海浪周期与波高的联合分布

依据线性海浪模式及波动的射线理论导出了周期与波高的一种联合分布,此分布与Longuet-Higgins(1983)得到的分布具有同等效益,但由此得出的波高分布仍为Rayleigh分布.     

由海浪波高与周期的一元分布函数构成二元分布函数的探讨

目前,在海洋、海岸工程中,对海浪波高与周期的一元概率分布,单独有较深入的研究。但对它们的二元分布(即联合分布),不管是理论上还是实践上,都探讨得很不够。六十年代,苏联的基于波高和周期相互独立的假设,给出了波高和周期的联合分布。七十年代,英国海洋学家Longuet-Higgins基于波浪是窄谱的假设,导出了波振幅和周期的联合分布。但由于这些假设都与实际的海浪现象,有较大的差异,因此,在实际应用上受到了很大限制。近年来,我国海洋工作者应用概率定理建立了浅水周期与波高的联合分布,开辟了一条新途径。     

海浪波面包线的计算及其分布函数的再推导

本文借助Hilbert变换技巧给出一种由波面记录计算波面包线的准确且简便的方法,并在线性海浪理论范围内和不受窄谱限制的条件下严格地再导波面包线的分布函数,最后,还用导出的波面包线分布函数讨论了海浪的波高分布问题.     

由模拟波面分析双峰谱型海浪的统计特征

采用目前国际上最新的随机波分析方法,由协方差矩阵的循环嵌套技术,对美国国家浮标44008站2002年6月一典型的双峰海浪谱资料进行谱分析.以实测平均谱为靶谱,对随机波面进行模拟.得到模拟波面估计谱与实测谱极为相近,谱峰及谱峰频率都基本一致.说明利用模拟波面研究海浪具有代表性,它可以反映实测海浪的特征.利用实测海浪谱密度,统计波特征量的周期概率分布,得到理论周期概率密度与估计周期概率密度分布相符较好,且与模拟波面的波周期分布也较好的一致.利用Longuet-Higgins(1983)模型计算了波高-周期联合概率密度分布.得到变换高斯过程计算的波高与周期联合分布与实测情况基本相同,更好地描述了波高-周期联合概率密度分布.     

非线性海浪波面与波高的统计分布

采用风浪谱参量化的方法将随机波面无因次化,把波面与波高概率分布的各阶矩展开为谱宽度根方的幂级数,并由此导出波面与波高的统计分布。结果表明,在准确至零阶和一阶时,风浪分别退化为静止海面和单色波;在准确至二阶时,波面为线性模型,即波面服从正态分布;而在准确至三阶以上时,波面分布与Longuet-Higgins导出的非线性海浪模型的Gram-Charlier形分布具有同效益;并在准确至三阶时,导出一种新的波高分布,此分布函数以Longuet-Higgins等给出的Rayleigh分布作为二阶近似的特例。     

海浪波群波高的统计分布

本文根据Rice和Longuet-Higgins提出的波群包络线统计理论,导出了波群包络线最大值和波群波高的统计分布.只要计算出海浪谱及各阶矩,便可由海浪波高得到波群波高,本文应用截断的P-M谱计算得到了理论分布曲线,并用外海和实验室资料进行了比较.     

风浪波高和周期的联合概率密度分布

本文采用有代表性的44008美国国家浮标站2003年1～3月实测的海浪谱密度资料,选取三次大风过程进行风浪谱分析。通过对实测平均海浪谱与PM谱、JONSWAP谱及Torsethaugen谱的比较,得到PM谱拟和最好。然后用国际上最先进的随机波分析方法,根据协方差矩阵的循环嵌套技术,以实测平均谱与PM谱为靶谱,对随机波面进行模拟。得到由模拟波面统计的特征值及估计的谱与实测谱结果极为相近,谱峰及谱峰频率都基本一致。说明利用模拟波面研究海浪具有代表性,它可以反映实测海浪的特征。利用Longuet-Higgins(1983)模型计算波高-周期联合概率密度分布,得到变换高斯过程计算的波高、周期联合分布与实测情况基本相同,更好地描述了波高-周期联合概率密度分布。     

