Evolution of surge in the sea of finite depth under the effect of wave-wave interactions

The wave-wave kinetic equation for surface gravity waves occurring in a deep sea and a sea of finite depth is solved numerically, using the Runge-Kutta technique. Spectral evolution was the result only of the waves’ being non-linear, without any contribution from wave generation and dissipation. The JONSWAP frequency spectra and the angular spectra of various widths were used to perform calculations. The existence of a steady angular wave spectrum, following its long evolution in a deep sea, has been confirmed here. For the sea of finite depth, a new result has been obtained. It exhibits the ‘focusing’ of the frequential and the angular spectra when the wavelength of a harmonic from the spectral maximum equals 2π, of the depth of the sea. With the depth further decreasing, the wave spectrum swiftly expands. The three-dimensional wave field in a deep sea becomes two-dimensional in the shallows. Translated by Vladimir A. Puchkin.     

The relationship between the amplitudinal characteristics of the high-frequency spectral components of wind-generated waves and the wind velocity over the sea

The relationship between the RMS amplitudes of the wind wave spectral components and the wind speed has been studied at ten frequencies in the band of 0.65–23 Hz. To measure the parameters of the high-frequenci waves, a resistance elevation wave gauge was operated, which was deployed in the Black See on an oceanographic platform near Katsively. The correlation between the wave amplitudes and the wind velocity at high frequencies of 5–23 Hz, corresponding to gravitation-capillary ripples, was found to reach a value of 0.8. At lower frequencies of 0.65–4.3 Hz, corresponding to short gravity waves, it dropped to 0.5–0.7. The response of spectral components to the wind speed variations in the gravity-capillary range is higher than in the range of short gravity waves. The results obtained differ from Phillips' idea about a saturated range for the frequency form of the spectrum of high-frequency gravity waves, since a linear dependence of the spectral amplitudes on the wind speed is established at a wind of force 1–8.Translated by Mikhail M. Trufanov.     

A comparison of observed and calculated directional wave spectra in the East China Sea

Directional wave spectra measured by a cloverleaf buoy in the East China Sea during AMTEX '75 have been compared with those calculated with the operational numerical MRI wave model developed at the Meteorological Research Institute of the Japan Meteorological Agency (J.M.A.). It is shown that the numerical wave model MRI can predict rather well, not only the frequency spectrum, but also the angular distribution function of the spectrum. The frequency dependence of the calculated angular distribution function is quite similar to that observed; the angular distribution is narrower for the spectral components near the peak spectral frequency but widens toward high frequencies and approaches the cos²-distribution.     

On the variability of the high-frequency part of the spectrum of wind-forced sea waves

Data on the temporal variability of sea wave spectral components in the frequency range 1–8 Hz, collected by a drifting vessel in the Pacific ocean (wind speed 1–10 m/s), are discussed in this paper. For the frequency range 3–6 Hz (wind speed 5–8 m/s), a weak variability of the ripples is observed, synchronous with long waves; in the remaining part of the spectral range studied the fluctuations are fortuitous. It is concluded that the wind plays a crucial role in forming the ripples' fluctuation characteristics in the high-frequency part of the spectrum.Translated by Vladimir A. Puchkin.     

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.     

Statistical characteristics of individual waves in laboratory wind waves I. Individual wave spectra and similarity structure

Statistical characteristics of individual waves in laboratory wind waves have been studied by use of a wind-wave tunnel. The individual waves are defined by actual undulations of the water surface at any instant, and are characterized by concentrated shearing stress and strong vorticity at their crests. A conspicuous self-similarity structure is found in the individual wave field. The similarity manifests itself as a simple spectral form, and as the statistical 3/2-power law between nondimensional wave height and wave period, and further as the -1/2-power relationship between nondimensional phase speed and frequency, for waves of the high frequency side. The normalized energy spectrum, specially defined for individual waves, has a form practically equivalent to the traditional spectrum for component waves in the main frequency range from 0.7 to 1.5 in the frequency normalized by the peak frequency, but does not have secondary peaks at harmonics. The phase speed of individual waves also coincides with that of component waves in the main frequency range.     

