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.     

Wave motion over a breakwater system of a horizontal plate and a vertical porous wall

A two-dimensional analytical solution is presented to study the reflection and transmission of linear water waves propagating past a submerged horizontal plate and through a vertical porous wall. The velocity potential in each fluid domain is formulated using three sets of orthogonal eigenfunctions and the unknown coefficients are determined from the matching conditions. Wave elevations and hydrodynamic forces acting on the porous wall are computed. Reflection and transmission coefficients are presented to examine the performance of the breakwater system. The present analytical solutions are found in fairly good agreement with the available laboratory data. The results indicate that the plate length, the porous-effect, the gap between plate and porous wall, and the submerged depth of the plate all show a significant influence on the reflected and transmitted wave fields. It is also interesting to note that the submerged plate plays an important role in reducing the transmitted wave height, especially for long incident waves.     

Wave reflection from coastal structures in design conditions

Based on an extensive database of more than 4000 data, this paper analyses wave reflection for various types of coastal structures in design conditions, such as smooth, rock and armour unit slopes. A new simple formula has been developed that relates the reflection coefficient to the breaker parameter and seems to fit all kinds of revetment materials by changing two coefficients. These coefficients depend only on the correct roughness factor, provided by recent research on overtopping discharges. The effects on reflection due to composite slopes and to low crests are also examined and proper extensions of the formula are provided.     

不规则波远破波对直墙的作用

基于物模试验、理论推理、因次分析和工程实例验证等综合分析方法,就不规则波远破波对直墙作用力的计算方法进行了研究,用推荐的方法得到的结果与工程实例符合较好.     

Analysis of Wave Height in Front of a Wave Absorbing Structure with Rubble Foundation

Wave absorbing structures have been widely applied in many countries. In the present paper, the wave heights in front of a vertical wave absorbing structure with rubble foundation as well as in the wave chamber of the structure are analysed using an approximative calculation method, and the dissipating effect of the structure is verified. On the basis of the results of regular waves, the relative wave heights of irregular waves in front of the wave absorbing structure as well as in the chamber have also been analysed.     

Wave radiation by a uniform cylinder in front of a vertical wall

In this paper, an exact analytical method is developed for the problem of wave radiation by a uniform cylinder in front of a vertical wall. Based on the image principle, the hydrodynamic problem of a cylinder in front of a vertical wall is transformed into the equivalent problem of double cylinders in unbounded fluid domain. Consequently, an analytical method of eigenfunction expansion is adopted to calculate the radiation of the cylinder due to the motion in surge, sway, roll and pitch, respectively. Moreover, numerical analysis has been carried out in detail in order to discuss the influences of the distance between the cylinder and the vertical wall and water depth on the added mass and radiation damping of the cylinder. It is shown that added mass and damping of the cylinder in front of a vertical wall are evidently different from those in case of the cylinder in unbounded fluid domain from the numerical results. It is also found that the added mass and radiation damping oscillate with wave number, and the oscillating frequency increases with the increasing of the distance between the cylinder and the wall.     

Wave Reflection Caused by Wave Overtopping and Sloping Top of Spructure

In this paper, the theoretical analysis and experimental studies are employed to investigate the reflection characteris-tics of partial standing waves caused by wave overtopping and sloping top of structures. Based on the principle of conser-vation of wave energy flux, the third-order Stokes wave theory is used to formulate the reflection coefficient at wave overtopping; the calculation results are regressed into an applied expression. A series of experiments of wave reflection for a vertical-wall structure with chamfered and overhanging upper sections are carried out to investigate the influence of top slope on wave reflection. The regularity of variation of wave reflection in this case is analysed based on the experimental results.     

Long Waves Induced by Wave Groups over a Trench

The second order long waves of the mean water free surface displacement induced by the wave groups over a trench are discussed in this paper. The incident wave groups are supposed to be superposed by 2 linear waves with different amplitudes, phases and slightly different frequencies. Some of the theoretical formulas and numerical results are presented.     

Long wave reflection from submerged trapezoidal breakwaters

This study addresses the reflection and transmission of long waves from a trapezoidal breakwater and a series of trapezoidal breakwaters, using the matching method. A systematic shape transfer is derived to determine wave reflection and transmission. The peak Bragg reflection of long waves from a series of trapezoidal breakwaters is shifted toward low frequency. In spite of the spacing between any pair of breakwaters, the top plane width and the arrangement of the series of breakwaters are found to be the two major parameters in designing multiply composite Bragg breakwaters.     

