Reflected and transmitted waves in a channel with side porous mattresses

The problem of wave propagation and wave damping in a channel with side porous mattresses of arbitrary shape protruding from the walls is studied. The solution was achieved by applying 3-D boundary element method and was employed to study wave field in the channel and to analyze the effect of the geometry of the mattresses and physical and hydraulic properties of porous material on wave damping. The results show that wave damping in the channel strongly depends on wave parameters, especially, on the wave number. Wave reflection and transmission decrease with increasing the wave number. The results also show that the wave field in the channel strongly depends on the geometry of the mattresses as well as on physical and hydraulic properties of porous material used to build these wave dampers. The geometry of the mattresses and physical and hydraulic properties of porous material have a moderate effect on wave reflection and a significant effect on wave transmission. The results show that wave transmission down the channel decreases with increasing the length and thickness of the mattresses. Moreover, wave transmission decreases with increasing the porosity and damping properties of porous media used to build the mattresses. The analysis shows that porous mattresses protruding from the channel walls are very efficient in damping water waves propagating down the channel and may be built in channels to reduce high waves and achieve desired wave conditions. Theoretical results are in reasonable agreement with experimental data.     

Interaction of non-breaking regular waves with a periodic array of artificial porous bars

A computational model is developed to investigate the wave damping characteristics of a periodic array of porous bars. The transmission and reflection coefficients as well as the wave energy dissipation are evaluated relating to the physical properties and geometric factors of bars. It is shown that the porosity, number, width and height of bars all play important roles in the wave damping characteristics, compared to other factors such as the intrinsic permeability. It is observed that like impermeable bars, permeable bars display Bragg phenomenon. However, Bragg reflection produced by permeable bars is smaller than that by impermeable bars. Permeable bars reflect smaller waves, transmit smaller waves and dissipate more wave energy. It is indicated that if the porosity increases, both the reflection and transmission coefficients decrease and more wave energy is dissipated. Further, it is found that the porosity controls the magnitude, but not the oscillation frequency of the reflection coefficient, which depends only on the number of bars.     

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。     

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.     

Wave reflection and transmission at permeable breakwaters of arbitrary cross-section

A theory is formulated to predict wave reflection and transmission at an infinite rubble-mound breakwater. The breakwater may be a multilayered structure with arbitrary cross-section. It is assumed that the incident wave is normal to the structure and the wave may be described by linear theory. A hybrid method has been applied to solve the boundary value problem.Comparison between experimental and theoretical results shows reasonable agreement.     

Water waves within a porous medium on an undulating bed

Water wave refraction–diffraction within a porous medium on an undulating seabed is considered based on linear wave theory. Using the model of wave-induced flow within a porous medium and Galerkin eigenfunction expansions, refraction–diffraction equations for surface waves are derived. With these equations, the wave reflection from a porous structure on a sloping beach is investigated and numerical results of reflection coefficients are obtained. A comparison between the present results with those in the literature is made for a special case and the agreement is satisfactory. This structure can be viewed as an idealized model of rubble-mound seawalls along coastlines.     

淹没矩形防波堤透反射系数特性研究

采用解析方法研究了斜向入射波作用下淹没矩形防波堤的透反射系数特性.首先利用特征函数展开法导出了绕射势函数的分析解和透反射系数的计算公式,然后利用边界元方法验证了解析解,在此基础上利用解析解分析了若干工况下的防波堤透反射特性.计算结果表明,淹没矩形防波堤截面的宽度、高度和相对位置以及入射角的改变都不同程度影响反射系数和透射系数.在中等深度条件下,对于一定频率的波浪,位置和尺寸适当的淹没矩形堤可以反射大部分斜向入射波.研究结果对设计淹没的矩形防波堤具有重要的参考价值.     

