Local properties of sea waves derived from a wave record

It is demonstrated that for linear deep sea waves with small directional scattering the particle motion at the sea surface and energy transmission may be retrieved from a wave record by means of the Hilbert transform. A physical interpretation of the envelope of the two-dimensional deep sea waves as well as a new method for wave group analysis is presented.     

Observations and Estimations of Directional Spectrum of Sea Waves

The directional spectrum is one of the basic characteristics of sea waves. The observations of directional spectrum of sea waves were successfully conducted at platform Bohai 8 during 1991 and 1992 using a wave gage array for the first time in China. Based on the field data, the directional spectrum which depends on the wave growth is given in this paper. Before observations, the effects of the type of gage array, the distance between the gages and the platform itself on the measured results and the precision of some methods for estimating the directional spectrum were investigated and compared with the methods of numerical simulations and model tests of multi-direcitonal irregular waves. This ensures the quality of the observations and estimations of the directional spectrum.     

分析海浪方向谱的扩展本征矢方法Ⅰ.方法的导出

基于交叉谱矩阵可以按本征值划分为信号和含有噪音部分的思想，提出了一种自直接测量数据估计海浪方向谱的方法。该方法称为扩展本征矢方法（EEV），可应用于单点测量系统、仪器阵列以及由二者构成的复合阵列。现有的某些估计方法（如最大似然方法及其扩展形式等）仅是此方法的某种特例。     

Estimation Approaches of ηUV,PUV and UV Directional Wave Spectra and Their Comparison

The observation and estimation of directional spectra of sea waves is one of the essential subjects of study of oceanic dynamics. On the basis of the irregular linear wave theory, estimation methods for i/UV, PUV and VV directional wave spectra are derived. By using ij and PUV data measured in-situ, directional wave spectra are estimated, meanwhile the virtues and defects of various spectra are comparied. This method provide a basis for the observations of sea waves.     

Estimation of mean spectral directions in random seas

A method for obtaining the directional spectrum, on assuming that the frequencies of the elementary waves are all different from one another, is re-proposed in a form suitable for applications to sea states near a coast. The method is applied to an interval of 10 h during which the sea state remained basically steady state off the beach at Reggio Calabria (east coast of the Straits of Messina). It is shown that the directional spectrum converges as the length of the time series data grows. A numerical simulation of a 10 h sea state confirms that the directional spectrum converges as the length of the time series grows, and the convergence is onto the known directional spectrum used to make the numerical simulation. Through the numerical simulation, it is proved that the method, generally, is suitable for applications even with short time series of wind waves (duration of about 100T_p). Finally, it is shown that the method is not necessarily inadequate even with short records of multimodal sea states with different modal directions, modal amplitude ratios and intermodal distances.     

海浪方向谱的现场观测与分析

方向谱是海浪的基本性质之一。本文在国内首次采用测波仪阵列法在渤海采油平台上成功地观测到海浪方向谱，给出了当地随波浪成长而变化的方向谱表达式。观测前采用数模和模型试验方法，对阵列的布置型式、测波仪间距和平台等对观测结果的影响，以及现有各种方向谱分析方法的精度等进行了对比分析，为提高观测精度，保证方向谱分析的质量提供了依据。     

A locally nonlinear interpretation of PUV measurements

A time domain method is presented for analyzing simultaneous measurements of pressure and the horizontal components of velocity obtained beneath irregular multidirectional wave fields. This new method differs from the usual linear directional analyses applied to PUV data in two important aspects. First, the essential nonlinearity of the measured waves is not sacrificed to achieve a solution. Therefore, predictions of sea surface elevation and directional kinematics throughout the water column accurately portray the actual nonlinear character of the waves. Second, the analysis method is `local' in that it can be applied to segments of PUV time series much shorter than an individual wave. The viability of the locally nonlinear methodology developed in this paper is proven by demonstrating agreement with higher-order theoretical steady waves. Predictions of sea surface elevation and wave kinematics are also made using actual measurements from PUV instruments at two ocean sites off the west coast of the United States.     