Wave interaction with a perforated wall breakwater with a submerged horizontal porous plate

This study examines the hydrodynamic performance of a new perforated-wall breakwater. The breakwater consists of a perforated front wall, a solid back wall and a submerged horizontal porous plate installed between them. The horizontal porous plate enhances the stability and wave-absorbing capacity of the structure. An analytical solution based on linear potential theory is developed for the interaction of water waves with the new proposed breakwater. According to the division of the structure, the whole fluid domain is divided into three sub-domains, and the velocity potential in each domain is obtained using the matched eigenfunction method. Then the reflection coefficient and the wave forces and moments on the perforated front wall and the submerged horizontal porous plate are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a perforated-wall breakwater with a submerged horizontal solid plate [Yip, T.L., Chwang, A.T., 2000. Perforated wall breakwater with internal horiontal plate. Journal of Engineering Mechanics ASCE 126 (5), 533–538] and a vertical wall with a submerged horizontal porous plate [Wu, J.H., Wan, Z.P., Fang, Y., 1998. Wave reflection by a vertical wall with a horizontal submerged porous plate. Ocean Engineering 25 (9), 767–779]. Numerical results show that with suitable geometric porosity of the front wall and horizontal plate, the reflection coefficient will be always rather small if the relative wave absorbing chamber width (distance between the front and back walls versus incident wavelength) exceeds a certain small value. In addition, the wave force and moment on the horizontal plate decrease significantly with the increase of the plate porosity.     

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.     

Drag force on a vegetation field due to long-crested and short-crested nonlinear random waves

This paper provides a practical method for estimating the drag force on a vegetation field exposed to long-crested (2D) and short-crested (3D) nonlinear random waves. This is achieved by using a simple drag formula together with an empirical drag coefficient given by Mendez et al. (1999), in conjunction with a stochastic approach. Here the waves are assumed to be a stationary narrow-band random process. Effects of nonlinear waves are included by adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D random waves.     

Bragg resonant reflection of carrier waves composing wave groups

Numerical analyses for the Bragg resonant reflection of carrier waves associated long waves due to sinusoidally varying seabeds are performed by using a set of coupled ordinary differential equations derived from the Boussinesq equations. The Boussinesq equations are firstly approximated with the Fourier decomposition. The coupled governing equations are then derived and used to simulate evolution of both short and long wave components. It is also found that wave groups are generated by two carrier waves with slightly different frequencies. The wave energy of the initial wave components is transferred to other harmonic components during propagation over a long distance. Evolution and reflection of both short and long waves were largely affected by nonlinearity.     

Experimental study of strong reflection of regular water waves over submerged breakwaters in tandem

A series of laboratory experiments was carried out to investigate the strong reflection of regular water waves over a train of submerged breakwaters. Rectangular and trapezoidal shapes of submerged breakwaters are employed and compared for reflecting capability of incident waves. Measured reflection coefficients of regular waves over impermeable submerged breakwaters are verified by comparing with those of the eigenfunction expansion method. A very good agreement is observed. Reflection coefficients of permeable submerged breakwaters are less than those of impermeable breakwaters. The trapezoidal shape is recommended for a submerged breakwater in terms of reflecting capability and practical application.     

分层流体中内孤立波在潜浮式竖直薄板上透射和反射

采用边缘层理论研究了两层流体系统中内孤立波在潜浮式竖直薄板上的透射和反射问题,提出了非线性演化方程的“初值”条件,分析了内孤立波与薄板非线性相互作用的效应。研究表明:流体层的密度比以及薄板伸入上下层的深度对于反射和透射波结构具有显著的影响,薄板伸入下层越深、密度差越小,则薄板阻碍孤立波透射的效率越高;透射波通常演化为单峰孤立波和迅速衰减的尾波,反射波演化为缓慢衰减的尾波列;对于具有小密度差的跃层结构,内孤立波在潜浮式竖直薄板上的透射及其演化近乎是无障碍的。     

The effects of a porous-elastic seabed on interfacial wave propagation

A theoretical model for the decay of progressive interfacial gravity waves propagating above a porous bed is developed assuming potential flow in a two-layer system with a free surface and a sharp interface. A new wave dispersion relation for two-layer flow above a quasi-static porous seabed is derived and investigated. The solutions for the nonlinear wave profile are derived using a perturbation method and the effects of geometric and flow parameters including bed characteristics, depth ratios and the densities of the two fluids are studied and discussed. Comparisons with existing analytical solutions for viscous interfacial wave attenuation over a rigid bed demonstrate the relative importance of the porous bed as a mechanism for wave decay. It is shown that the influence of a porous seabed on wave propagation is significant when the depth of the lower layer, normalised by the wavenumber, is less than π.     

An empirical formula for friction coefficient of a perforated wall with vertical slits

The friction coefficient in the permeability parameter of a perforated wall has been estimated on the basis of a best fit between measured and predicted values of such hydrodynamic coefficients as reflection and transmission coefficients. In the present study, an empirical formula for the friction coefficient is proposed in terms of known variables, i.e., the porosity and thickness of the perforated wall and the water depth. This enables direct estimation of the friction coefficient without invoking a best fit procedure. To obtain the empirical formula, hydraulic experiments are carried out, the results of which are used along with other researchers' results. The proposed formula is used to predict the reflection and transmission coefficients of various types of structures including a perforated wall. The concurrence between the experimental data and calculated results is good, verifying the appropriateness of the proposed formula. It is also shown that the proposed formula can be used for irregular waves as well.