Wave Height Transformation and Set-up Between a A Submerged Permeable Breakwater and A Seawall

In this study, we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall. Modified time-dependent mild-slope equations, which involve parameters of the porous medium, were used to calculate the wave height transformation and the mean water level change around a submerged breakwater. The numerical solution is verified with experimental data. The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall. In contrast to cases without a seawall, the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall. Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater. We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.     

Wave transformation over submerged permeable breakwater on porous bottom

A numerical model is presented in this study to investigate the wave transformation over a submerged permeable breakwater on a porous slope seabed. For this purpose, the time-dependent mild-slope equation is newly derived for waves propagating over two layers of porous medium. This new mild-slope equation involves the parameters of the porous medium, and it is a type of hyperbolic differential equation, therefore numerically efficient. The validity of the present model is verified based on the comparisons with the previous experiments. The effects of the permeable properties of both the porous seabed and the submerged permeable breakwater are discussed in detail. The geometry of the submerged permeable breakwater to the wave transformation is also investigated based on the numerical solutions.     

聚焦波作用下透水潜堤消波特性数值模拟研究

基于非静压数值计算模型,本文系统研究了聚焦波作用下透水潜堤的消波特性,通过设置合理的计算工况,详细分析了波高、堤顶水深、谱峰周期、孔隙率以及堤顶宽度5种因素对透水潜堤消波特性的影响。与此同时,本文将透水潜堤的计算结果同不透水潜堤的计算结果进行了对比分析。计算结果表明：透水潜堤对聚焦波的消减作用要强于不透水潜堤,从而说明,透水潜堤能更有效地降低畸形波对海岸基础设施的影响;波高和堤顶水深是影响潜堤消波特性的重要因素,随入射波高增加、堤顶水深减小,透水潜堤对波浪的消减作用逐渐增强。透水潜堤对长周期波浪的消波效果较差。在本文考虑的孔隙率范围内,孔隙率越大,透水潜堤消波效果越好;当孔隙率为0.4,堤顶宽度为0.612 5 m时,透水潜堤可消减54%的入射波能,比不透水潜堤对入射波能的消减增加36.1%。本文研究结果可为进一步认识透水潜堤的消波特性和海岸防护工程设计提供相应的参考。     

多向聚焦波作用下透水潜堤消波特性数值模拟研究

本文采用非静压模型NHWAVE建立高精度三维波浪数值水槽,对多向聚焦波作用下透水和不透水潜堤消波特性进行数值模拟研究。通过计算结果与实验数据的对比,验证了该模型模拟多向聚焦波产生传播及多孔介质内流动的能力,进一步考虑了有效波高、水深、谱峰周期和传播角度等因素对潜堤消波特性的影响。结果表明：潜堤对多向聚焦波的最大波幅、最大水位、沿水深平均最大流速和波能均有显著消减作用,且透水潜堤因孔隙介质的存在消波性能更好。随着有效波高增大,堤顶处波浪破碎点前移,不透水潜堤消波性能受波高影响较大。水深越大,潜堤消波性能越低。透水潜堤对长周期波浪消减效果较差。传播角度越小,聚焦位置处波幅越大,波浪非线性作用越强。研究结果可为我们进一步保护沿海设施免受极端海洋环境的影响提供一定的参考     

没水倾斜板式防波堤消波性能分析

提出了一种将波浪中倾斜板问题等效化简为波浪中水平板单元组的方法,该方法建立在使用分离变量法求解水工结构边值问题的基础上,并使用伽辽金法精确求解连续边界条件,确定考虑衰减波态的速度势函数,从而求解没水倾斜板结构的消波性能。等效化简法计算精度于边界元法相当,且计算单元数量少、开销低。基于二维线性势波理论,对没水倾斜板式防波堤消波性能分析显示,没水板的倾斜角度、没水深度与板长是结构消波性能的控制因素:没水倾斜板防波堤的消波性能优于没水水平板防波堤的消波性能,随着没水板结构的倾斜角度增大,没水倾斜板结构的波浪透射系数显著减小,且长板优于短板,浅板优于深板;与前人的水槽实验对比显示,相对没水深度与波陡影响结构的消波性能,且波陡造成的波浪破碎贡献了显著的波能消耗。该结论对板式防波堤的结构配置、优化设计有重要意义。     

Scattering of water wave by a submerged horizontal plate and a submerged permeable breakwater

Based on a two-dimensional linear water wave theory, this study develops the boundary element method (BEM) to examine normally incident wave scattering by a fixed, submerged, horizontal, impermeable plate and a submerged permeable breakwater in water of finite depth. Numerical results for the transmission coefficients are also presented. In addition, the numerical technique's accuracy is demonstrated by comparing the numerical results with previously published numerical and experimental ones. According to that comparison, the transmission coefficient relies not only on the submergence of the horizontal impermeable plate and the height of the permeable breakwater, but also on the distance between horizontal plate and permeable breakwater. Results presented herein confirm that the transmission coefficient is minimum for the distance approximately equal to four times the water depth.     

