of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core

The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction method. Numerical results of the present model are compared with the experimental data of different researchers. Numerical examples are given to examine the effect of rock fill on the reflection coefficient. The differences between regular and irregular waves are also investigated by means of theoretical and experimental results. It is found that the minimum reflection coefficient of irregular waves is larger than that of corresponding regular waves, but the contrary is the case for the maximum reflection coefficient.     

The reflection of regular and irregular waves by a partially perforated caisson breakwater on a step bed

This study examines the reflection of regular and irregular waves from a partially perforated caisson breakwater located on a step bed. The step bed is treated as an idealized rubble mound foundation. Based on the linear potential theory, an analytical solution is developed to calculate the reflection coefficient of the structure subjected to regular waves. The matched eigenfunction expansion method is used for the solution. The regular wave method is also extended to irregular waves using a linear transfer function. The calculated results obtained for limiting cases are exactly the same as corresponding results given by the previous researchers. The present predictions also agree well with experimental data in the published literatures. Numerical experiments are conducted to examine the variations of the reflection coefficient versus its main effect factors, and some interesting results are presented.     

Hilbert Transform Applied to Separation of Waves

The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is ap-plicable to both regular and irregular trains of waves. The wave data series measured with two wave gauges in the experi-ments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily ob-tained. The arrival of reflected waves can also be detected for improvement of the accuracy of the reflection coefficient.The reflection performance of the physical model can be estimated exactly without calculation of wave height and phasedifference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conduct-ed and compared with Goda‘s method and satisfactory results are obtained.     

Hilbert Transferin Applied to Separation of Waves

The analytical method (AM) for separation of composite waves is presented based on the Hilbert transform. It is ap-plicable to both regular and irregular trains of waves. The wave data series measured with two wave gauges in the experi-ments are separated into two series of incident and reflected waves. Then, the reflection coefficient can be easily ob-tained. The arrival of reflected waves can also be detected for improveraent of the accuracy of the reflection coefficient. The reflection performance of the physical model can be estimated exactly without calculation of wave height and phase difference. Numerical samples developed to test the method are proved to be accurate. Physical experiments are conduct-ed and compared with Goda s method and satisfactory results are obtained.     

Wave reflection from partially perforated-wall caisson breakwater

In 1995, Suh and Park developed a numerical model that computes the reflection of regular waves from a fully perforated-wall caisson breakwater. This paper describes how to apply this model to a partially perforated-wall caisson and irregular waves. To examine the performance of the model, existing experimental data are used for regular waves, while a laboratory experiment is conducted in this study for irregular waves. The numerical model based on a linear wave theory tends to over-predict the reflection coefficient of regular waves as the wave nonlinearity increases, but such an over-prediction is not observed in the case of irregular waves. For both regular and irregular waves, the numerical model slightly over- and under-predicts the reflection coefficients at larger and smaller values, respectively, because the model neglects the evanescent waves near the breakwater.     

An application of Boussinesq equations to Bragg reflection of irregular waves

A numerical model based on the second-order fully nonlinear Boussinesq equations of Wei et al. [1995. Journal of Waterway, Port, Coastal and Ocean Engineering 121 (5), 251-263] is developed to simulate the Bragg reflection of both regular and irregular surface waves scattered by submerged bars. Particularly for incident regular waves, the computed results are observed to agree very well with the existing experimental data as presented by Davies and Heathershaw [1984. Journal of Fluid Mechanics 144, 419-446] and Kirby and Anton [1990. Proceedings of the 22nd International Conference on Coastal Engineering, ASCE, New York, pp. 757–768). In the case of incident irregular waves, the simulated results reveal that the distribution of Bragg reflection from irregular waves becomes more flat than that of regular waves. Due to lack of experimental data, the numerical results for incident irregular waves are compared with those of the evolution equation of the mild-slope equation [Hsu et al., 2002 Proceedings of the 24th Ocean Engineering Conference in Taiwan, pp. 70–77 (in Chinese)]. In addition, several parameters such as the number of bars, the relative height of bars and the spacing of bars affecting Bragg reflection are also discussed.     

