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。     

波浪在可渗海床上传播时的衰减

在以往的波浪理论研究中,通常假定海床是不可渗的。但在浅水区,海床的可渗性对波浪的传播有一定影响,它能引起波高的衰减,同时波浪也能够引起海床的变形、滑动、甚至液化。当海床的弹性小,渗透性大时,波浪与可渗海床的这种相互作用更为明显。本文通过对波浪场控制方程－拉普拉斯方程和弹性海床的控制方程－比奥方程联合解析求解,给出了海床土体响应、孔隙水压变化规律,以及波高在传播过程中的衰减。     

渗透海床上矩形Bragg防波堤对波浪反射的研究

与海床不可渗透的情况相比,波浪在可渗透海床上传播时会发生波能衰减。本文将基于可渗透海床上一维修正型缓坡方程,建立方程求解的有限差分模型。将通过与不可渗透海床上矩形Bragg防波堤对波浪反射系数解析解的对比,验证有限差分模型的正确性和适用性。将进一步研究海床可渗透情况下,海床的渗透性参数、坝体的相对宽度、数量、浸没度对波浪反射系数的影响及其与海床不可渗透情况下的差异。本文研究发现,Bragg共振发生时的反射系数随坝体数量的增多而增大,随海床渗透性参数和坝体浸没度的增大而减小,并且存在一个坝体相对宽度值会使Bragg共振反射达到最大。相较于海床不可渗透的情况,发生Bragg共振反射的波浪频率几乎相同,但反射系数减小,而且零反射（或全透射）现象不再存在。     

无限深可压缩海床上圆墩柱波浪渗流压力解析解

对建在海床上的海洋工程建筑物,波浪引起的渗流力是不可忽视的环境因素之一.我们给出了圆墩柱下无限深可渗可压缩海床中波浪渗流压力的封闭形式的解析解,进而可以给出作用在墩柱底面上的渗流力和力矩的解析表达式.假定海床土介质是可变形的,孔隙流体是可压缩的,渗流遵从达西定律,则渗流压力的控制方程为▽²p=CM_s∂P/∂t.海底面上的波浪压力由线性波浪理论计算.     

波浪在陡坡上的传播变化

利用数值方法和物理模型分析以反射为主的陡坡上波浪传播变形特征。数值方法采用标记单元法,为处理倾斜反射边界对斜坡前波浪运动的影响,提出了“台阶镜像法”。通过１：１．５光滑斜坡上物理模型试验,分析了不完全立波的运动特性,说明强反射光滑陡坡坡前波浪运动呈明显的立波状态,它与直墙反射的主要判别是坡前第一波节点和腹点位置向岸推移。本试验得到的波浪反射、爬高和回落特征值与港口工程规范给定结果接近。     

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。     

网衣对波浪传播影响的三维数值模拟

为研究网衣对波浪传播的影响,采用多孔介质模型模拟网衣,建立了模拟网衣与波浪相互作用的三维数值波浪水槽模型。基于该数值模型研究了波浪经过网衣作用后波高衰减的变化规律,并与物理模型试验结果进行比较。通过对比数值模拟和物理模型试验的结果,证明了该三维数值模型模拟网衣对波浪传播影响的可行性。     

波浪在陡坡上的传播变形

利用数值方法和物理模型分析以反射为主的陡坡上波浪传播变形特性。数值方法采用标记单元法,为处理倾斜反射边界对斜坡前波浪运动的影响,提出了“台阶镜像法”。通过1：1．5光滑斜坡上物理模型试验,分析了不完全立波的运动特性,说明强反射光滑陡坡坡前波浪运动呈明显的立波状态,它与直墙反射的主要差别是被前第一波节点和腹点位置向岸推移。本试验得到的波浪反射、爬高和回落特征值与港口工程规范给定结果接近。     

波浪在缓变海底上传播的一个简单数学模型

基于Liu和Shi(2008)的波浪势函数零阶、一阶近似解,采用四阶龙格-库塔法,对缓变海底上一维波浪传播理论模型进行了数值求解,并对波浪在定常坡度的斜坡地形、双曲正切地形为例的传播、变形进行了研究。为了更逼真地描述流体质点的波动特性,将在Euler坐标系下得到的解转换至Lagrange坐标下的解,并绘制Lagrange坐标下坡度为0.2的海滩上的一个波周期内临近破碎前的波形的详细变化过程。此外,计算得到了变水深区域波浪速度势以及自由面的分布,并与Athanassoulis and Belibassakis[34]的结果进行了对比,表明本文模型比保留了六个瞬息项的后者更有效。     

On waves propagating over poro-elastic seabed

In this study, an analytical solution is developed for the problem of periodic waves propagating over a poro-elastic seabed of infinite depth. Water waves above the seabed are described using the linear wave theory. The poro-elastic seabed is modelled based on the Biot theory in which the inertia effect and Darcy's friction are added. Continuity of dynamic pressure and flow flux at the interfacial seabed surface are considered. Adopting an approach similar to Hsu et al. (1993), the governing equations for the pore pressure and displacements of the poro-elastic medium are derived. The present analytic solution compares favorably well with experimental results by Yamamoto et al. (1978), and analytical results by Song (1993) for the case of fine sand. Using the present theory, variations of the wavelength and fluid pressure caused by coupling of waves and the poro-elastic seabed are discussed. Results show that higher elasticity of the poro-elastic seabed induces larger interface pressure, but higher permeability causes smaller pressure on the seabed interface. The wave length is affected by the poro-elastic seabed and becomes shorter for softer seabed and shallower water depth.     

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.     

