. The existing models are also modified by changing the breaker height formulas in the dissipation models. The accuracy of most existing models is improved significantly by using the suitable breaker height formula.     

渔港港内作业水域泊稳条件的研究

就渔港港内作业水域泊稳条件研究课题查阅了国内外有关资料,走访了多年从事渔港建设、管理的专家,并选择了两条代表性船型,进行了不同边界、不同载态情况下的模型试验及分析。试验与调查结果符合良好,在此基础上给出了１００～６００ＨＰ渔船装卸作业允许波高的近似计算公式。     

Prediction of wave parameters by using fuzzy logic approach

The purpose of this study is to investigate the relationship between wind speed, previous and current wave characteristics. It is expected that such a non-linear relationship includes some uncertainties. A fuzzy inference system employing fuzzy IF–THEN rules has an ability to deal with ill-defined and uncertain systems. Compared with traditional approaches, fuzzy logic is more efficient in linking the multiple inputs to a single output in a non-linear domain. In this paper, a sophisticated intelligent model, based on Takagi–Sugeno (TS) fuzzy modeling principles, was developed to predict the changes in wave characteristics such as significant wave height and zero up-crossing period due to the wind speed. Past measurements of significant wave height values and wind speed variables are used for training the adaptive model and it is then employed to predict the significant wave height amounts for future time intervals such as 1, 3, 6 and 12 h. The verification of the proposed model is achieved through the wave characteristics time series plots and various numerical error criterias. Also the model results were compared with classical Auto Regressive Moving Average with exogenous input (ARMAX) models. For the application of the proposed approach the offshore station located in the Pacific Ocean was used.     

印尼ADIPALA海域较长周期波浪统计特征分析

对印尼ADIPALA海岸观测的较长周期波浪数据进行了统计分析,给出了不同统计波高特征值之间的关系以及统计特征周期和相对水深的关系;并就波浪统计中的波高分布,采用威布尔分布形式进行拟合,得到波高累积分布;给出了最大波高计算公式,可为工程设计提供参考。     

Design weight of armour stone considering the effect of extreme waves

In this study, waves with the heights higher than H_1/3 in an irregular wave train are called as extreme waves and defined with the help of extreme wave parameter, α_extreme. In order to see the effect of extreme waves on the design weight of armour stone, stability analysis is carried out based on the hydraulic model test results. The test results of high α_extreme cases (HE) and low α_extreme cases (LE) are compared with currently used van der Meer's formulae with permeability factor P=0.4 and 0.45 and Hudson formula by using H_1/3 and H_1/10 in terms of the design weight of armour stone. As a result of the comparison, it is found that Hudson formula by using H_1/3 underestimates the necessary armour weight. Usage of H_1/10 instead of H_1/3 in Hudson formula doubles the weight which seems overestimated when Irribaren number is away from the transition zone in which both wave run-up and run-down forces become effective. However, it seems underestimated near the transition zone where experiment case HE gives higher armour weights. When the design weight of armour stone is calculated by van der Meer's formulae with P=0.4, it may be necessary to increase the weight up to 30% in the case of high extreme waves. On the other hand, van der Meer's formulae may overestimate the weight 14% when the extreme waves are low.     

斋堂岛东南海域波浪特征及海浪谱分析

利用斋堂岛东南海域2013年至2014年的实测波浪资料,统计分析了本海域波浪特征,为波浪能资源评估提供基本波浪参数。统计结果表明,本海域年平均有效波高为0.60 m,最大波高为5.30 m,平均周期为3.3 s,最大周期为8.3 s,常浪向为E-SE向。本文亦讨论了本海域波高分布和波高与周期的关系,并基于JONSWAP谱谱型的基本结构,拟合得到适用于本海域的海浪谱谱型,可为海洋能发电装置的布设及相应的工程建设提供一定的参考。     

Wave height distributions in bimodal sea states from offshore basins

The paper presents results for the distribution of wave heights from laboratory generated bimodal sea states. Data collected at the DHI offshore basin are analyzed and compared with results based on wave records from the MARINTEK offshore basin. The comparisons are done for three groups of mixed sea states: wind-sea dominated, swell-dominated and energy-equivalent, determined on the basis of the parameter sea-swell energy ratio (SSER), which have been generated according to the model of Guedes Soares (1984). In some sea states abnormal or freak waves have been observed.The quasi-determinism theory of Boccotti is used to expand some linear narrowband models to second order, thus providing validation of the adequacy of the equations to represent the linear components of the wave heights. Also, the data are compared with the predictions of a third order model using as a nonlinear correction the coefficient of kurtosis. Due to the coexistence of wind-sea and swell, the core of the autocovariance function in some cases demonstrates a global minimum which is the second local minimum in the sequence. This can affect the fitting ability of distributions whose parameters depend on the form of the autocorrelation function or its envelope.The results for MARINTEK and DHI data show similar patterns of fit between predicted and observed exceedance probabilities for the considered classes of bimodal spectra.     

Seasonality and duration in extreme value distributions of significant wave height

This paper presents a statistical model to characterize the long-term extreme value distribution of significant wave height, conditioning to the duration of the storm and accounting for seasonality. A time-dependent version of the peak over threshold (POT) approach is used to build the model, which is then applied to specific reanalysis time series and NOAA buoy records. The model considers the annual and semiannual cycles which are parameterized in terms of harmonic functions. The inclusion of seasonal variabilities substantially reduces the residuals of the fitted model. The information obtained in this study can be useful to design maritime works, because (a) the model improves the understanding of the variability of extreme wave climate along a year and (b) the model accounts for the duration of the storm, which is a key parameter in several formulations for rubble mound breakwater design.     

三阶Stokes型随机波浪载荷谱研究

应用非线性谱分析理论,对三阶Stokes型随机波浪载荷谱进行了分析,将波面方程及海水质点的水平速度用一阶波面的非线性组表示,导出了随机波浪谱的表达式。为了便于求解随机波浪的载荷谱,将阻力项展开为幂级数式,并应用非线性谱分析理论,确定了幂级数的系数,进而将波浪载荷表示为一阶波面及其导数的非线性组合,最后得出波浪载荷谱密度的表达式,并应用数值分析方法,得出单位桩柱波浪力及总波浪力谱密度。