The energy cycle of wind waves on the sea surface

The problems of wind-induced waves on the sea surface are considered. To this end, the empirical fetch laws that determine variations in the basic periods and heights of waves in relation to their fetch are used. The relation between the fetch and the physical time is found, as are the dependences of the basic characteristics of waves on the time of wind forcing. It is found that about 5% of wind energy dissipated in the near-water air layer contributes to the growth of wave heights, i.e. wave energy, although this quantity depends on the age of waves and the exponent in the fetch laws. With consideration for estimates of the probability distribution functions for the wind over the world ocean [11], it is found that the rate of wind-energy dissipation in the near-water air layer is on the order of 1 W/m². The calculations of wind waves [19] for the world ocean for 2007 have made it possible to assess the mean characteristics of the cycle of wave development and their seasonal variations. An analysis of these calculations [19] shows that about 20% of wind energy is transferred to the water surface. The remaining amount (80%) of wind energy is spent on the generation of turbulence in the near-water air layer. About 2%, i.e., one tenth of the energy transferred to water, is spent on turbulence generation due to the instability of the vertical velocity profile of the Stokes drift current and on energy dissipation in the surf zones. Of the remaining 18%, 5% is spent directly on wave growth and 13% is spent on the generation of turbulence during wave breaking and on a small-scale spectral region. These annually and globally mean estimates have a seasonal cycle with an amplitude on the order of 20% in absolute values but with a smaller amplitude in relative values. According to [19] and to the results of this study, the annually mean height of waves is estimated as 2.7 m and their age is estimated as 1.17.     

Nonlinear properties of laboratory wind waves at energy containing frequencies

Nonlinear properties of wind waves in a wind-wave tunnel are investigated by measuring the probability density distribution of surface elevation. The surface elevation distribution of raw records are found to have a positive skewness (K ₃=0.21 to 0.43) and a negative kurtosis (K ₄=–0.74 to –0.41) with magnitude depending of fetch and wind speed. The values of skewness are in qualitative agreement with a prediction of the weak interaction theory for a random wave field incorporating the effects of second harmonics (Tayfun, 1980), but the values of kurtosis are different in sign from the prediction.To examine the nonlinear properties of energy containing components, higher harmonic components are excluded from the wave records by using a kind of a band-pass filter. The surface elevation distributions of the filtered waves show a sharp decrease in skewness , but the distributions remain highly non-Gaussian with a large negative kurtosis almost independent of the fetch and wind speed . It is concluded that the negative kurtosis is due to the non-random character of the phase and amplitude among the energy containing components, and that nonlinear interactions occur amongst the energy containing frequencies.     

Measurement of skin friction distribution along the surface of wind waves

Measurements of local values of the skin friction have been made at many points along the surface of representative wind wave crests in a wind wave tunnel, by use of the distortion of hydrogen-bubble lines. The results obtained at 2.85-m fetch under 6.2 m s^–1 mean wind speed show that the intensity of the skin friction varies greatly along the surface of wind waves as a function of the phase angle. It increases rather continuously at the windward surface toward the crest, attains a value of about 12 dyn cm^–2 near the crest, decreases suddenly just past the crest, and the value at the lee surface is substantially zero Values of the skin friction thus determined along the representative wind waves give an average value of 3.6 dyn cm^–2, rather exceeding the overall stress value of 3.0 dyn cm^–2, which has been estimated from the wind profile. The results are interpreted as that the skin friction bears most of the shearing stress of wind, and that it exerts most intensively around the representative wave crests at their windward faces.     

辽宁沿海地区风能资源时空分布的初步分析

利用1997～2007 年辽宁省7 个海洋站和2007～2008 年3 个临时观测站的实测数据, 使用GIS 的反距离加权插值法, 初步分析了辽宁省沿海风能资源时空分布。结果为： 辽东湾沿岸风能资源丰富, 年平均风功率密度可达250 W/m2, 大连南部和东南沿海风能资源次之, 年平均风功率密度达到175 W/m2,丹...     

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

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Directional spectrum methods for deterministic waves

This work discusses developments related to the generation and measurement of directional wave spectra in multi-directional wave tank using deterministic waves. The details of the generation method, based on the single summation method described by Jefferys (1987), are given and the capacity of the Edinburgh curved wave tank to generate such waves is assessed. The Maximum Likelihood Method (MLM) and one of its derivative, The Modified Maximum Likelihood Method (MMLM) (Isobe and Kondo, 1985), are adapted to the characteristics of deterministic waves. The methods are assessed both with simulated waves and real wave elevations from the Edinburgh curved tank. Both methods show very satisfactory results with very stable angular spreading estimates and good tracking of mean directions of propagation across frequencies. The adapted MLM compares favourably with the industry standard, the Bayesian Directional Method, while only taking a fraction of the time needed to the BDM to produce its spectral estimates.     