双层局部开孔板沉箱对波浪反射的理论研究

提出了一种用于研究由双层开孔板和一个不透水后板的开孔结构对斜向波反射率的理论分析方法。整个流域被分成三个子域，在每个子域内应用特征函数展开法以得到该域内包含未知展开系数的势函数的表达式，在速度势的展开中，考虑了非传播模态波浪的影响。通过匹配开孔板处的边界条件可以求解待定的展开系数，继而求解双层开孔板防波堤结构对斜向波的反射率。数值计算结果与试验结果进行了比较，符合较好。并进一步讨论了几个重要因素对反射系数的影响。     

Extended mild-slope equation for random waves

A time-dependent extended mild-slope equation is derived from the elliptic equation of Chamberlain and Porter [J. Fluid Mech. 291 (1995) 393] using the Taylor series technique. Numerical tests are made on a horizontally one-dimensional case for regular waves over sloping beds and for both regular and irregular waves over a ripple patch. Numerical results prove that the proposed model gives accurate results for both regular and irregular waves over rapidly varying topography.     

港域波浪数学模型的改进与验证

通过物理模型对改进的港内波浪传播变形数学模型进行验证。该数学模型以推广的时变缓坡方程为控制方程,采用含松弛因子的ADI法求解,并对波浪反射和透射边界模拟方法进行改进。先通过物理模型试验确定斜向浪入射条件下抛石防波堤前的波浪反射系数,作为数学模型中部分反射边界模拟的依据。然后进行了一个典型港口内波浪折射、绕射和反射的模型试验,测量港内波浪分布。对比模型试验和数学模型计算的结果表明,数学模型可较好地模拟港内复杂地形和边界条件下规则波和不规则波的传播变形。     

Application of desingularized approach to water wave propagation over three-dimensional topography

A numerical approach based on desingularized boundary element method and mixed Eulerian–Lagrangian formulation [Zhang et al., 2006. Wave propagation in a fully nonlinear numerical wave tank: a desingularized method. Ocean Engineering 33, 2310–2331] is extended to solve the water wave propagation over arbitrary topography in a three-dimensional wave tank. A robust damping layer applicable for regular and irregular incident waves is employed to minimize the outgoing wave reflection back into the wave tank. Numerical results on the propagation of regular and irregular incident waves over the flat bottom and linear incident waves over an elliptical shoal show good concurrence with the corresponding analytical solutions and experimental data.     

The reflection of oblique waves by an infinite number of partially perforated caissons

This study examines the reflection of obliquely incident waves by an infinite array of partially perforated caissons. Based on the linear potential theory, an analytical solution of the present problem was developed by means of the matched eigenfunction expansion method. The solution was obtained in a single strip consisting of the semi-infinite narrow region in front of a caisson and the fluid domain inside this caisson. It was then extended to the whole fluid domain by using the periodicities of the structure and the incident waves along the length of the caissons. The present model was validated by comparing the reflection coefficients of several limiting cases with the corresponding results obtained by previous researchers. Numerical experiments were also conducted to examine the variations of the reflection coefficient versus its main effect factors. The numerical results indicate the differences between the present model and the previous limiting cases, and some helpful results are recommended for practical engineering.     

基于激波捕捉类Boussinesq模型对岛礁地形上波浪传播的数值模拟

为了探究激波捕捉类Boussinesq模型在模拟岛礁地形上规则波和不规则波传播的可行性,采用基于完全非线性Boussinesq方程并具有激波捕捉能力的数值模型Funwave-TVD对规则波和不规则波在岛礁地形上的传播进行了数值模拟,通过与试验数据对比,分析模型中空间步长的影响,验证模型在模拟波高、平均水位分布以及波谱空间演变的能力,结果表明:采用合适的空间步长,模型能较好地模拟规则波和不规则波在岛礁地形上的传播和演化过程。对于规则波,较小的空间步长可改善破碎点处波高峰值的预测,并能更好地预测波浪破碎后波高的空间分布,相比结合经验破碎的Boussinesq模型,Funwave-TVD能更好地模拟规则波在岛礁地形上的破碎,以及破碎以后行进涌波的再生成过程;对于不规则波,Funwave-TVD总体而言能较好地模拟涌浪有效波高、次重力波的生成及空间演化和平均水位,但会低估礁坪上次重力波波高,较粗的空间步长也会低估礁坪上涌浪有效波高。     

Separation of Waves by Interpolation Method

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Verification of A Numerical Harbour Wave Model

A numerical model for wave propagation in a harbour is verified by use of physical models.The extended time-dependent mild slope equation is employed as the governing equation,and the model is solved by use of ADI method containing the relaxation factor.Firstly,the reflection coefficient of waves in front of rubble-mound breakwaters under oblique incident waves is determined through physical model tests,and it is regarded as the basis for simulating partial reflection boundaries of the numerical model.Then model tests on refraction,diffraction and reflection of waves in a harbour are performed to measure wave height distribution.Comparative results between physical and numerical model tests show that the present numerical model can satisfactorily simulate the propagation of regular and irregular waves in a harbour with complex topography and boundary conditions.     

