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.     

论风浪的局域结构──Ⅰ.风浪的局域结构与局域小波能谱

基于小波变换,引入了能刻画风浪局域结构的局域小波能谱。论述了风浪的整体结构与局域结构。指出了在不同时间尺度上,风浪具有不同的局域化特征。提出了风场演化过程中整体的共振在线性相互作用是否存在的质疑。     

Hilbert Transferin Applied to Separation of Waves

The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is ap-plicable to both regular and irregular trains of waves. The wave data series measured with two wave gauges in the experi-ments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily ob-tained. The arrival of reflected waves can also be detected for improveraent of the accuracy of the reflection coefficient. The reflection performance of the physical model can be estimated exactly without calculation of wave height and phase difference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conduct-ed and compared with Goda s method and satisfactory results are obtained.     

Analysis of wave groups by wave envelope-phase and the Hilbert Huang transform methods

The wave groups are studied by both conventional wave analysis methods and by the non-stationary Hilbert Huang Transform (HHT) method. Full-scale wave records containing abnormal waves are used. Instantaneous quantities, such as envelope, phase and frequency, are adopted to study the wave grouping. A refined definition of wave group is proposed considering that the wave process is simultaneously amplitude and frequency modulated. The validation of the proposed definition is conducted by analysis of numerical simulation data. Group parameters are proposed based on the time-frequency distribution of energy. An attempt is made to find the relationship between the characteristics of abnormal waves and the group characteristics.     

基于小波变换法定义的波群参数

通过小波变换分析的波能过程定义了两个描述波浪群性的参数,由数值模拟波浪和实测波浪资料对其与常用的波群参数进行对比分析,结果表明基于小波波能过程定义的群性参数是有效的,从而展示了小波变换用于在时频域上分析波群的能力。详细探讨了波浪记录长度对群性参数稳定性的影响,分析结果表明,波浪观测长度对于波群参数的影响较大,在考虑波浪群性的波浪模拟及分析时,建议模拟时间长度应在400~500个波以上。     

Laboratory study of wave and turbulence characteristics in narrow-band irregular breaking waves

Wave elevations and water particle velocities were measured in a laboratory surf zone created by the breaking of a narrow-band irregular wave train on a 1/35 plane slope. The incident waves form wave groups that are strongly modulated. It is found that the waves that break close to the shoreline generally have larger wave-height-to-water-depth ratios before breaking than the waves that break farther offshore. After breaking, the wave-height-to-water-depth ratio for the individual waves approaches a constant value in the inner surf zone, while the standard deviation of the wave period increases as the still water depth decreases. In the outer surf zone, the distribution of the period-averaged turbulent kinetic energy is closely correlated to the initial wave heights, and has a wider variation for narrow-band waves than for broad-band waves. In the inner surf zone, the distribution of the period-averaged turbulent kinetic energy is similar for narrow-band waves and broad-band waves. It is found that the wave elevation and turbulent kinetic energy time histories for the individual waves in a wave group are qualitatively similar to those found in a spilling regular wave. The time-averaged transport of turbulent kinetic energy by the ensemble-averaged velocity and turbulence velocity under the irregular breaking waves are also consistent with the measurements obtained in regular breaking waves. The experimental results indicate that the shape of the incident wave spectrum has a significant effect on the temporal and spatial variability of wave breaking and the distribution of turbulent kinetic energy in the outer surf zone. In the inner surf zone, however, the distribution of turbulent kinetic energy is relatively insensitive to the shape of the incident wave spectrum, and the important parameters are the significant wave height and period of the incident waves, and the beach slope.     

海浪局部频率及波面水质点局部速度的统计分布

根据平稳正态随机过程和Ｈｉｌｂｅｒｔ变换的性质,推导了海浪局部频率及波面水质点局部速度的统计分布,以Ｐｉｅｒｓｏｎ－Ｍｏｓｃｏｗｉｔｚ谱为例进行了讨论。本文的结果为解释与海上结构物ｒｉｎｇｉｎｇ现象产生有关的海浪事件提供了一种可能的参考依据。     

Hilbert Transform Applied to Separation of Waves

The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is ap-plicable to both regular and irregular trains of waves. The wave data series measured with two wave gauges in the experi-ments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily ob-tained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient.The reflection performance of the physical model can be estimated exactly without calculation of wave height and phasedifference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conduct-ed and compared with Goda‘s method and satisfactory results are obtained.     