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.     

Dynamic pressure distribution on large circular cylinders caused by wind generated random waves

A technique has been developed to evaluate the dynamic pressures on cylindrical structures due to irregular waves based on McCamy and Fuchs linear diffraction theory and principle of superposition. Experiments have been conducted in Hydraulic Engineering Laboratory, Indian Institute of Technology, Madras to examine the dynamic pressures excited by irregular waves on circular cylinders of large diameter. The pressures around the cylinder at representative locations were measured and compared with calculated pressures. The spectral density functions computed from pressure time series measured in the laboratory agree well with the calculated pressure spectral densities. The agreement is good and encouraging.     

Statistical characteristics of individual waves in laboratory wind waves

On the basis of data on the statistical characteristics of individual waves in laboratory wind waves reported in part I of this series, a self-consistent similarity regime is found to exist among properties of the individual waves, such as the nondimensional frequency, the wave number, the phase speed, and the steepness. Also, it is shown that forms of past empirical formulas for the development of the peak wave can be derived starting from the 3/2-power law, as an extension of the persent laboratory experimental data. In the derivation, only values of the coefficient of the 3/2-power law, and the fraction of momentum transferred from the wind retained by the wind waves, remain on an empirical basis.     

海浪产生磁场的能量分布计算

结合前人在海浪功率谱研究以及海浪产生磁场两方面的研究,求出了海浪-磁场系统的传递函数,计算了传递函数的峰值、对应的峰值频率,分析了这些指标随高度的变化.根据理论分析,给出了感应磁场总功率的表达式和峰值频率满足的方程,指出海浪感应磁场是一个窄带随机过程.最后选择几种典型的海浪谱,计算了它们感应的磁场功率谱以及总功率、功率谱峰值、峰值频率以及等效噪声带宽.     

Forced convection accompanying wind waves

Wind-wave tunnel experiments reveal, by use of techniques of the flow visualization, that wind waves are accompanied by the wind drift surface current with large velocity shear and with horizontal variation of velocity relative to the wave profile. The surface current converges from the crest to a little leeward face of the crest, making a downward flow there, even though the wave is not breaking. Namely, wind waves are accompanied by forced convections relative to the crests of the waves. Since the location of the convergence and the downward flow travels on the water surface as the crest of the wave propagates, the motion as a whole is characterized by turbulent structure as well as by the nature of water-surface waves. In this meaning, the term of real wind waves is proposed in contrast with ordinary water waves. The study of real wind waves will be essential in future development of the study of wind waves.     

A new scheme of nonlinear energy transfer among wind waves: RIAM method-algorithm and performance-

A numerical scheme for calculating the nonlinear energy transfer among wind waves (RIAM method) was developed on the basis of the rigorous method of Masuda. Then the performance of the RIAM method was examined by applying it to various forms of wind-wave spectra and different situations of wind-wave evolution, in comparison mainly with the WAM method. The computational time of the Masuda method was reduced by a factor of 300 by the RIAM method, which is still 2000 times slower than the WAM method simply because the RIAM method processes thousands of resonance configurations whereas the WAM method does only one. The RIAM method proves to give accurate results even for spectra of narrow band widths or bimodal spectra, whereas the WAM method often calculates an unrealistic magnitude and pattern of nonlinear energy transfer functions. In the duration-limited evolution of wind-wave spectra, the RIAM method yields a unimodal directional distribution on the low-frequency side of the spectral peak, whereas the WAM method produces a spurious bimodal one there. At higher frequencies, however, both methods give a bimodal directional distribution with two oblique maxima. The RIAM method enhances the growth of the total energy and peak period of wind waves in comparison with the WAM method. Nevertheless, Toba's constant of his 3/2-power law approaches almost the same standard value of 0.06 in both methods. For spectra of a narrow band width or for those perturbed by a small hump or depression, the RIAM method tends to recover the monotonic smoother form of spectrum whereas the WAM method often yields unrealistic humps or depressions.     

