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.     

Radar Investigation of the Structure of Wind Waves

Radar data from three experiments are analysed. Scatter characteristics of 50 cm wind-generated waves have been investigated with a C-band radar in a large wind-wave tank. Evidence of wave groups in sea clutter from the west coast of Scotland in the Sound of Sleat is also presented. The spectrum of the waves in the sound is narrow-banded and the waves are young, like the wind-wave spectrum in the laboratory. Clutter measurements, collected on the English south coast at Portland, of more ocean-like waves with broad band spectra also suggest the presence of wave groups. Evidence of the presence of wave groups is demonstrated in range-time images, as well as in the Fourier domain. Some ad hoc processing schemes, the normalised variance and binary threshold techniques, were successfully applied to enhance the appearance of the wave groups. The wind waves change frequency with fetch in the wave tank and the downshifting process is investigated using range-frequency maps of the radar data. The waves appear to change frequency in discrete steps that are associated with wave breaking events. The difference in wave period before and after breaking could be measured, and a wave crest was shown to be lost to compensate for the change in period, as expected. Some downshifting could also be measured in the Sound of Sleat. The ratio of wave group frequency and wave frequency is inaccordance with Benjamin-Fier sideband instability theory, as it is for the data measured at Portland. This revised version was published online in July 2006 with corrections to the Cover Date.     

Computation of Diffraction of Irregular Waves Behind Double Jetty

The coefficient of deffraction of regular waves behind the double jetty has been computed in this paper at first by using the singularity distribution method. The model tests conducted for diffraction of irregular waves with a unidirectional frequency spectrum have confirmed good agreement between the data measured in experiments and the results computed by the singularity distribution method plus the linear superposition method for the energy of component waves in the directional frequency spectra. Therefore, this technique for component waves in the directional spectra has been further used to compute diffraction of irregular waves of multidirection, including the employment of a directional distribution function of the cos2 type, as well as the Bretschneider-Misuyann frequency spectrum.     

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.     

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.     

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.     

Statistical Distribution of Surface Slope in A 3-D Ocean Wave Field

—A joint probability density function(PDF)for surface slopes in two arbitrary directions is de-rived on the basis of Longuet-Higgins's linear model for three-dimensional(3-D)random wave field.andthe correlation moments of surface slopes.as parameters in the PDF.are expressed in terms of directionalspectrum of ocean waves.So long as the directional spectrum model is given.these parameters are deter-mined.Since the directional spectrum models proposed so far are mostly parameterized by the wind speedand fetch.this allows for substituting these parameters with the wind speed and fetch.As an example.thewind speed and fetch are taken to be 14 m s and 200 km.and the Hasselmann and Donelan directionalspectra are.respectively.used to compute these parameters.Some novel results are obtained,One of the in-teresting results is that the variances of surface slope in downwind and cross-wind directions determined bythe Donelan directional spectra are close to those measured by Cox and Munk(1954).Some discussionsare m     

由模拟波面统计分析波高－周期联合分布

阐述以实测或拟合海浪谱为靶谱，用等能量分割法作波面数值模拟，从而利用模拟波面统计分析波高（Ｈ）－周期（Ｔ）联合分布。对波候的Ｈ－Ｔ联合分布、长时段海浪连续记录的Ｈ－Ｔ联合分布以及风浪、涌浪和混合浪的Ｈ－Ｔ联合分布进行了讨论。结果表明，只要已知特征波高和周期，就可反演出模拟波面，进而估测Ｈ－Ｔ联合分布情况，这对了解与各种特征波高对应的周期问题及在海洋工程应用上有一定的参考意义。     

Modification of SAR spectra associated with surface wind fields in the sea off the Kii Peninsula: A case study

