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.     

Reflection of Short Waves

—According to the energy equation,the relation between reflection and energy losses for shortwaves from mild beaches is established and analysed.A reflection coefficient varying with position and en-ergy losses is proposed.Different reflection tests are conducted to check the theoretical analysis.A modi-fied method to estimate the reflection coefficient at varied water depths is suggested based on the linearwave theory.The study indicates that the reflection coefficient from mild beaches has a changing trend forshort waves approaching shoreline.     

Tests and Applications of An Approach to Absorbing Reflected Waves Towards Incident Boundary

If the upstream boundary conditions are prescribed based on the incident wave only, the time-dependent numerical models cannot effectively simulate the wave field when the physical or spurious reflected waves become significant. This paper describes carefully an approach to specifying the incident wave boundary conditions combined with a set sponge layer to absorb the reflected waves towards the incident boundary. Incorporated into a time-dependent numerical model, whose governing equations are the Boussinesq-type ones, the effectiveness of the approach is studied in detail. The general boundary conditions, describing the down-wave boundary conditions are also generalized to the case of random waves. The numerical model is in detail examined. The test cases include both the normal one-dimensional incident regular or random waves and the two-dimensional oblique incident regular waves. The calculated results show that the present approach is effective on damping the reflected waves towards the incident wave boundary.     

Numerical Simulated Study on the Separation of Oblique Incident and Reflected Waves

The Goda's method of separating the frequency spectrum of the unidirectional incident and reflected waves is improved. The proposed method can be applied to the separation of oblique incident and reflected waves and the two wave gauges can be arranged in an arbitrary angle in front of a structure. When the projected distance of the two probes on the incident wave direction is the multiple ofthe half length of the incident waves, the singular problem will emerge by using the method. It is advised that when the projected distance of the two measured points on the incident wave direction is 0.05～0.45 times the wave length of peak frequency wave, good results can be obtained. The simulated resultant waves are separated by the method of numerical simulation and the separated wave spectra are basically corresponding to the target spectra input. The wave trains calculated by the separated incident and reflected wave frequency spectrum are approximated to the input wave trains and the reflected coefficient can be derived correctly. Therefore, the method proposed in this paper is reliable.     

Reflection of Oblique Incident Waves by Breakwaters with Partially-Perforated Wall

The reflection of oblique incident waves from breakwaters with a partially-perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigenfunction expansion method is applied to expand velocity poten-tials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with experimental data. The effect of porosity, the relative chamber width, the relative water depth in the wave absorbing chamber and the water depth in front of the structure are discussed.     

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.     

非线性相互作用对高频方向谱估计的影响

海浪组成波之间的三阶非线性相互作用产生的高次谐波,不仅改变了波面的外观形状,而且使得高频域不再满足通常的线性频散关系,当ｆ＞１．７ｆｐ时,频散关系应修改为ω２＝２ｇｋ。用最大似然法（ＭＬＭ）分析方向分布的结果表明：在二倍峰频附近,方向分布再次变窄,且能量在方向上的集中程度与海浪的成长状态有关,得到的高频方向分布跟Ｃａｕｄａｌ和Ｈａｕｓｅｒ（１９９６）的微波遥感结果定性一致。     

Laboratory Study on the Interaction Between Regular Obliquely Incident Waves and Vertical Walls

The characteristics of wave forces are studied based on physical model tests with regular waves. The ratio of obliquely incident wave forces to normally incident wave forces on unit length of a vertical wall is related with various factors. A linear reduction of the mean force of obliquely incident waves is confirmed with an increase in the relative caisson length. Also the characteristics of reflection coefficient of diagonal waves are discussed.     

A Calculation Method for Incidence and Reflection of Irregular Waves Along Seawalls

Some researches have been made in this aspect.In the method by Walton Jr.(1992),incidentwaves are supposed to be the overlapping result of M component waves with different frequencies whichmay take different directions,the direction of incident waves should be available in advance,but in fact thedirection of incident waves is not available.In our study,incident waves are supposed to be composed ofM overlapping component waves with different frequencies,and different frequencies have different direc-tions.Based on the irregular wave reflection theory,the calculation formulas of wave direction,complexamplitude of incident waves,and complex amplitude of reflected waves in surface which are composed ofcomponent waves are derived by means of discrete Fourier transform.Then,the frequency spectra of inci-dent waves and reflected waves and the reflection coefficient of waves with corresponding frequencies areobtained.Verification of the method and the calculation results from in-situ measured data indicate thatt     

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.     