Spectral distribution of wave energy dissipation by salt marsh vegetation

Spectral energy dissipation of random waves due to salt marsh vegetation (Spartina alterniflora) was analyzed using field data collected during a tropical storm. Wave data (significant wave heights up to 0.4 m in 0.8 m depth) were measured over a two-day period along a 28 m transect using 3 pressure transducers. The storm produced largely bimodal spectra on the wetland, consisting of low-frequency swell (7–10 s) and high-frequency (2–4.5 s) wind-sea. The energy dissipation varied across the frequency scales with the largest magnitude observed near the spectral peaks, above which the dissipation gradually decreased. The wind-sea energy dissipated largely in the leading section of the instrument array in the wetland, but the low-frequency swell propagated to the subsequent section with limited energy loss. Across a spectrum, dissipation did not linearly follow incident energy, and the degree of non-linearity varied with the dominant wave frequency. A rigid-type vegetation model was used to estimate the frequency-dependent bulk drag coefficient. For a given spectrum, this drag coefficient increased gradually up to the peak frequency and remained generally at a stable value at the higher frequencies. This spectral variation was parameterized by employing a frequency-dependent velocity attenuation parameter inside the canopy. This parameter had much less variability among incident wave conditions, compared to the variability of the bulk drag coefficient, allowing its standardization into a single, frequency-dependent curve for velocity attenuation inside a canopy. It is demonstrated that the spectral drag coefficient predicts the frequency-dependent energy dissipation with more accuracy than the integral coefficient.     

Modulation of short wind waves by a long surface wave: a mechanism for feedback with an air flow

The paper concentrates on the evolution of a spectrum of short wind waves (SW) along the profile of a long surface wave (LW). Short wave spectral variations are considered in the relaxation approximation. The SW spectrum is modulated by the orbital velocities of long waves and by the variations of wind stress along the LW profile. The latter effect occurs due to wind flux perturbations induced by both the long wave proper and variations of the sea surface roughness induced by the SW modulations. To describe this effect, a feedback mechanism is introduces—the growth of energy of short waves results in the larger roughness of the sea surface, thereby contributing to the local wind stress, which facilitates, in turn, the growth of short waves. With moderate and strong winds being involved, this effect (aerodynamic feedback) is shown to be dominant in the short wave spectrum modulation. The mechanism becomes more efficient with intensification of the wind and decreasing of the long waves' frequency. Results of model calculations are in agreement with the known experimental data. Translated by Vladimir A. Puchkin.     

Directional energy distribution of wind waves

Two-dimensional ocean wave spectrum developing under the atmospheric surface pressure fluctuations is linearly correlated with that of wind pressure itself, so that angular distribution of energy of ocean surface waves can be determined by directional properties of surface pressure fluctuations with the same frequency to the surface wave.From empirically determined spectral formula of the atmospheric surface pressure fluctuations the coefficients of Fourier series expanded around mean direction of wind are analytically integrated, from which r.m.s. angular distribution, spectral peakedness and long-crestedness are calculated, compared with previously proposed empirical formulae and observations carried out by ultrasonic current meter.     

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.     

SWAN模型对实验室小尺度浅水波浪模拟研究

基于浅水斜坡地形的物理模型试验数据,考察SWAN模型对实验室小尺度浅水波浪的模拟效果,进而检验其浅水项的模拟精度。模拟中采用直接输入初始测点的实测海浪谱进行造波,重点考察浅水中三波相互作用和变浅破碎两个源项,对不同工况下,SWAN模式在水深条件变化下的有效波高、谱平均周期、海浪谱演化的模拟能力进行研究。研究表明:模拟的有效波高较符合实测波浪的增长和衰减,但谱平均周期计算值明显偏小;海浪谱的能量转移机制同实测有较大区别,频谱模拟结果出现高频高估、低频低估现象。对两个源项进行对比分析得出三波相互作用对海浪谱的能量转换影响远大于变浅破碎耗散。想要提高近岸区谱平均周期和海浪谱的模拟精度则SWAN模型中三波非线性项的计算精确度仍需更多研究和改进。     

Water-temperature effect on the spectral density of wind gravity waves and on sea-surface roughness