聚焦波浪在浅堤上传播变形高精度数值模拟研究

基于开源程序REEF3D,通过建立高精度二维数值波浪水槽,系统研究了聚焦波浪在浅堤上传播变形的规律,着重分析了聚焦波浪通过浅堤的水动力过程及能量变化规律,讨论了不同波浪要素对聚焦波浪传播特性的影响。除此之外,还考虑了双浅堤布置对聚焦波浪传播变形的影响。研究结果表明:极端波浪通过浅堤时,堤顶水深越小,波浪主频能量衰减越显著。在给定堤顶水深条件下,聚焦点与浅堤的相对位置对聚焦波浪能量的衰减影响较小。在双浅堤布置条件下,随着浅堤间距的增加,上下游浅堤的相互影响逐渐减弱,高频段的波浪能量也随之减小。     

Numerical study for waves propagating over a porous seabed around a submerged permeable breakwater: PORO-WSSI II model

The phenomenon of the wave, seabed and structure interactions has attracted great attentions from coastal geotechnical engineers in recent years. Most previous investigations have based on individual approaches, which focused on either flow region or seabed domain. In this study, an integrated model (PORO-WSSI II), based on the Volume-Averaged/Reynolds-Averaged Navier-Stokes (VARANS) equations and Biot's poro-elastic theory, is developed to investigate the mechanism of the wave-permeable structure-porous seabed interactions. The new model is verified with the previous experimental data. Based on the present model, parametric studies have been carried out to investigate the influences of wave, soil and structure parameters on the wave-induced pore pressure. Numerical results indicated: (i) longer wave period and larger wave height will obviously induce a higher magnitude of pore pressure at the leading edge of a breakwater; (ii) after a full wave-structure interaction, the magnitude of pore pressure below the lee side of a breakwater decreases with an increasing structure porosity while it varies dramatically with a change of structure height; and (iii) the seabed thickness, soil permeability and the degree of saturation can also significantly affect the dynamic soil behaviour.     

柔性水囊潜堤消波特性的溃坝水槽试验研究

柔性水囊潜堤由橡胶制成,内部充水,具有结构简单、造价低廉等优点,能较好满足人工岛、跨海桥梁、海洋平台等基础设施建设工程对简单便携、拆装方便的临时防波堤的需求。为了探究柔性水囊潜堤的消波特性,在溃坝水槽内开展溃坝波与半圆柱形柔性水囊潜堤相互作用的试验研究,重点探究柔性水囊潜堤与溃坝波相互作用过程中水位变化特性,并与半圆柱刚性潜堤的性能进行比较;同时分析柔性水囊潜堤内部初始水压和浸没深度等参数对其消波性能的影响。结果表明：柔性水囊潜堤能够用作临时防波堤来衰减波浪;与半圆柱刚性潜堤相比,柔性水囊潜堤在降低溃坝波无量纲最大水位、提高消波性能方面更具优势;内部初始水压是影响柔性水囊潜堤消波性能的重要因素,适当降低内部初始水压,有利于增强柔性潜堤的变形程度,进而增加波能耗散,可获得更好的消波效果;而增加浸没深度即潜深,会使得柔性水囊潜堤对溃坝波的影响程度降低,消波效果减弱。     

Parameterisation and transformation of wave asymmetries over a low-crested breakwater

This paper presents the results of an investigation of the transformation of wave skewness and asymmetry as waves propagate obliquely over low-crested breakwaters, (LCBs), based on an analysis of measurements collected in the DELOS project. Considering the effect of the local Ursell number on wave asymmetries, a set of practical empirical formulae were established using least squares regression for both smooth and rubble mound LCBs. Predictions are in good agreement with measurements. Wave skewness on both sides of LCBs is linearly correlated for rubble mound LCBs but weakly correlated for smooth LCBs. While wave asymmetry on both sides of LCBs has a weakly quadratic correlation. The effect of the relative freeboard on the relationships of wave asymmetries between both sides is significant for rubble mound LCBs, but the same does not hold for smooth LCBs. With the presence of LCBs, wave skewness retains a positive sign on both sides but asymmetry changes from negative on the incident side to positive on the transmission side. Bispectral analysis shows that positive skewness and negative asymmetry arises from self–self and sum interactions but positive asymmetry is due to difference interactions between frequencies. The findings provide improved understanding of changes in wave skewness and asymmetry in the vicinity of structures, which may help mitigate scour and improve the stability of breakwaters.     

Comparison between characteristics of mild slope equations and Boussinesq equations

Boussinesq-type equations and mild-slope equations are compared in terms of their basic forms and characteristics. It is concluded that linear mild-slope equations on dispersion relation are better than non-linear Boussinesq equations. In addition, Berkhoffexperiments are computed and compared by the two models, and agreement between model results and available experimental data is found to be quite reasonable, which demonstrates the two models＇ capacity to simulate wave transformation. However they can deal with different physical processes respectively, and they have their own characteristics.     