北礵岛附近海域夏季海浪波高-周期分布特征

利用2016年夏季(6—8月)北礵岛附近海域的实测波浪数据,统计分析该海域海浪的波高特征值,探讨各特征波高与平均波高及有效波高之间的关系,找出较适用于该海域的波高分布、周期分布以及波高和周期的联合分布。结果表明:该海域有效波高的平均值为0.73 m,最大值为2.96 m,平均周期的平均值为4.50 s;各特征波高与平均波高及有效波高的比值普遍小于Rayleigh分布理论值;采用双参数Weibull分布,利用最小二乘法拟合出的波高分布和周期分布较适用于该海域。根据实测波高和周期联合分布结果,与已有的波高和周期理论分布进行对比,发现Longuet-Higgins改进分布和孙孚分布较适用于该海域的波高和周期联合分布特征。     

基于Copula函数的联合概率法在海洋工程中的应用

本文介绍了Copula函数的定义、属性和几种特殊的Copula函数.将Copula函数应用到近海工程中,用其建立了最大有效波高和最大风速的联合分布函数并检验,结果表明:Copula函数能够比较好的模拟实际的联合概率分布。通过Copula方法,可以由边缘分布和一个连接它们的Copula函数来得出联合分布函数,发挥其描述相关性尤其是尾部相关性的优势。该方法在近海工程的工程可靠度、设计标准和失效概率的计算中具有广泛的应用前景。     

海浪局部振幅和局部周期的统计分布

根据平稳正态随机过程及其Hilbert变换的性质,在不受窄谱限制的条件下,严格导出海浪局部振幅A局部周期T的分布函和联合分布函数,并以在实验室水槽中产生的三种不同谱宽度的波浪作了验证,结果比较满意。     

The distribution of zero-crossing wave heights and periods in a stationary sea state

Existing theoretical distributions of wave height and period do not reflect measured joint distributions from field data. A simulation methodology is introduced to retain the essential features of the theoretical background in Gaussian random noise but to avoid further compromising assumptions in the interpretation of height and period in the amplitude domain. A joint distribution can be associated directly with an empirical or measured variance spectrum. Spectral shape appears to dominate the detail of predicted joint distributions. There is generally a much sharper decay in probability levels at higher periods than is predicted by theoretical models. For Jonswap spectra, there is a dominant central ridge and a distinct bimodal structure in the joint distribution, features that are not evident in symmetric Gaussian spectral forms. The wave height distributions for Jonswap spectra differ little from the Rayleigh distribution, except at extreme wave heights where Rayleigh overpredicts. The period distributions are strongly sensitive to spectral shape. In the conditional distribution of periods, given the height, the asymptotic median period at extreme wave heights is significantly longer than the mean period for Jonswap spectra, but not for symmetric Gaussian forms.     

On the long-term joint distribution of characteristic wave height and period and its application

By analysing the scatter diagrams of characteristic the wave height H and the period T on the basis of instrumental data from various ocean wave stations, we found that the conditional expectation and standard deviation of wave period for a given wave height can be better predicted by using the equations of normal linear regression rather than by those based on the log- normal law. The latter was implied in Ochi' s bivariate log-normal model(Ochi. 1978) for the long-term joint distribution of H and T. With the expectation and standard deviation predicted by the normal linear regression equations and applying proper types of distribution, we have obtained the conditional distribution of T for given H. Then combining this conditional P(T / H) with long-term marginal distribution of the wave height P(H) we establish a new parameterized model for the long-term joint distribution P(H,T). As an example of the application of the new model we give a method for estimating wave period associated with an extreme w     

海浪的条件特征周期

在海浪波面高度为正态分布的假定下,导出一种以给定波高为条件的条件周期概率密度函数.与风浪槽中测量数据比较,结果表明,在窄谱情况下此概率密度函数与实验室风浪的实际符合良好.根据此密度函数定义了3种条件特征周期,并导出它们与平均周期的关系式.根据这些关系对有关海洋工程上的一些问题作了解释和讨论.     

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.     

Long-Term Joint Distribution of One-Tenth Large (or Significant) Wave Height with Average Period

- In this paper, by using the wave data from a few oceanographic observation stations in the coastal zone of the Yellow Sea, the East China Sea and the South China Sea, the long-term joint distribution of the one-tenth large (or significant) wave height with average period is studied. The statistical data demonstrate that the long- term distribution of the one- tenth wave height or average period fits the log-normal distribution, thus the joint distribution also fits the two-dimensional log-normal distribution. Then the conditional probability distribution of the average period is derived, and the range as well as the mode of the average wave period corresponding to a certain return period of wave height can be calculated easily.     