The results of hourly measurements of sea roughness and hydrometeorological parameters, which were automatically taken from special buoys over a long period of time, were used. These buoys were located in the open regions of both the Atlantic and Pacific oceans in different climatic zones; the mean water-surface temperature around the buoys varies from 1–3°C to 26–28°C. In addition to measurement results, the tables contain data on the spectral density of sea roughness for a wide range of frequencies. An analysis of these data, which was made for a short-wave region of the wind-wave spectrum, for the first time revealed a noticeable watertemperature dependence of the spectral density of wind waves within the frequency range 0.30–0.40 Hz, which corresponds to wave lengths of 9-4 m. The presence of such dependence is explained by a rapid temperature change in kinematic sea-water viscosity. Earlier, we indicated the temperature dependence of only very short spectral components that relate to a centimetric wavelength range. The statistical significance of the watertemperature effect on the spectral density of waves of the indicated frequency is supported by the results of a variance analysis. Temperature variations in the parameter of sea-surface roughness, which is determined, first of all, by the energy of the spectral shortwave region, are estimated. Altimetry is the basic method which is used in remotely determining the velocity of near-water wind. This method allows one to obtain records of deviations of the sea surface from the geoid surface and to calculate (on the basis of these records) the spectral density of wave components of almost any frequency. It is known that the wave-spectrum components in the region of low frequencies are almost always affected by ripple. Consequently, the energy of these components is determined not only by wind forcing, and only the components in the range of frequencies exceeding approximately 0.3 Hz are purely windy. Therefore, using the results of sea-surface altimetry in order to determine the velocity of near-water wind, one should use the spectral densities of wave components in this frequency region. The water-temperature dependence of the spectral density of short wind waves is manifested only in a certain frequency interval, which supports this recommendation.     

深水随机波列中畸形波统计特征的研究

本文基于Longuet-Higgins随机波浪模型和JONSWAP谱,进行了大量深水随机波的模拟,获取了畸形波发生概率稳定的随机波列,并对随机波列中的畸形波进行了分析。结果表明,畸形波发生的概率小于基于Rayleigh分布预测结果,且随谱宽的减小而增大。在固定时间段内,畸形波发生的频次服从泊松分布,时间间隔服从指数分布,且随着谱宽的增大,畸形波的发生频次减小,相邻畸形波的发生时间间隔增加。通过小波变换方法分离随机波中的波群,研究了出现畸形波的波群特征,发现一个波群中最多会出现4个畸形波,但是在发生畸形波的波群中,单个畸形波的概率最大。随着谱宽减小,一个波群中包含多个畸形波的概率增加。另外,出现畸形波的波群时间长度服从广义极值分布,随着谱宽减小,畸形波波群的时间跨度增加。     

Numerical Study of Two-Dimensional Focusing Waves

Two-dimensional focusing waves are generated and investigated by numerical method. The numerical model is developed by introducing the wave maker boundary on the high-order spectral （HOS） method proposed by Dommermuth and Yue in 1987 and verified by theoretical and experimental data. Some cases of focusing waves considering different parameters such as assumed focusing amplitudes, frequency bandwidth, central frequency and frequency spectrum are generated. Characteristics of the focusing wave including surface elevations, the maximum crest, shift of focusing points and frequency spectra are discussed. The results show that the focusing wave characteristics are strongly affected by focusing amplitudes, frequency bandwidth, central frequency and frequency spectrum.     

Estimation of Wind Wave Frequency Spectra by Use of the Arcsine Law

In the present study,the surface elevation of wind waves oberved in laboratory and in the Bohai Sea are adopted for the estimation of the wind wave frequency spectrum by use of the method of the arcsine law(MAL).The traditional method uses the surface elevation to calculate the correlation and then estimate the frequency spectrum while the MAL,presented by Yu and Lan(1979),uses the time sequence of zero-crossing points of surface elevation rather than directly the surface elevation to calculate the correlation.66 sets of wind wave data obtained in laboratory and 420 sets of data observed in the Bohai Sea are adopted for the examination of the method introduced by Yu and Lan.Results show that the MAL can give reliable estimation of wind wave spectra.Correlation and form of spectra estimated by the MAL are similar to those estimated by the traditional method.The peak frequency and the spectral density in peak frequency by the MAL are close to those obtained by the traditional method.     