Wave motion over a submerged breakwater with an upper horizontal porous plate and a lower horizontal solid plate

This study examines the hydrodynamic performance of a modified two-layer horizontal-plate breakwater. The breakwater consists of an upper submerged horizontal porous plate and a lower submerged horizontal solid plate. By means of the matched eigenfunction expansion method, a linear analytical solution is developed for the interaction of water waves with the structure. Then the reflection coefficient, the transmission coefficient, the energy-loss coefficient and the wave forces acting on the plates are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a single submerged horizontal solid plate and a single submerged horizontal porous plate. Numerical results show that with a suitable geometrical porosity of the upper plate, the uplift wave forces on both plates can be controlled at a low level. Numerical results also show that the transmission coefficient will be always small if the dimensionless plate length (plate length versus incident wavelength) exceeds a certain moderate value. This is rather significant for practical engineering, as the incident wavelength varies over a wide range in practice. Moreover, it is found that the hydrodynamic performance of the present structure may be further enhanced if the lower plate is also perforated.     

Asymptotic analysis of the interaction between linear long waves and a submerged floating breakwater of wavy surfaces

In this work, we carried out an asymptotic analysis, up to the second order in a regular expansion, of the interaction of linear long waves with an impermeable, fixed, submerged breakwater composed of wavy surfaces. Below the floating breakwater, there is also a step with a wavy surface. The undulating surfaces are described by sinusoidal profiles. The effects of three different geometric parameters — the amplitude of the wavy surfaces and the submerged length and width of the structure — on the reflection and transmission coefficients are analyzed. The hydrodynamic forces are also determined. The governing equations are expressed in dimensionless form. Using the domain perturbation method, the small wavy surfaces of the breakwater are linearized. The wavy surfaces of the breakwater generate larger values of the reflection coefficient than those obtained for breakwaters with flat surfaces, and the largest values of this coefficient are obtained when the length of the breakwater is of the same order of magnitude as the wavelength. The asymptotic solution is compared with the theoretical solutions that have been reported in the specialized literature and with a numerical solution. The present mathematical model can be used as a practical reference for the selection of the geometric configuration of a submerged floating breakwater under shallow flow conditions.     

孤立波与升沉水平板相互作用数值模拟研究

合理的刚度和潜深设计可以使升沉水平板获得优异的消浪性能。基于考虑流体黏性的二维不可压缩Navier-Stokes方程,以高阶紧致插值CIP(constrained interpolation profile)方法求解方程对流项,采用VOF(volume of fluid)方法重构自由液面,构建二维数值波浪水槽。采用试验数据验证模型后,研究孤立波与升沉水平板相互作用,分析相对刚度K*、相对潜深d/h、相对波高H/h对于升沉板的消浪性能和运动响应的影响,揭示升沉板对孤立波的消浪机理。研究表明:在孤立波通过时,升沉板会经历一个先上升后下降的运动,随后非线性自由振动,板下方水体近似均匀流动,且水流的垂向流动与板的垂荡方向一致;升沉板主要通过不对称涡旋脱落、浅水变形、波浪反射与辐射波转化等方式消耗孤立波能量;一定条件下,采用最优相对刚度K*=4.0和最优相对潜深d/h=0.52可以取得良好的消浪效果,此时透射系数最小,同时升沉板的运动响应在合理的范围内。     

Numerical study on the interaction among a nonlinear wave,composite breakwater and sandy seabed

Most previous investigations related to composite breakwaters have focused on the wave forces acting on the structure itself from a hydrodynamic aspect. The foundational aspects of a composite breakwater under wave-induced cyclic loading are also important in studying the stability of a composite breakwater. In this study, numerical simulations were performed to investigate the wave-induced pore water pressure and flow changes inside the rubble mound of the composite breakwater and seabed foundation. The validity and applicability of the numerical model were demonstrated by comparing numerical results with existing experimental data. Moreover, the present model clearly has shown that the instantaneous directions of pore water flow motion inside the seabed induced by surface waves are in good agreement with the general wave-induced pore water flow inside the seabed. The model is further used to discuss the stability of a composite breakwater, i.e., the interaction among nonlinear waves, composite breakwater and seabed. Numerical results suggest that the stability of a composite breakwater is affected by not only downward shear flow generating on the seaward slope face of the rubble mound but, also, a high and dense pore water pressure gradient inside the rubble mound and seabed foundation.     

Simulation of the nonlinear dynamic interactions between waves, a submerged breakwater and the seabed

This study employed direct numerical simulation to simulate the fully nonlinear interaction between the water waves, the submerged breakwater, and the seabed under differing wave conditions. In the numerical simulation, the laminar flow condition in the seabed was applied to evaluate the more exact fluid resistance acting on the porous media. Varying incident wave conditions were applied to the flow field resulting from the wave–structure–seabed interaction, and the variation in the pore water pressure beneath the submerged breakwater was investigated along the cross-section of the submerged breakwater. Structural safety and scouring were also considered on the basis of the numerical results for the flow field around the structure and the variation of the pore water pressure.