Analysis and simulation of wave records through fast Hartley transform

The Hartley transform, a real-valued alternative to the complex Fourier transform, is presented as an efficient tool for the analysis and synthesis of ocean surface wave records. Basic theoretical properties of this real-valued transform are briefly reviewed. Similarities and differences between Fourier and Hartley integral transforms, as well as computational benefits and disadvantages between numerical algorithms used to evaluate their discrete versions, are presented. The fast Hartley transform algorithm is used to simulate stationary Gaussian time series of the sea surface elevation and to estimate the spectral density function, the Hilbert transform and the envelope function of wave records.     

Capillary waves understood by an elementary method

The central physics of capillary waves (or ripples) can be understood by an elementary method which makes use of the balance of static and dynamic pressure differences along the surface streamline between crest and trough, in the steady reference frame, and conservation of mass through vertical cross-sections beneath crest and trough. Basically Einstein’s (1916) model of surface gravity waves is adapted for the purpose of explaining the existence of capillary waves of infinitesimal amplitude. One product of the physical understanding, the phase speed of capillary waves, is derived as a function of the wave length and surface tension and the result agrees exactly with that obtained by the classical mathematical procedure. In the elementary method it is not necessary to assume irrotational flow, upon which the classical theory is founded, nor are perturbation expansions of the nonlinear fluid equations employed. The extension to capillary-gravity waves, by including the acceleration of gravity in the physical model, is straightforward, and the calculated phase speed of these waves is identical to what is found in the text books as well.     

Calculation of slowly varying drift forces

A new method for approximating time dependent drift forces in irregular, long or short crested sea is presented. The approximation is based on the assumption that the wave energy spectrum is narrow-banded. The drift forces may be computed from the spectrum or directly from a time record of waves by using Hilbert transforms. Numerical calculations are made for drift forces and corresponding motions of a floating box, and the method is compared to a commonly used method due to Newman. The two methods are found to agree very well.     

Hilbert变换在海浪波高与周期联合分布函数中的应用

Longuet-Higgins(1983)[1]导出了波高与周期的联合分布函数,此分布函数虽然与实际数据符合良好,但存在很大的缺陷,如:由此分布函数得出的波高分布为形式较为复杂的非Rayleigh分布,很难应用于工程计算中。孙孚(1988a)[2]应用射线理论导出了一种波高与周期联合分布,虽然弥补了Longuet-Higgins的一些缺陷,但推导过程过于复杂。本文在窄谱假定下通过应用Hilbert变换方法得出新的分布函数并与前两者比较,表明Hilbert变换的方法不但简便,而且完全克服Longuet-Higgins的不足,可以方便的应用于工程计算中。本文也为Hilbert变换的方法在工程中的应用提供了理论依据。     

风浪局域小波谱峰的涨落

将湍流研究中已得到有效应用的局域小波能谱概念引入到风浪研究.分析了实验室不同风速下风浪的局域小波能谱.结果表明,局域小波谱峰值存在着显着的涨落,涨落的方差随风速的增加而增大.这不仅体现了风浪的局域结构,还意味着通常风浪谱的应用中除了要考虑平均意义下的频谱峰值外,还必须考虑局域小波谱峰值的涨落方差.     

Two-dimensional continuous wavelet transform of simulated spatial images of waves on a slowly varying topography

The wavelet transform (WT) is now recognized as a useful, flexible, and efficient technique to analyze intermittent, non-stationary and inhomogeneous signals as well as images which are obtained from experimental or in situ measurements. In this study, the two-dimensional continuous wavelet transform (2-D CWT) was introduced to analyze the spatial image of waves. The numerical algorithm of 2-D CWT was developed and testified in simulated wave field of regular and random waves. Some more simulated wave fields of various wave conditions and sea bed slopes were then assumed to verify the analytical accuracy of this new technique. The comparisons of estimations to theoretical values for several wave parameters show that the 2-D CWT is capable of identifying the directional spectra and wave properties in shallow water.     