Wave damping characteristics of vertically stratified porous structures under oblique wave action

The characteristics of wave damping for the vertically stratified porous breakwaters are investigated under oblique wave action. It is found that for common angles of incidence, the wave damping efficiency of a vertically stratified porous structure behaves very similar to a simple structure. The reflection coefficient decreases with increasing angle of incidence while the transmission coefficient only slightly increases as the angle of incidence increases. It is shown that the wave energy loss is in direct proportional to the structure thickness and its porosity regardless of the angle of incidence. Considering small transmission coefficient as a basic requirement and if a moderate reflection coefficient is accepted, a structure thickness of b/h=1 is proposed. In this situation, since the structure does not have a very large thickness, adopting a vertically stratified structure is not an effective way to improve its wave damping efficiency.     

消浪室宽度对可渗明基床开孔沉箱消浪性能影响研究

开孔沉箱是将传统沉箱的前壁开孔,使沉箱前的入射波浪与反射波浪非同相位叠加,达到消能目的。消浪室是开孔沉箱的重要特征结构,其宽度对开孔沉箱的消浪性能具有重要影响。针对可渗明基床开孔沉箱,赋予消浪室宽度以较大的变化范围,开展专项物模试验,研究探讨了在规则波与不规则波作用下,相对消浪室宽度对可渗明基床开孔沉箱前波高反射系数的影响规律,发现反射系数随相对消浪室宽度的增加呈减小—增大—减小的振荡特性,这一发现有别于前人的研究成果,对工程中开孔沉箱消浪室结构的优化设计具有借鉴意义。同时,对试验工况进行数值模拟和解析计算,以物模试验值为标准,评价两种方法在研究相对消浪室宽度对开孔沉箱波高反射系数影响时的规律把握能力及计算精度,对工程中应用这两种方法给出相关建议。     

NWF: Propagation of Tsunami and its Interaction with Continental Shelf and Vertical Wall

In this article, tsunamis represented as solitary waves was simulated using the fully nonlinear free surface waves based on Finite Element method developed by Sriram et al. (2006). The split up of solitary wave while it propagates over the uneven bottom topography is successfully established. Wave transmission and reflection over a vertical step introduced in the bottom topography is in good agreement with the experimental results from Seabra-Santos et al. (1987). The wave transformation over a continental shelf with different smooth slopes reveals that the solitary wave reflection increases while the continental slope varies from flat to steep. The interaction of the solitary wave with a vertical wall for different wave steepness has been analysed. The reflected shape of the profile is in good agreement with the observation made by Fenton and Rienecker (1982) and an increase in wave celerity is observed.     

Tentative engineering approach to scour around breakwaters in random waves

An approach by which the scour depth and protection layer width around the head of vertical-wall breakwaters, the scour and deposition depths as well as the protection layer widths at the round head of rubble-mound breakwaters in random waves can be derived is presented. Here the formulas for scour depth by Sumer and Fredsøe (1997) for vertical-wall breakwaters for regular waves and Fredsøe and Sumer (1997) for rubble-mound breakwaters for irregular waves are used. They are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the scour and deposition depths as well as protection layer widths in random waves. Comparisons are made between the present approach and the Fredsøe and Sumer (1997) random wave scour data for rubble-mound breakwaters.     

Examination of Extraordinary Transmission of Waves Propagation through Gaps of Vertical Thin Barriers in Channels by A Hypersingular Boundary Element Method

The extraordinary transmission(ET) phenomenon is examined for waves propagating through gaps of vertical thin barriers in channels with a hypersingular boundary element method model on the linear potential theory, and an estimate formula based on small gap approximation for predicting the number of ET frequencies is proposed.Numerical computations are carried out to examine the influences of barrier number, barrier interval, gap size, gap position and barrier arrangement on extraordinary transmission and wave height in the channel. It shows that all of those factors evidently affect the extraordinary transmission frequencies. The contours of wave amplitude show that very high waves can be excited in the basins between barriers at the extraordinary transmission frequencies. Proper arrangement of barriers in a channel can avoid the occurrence of ET phenomenon and reduce wave height in the channel.     

