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.     

Analysis of Wave Directional Spreading by Bayesian Parameter Estimation

A spatial array of wave gauges installed on an observatoion platform has been designed and arranged to measure the lo-cal features of winter monsoon directional waves off Taishi coast of Taiwan. A new method, named the Bayesian Parameter Estimation Method(BPEM) , is developed and adopted to determine the main direction and the directional spreading parame-ter of directional spectra. The BPEM could be considered as a regression analysis to find the maximum joint probability of parameters, which best approximates the observed data from the Bayesian viewpoint. The result of the analysis of field wave data demonstrates the highly dependency of the characteristics of normalized directional spreading on the wave age. The Mit-suyasu type empirical formula of directional spectrum is therefore modified to be representative of monsoon wave field. More-over, it is suggested that Smax could be expressed as a function of wave steepness. The values of Smax decrease with increas-ing steepness. Finally, a local directi     

海浪双峰方向分布的一种物理解释

用 １８个波高计组成的直径为 ４０ｃｍ的圆形阵列在大型风浪槽内系统地测量了风浪和涌浪方向谱。用两种分辨力较高的方向谱估计方法最大似然法（ＭＬＭ）和贝叶斯方法（ＢＤＭ）分析的结果表明：风浪高频域出现的依赖于估计方法的双峰方向分布是一种物理假象;在较成长的涌浪低频域,得到跟传播方向对称、两峰间隔大约６０°－９０°非常规则的双峰方向分布,它跟频率和涌浪的成长状态有关,而跟估计方法无关,这种现象可以用非线性波－波相互作用过弱,在不同方向之间不能有效传递能量来解释。     

On the determination of directional wave spectra for practical applications

The performance of various directional instruments for practical oceanographic and coastal engineering applications is examined. The emphasis is put on the application of conventional current meters equipped with high resolution pressure sensors and three element arrays. Two simulation techniques have been used to produce input data with known frequency spectrum and known directional spreading. The directional spreading is determined by the maximum likelihood method and the resulting spreading is compared with the input spreading. The performance of a conventional current meter equipped with a high resolution pressure sensor depends on the width of the directional spreading of surface waves and on the frequencies under consideration. Even for very narrow directional spreading, the current meter response is acceptable for practical applications and for shallow water deployment. In general, the current meter directional response does not depend on the direction of the incident waves. The spatial array of three wave staffs deployed in shallow water shows a similar performance to that of the current meters when the dimension of the spatial array is of the order of 1 m. This performance also does not depend on the direction of the incident waves.     

风浪方向分布模式的比较

本文对目前常用的几种风浪方向分布模式进行了分析对比，进而根据由浪高仪阵列和ＥＮＤＥＣＯ９５６测波浮标在我国各海区测得的风浪方向谱，从波能方向分布、方向累积分布、方向分布的峰值和标准差四个方面，与光易恒、Ｈａｓｓｅｌｍａｎｎ和Ｄｏｎｅｌａｎ等分别由观测得到的经验方向分布以及文圣常等由解析方法得到的风浪方向谱进行了比较，结果表明：Ｄｏｎｅｌａｎ分布与实测结果比较一致，文圣常谱也较接近。此外，笔者在渤海由仪器阵列实测方向谱拟合得到的方向分布（改进的光易模式）与各地实测资料也比较符合。     

Study on Measurement Methods of Multi-Directional Waves—Wave Gauge Array Method

- Measuring multi-directional waves with the wave gauge array is one of the fundamental and easily realised methods. In this paper, the wave gauge array is described and the effects of the gauge spacing, the array orientations, etc. of the three array arrangements, i. e., linear array, T-type array and pentagon array, on the resolution of the directional spreading of waves, are investigated experimentally. This study can be used as a reference in the experimental study and the field measurement of directional waves.     

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.     

Statistical Analyses of Wave Height Distribution for Multidirectional Irregular Waves over A Sloping Bottom

The main objective of this paper is to examine the influences of both the principal wave direction and the directional spreading parameter of the wave energy on the wave height evolution of multidirectional irregular waves over an impermeable sloping bottom and to propose an improved wave height distribution model based on an existing classical formula. The numerical model FUNWAVE 2.0, based on a fully nonlinear Boussinesq equation, is employed to simulate the propagation of multidirectional irregular waves over the sloping bottom. Comparisons of wave heights derived from wave trains with various principal wave directions and different directional spreading parameters are conducted. Results show that both the principal wave direction and the wave directional spread have significant influences on the wave height evolution on a varying coastal topography. The shoaling effect for the wave height is obviously weakened with the increase of the principal wave direction and with the decrease of the directional spreading parameter. With the simulated data, the classical Klopman wave height distribution model is improved by considering the influences of both factors. It is found that the improved model performs better in describing the wave height distribution for the multidirectional irregular waves in shallow water.     

