适用于沙坝上Bragg反射的二阶Boussinesq方程数学模型及其数值验证

在二阶 Boussinesq 方程基础上,通过引入含水深导数项对该方程进行了理论上的改进,使得该方程在应用于无限沙坝 Bragg反射问题时与理论解析解在更大范围内符合.基于该改进的高阶 Boussinesq 方程,在非交错网格下建立了混合 4 阶的Adams-Bashforth- Moulton 格式的数学模型.将数值模型应用到有限个连续沙坝上波浪传播变形问题的数值模拟中,通过两点法给出数值波浪反射系数,将这些反射系数与已有的实验数据进行对比,对比表明改进后的模型计算出的反射系数与实验结果吻合更好,这验证了本文理论改进的有效性.     

Boussinesq类方程描述有限沙坝地形Bragg反射的性能比较

利用Boussinesq方程,采用线性摄动展开法,求解波浪正向通过有限沙坝地形的一阶反射波解,研究比较Boussinesq类方程描述沙坝地形对波浪的反射作用的性能。通过研究反射系数并与势流理论结果及实验结果对比,发现:邹志利的高阶方程、张永刚及Madsen的方程适用的水深范围较广,而Nwogu和Peregrine的方程仅在共振点附近有效;当入射波的波长为沙坝波长两倍时,反射波产生共振效应(即Bragg反射),反射系数与沙坝振幅和水深的比值以及地形中沙坝的条数成正比;相对势流理论的共振时的反射系数,以张永刚为代表的一系列Boussinesq方程色散精度越高,适用水深范围越广,而高阶方程适用的水深很浅。     

透空式防波堤周围的非线性波浪传播的数值模拟

对非线形波浪在透空式防波堤周围的波浪变形进行了数值模拟,在Boussinesq波浪方程中加入与透空建筑物有关的新的耗散项,从而界定了透空建筑物引起的部分反射和透射,波浪折射衍射的传播过程通过控制方程求解。波浪控制方程通过有限差分方法求解。模型应用于模拟波浪经过具有部分反射的群桩式透空结构,结果表明透空式防波堤可以有效地衰减波浪,是重力式结构的一种替代形式。     

波浪在局部可渗透水平海床上传播的解析解

本文建立了波浪在局部可渗透水平海床上传播的解析解,并研究了波浪在局部可渗透海床上的透射、反射问题。研究中将计算域划分为4个区域,中间区域为流域,海底可渗透,其下区域为多孔介质海床,左右两个区域也为流域,但海底不可渗透。应用线性波浪理论,建立了各流域包含非传播模态的速度势表达式,给出了海床内部的压强表达式,并利用交界面上匹配条件,求解了表达式中的待定系数。基于该解析模型,探讨了海床渗透系数、相对水深、渗透海床长度对波浪传播变形的影响。结果表明,波高沿程衰减,强度随渗透系数、渗透海床长度的增加以及相对水深的减小而变大;局部可渗透海床会引起波浪的反射和透射,随着海床长度的增加,反射系数振荡变化,并最终趋于常数,透射系数指数衰减,并最终趋于0。     

波浪在三维圆形岛地形上的绕射研究

波浪在传播过程中遇到岛屿就会发生绕射。本文使用混合元方法对修正型缓坡方程进行了数值求解,并与KUO et al的解析解进行了比较验证。在此基础上研究了工程尺度背景下,波浪在三维圆形岛地形上的绕射,计算了不同入射波浪周期、浅滩形状参数和岛屿尺寸情况下,沿波浪传播方向断面上和岛屿岸线上的相对波高大小。计算结果表明：随着入射波周期的减小、浅滩形状参数的增大和岛屿尺寸的减小,圆形岛迎浪侧的相对波高振荡幅度、圆形岛背浪侧的相对波高大小以及岛屿岸线上的相对波高振幅和大小均随之增大。不同情况下,岛屿岸线上的相对波高最大值大多数发生在迎浪点,个别发生在迎浪点两侧20°~25°处;最小值发生在背浪点两侧30°附近。     

波浪周期性作用对海床基回收的影响研究

针对海床基回收过程中波浪对回收绳索的冲击响应问题,通过对回收船—回收绳体系的运动响应进行数值模拟仿真,模拟回收绳索的松弛—张紧动态响应过程,分析波浪周期性作用对回收绳索冲击张力的影响。研究结果表明,冲击张力与波高成线性关系且不同周期条件下冲击张力随波高增加量差异较大,冲击张力对波浪周期的响应极为敏感,长周期波浪冲击响应较小,而短周期波浪冲击响应较大,易超出回收绳索的极限负荷,特别是当波长达到船长两倍左右时冲击张力达到最大;随着水深增加,冲击张力呈指数衰减,因此在浅水区波浪周期性作用对海床基的回收影响更大。     

高阶边界元方法求解规则波在三维局部渗透海床上的传播

基于线性势流理论,利用高阶边界元法研究了规则波在三维局部渗透海床上的传播。根据Darcy渗透定律推导出渗透海床的控制方程,利用渗透海床顶部和海底处法向速度和压强连续条件得到渗透海床顶部满足的边界条件。根据绕射理论,利用满足自由水面条件的格林函数建立了求解渗透海床绕射势的边界积分方程,采用高阶边界元方法求解边界积分方程进而得到自由水面的绕射势和波浪在局部渗透海床上传播过程中幅值的变化情况。通过与已发表的波浪对圆柱形暗礁的时域全绕射结果对比,证明了本文建立的频域方法计算波幅的正确性和有效性。利用这一模型研究了三维矩形渗透海床区域上波浪的传播特性,并分析了入射波波长、海床渗透特性系数等参数对波浪传播的影响。     