Approximation to the hydrodynamics of floating pontoons under oblique waves

The hydrodynamic properties of long rigid floating pontoon interacting with linear oblique waves in water of finite arbitrary depth are examined theoretically. The flow is idealized as linearized, velocity potentials are expressed in the form of eigen-function expansions with unknown coefficients. The fluid domain is split into three regions, region (1) wave-ward of the structure, region (2) in the lee of the structure, and region (3) beneath the structure. The different hydrodynamic quantities of interest such as the exciting forces, added mass and damping coefficients, reflection and transmission coefficients were studied for an applicable range of wave/structure parameters. Assuming rigid body motions, dynamic responses of the moored structure is approximately calculated through three equations of motion. Floating pontoons proved to be a convenient alternative for protection from waves in shallow water. The present method of solution was found to be computationally efficient, and results are comparable to those obtained through other techniques.     

Numerical simulation of non-linear regular and focused waves in an infinite water-depth

Inviscid three-dimensional free surface wave motions are simulated using a novel quadratic higher order boundary element model (HOBEM) based on potential theory for irrotational, incompressible fluid flow in an infinite water-depth. The free surface boundary conditions are fully non-linear. Based on the use of images, a channel Green function is developed and applied to the present model so that two lateral surfaces of an infinite-depth wave tank can be excluded from the calculation domain. In order to generate incident waves and dissipate outgoing waves, a non-reflective wave generator, composed of a series of vertically aligned point sources in the computational domain, is used in conjunction with upstream and downstream damping layers. Numerical experiments are carried out, with linear and fully non-linear, regular and focused waves. It can be seen from the results that the present approach is effective in generating a specified wave profile in an infinite water-depth without reflection at the open boundaries, and fully non-linear numerical simulations compare well with theoretical solutions. The present numerical technique is aimed at efficient modelling of the non-linear wave interactions with ocean structures in deep water.     

Depositional elements associated with a basin floor channel-levee system: case study from the Gulf of Mexico

The seismic geomorphology and seismic stratigraphy of a deep-marine channel-levee system is described. A moderate to high-sinuosity channel trending southeastward across the northeastern Gulf of Mexico basin floor, and associated depositional elements are well imaged using conventional 3D multi-channel seismic reflection data. Depositional elements described include channels, associated levees, a channel belt, avulsion channels, levee crevasses, frontal splays, sediment waves, and mass transport complexes. Distinguishing morphologic and stratigraphic characteristics of each depositional element are discussed. These deposits are presumed to be associated with repeated deep-marine turbidity flows and other mass transport processes.     

Damping long waves by a multi-channel structure

In this paper, a multi-channel structure was developed to attenuate waves with various wave periods. By ignoring energy losses and the factor of channel width, a simple and straightforward method was used to tackle this problem. The theoretical solution showed that a single reflected channel structure could attenuate waves of a certain wave period, while a multi-channel structure could attenuate waves with various wave periods. If an interval of 0.05<relative water depth<0.15 is concerned, a structure consisting of four reflected channels could provide a transmission coefficient of less than 0.2. Experimental tests were conducted to verify the theoretical solutions. Both theoretical solution and experimental data indicated that waves with various wave periods would be effectively attenuated after passing through the multi-channel structure. Although some factors are neglected in treating this problem, the method is applicable. An allowed transmission coefficient can be provided by a multi-channel structure only if the computed peak value is not larger than that value.     

RANS modelling applied to random wave interaction with submerged permeable structures