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。     

The form of the asymptotic depth-limited wind-wave spectrum: Part III — Directional spreading

The directional spreading of both the wavenumber and frequency spectra of finite-depth wind generated waves at the asymptotic depth limit are examined. The analysis uses the Wavelet Directional Method, removing the need to assume a form for the dispersion relationship. The paper shows that both the wavenumber and frequency forms are narrowest at the spectral peak and broaden at wavenumbers (frequencies) both above and below the peak. The directional spreading of the wavenumber spectrum is bi-modal above the spectral peak. In contrast, the frequency spectrum is uni-modal. This difference is shown to be the result of energy in the wind direction being displaced from the linear dispersion shell. A full parametric relationship for the directional spreading of the wavenumber spectrum is developed. The analysis clearly shows that typical dispersion relationships are questionable at high frequencies and that such effects can be significant. This result supports greater attention being focussed on the routine recording of wavenumber spectra, rather than frequency spectra.     

Directional spread parameter at intermediate water depth

The characteristics of directional spread parameters at intermediate water depth are investigated based on a cosine power ‘2s' directional spreading model. This is based on wave measurements carried out using a Datawell directional waverider buoy in 23 m water depth. An empirical equation for the frequency dependent directional spreading parameter is presented. Directional spreading function estimated based on the Maximum Entropy Method is compared with those obtained using a cosine power ‘2s' parameter model. A set of empirical equations relating the directional spreading parameter corresponding to the peak of wave spectrum to other wave parameters like significant wave height and period are obtained. It shows that the wave directional spreading at peak wave frequency can be related to the non-linearity parameter, which allows estimation of directional spreading without reference to wind information.     

A proposed directional function and wind-wave directional spectrum

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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.     

遗传算法在多向随机波浪反射分析中的应用

通过数值模拟方法研究了遗传算法在分析多向入、反射波浪共存场中入射波浪的方向分布、波浪的反射系数和反射面位置的应用.对入射波浪的方向分布、波浪的反射系数和反射面位置通过遗传优化模拟和理论互谱的差别组成适应函数来确定.数值模拟结果表明,在多向入、反射波浪场中遗传算法能够精确地分离入、反射波浪,而且不需要预先确定反射面位置,因此遗传算法能够很好地被应用于分析多向随机波浪从斜坡堤等反射面位置不明确的建筑物的反射问题.     

Numerical Simulation of Multi-Directional Random Seas

Multi-directional irregular waves are simulated on the basis of the given directional spectrum using a double summation model, a single direction per frequency model and a single summation model. Their results are compared. It is shown that the single direction per frequency model proposed in this paper can generate a realistic wave field. The effects of the model parameters on the simulated results are also studied in this paper and corresponding suggestions are given.     

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。     

A laboratory study of directional spectra with maximum likelihood method-Ⅰ Developing wind wave

measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of wind-generated waves in deep water are systematically determined by using maximum likelihood method The investigations reveal that the angular spreading of the wave energy is consistent with cos^2s(θ/2) proposed by Longuet-Higgins et al.(1963, Ocean Wave Spectra, 111-136), if the bimodal distributions of wave energy are not taken into account. Bimodality occurring on higher frequency than peak frequency is too rare to affect our whole resalts. Surprisingly, a much broader directional spreading than that of the field, which is interpreted by the strongly nonlinear energy transfer because of the very young waves in laboratory, is found. The parameter s depends on frequency in the same way as observed by Mitsuyasu et al.(1975, Journal of Physical Oceanography, 5, 750-760) and Hasselmann et al.(1980, Journal of Physical Oceanography, 10, 1264-1280) in the field, and the relationship between the four nondimensional parameters s_m, f_o, b₁ and b₂, determining the directional width, and ū₁₀ (corresponding to the inverse of wave age) are given respectively. The observed distributions are found to agree well with the suggestion of Donelan et al.(1985, Philosophical Transaction of Royal Society of London, A315, 509-562) when applied to field waves.     

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     

Modelling storm impacts on beaches, dunes and barrier islands

A new nearshore numerical model approach to assess the natural coastal response during time-varying storm and hurricane conditions, including dune erosion, overwash and breaching, is validated with a series of analytical, laboratory and field test cases. Innovations include a non-stationary wave driver with directional spreading to account for wave-group generated surf and swash motions and an avalanching mechanism providing a smooth and robust solution for slumping of sand during dune erosion. The model performs well in different situations including dune erosion, overwash and breaching with specific emphasis on swash dynamics, avalanching and 2DH effects; these situations are all modelled using a standard set of parameter settings. The results show the importance of infragravity waves in extending the reach of the resolved processes to the dune front. The simple approach to account for slumping of the dune face by avalanching makes the model easily applicable in two dimensions and applying the same settings good results are obtained both for dune erosion and breaching.     

多向不规则波有效试验区的扩展法

实验室中一般采用分段式造波机来产生斜向或多向波，但其中存在几个问题，最主要的是有效试验区较小。扩大有效试验区的常用方法是采用边墙反射法。本文首先叙述了应用边墙反射产生斜向波和多向波的方法，通过物理模型试验对该方法进行了验证，试验结果表明采用边墙反射的确可以扩大有效试验区的范围。