Statistical properties of successive wave heights and successive wave periods

Two successive wave heights are modeled by a Gaussian copula, which is referred to as the Nataf model. Results with two initial distributions for the transformation are presented, the Næss model [Næss A. On the distribution of crest to trough wave heights. Ocean Engineering (1985);12(3):221–34] and a two-parameter Weibull distribution, where the latter is in best agreement with data. The results are compared with existing models. The Nataf model has also been used for modeling three successive wave heights.Results show that the Nataf transformation of three successive wave heights can be approximated by a first order autoregressive model. This means that the distribution of the wave height given the previous wave height is independent of the wave heights prior to the previous wave height. Thus, the joint distribution of three successive wave heights can be obtained by combining conditional bivariate distributions. The simulation of successive wave heights can be done directly without simulating the time series of the complete surface elevation.Successive wave periods with corresponding wave heights exceeding a certain threshold have also been studied. Results show that the distribution for successive wave periods when the corresponding wave heights exceed the root-mean-square value of the wave heights, can be approximated by a multivariate Gaussian distribution.The theoretical distributions are compared with observed wave data obtained from field measurements in the central North Sea and in the Japan Sea, with laboratory data and numerical simulations.     

广东阳西近岸海域波浪的分布特征

通过对广东阳西近岸测站1a实测波浪资料及岸边同期风资料的整理与分析,探讨了该海域的波浪特性,得出研究海域不分方向H1/10年平均值为1.00 m,常浪向为SE向,出现的频率为38.35%,强浪向为SE向,观测期间的最大波高出现在0814号"黑格比"台风期间,Hmax值为8.31 m.用已有的理论分布函数对实测统计数据进行拟合,筛选出研究海域的波高分布、周期分布及波高与周期联合分布的特征,结果表明双参数威布尔理论波高分布、杨正己威布尔周期分布、朗格-赫金斯83模式或者孙孚模式较为适用于本海区的波高分布、周期分布、波高周期联合分布;结合相应的风速风向资料,运用回归分析方法,建立了该地区的波高与风速之间、波高与波周期之间的关系.     

Estimating the potential of ocean wave power resources

The realistic assessment of an ocean wave energy resource that can be converted to an electrical power at various offshore sites depends upon many factors, and these include estimating the resource recognizing the random nature of the site-specific wave field, and optimizing the power conversion from particular wave energy conversion devices. In order to better account for the uncertainty in wave power resource estimates, conditional probability distribution functions of wave power in a given sea-state are derived. Theoretical expressions for the deep and shallow water limits are derived and the role of spectral width is studied. The theoretical model estimates were compared with the statistics obtained from the wave-by-wave analysis of JONSWAP based ocean wave time-series. It was shown that the narrow-band approximation is appropriate when the variability due to wave period is negligible. The application of the short-term models in evaluating the long-term wave power resource at a site was illustrated using wave data measured off the California coast. The final example illustrates the procedure for incorporating the local wave data and the sea-state model together with a wave energy device to obtain an estimate of the potential wave energy that could be converted into a usable energy resource.     

基于波高和周期双指标的福建海域海浪危险性分析

现行的海浪危险性评估方法仅以波高作为指标,没有考虑波浪周期对海上建筑物和船舶航行安全的影响。基于1979-2016年福建外海海浪数值后报结果,建立了基于周期的海浪强度和危险性等级划分标准,提出了基于波高和周期双指标的福建海域海浪危险性分析方法。结果表明,双指标下海浪危险等级分布结合了波高单指标下环状分布和周期单指标下带状分布的特点,以台湾海峡中南部海域海浪危险等级最高,闽南近岸海域海浪危险等级高于闽东和闽中海域,总体危险等级分布呈现南高北低的特征;双指标下的福建外海海浪危险等级分布比单指标考虑更为全面,不仅包含波高对结构物的影响还考虑了周期对浮式结构物和防波堤的作用,更加贴近真实情况下的海浪危险性特征。     

The long wave climbing a shore in a bay of variable cross-section

The long wave climbing a shore is studied assuming the shelf surface to be a tilted parabolic cylinder. Asymptotic formulae have been derived which permit extreme values of water surface elevation and velocity at the water's edge to be calculated, when the incident wave has an arbitrary form. For the case where the impinging wave is a simple harmonic, we have derived an accuration solution for evolution of the wave height at the water's edge.Translated by V. Puchkin.