This paper is the second part of the work presented by Garcia et al. [Garcia, N., Lara, J.L., Losada, I.J., 2004. 2-D numerical analysis of near-field flow at low-crested breakwaters. Coastal Engineering 51 (10), 991–1020]. In the mentioned paper, flow conditions at low-crested rubble-mound breakwaters under regular wave attack were examined, using a combination of measured data of free surface, bottom pressure and fluid velocities from small-scale experiments and numerical results provided by a VOF-type model (COBRAS) based on the Reynolds-Averaged Navier–Stokes (RANS) equations. This paper demonstrates the capability of the COBRAS model to reproduce irregular wave interaction with submerged permeable breakwaters. Data provided by the numerical model are compared to experimental data of laboratory tests, and the main processes of wave–structure interaction are examined using both experimental and numerical results. The numerical model validation is carried out in two steps. First, the procedure of irregular wave generation is verified to work properly, comparing experimental and numerical data of different cases of irregular wave trains propagating over a flat bottom. Next, the validation of the numerical model for wave interaction with submerged rubble-mound breakwaters is performed through the simulation of small-scale laboratory tests on different incident wave spectra. Results show that the numerical model adequately reproduces the main aspects of the interaction of random waves with submerged porous breakwaters, especially the spectral energy decay at the structure and the spectrum broadening past the structure. The simulations give good results in terms of height envelopes, mean level, spectral shape, root-mean-square height for both free surface displacement and dynamic pressure inside the breakwater. Moreover, large-scale simulations have been conducted, on both regular and irregular incident wave conditions. The overall pattern of the wave interaction with a large-scale submerged breakwater is adequately reproduced by the numerical model. The processes of wave reflection, shoaling and breaking are correctly captured. The good results achieved at a near prototype scale are promising regarding the use of the numerical model for design purposes.     

Transmission and reflection of the Rossby waves in a stratified ocean with bottom topography

Transmission and reflection coefficients are calculated for Rossby waves incident on a bottom topography with constant slope in a continuously stratified ocean. The characteristics of the coefficients are interpreted in terms of the quasigeostrophic waves on the slope. In the parameter range where only the barotropic Rossby waves can propagate in the region outside the slope, the bottom trapped wave plays the same role as the topographic Rossby wave in a homogeneous ocean, and hence the transmission is weak unless phase matching takes place. When both of the barotropic and baroclinic Rossby waves can propagate outside the slope, the total transmission can be strong. The bottom trapped wave affects the transmission and reflection, and it leads to the possibility that the Rossby wave is transmitted as a mode different from the incident mode. When the number of the wavy modes on the slope is smaller than that of the Rossby wave modes outside the slope, strong reflection occurs.The results for an ocean with linear distribution of the squared Brunt-Väisälä frequency are compared to those in a uniformly stratified ocean. The weakening of the stratification near the bottom is almost equivalent to reducing the effect of the slope.     

新型直立式透空堤消浪性能数值研究

为使防波堤同时具有良好的掩护效果和水体交换能力,提出了两种带有透浪通道的新型直立式防波堤。基于Fluent求解器建立了三维数值波浪水槽,通过与试验结果对比,验证了该数值水槽求解波浪与透空堤作用具有较高的精度。对两种防波堤在规则波作用下的透浪特性进行了研究,结果表明:透射系数K_t与透空率呈正线性相关,且可通过调整透浪通道间距,使相同透空率下K_t降低20%～30%。对同一结构,K_t随相对波长的增大而显著增大,但受相对波高的影响较小。在透空率大于0.16后,异型沉箱防波堤的消浪性能明显优于错位沉箱。基于数值计算结果,给出了以上两种透空堤波浪透射系数的经验公式。     

Reflection of irregular waves from perforated-wall caisson breakwaters

An analytical model has been developed that predicts the reflection of irregular waves normally incident upon a perforated-wall caisson breakwater. To examine the predictability of the developed model, laboratory experiments have been conducted for the reflection of irregular waves of various significant wave heights and periods impinging upon breakwaters having various wave chamber widths. For frequency-averaged reflection coefficients, though the overall agreement is fairly good between measurement and calculation, the model somewhat over-predicts the reflection coefficients at larger values, and under-predicts at smaller values. The model also underestimates the energy loss coefficients as wave reflection becomes larger. These differences occur because the model neglects the evanescent waves near the breakwater, which increase the energy loss at the perforated wall. The frequency-averaged reflection coefficient shows a minimum when the wave chamber width is approximately 0.2 times the significant wavelength, and it decreases with increasing wave steepness. Finally, it is shown that the reflection of irregular waves from a perforated-wall caisson breakwater depends on the wave frequency, so that the reflected wave spectrum shows a frequency dependent oscillatory behavior.