Bubble Size Distribution for Waves Propagating over A Submerged Breakwater

Experiments are carried out to study the characteristics of active bubbles entrained by breaking waves as these propagate over an abruptly topographical change or a submerged breakwater. Underwater sounds generated by the entrained air bubbles are detected by a hydrophone connected to a charge amplifier and a data acquisition system. The size distribution of the bubbles is then determined inversely from the received sound frequencies. The sound signals are converted from time domain to time-frequency domain by applying Gabor transform. The number of bubbles with different sizes are counted from the signal peaks in the time-frequency domain. The characteristics of the bubbles are in terms of bubble size spectra, which account for the variation in bubble probability density related to the bubble radius r. The experimental data demonstrate that the bubble probability density function shows a - 2.39 power-law sealing with radius for r 〉 0. 8 mm, and a- 1.11 power law for r 〈0.8 mm.     

Bble Size Distribution for Waves Propagating over A Submerged Breakwater

Experiments are carried out to study the characteristics of active bubbles entrained by breaking waves as these propagate over an abruptly topographical change or a submerged breakwater. Underwater sounds generated by the entrained air bubbles are detected by a hydrophone connected to a charge amplifier and a data acquisition system. The size distribution of the bubbles is then determined inversely from the received sound frequencies. The sound signals are converted from time domain to time-frequency domain by applying Gabor transform. The number of bubbles with different sizes are counted from the signal peaks in the time-frequency domain. The characteristics of the bubbles are in terms of bubble size spectra, which account for the variation in bubble probability density related to the bubble radius r. The experimental data demonstrate that the bubble probability density function shows a-2.39 power-law scaling with radius for r＞0.8 mm, and a-1.11 power law for r＜0.8 mm.     

A Three-Point Method for Separating Incident and Reflected Waves over A Sloping Bed

This study presents a three-point method for separating incident and reflected waves to explain normally incident waves' propagating over a sloping bed. Linear wave shoaling is used to determine changes in wave amplitude and phase in response to variations of bathymetry. The wave reflection coefficient and incident amplitude are estimated from wave heights measured at three fixed wave gauges with unequal spacing. Sensitivity analysis demonstrates that the proposed method can predict the reflection and amplitude of waves over a sloping bed more accurately than the two-point method.     

海浪方向谱估计方法的比较

分别利用数值模拟和实测资料对目前被认为分辨力较高的最大似然法(MLM)、扩展本征矢方法(EEV)、扩展最大滴方法(EMEP)以及贝叶斯方法(BDM)等四种海浪方向谱估计方法的可靠性进行了分析,从不同频率、不同噪声水平和不同方向集中度三个角度检验其再现性、稳定性和实用性,结果表明MLM、EEV和BDM大致给出相同的方向分布,其中BDM的再现性最好,但实用性逊于MLM和EEV,EMEP由于稳定性差,不适用于实测资料的分析.     

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.     

Experimental Study of Hydrodynamic Loading on Submarine Composite Pipelines under the Action of Waves and Current

- This article is aimed at the experimental study of the hydrodynamic loading induced by waves and current acting on the JZ 20-2 submarine composite pipelines. The corresponding hydrodynamic coefficients obtained in this experimental study can be applied to engineering projects.     

Reply to “Discussion of wave setup and setdown generated by obliquely incident waves” by F. Shi and J.T. Kirby

The authors are grateful to the derivation and correction addressed by Shi and Kirby (2008) for the calculation of the wave setup and setdown induced by obliquely incident waves. The mathematical equations for the expression of setup and setdown are rederived in which the velocity potential is expanded to the second-order on the still water lever. The correct form of setdown presented by Shi and Kirby is confirmed in the present paper.     

斜向波浪入射角和反射系数确定方法

在海岸工程和水池实验中常常需要同时确定斜向波浪的传播方向和与海岸结构物相遇时的反射系数。应用三点浪高仪测波和迭代求解方法,建立了同时确定斜向波浪入射角和反射系数的分析方法。通过模拟数值信号,研究了测点不同排列方式、不同波浪入射方向、不同入射频率下本方法的分析灵敏程度。数值研究表明当测点间距指标p和q不同时趋于零时,任何一种排列方式求得的波浪反射系数和波浪入射角均具有很高的分析精度。     

锁相波浪场入、反射波方向谱及反射系数估算

通过数模波浪和物模实验，比较分析了估算多向不规则入射波与反射波相互叠加的锁相波浪场方向分布和反射系数方向分布的改进的贝叶斯估计法MBDM和扩展的最大似然法MMLM的性能。数模试验检验了不同波浪条件、不同波浪测量系统和结构物的不同反射特性等情况下的估算结果，同时还比较了两种分析方法的计算速度和稳定性，结果显示，对于波浪的方向分布估计，MBDM优于MMLM，对于反射系数的方向分布估计以及计算速度和稳定性，MMLM优于MBDM。     

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.