A representation for the frequency spectrum of wind-generated waves

This paper proposes the following generalized representation for a wind-wave frequency spectrum:

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where E = ∫S(f)df is the variance of the surface displacement; f_m is the frequency of the spectral peak; and C_i's, i = 1,2,3, are dimensionless parameters that can be determined from the internal spectral parameters of a given spectrum.When applied to 234 sets of wave spectra recorded in the Great Lakes, this representation has been realistic, accurate, and capable of representing widely varied wave processes. The C_i's are clearly related to wave growth processes; they are large during early growth, decrease as waves grow, and reach approximate equilibrium when waves are fully developed.     

星载高级合成孔径雷达波模式算法及其反演数据精度验证

搭载在欧洲环境卫星(ENVISAT)上的高级合成孔径雷达(Advanced Synthetic Aperture Radar,ASAR)二级波模式数据提供了诸多海浪信息包括有效波高、波向、波长和二维海浪谱等,在海浪预报模式中具有重要作用。本文拟利用浮标观测数据对ASAR波模式算法及其反演数据精度进行对比验证。由于SAR卫星在海面的特殊成像机制,不同海况下会有不同的测量结果,通过与美国国家浮标中心(NDBC)的浮标数据对比,显示ASAR有效波高在高海况下低估和在低海况下高估的现象,在中等海况下的测量结果较优。通过研究ASAR数据集中对应的海浪谱,按照能量与方向分布可分为四种类型:单一方向海浪谱(Ⅰ类谱),180°方向模糊海浪谱(Ⅱ类谱),海浪两个方向且能量分布杂乱(Ⅲ类谱),多个传播方向且谱型杂乱海浪谱(Ⅳ类谱)。探究在不同类型下的海浪参数的精度,结果表明在单一波向正常海浪谱情况下,有效波高、波向与浮标数据一致性较好,存在180°方向模糊的对称海浪谱仅有效波高精度较高,谱型杂乱的海浪谱海浪有效波高和波向反演结果均较差。     

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。     

不规则波下船舶运动响应特征数值分析

针对不规则波浪作用下Wigley型船的运动响应问题进行了系统的研究,采用统计学方法深入探讨了船舶不规则运动幅值和响应周期的分布规律,并通过傅里叶变换对船舶运动响应进行了频谱特征分析。结果表明,船舶横摇方向与升沉和纵摇方向随机运动的响应特征有显著差异。在升沉与纵摇方向,波浪谱峰频率远离自振频率,前十分之一大振幅运动对应周期离散性较小,基本稳定在波浪谱峰周期附近,但小振幅运动周期分布离散性较大,频谱分析指出船舶升沉与纵摇运动响应频谱在波浪谱峰频率附近出现明显峰值。而在横摇方向,波浪谱峰频率与自振频率相耦合,不同振幅的横摇运动响应周期均稳定在自振周期附近,且周期离散性较小,频谱分析也表明横摇运动响应频谱主要集中于船舶运动自振频率附近。     

Taylor Dispersion of Contaminants by Dual-peak Spectral Random Waves

Recent extensive and important studies have provided detailed information and compelling evidence on how the presence of waves influences the vertical diffusivity/dispersivity in the coastal environment, which can affect various water quality considerations such as the distribution of suspended sediments in the water column as well as the potential of eutrophication. Comparatively, how the presence of waves influences the horizontal diffusivity/dispersivity has received only scant attention in the literature. Our previous works investigated the role played by the Taylor mechanism due to the wave-induced drift profile which leads to the longitudinal dispersion of contaminants in the horizontal direction, under regular sinusoidal waves and random waves with single-peak spectra.Natural waves in the coastal environment, however, often possess dual-peak spectra, comprising both higher frequency wind waves and lower frequency swells. In this study, the Taylor dispersion of contaminants under random waves with dual-peak spectra is examined through analytical derivation and numerical calculations. The effects of various dual-peak spectral parameters on the horizontal dispersion, including the proportion of lower frequency energy, peak frequency ratio and spectral shape parameter, are investigated. The results show that the relative energy distribution between the dual peaks has the most significant effect. Compared with single-peak spectra with equivalent energy, the Taylor dispersion with dual-peak spectra is stronger when the lower frequency is close to the peak frequency of the single-peak spectrum, and weaker with the higher frequency instead. Thus, it can be concluded that with a dual-peak wave spectrum, wind-dominated seas with higher frequency lead to stronger dispersion in the horizontal direction than swell-dominated seas with lower frequency.