Using surface wave parameters and a high-resolution surface wind field derived from Synthetic Aperture Radar (SAR) image mode data, we have investigated the spatial modification of SAR spectra. We found a surface wind front, formed by sheltering effect of the Kii Mountains, separating high and low wind-speed regions in a sea area of an European Remote-Sensing Satellite (ERS) SAR image off the Kii Peninsula. A swell system propagating westward dominates in the whole sea area covered by the SAR image. The wavelength retrieved from the SAR spectra in the sheltered (non-sheltered) region is longer (shorter). Since the distributions of surface wave parameters and surface wind speed are so well correlated, it can be considered that the SAR spectra are modified differently by the sheltered/non-sheltered surface winds. In order to examine the phenomena observed on the SAR image we have estimated the wind-wave SAR spectrum using the SAR surface winds, a wind-wave spectrum model and a SAR wave imaging model. We assume that the SAR spectrum related to the swell is homogeneous in the area imaged by SAR, and that the SAR spectrum of the wind-wave components causes the observed SAR spectra modification. Differences between the observed SAR spectra and the estimated SAR spectra in the sheltered and non-sheltered regions agree well with each other. In the present case, it can be concluded that the observed SAR spectra can be regarded as a linear combination of the wind-wave SAR spectra and the swell SAR spectra.     

Retrieval of surface wave parameters from sar images and their validation in the coastal seas around Japan

We have developed a scheme to retrieve surface wave parameters (wave height and wave propagation direction) from European Remote-Sensing Satellite (ERS) Synthetic Aperture Radar (SAR) image mode data in coastal seas around Japanese coastlines. SAR spectra are converted to surface wave spectra of swell-dominated or wind-wave dominated cases. The SAR spectrum and SAR-derived wind speed are used to derive the surface wave spectrum. The wind-wave dominated case and swell-dominated case are differentiated by a wind speed of 6 m/s, and processed in different ways because of their different degree of nonlinearity. It is indicated that the cutoff wavelength for retrieval of the wind-wave dominated spectrum is proportional to the root of significant wave height, which is consistent with the results of previous studies. We generated 66 match-ups using the SAR sub-images and the in-situ surface wave parameters, which were measured by wave gauges installed in near-shore seas. Among them, there are 57 swell-dominated cases, and 9 wind-wave dominated cases. The significant wave heights derived from SAR and from in-situ observation agree with the bias of 0.09 m, the standard deviation of 0.61 m and the correlation coefficient of 0.78. The averaged absolute deviation of wave propagation directions is 18.4°, and the trend of the agreement does not depend on the wave height. These results demonstrate that the SAR surface wave spectrum retrieved by the present system can be used to observe the surface wave field in the coastal seas around Japan.     

A New Maximum Entropy Probability Function for the Surface Elevation of Nonlinear Sea Waves

Based on the maximum entropy principle a new probability density function （PDF） f（x） for the surface elevation of nonlinear sea waves, X, is derived through performing a coordinate transform of X and solving a variation problem subject to three constraint conditions of f（ x ）. Compared with the maximum entropy PDFs presented previously, the new PDF has the following merits： （1） it has four parameters to be determined and hence can give more refined fit to observed data and has wider suitability for nonlinear waves in different conditions; （2） these parameters are expressed in terms of distribution moments of X in a relatively simple form and hence are easy to be determined from observed data; （3） the PDF is free of the restriction of weak nonlinearity and possible to be used for sea waves in complicated conditions, such as those in shallow waters with complicated topography; and （4） the PDF is simple in form and hence convenient for theoretical and practical uses. l.aboratory wind-wave experiments have been conducted to test the competence of the new PDF for the surface elevation of nonlinear waves. The experimental results manifest that the new PDF gives somewhat better fit to the laboratory wind-wave data than the well-known Gram-Charlier PDF and beta PDF.     