Physical model of the spectrum of capillary-gravity waves

A model for the spectrum of capillary waves has been constructed. These waves are generated at the crests of short gravity waves and decay due to viscosity. Capillary wave generation leads to short gravity wave dissipation. Using empirical data on the short gravity wave dissipation spectrum, a relation for the capillary wave spectrum is derived from the equation of energy balance of capillary waves. The capillary wave spectrum is matched with the known Donelan-Pierson spectrum for short gravity waves. The obtained relation for the spectrum of wind-generated ripple is compared with the data of laboratory experiments. Translated by Vladimir A. Puchkin.     

Fluctuations of peak energy and peak frequency of local wavelet energy spectrum for wind waves

Ｆｌｕｃｔｕａｔｉｏｎｓ　ｏｆ　ｐｅａｋ　ｅｎｅｒｇｙ　ａｎｄ　ｐｅａｋ　ｆｒｅｑｕｅｎｃｙ　ｏ　ｌｏｃａｌ　ｗａｖｅｌｅｔ　ｅｎｅｒｇｙ　ｓｐｅｃｔｒｕｍ　ｆｏｒ　ｗｉｎｄ　ｗａｖｅｓTXＦｌｕｃｔｕａｔｉｏｎｓｏｆｐｅａｋｅｎｅｒｇｙａｎｄｐｅａｋ...     

双曲余弦海脊上海啸俘获波的解析与数值研究

海啸能被大洋海脊引导以俘获波的形式沿其传播上万千米,且因其特殊的运动方式,携带巨大能量影响远场地区的港口,严重威胁海岸安全。本文首先基于线性浅水方程,推导了双曲余弦平方海脊上俘获波的波面解,其为μ阶ν次的连带勒让德函数的第一类解和第二类解的组合。进一步推导出其对应的频散关系,其中对于确定的频率ω,存在无穷多个波数k_y与之对应。采用MIKE21-BW模型,模拟了产生于海脊脊顶处的海啸在理想双曲余弦平方海脊上的传播变形过程。结果表明,小部分能量以自由先驱波进行传播,海啸波的波能大部分被海脊俘获。海脊俘获波沿着海脊方向为行进波,随着海啸波传播时间的增加,波浪在沿着海脊方向的延展范围也逐渐增大,波高逐渐减小、波的个数逐渐增加。俘获波能量主要由不同频率以相同速度传播的具有孤立波特性的波浪成分和能量主要集中在特定频率范围内的波浪成分组成。     

Flow under standing waves: Part 1. Shear stress distribution,energy flux and steady streaming

The conditions for energy flux, momentum flux and the resulting streaming velocity are analysed for standing waves formed in front of a fully reflecting wall. The exchange of energy between the outer wave motion and the near bed oscillatory boundary layer is considered, determining the horizontal energy flux inside and outside the boundary layer. The momentum balance, the mean shear stress and the resulting time averaged streaming velocities are determined. For a laminar bed boundary layer the analysis of the wave drift gives results similar to the original work of Longuet–Higgins from 1953. The work is extended to turbulent bed boundary layers by application of a numerical model. The similarities and differences between laminar and turbulent flow conditions are discussed, and quantitative results for the magnitude of the mean shear stress and drift velocity are presented. Full two-dimensional simulations of standing waves have also been made by application of a general purpose Navier–Stokes solver. The results agree well with those obtained by the boundary layer analysis. Wave reflection from a plane sloping wall is also investigated by using the same numerical model and by physical laboratory experiments. The phase shift of the reflected wave train is compared with theoretical and empirical models.     

Nonlinear effects of the distribution of amplitudes of sea waves

The effect of nonlinearities, such as wave-breaking and vertical asymmetry associated with sea waves, on the distribution of wave amplitudes is explored. Semiclosed theoretical expressions are derived to describe the distributions of breaking-limited crest and trough amplitudes for Stokes-type nonlinear sea waves. These are compared with the conventional Rayleigh distribution appropriate to linear wave amplitudes. The construction of nonlinear wave envelopes with the fast Fourier transform technique is described. The technique can be utilized to enlarge the data base in empirical analyses of field records which typically contain limited information on amplitude characteristics. The theoretical distributions and the proposed data enlargement technique are demonstrated with the analysis of a nonlinear wave record.