Directional spreading of waves in the nearshore zone

The directionality of waves inside a groin field near the German coastal zone of the island of Norderney is studied in the frequency domain. The maximum entropy method is adopted to estimate the directional spreading function. The various characteristics of the directional distribution of waves have been presented for the locations both inside and outside the groin field. The variation of directional spreading with depth and the importance of study of directional waves in coastal regions are discussed.     

Directional spreading of waves in the nearshore zone

The directionality of waves inside a groin field near the German coastal zone of the island of Norderney is studied in the frequency domain. The maximum entropy method is adopted to estimate the directional spreading function. The various characteristics of the directional distribution of waves have been presented for the locations both inside and outside the groin field. The variation of directional spreading with depth and the importance of study of directional waves in coastal regions are discussed.     

Negative correlations of variations in near-water wind and surface wind waves

The relationship between the intensity of surface wind waves and near-water wind is analyzed. The data of measuring wind waves and near-water wind under natural conditions in the Black Sea (July 2004) and Norwegian Sea (June 2003, 16th cruise of the R/V Akademik Sergei Vavilov) are used. A phenomenon of negative correlations has been found between the intensity of wind waves and near-water wind in regions of substantial restructuring of wind waves in the field of inhomogeneous flows: wind-wave amplification during wind decay and vice versa. Examples of such observations are presented, a theoretical model is constructed for the observed phenomenon, and a good agreement is obtained between theory and experiment.     

分段式造波机生成波浪的方向谱分析

采用声学多普勒流速仪(ADV)和多点测波仪的实验资料,对分段式造波机生成的多向随机波浪进行方向谱分析.结果表明,分段式造波机生成的多向随机波浪的时间平稳性优于空间均匀性;贝叶斯方法(BDM)适合于流速实验资料和阵列波浪资料的方向谱分析,给出的方向谱满足随机波浪的内禀性质(如光滑性、连续性等);流速资料和阵列波浪资料给出的方向谱具有相当的精度,但与测速的深度有关;三参量(如三点波浪、两个方向的速度分量和一点波浪等)可给出具有相当精度的方向谱;给出了衡量方向谱精度的初步标准.     

Internal flow structure of short wind waves

For wind waves generated in a wind-wave tunnel, the surface pressure and also the pressure distribution along the internal streamlines were calculated from the measured internal velocity field. In distinct waves, with wave height comparable with or larger than the mean, the surface pressure is found to vary drastically in a narrow region around the crest, showing a dominant minimum near the crest. On the other hand, the pressure distribution along the streamline shows systematic variations that are nearly in phase with the streamline profile. It is shown that the occurrence of the pressure in phase with the streamline profile is linked with the internal vorticity distribution, especially with the presence of a high vorticity region below the crest described in Part I of this study. As a result of the occurrence of such pressure variations, the dispersion relation is modified by about 10% from that for linear irrotational waves. It is argued from the present measurements that the dispersion relation and also the energy transfer from wind into wind waves are strongly affected by the internal vortical structure so that the assumption of irrotational gravity waves cannot be applied to the wind waves being studied.     

Internal flow structure of short wind waves

The minimum value of wind stress under which the flow velocity in short wind waves exceeds the phase speed is estimated by calculating the laminar boundary layer flow induced by the surface tangential stress with a dominant peak at the wave crest as observed in previous experiments. The minimum value of the wind stress is found to depend strongly on, the ratio of the flow velocity just below the boundary layer and the phase speed, but weakly onL, the wavelength. For wind waves previously studied (=0.5,L=10 cm), the excess flow appears when the air friction velocityu _* is larger than about 30 cm sec^–1. The present results confirm that the excess flow found in my previous experiments is associated with the local growth of a laminar boundary layer flow near the wave crest.     

Internal flow structure of short wind waves

The internal flow structure of wind waves in a wind-wave tunnel was investigated on the bases of the measured vorticity distributions, streamline patterns, internal pressure fields, and stress distributions at the water surface for some waves in the field. In part I the experimental method and the internal vorticity structure relative to the individual wave crests are described. The measured vorticity distributions of distinct waves (waves with waveheight comparable with or larger than that of significant wavesH _1/3) in the field indicate that the surface vorticity layer is extraordinarily thickened near the crest, and the vorticity near the water surface shows a particularly large value below the crest. The flow near the crest of distinct waves is found to be in excess of the phase speed in a very thin surface layer, and the tangential stress distribution has a dominant peak near the crest. It is argued that the occurrence of the region of high vorticity in distinct waves is associated with the local generation of vorticity near the crest by tangential stress which attains a peak, under the presence of excess flow.