Multidirectional wave transformation around detached breakwaters

The performance of the new wave diffraction feature of the shallow-water spectral model SWAN, particularly its ability to predict the multidirectional wave transformation around shore-parallel emerged breakwaters is examined using laboratory and field data. Comparison between model predictions and field measurements of directional spectra was used to identify the importance of various wave transformation processes in the evolution of the directional wave field. First, the model was evaluated against laboratory measurements of diffracted multidirectional waves around a breakwater shoulder. Excellent agreement between the model predictions and measurements was found for broad frequency and directional spectra. The performance of the model worsened with decreasing frequency and directional spread. Next, the performance of the model with regard to diffraction–refraction was assessed for directional wave spectra around detached breakwaters. Seven different field cases were considered: three wind–sea spectra with broad frequency and directional distributions, each coming from a different direction; two swell–sea bimodal spectra; and two swell spectra with narrow frequency and directional distributions. The new diffraction functionality in SWAN improved the prediction of wave heights around shore-parallel breakwaters. Processes such as beach reflection and wave transmission through breakwaters seem to have a significant role on transformation of swell waves behind the breakwaters. Bottom friction and wave–current interactions were less important, while the difference in frequency and directional distribution might be associated with seiching.     

分析海浪方向谱的EEV方法的一种迭代形式

将Pawka为改进最大似然方法（MLM）而提出的迭代方案应用于扩展本征关方法（EEV），作为EEV的一种迭代形式（IEEV）。用模拟数据检验了IEEV的合理性，并与EEV作了比较。计算结果表明，IEEV的估计性状较EEV有改善。最后将IEEV及EEV用于分析仪器阵列的外海观测数据。     

Detection of nonlinear waves and their contribution to ocean wave spectra Part I: Theoretical consideration

This is a Part I of a paper of nonlinearities of wind waves in the deep open ocean. First, considerations are given in order to verify the theoretical expression for bound waves from observed data. We compare the contribution of bound waves and double Bragg scattering to the second-order scattering, and we show that the contribution of bound waves is larger, and that bound waves can be detected by measuring the Doppler spectra of HF (high-frequency) radio wave scattering from the sea surface. Moreover, if the theory of the HF radio wave scattering from the sea surface is verified, so is the second-order perturbation theory for bound waves. Then, the contributions of bound waves to ocean wave spectra are investigated on the basis of the nonlinear theory. The bound waves are shown to modify frequency spectra and wave directional distributions at higher frequencies, and it is shown that although the modifications of frequency spectra are smaller for a two-dimensional field case than for a one-dimensional field case, they are not negligible at higher frequencies. On the other hand, the modifications of wave directional distributions are shown to be significant at higher frequencies. These discussions become significant only when bound wave predictions are verified in the open ocean. Consequently, it is shown that nonlinearities of water waves are important in considering both radio wave scattering from the sea surface and the detailed structures of ocean wave spectra at high frequencies.     

Rogue waves during Typhoon Trami in the East China Sea

As concluded from physical theory and laboratory experiment,it is widely accepted that nonlinearities of sea state play an important role in the formation of rogue waves;however,the sea states and corresponding nonlinearities of real-world rogue wave events remain poorly understood.Three rogue waves were recorded by a directional buoy located in the East China Sea during Typhoon Trami in August 2013.This study used the WAVEWATCHⅢmodel to simulate the sea state conditions pertaining to when and where those rogue waves were observed,based on which a comprehensive and full-scale analysis was performed.From the perspectives of wind and wave fields,wave system tracking,High-Order Spectral method simulation,and some characteristic sea state parameters,we concluded that the rogue waves occurred in sea states dominated by second-order nonlinearities.Moreover,third-order modulational instabilities were suppressed in these events because of the developed or fully developed sea state determined by the typhoon wave system.The method adopted in this study can provide comprehensive and full-scale analysis of rogue waves in the real world.The case studied in this paper is not considered unique,and rules could be found and confirmed in relation to other typhoon sea states through the application of our proposed method.     

不规则波作用下的船舶撞击作用

随着波谱理论研究的发展,各种海工结构及船舶的荷载及其内力分析也日趋应用不规则波的计算方法。目前对于外海码头在波浪作用下的船舶撞击荷载还应用规则波的研究方法,对其应用不规则波分析方法的途径以及在考虑波谱作用后会有怎样的结果等问题目前还较少研究。本文试图对此问题进行初步的分析。     

Directional seas should be ergodic

Directional seas are often modelled as a double summation of plane sinusoidal waves from different directions at a set of discrete frequencies. Unfortunately, this model is commonly used in a way which produces unrealistic standing wave phenomena and hence is not ergodic. Consequently, time averages of variables are not necessarily the same as space averages and averages over different realisations. The resulting point spectrum is randomly distributed about the target point spectrum as required, but the time history generated is only representative of a short record of the target sea. In this note, the basis of the phenomenon and its consequences for both wave tank and computer simulation work are described. Two alternative techniques of directional wave generation are discussed.