Statistical properties of microwave backscattering from laboratory wind-wave surfaces

The microwave backscattering from wind-wave surfaces is observed in a windwave tunnel under various conditions of the wind and wind waves, and its statistical features are investigated. The dependence of the backscattered power on the wind speed and the incident angle shows similar features to those predicted by models proposed previously. However, the dependence of the backscattered power on the incident angles also corresponds to the asymmetrical feature of the wind-wave surfaces with respect to the wind direction. The spectral analyses of time series of the backscattered intensity show that the propagating speed of fine structures of the wind-wave surface contributing to the backscattering at large incident angles does not coincide with the phase speed of the freely propagating Braggwaves. Atupwind incidence, the surface structures of wind waves contributing to the backscattering propagates with the dominant waves at their phase speed. This result is inconsistent with the two-scale model in which the Bragg waves are simply superimposed on longer waves, but is consistent with the results of optical observation by Ebuchiet al. (1987). At downwind incidence, the propagating speed is slower than the phase speed of the dominant waves.     

A Comparative Study of the Statistical Distributions of Wave Heights

Distribution of wave heights and surface elevations of wind-driven waves are studied.Recordsof surface elevations obtained from both field observations and laboratory measurements are analyzed.Wave heights can be approximated by normal,two-parameter Weibull,and/or Rayleigh distribution.However,while the first two models may have almost equal probabilities to fit measured data quite satis-factorily,the Rayleigh distribution does not appear to be a good model for the majority of the cases stu-died.Surface elevations from field data are well described by the Gaussian model,but as with increasingwind speeds,water surface in a wind-wave flume deviates from normality,and the Edgeworth's form ofthe type A Gram-Charlier series is then applied.     

Ⅲ变浅作用下列率谱和频率谱的实验研究

为研究变浅作用下的非线性海浪，本文利用并矢相关谱估计方法，设计并进行了多种强度下，由深水传入近岸浪变浅作用下，列率谱和频率谱随水深和坡度变化的实验比较研究。     

Physical Investigation of Directional Wave Focusing and Breaking Waves in Wave Basin

An experimental scheme for the generation of directional focusing waves in a wave basin is established in this paper. The effects of the directional range, frequency width and center frequency on the wave focusing are studied. The distrihution of maximum amplitude and the evolution of time series and spectra during wave packet propagation and the variation of water surface parameters are extensively investigated. The results reveal that the characteristics of focusing waves are significantly influenced hy wave directionality and that that breaking criteria for directional waves are distinctly different from those for unidirectional waves.     

滆湖北部人工地形重塑下风浪场变化研究

风浪是影响浅水湖泊物理生境环境重要的水动力要素之一。基于滆湖实测风浪数据, 建立了滆湖风浪模型, 验证结果表明模型可以较好模拟滆湖风浪随风场变化情况。在此基础上开展滆湖北部水域在人工地形重塑工程实施后的风浪变化情况分析。结果表明, 不同季节盛行风下, 风浪强度和湖底扰动强度均有一定程度的衰减, 这有利于水体透明度和水底光照条件的改善。风浪强度的衰减使得具有有利于水生植物生长与发育风浪条件的水域面积显著扩增。人工地形重塑的实施, 有利于滆湖北部水域水生植被物理生境环境改善, 从而为滆湖北部水域水生植被的修复提供较好的环境支撑, 也为其他浅水湖泊地形重塑工程的实施提供借鉴。     

Analysis of Directional Spectra and Reflection Coefficients in Incident and Reflected Wave Field

In this paper, the modified Bayesian method for the analysis of directional wave spectra and reflection coefficients is verified by numerical and physical simulation of waves. The results show that the method can basically separate the incident and reflected directional spectra. In addition, the effect of the type of wave gage arrays, the number of measured wave properties, and the distance between the wave gage array and the reflection line on the resolution of the method are investigated. Some suggestions are proposed for practical application.     

风浪槽内风浪外频谱谱形的一些特征

利用实验室风浪槽内测得的波面序列资料估计风浪外频谱。通过与实测风浪内频谱的比较,研究实测风浪外频谱的谱形特征,探讨海浪外频谱与内频谱的相似性问题。此外,还检验一种理论海浪外频谱。     

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     

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。