波浪作用下沙质海床上大直径圆筒结构动态响应的实验研究

通过物理模型实验,对沙质海床上沉入式大直径圆筒结构对波浪的动态响应进行了较系统的实验研究。实验中考虑了大直径圆筒、波浪和海床三者之间的耦合作用,并实时记录了大直径圆筒结构的动态响应。实验数据分析表明,大直径圆筒在波浪作用下的动态响应以大圆筒随波浪的前后摆动为主,其摆动轴心并不是固定不变的。最后通过回归分析给出了估算大直径圆筒摆动转角幅值的经验公式。     

基于Boussinesq方程近岸波浪演变的数值研究

首先对目前描述近岸波浪传播变形的数学模型进行了回顾与总结;对不同数学模型的特点、适用范围和发展情况进行了阐述与对比。应用基于Boussinesq方程的Coulwave模式针对几个经典实验地形进行了数值实验,数值结果和实验实测数据吻合较好。此外,分别采用不同的近岸波浪模型模拟了某渔港附近波浪的传播变形,结果表明:当考虑波浪的折射、绕射、反射联合作用时,Coulwave模式计算结果明显较缓坡方程及SWAN模型计算结果更加合理。     

双层直立圆弧型防波堤上绕射波浪力的解析计算

基于微幅波绕射理论,应用特征函数展开法,推导了双层直立圆弧型透空防波堤的波浪绕射解析解,从而将已有的比例边界有限元法拓展为解析算法,并据此对外层与内层防波堤所受波浪载荷进行了解析计算。计算结果表明:应用本文方法对直立透空圆环柱的绕射波浪载荷进行验证计算,所得结果与现有的解析解完全吻合,说明方法可靠。双层堤较单层堤能更有效地减弱波浪作用。波浪的入射角度和特征参数、防波堤张角与半径、防波堤透空系数以及水深等因素的相对变化对双层堤的波浪作用均存在一定影响。     

Bragg reflection of water waves by multiple floating horizontal flexible membranes with submerged rectangular bars on the seabed

Bragg reflection of water waves by multiple floating horizontal flexible membranes is investigated based on the linear wave theory and the assumption of small membrane response. Under the floating horizontal membranes, periodical submerged rectangular bars are arranged on the flat seabed. The total reflection and transmission coefficients are obtained by using the eigenfunction expansion method and the wide spacing approximation. The calculated coefficients are validated with the results available in the literature, which shows that the present method is applicable. The characteristics of Bragg reflection are systematically investigated by changing various parameters including the height of the rectangular bars, the number, the tension, the spacing, and the length of the flexible membranes. The results can help designing multiple floating horizontal flexible membranes as effective floating breakwaters by taking advantage of Bragg reflection.     

恒定流对潜堤波浪反射系数影响研究

为研究恒定均匀流对直立潜堤波浪反射系数的影响,采用了高阶边界元方法和混合欧拉-拉格朗日时间步进方法更新瞬时自由水面,运用基于二次形状函数的网格重分方案结合四阶龙格库塔方法更新时间积分,并运用两点法得到淹没潜体前的反射系数。将数值模拟得到的波面数据与物理模型试验结果进行对比,两者吻合良好。通过数值模拟研究给出了入射波周期、水流流速、潜堤相对宽度和相对淹没深度对反射系数的影响。结果表明,水流流速和潜堤相对淹没深度对反射系数影响较大,潜堤相对宽度的影响相对较小;水流的存在会使入射波周期等参数对反射系数的影响程度发生改变,在实际工程设计时应考虑水流对潜堤防浪效果的影响。     

On the wave damping due to a permeable seabed

Laboratory experiments were performed to study the wave damping induced by a porous bed. During the propagation of waves over a porous medium the wave characteristics change: a significant wave height attenuation of about 20–30% is observed and, in almost all cases, an increase in wavelength. The wave decay is found to depend on the wave characteristics like the wave height, the wavelength and the wave shape. We have also studied the influence of the geometric properties of the porous bed (i.e. thickness and length) on the wave dissipation. It is found that the attenuation of the wave height increases with the permeable bed thickness and that there is a maximum wave dissipation for a length of the porous seabed equal to 2.0–2.5 times the wavelength. A comparison is also made of our findings with available literature results. A parametric study of the wave damping has been performed by varying the values of the resistance coefficients derived by both literature and experiments. Literature analytical models have been applied by using the resistance coefficients that better describe our flow conditions. All models in use underpredict the observed wave attenuation for any sensible values of the resistance coefficients.     

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。     

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。     

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.     

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.     

Cnoidal water wave induced seepage in a permeable seabed with a defined thickness

Extreme waves can induce seepage in a seabed and cause problems to marine structures in coastal regions. In this study, the seepage under cnoidal waves was studied using the transient seepage equation. An analytical solution is presented for the pore pressure in a seabed of defined thickness. Parametric studies were carried out to examine the influence of air content in the pore water, and of the soil hydraulic conductivity on the seepage. It has been shown that the air content and the soil hydraulic conductivity can affect the pore pressure response significantly. An increase in the air content or a decrease in the soil hydraulic conductivity will increase the magnitude of the pore pressure gradient and results in the pore pressure varying sharply. The liquefaction potential of a seabed under cnoidal waves is discussed. Consequently, comparative studies are carried out to show that the soil shear modulus and Poisson constant can influence the difference between the transient seepage equation and Biot's equation, and the transient seepage equation is a limit of Biot's equation.     

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.