Standing waves also occur near reflectors in the sea and test tanks; their effects on point and directional wave measurements are discussed.     

论运动坐标系中的海浪谱

基于Galieo变换，导出了运动坐标系与静止坐标系中海浪谱间的关系。由于海浪是频散的，两者间的关系是频率相关的。运动坐标系中的海浪频谱是与静止坐标系中的海浪方向谱相联系的。以文氏谱作为静止坐标系中的海浪频谱，给出了不同速度下运动坐标系中的海浪频谱。     

胶州湾双峰谱型波浪的统计特征

本文对胶州湾实测双峰海浪谱的资料进行了统计分析和谱分析，探讨了双峰谱型海浪的波要素概率分布及其群性特征，并与单峰谱型海浪进行了比较．最后通过双峰谱的合成波高、周期与实测值的比较，对采用能量迭加方式的式（９）和式（８）进行一些讨论，主要结果列于本文最后一节．     

分析海浪方向谱的扩展本征矢方法

采用Ｌｏｎｇｕｅｔ－Ｈｉｇｇｉｎｓ形式的方向分布函数作为已知谱，用模拟数据检验了作者是所提出的估计方法ＥＥＶ合理性，并与扩展最大似然方法（ＥＭＬＭ）及Ｌｙｇｒｅ等（１９８６）的最在熵方法（ＭＥＭ）作了比较，在验证和比较中，使用纵摇－横摇浮标，星形阵形和ＣＥＲＣ阵列作为复合阵列，计算表明，ＥＥＶ优于ＥＭＬＭ和ＥＭＥ。最后将ＥＥＶ和ＥＭＬＭ两种方法应用于仪器阵列的外海观测数据，得到了比较合理的海浪方向     

Detection of nonlinear waves and their contribution to ocean wave spectra Part II: Observation

This is a Part II of a paper of nonlinearities of wind waves in the deep open ocean. As shown in Part I, bound waves in deep sea are detectable by extracting secondorder Doppler spectra from the Doppler spectra of HF (high-frequency) radio waves scattered from the sea surface. There is a remarkable agreement between the calculated and measured Doppler spectra, considering the noise levels in measured Doppler spectra and the uncertainties in directional properties. The theoretical expression for bound waves is thus verified. Furthermore, the upper limit in calculating the Doppler spectra for the second-order approximation is presented from field observations, although we cannot conclude that it is equivalent to the limitation of the second-order bound wave theory. It is shown that analysis of radio wave scattering by the sea surface is one useful means of understanding the nonlinear properties of ocean waves.     

New simplified formulas for ELF subsurface-to-subsurface propagation

New formulas for the electric and magnetic fields produced by the four elementary dipole antennas have been developed for the subsurface-to-subsurface propagation case. The formulas are of rather simple, but useful, form and are completely general (i.e., the air can easily be replaced by the sea bottom). They are valid at any frequency and at any range beyond a certain minimum distance for the flat-earth case. They are especially applicable at extremely low frequency (ELF) for the air/sea and sea/ seabed propagatipn cases. The main restrictions on these formulas are 1) the square of the index of refraction is greater than or equal to 10 and 2) the horizontal separation is greater than or equal to 3 times the sum of the depths of burial of the transmitting and receiving point sources. With these new formulas, computer evaluation can be reduced to fractions of a minute, compared with hours for the complete numerical evaluation of the exact Sommerfeld integrals. The formulas also exhibit an interference pattern set up under certain close-range conditions. The three waves (direct, modified mirror image, and lateral) may interfere, either constructively or destructively, with each other.     

一种实体嵌入的三维海浪可视化方法

针对实体嵌入对海面的随机干扰问题,提出一种海浪三维可视化方法。该方法采用扰动的思想改进了海浪的数学模型,并利用信息更加全面的方向谱描述海浪,进而将方向谱和改进海浪模型共同应用于海浪的三维可视化,形象展示实体嵌入时对海浪的随机性影响,并给出了三维实体的建模方法。通过多组实体嵌入的海浪可视化仿真试验的比较与分析,验证了本文提出方法的有效性。