Implementation and evaluation of alternative wave breaking formulas in a coastal spectral wave model

This paper describes methods and results of research for incorporating four different parameterized wave breaking and dissipation formulas in a coastal wave prediction model. Two formulations assume the breaking energy dissipation to be limited by the Rayleigh distribution, whereas the other two represent the breaking wave energy by a bore model. These four formulations have been implemented in WABED, a directional spectral wave model based on the wave action balance equation with diffraction, reflection, and wave–current interaction capabilities. Four parameterized wave breaking formulations are evaluated in the present study using two high-quality laboratory data sets. The first data set is from a wave transformation experiment at an idealized inlet entrance, representing four incident irregular waves in a slack tide and two steady-state ebb current conditions. The second data set is from a laboratory study of wave propagation over a complex bathymetry with strong wave-induced currents. Numerical simulation results show that with a proper breaking formulation the wave model can reproduce laboratory data for waves propagating over idealized or complicated bathymetries with ambient currents. The extended Goda wave breaking formulation with a truncated Rayleigh distribution, and the Battjes and Janssen formulation with a bore model produced the best agreement between model and data.     

Water surface resonance in the L-shaped channel of seawater exchange breakwater

The resonance period of the L-shaped channel in the caisson is predicted analytically for the seawater exchange breakwater of “Applicability Study of the Seawater Exchange Breakwater (1). Korea Ministry of Maritime Affairs and Fisheries (in Korean) (1999a)”. Hydraulic experiments are conducted for a composite breakwater with a rear reservoir that is one of the seawater exchange breakwaters developed by them. For regular waves, the water surface elevation in the channel and the flow rate through the breakwater are measured. For irregular waves, the flow rate through the breakwater and the reflection coefficient on the breakwater are measured. The resonant maximum values in both the surface elevation and the flow rate, and the resonant minimum values in the reflection coefficient are all at wave periods slightly longer than analytically predicted ones. The measured resonance period for irregular waves is closer to the predicted one than for regular waves. If the resonance period of the L-shaped channel is fitted to the dominant period of incident waves, there would be high efficiency of seawater exchange between inside and outside the harbor.     

Wave Reflection Coefficient Spectrum

1 .IntroductionWavereflectionfromstructuresisanimportantfactorforthedesignofthestructures .Therehavebeenmanyresearchesonwavereflectionwithregularwavesandmonochromaticirregularwaves .Miche( 1 951 )proposedanon dimensionalMichenumberMfornormallyincidentirregularwavesconsideringwavebreakingbecauseofthedeepeningofwavesteepnessontheslopeofbreakwaters .ThereflectioncoefficientisproportionaltoM ,i.e .,Kr ∝M =4g( 2π) 5/ 2tan5/ 2 α(Hsf2p) ( 1 )wheregisthegravitationalacceleration ,Hsthesignifican…     

Numerical Simulation of Sand Shoreline Evolution Under Action of Regular Waves and Irregular Waves

Based on the singleline theory, a numerical simulation is presented to predict the shoreline evolution on sand beach. A parabolic equation of longshore sediment transport and boundary conditions are proposed. The combined effect of wave diffraction and refraction on the shoreline evolution on the downdrift side of the breakwater is taken into account and is calculated using the theory of regular waves and irregular waves. The present model is verified by the field observation data of erosion for half a year on the downdrift side of a harbor, and compared with some experimental results. The numerical results are in good agreement with the field measured and experimental data.     

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.     

Investigation of Π-type breakwaters performance under regular and irregular waves

In this paper, performance of solid and perforated Π-type breakwaters was investigated experimentally. Both regular and irregular waves were used during testing. Four depths of immersions were selected for each breakwater and wave type. Different wave groups were generated over these breakwaters, and the transmission, reflection and energy-dissipation characteristics were determined. The results of the experimental study were evaluated and some empirical expressions based on the results were suggested to define the transmission, reflection and energy-dissipation coefficients for different immersion depths of solid and perforated breakwaters under regular and irregular waves. Moreover, performance of solid and perforated Π-type breakwaters were compared with that of solid and perforated U-type breakwaters investigated by Günaydın and Kabdaşlı [2006. Performance of solid and perforated U-type breakwaters under regular and irregular waves. Ocean Engineering 31, 1377–1405]. These comparisons showed that the most reasonable model and wave type are selected to determine requiring performance parameters.