Ocean waves propagating over a porous seabed of finite thickness

In the past few decades, considerable efforts have been devoted to the phenomenon of wave-seabed interaction. However, conventional investigations for determining wave characteristics have been focused on the wave nonlinearity. On the other hand, most previous works have been only concerned with the seabed response under the wave pressure, which was obtained from the assumption of a rigid seabed. In this paper, the inertia forces and employing a complex wave number are considered in the whole problem. Based on Biot’s poro-elastic theory, the problem of wave-seabed interaction is first treated analytically for a homogeneous bed of finite thickness and a new wave dispersion relationship is also obtained, in which the soil characteristics are included. The numerical results indicate that the effects of soil parameters significantly affect the wave characteristics (such as the damping of water wave, wave length and wave pressure). Furthermore, the effects of inertia forces on the wave-induced seabed response cannot always be ignored under certain combination of wave and soil conditions.     

On waves propagating over a submerged poro-elastic structure

In this paper, the problem of incident waves propagating over a submerged poro-elastic structure is studied theoretically. A linear wave theory is used to describe the wave motion. The submerged poro-elastic structure is modeled based on Biot's theory, in which the fluid motion is described using the potential wave theory of Sollitt and Cross (1972). In the present approach, the problem domain is divided into four subregions. Using general solutions for each region and matching dynamic and kinematic conditions for neighboring regions, analytic solutions are derived for the wave fields and poro-elastic structure. The present analytic solutions compare very well with simplified cases of impermeable, rigid structures, and with those of porous structures. Using the present analytic solution, the effects of a poro-elastic submerged structure on waves are studied. The results show that softer poro-elastic structures can induce higher reflection and lower transmission from incident waves. For low permeability conditions, the elasticity of the structure can induce resonance, while higher permeability can depress the resonant effects.     

An analytic solution to the mild slope equation for waves propagating over an axi-symmetric pit

An analytic solution to the mild slope equation is derived for waves propagating over an axi-symmetric pit located in an otherwise constant depth region. The water depth inside the pit decreases in proportion to an integer power of radial distance from the pit center. The mild slope equation in cylindrical coordinates is transformed into ordinary differential equations by using the method of separation of variables, and the coefficients of the equation in radial direction are transformed into explicit forms by using the direct solution for the wave dispersion equation by Hunt (Hunt, J.N., 1979. Direct solution of wave dispersion equation. J. Waterw., Port, Coast., Ocean Div., Proc. ASCE, 105, 457–459). Finally, the Frobenius series is used to obtain the analytic solution. Due to the feature of the Hunt's solution, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth waters. The validity of the analytic solution is demonstrated by comparison with numerical solutions of the hyperbolic mild slope equations. The analytic solution is also used to examine the effects of the pit geometry and relative depth on wave transformation. Finally, wave attenuation in the region over the pit is discussed.     

Harmonic generation by waves propagating over a submerged step

Harmonic generation by waves propagating over a two-dimensional submerged step is investigated. A nonlinear theory correct to second order is presented for steps of infinite and finite lengths subjected to single harmonic waves.The boundary value problem for the second-order scattered velocity potential is linearly decomposed into two separate boundary value problems, each having only one inhomogeneous boundary condition.Theoretical results indicate that the higher harmonics are generated in the shallow-water region over a step and then are transmitted to the deeper water as free waves.Numerical calculations compare favourably with existing experimental data.     

A 3-D model for ocean waves over a Columb-damping poroelastic seabed

The evaluation of the wave-induced seabed instability in the vicinity of a breakwater is particularly important for coastal and geotechnical engineers involved in the design of coastal structures. In this paper, an analytical solution for three-dimensional short-crested wave-induced seabed instability in a Coulomb-damping porous seabed is derived. The partial wave reflection and self-weight of breakwater are also considered in the new solution. Based on the analytical solution, we examine (1) the wave-induced soil response at different location; (2) the maximum liquefaction and shear failure depth in coarse and fine sand; (3) the effects of reflection coefficients; and (4) the added stresses due to the self-weight of the breakwater.     

Propagation of solitary waves over a submerged permeable breakwater

We study the interactions between a non-breaking solitary wave and a submerged permeable breakwater experimentally and numerically. The particle image velocimetry (PIV) technique is employed to measure instantaneous free surface displacements and velocity fields in the vicinity of a porous dike. The porous medium, consisting of uniform glass spheres, is mounted on the seafloor. Due to the limited size of each field of view (FOV) for high spatial resolution purposes, four FOVs are set in order to form a continuous flow field around the structure. Quantitative mean properties are obtained by ensemble averaging 30 repeated instantaneous measurements. The Reynolds decomposition method is then adopted to separate the velocity fluctuations for each trial to estimate the turbulent kinetic energy. In addition, a highly accurate two-dimensional model with the volume of fluid interface tracking technique is used to simulate an idealized volume-averaged porous medium. The model is based on the Volume-Averaged Reynolds Averaged Navier–Stokes equations coupled with the non-linear k–ε turbulence closure solver. Comparisons are performed between measurements and numerical results for the time histories of the free surface elevation recorded by wave gauges and the spatial distributions of free surface displacement with the corresponding velocity and turbulent kinetic energy around the permeable object imaged by the PIV system. Fairly good agreements are obtained. It is found that the measured and modeled turbulent intensities on the weather side are much larger than those on the lee side of the object, and that the magnitude of the turbulent intensity increases with increasing wave height of a solitary wave at a constant water depth. The verified numerical model is then used to estimate the energy reflection, transmission and dissipation using the energy integral method by varying the aspect ratio and the grain size of the permeable obstacle.     

Analytical solutions for long waves over a circular island

In this study, we derive an analytical solution for long waves over a circular island which is mounted on a flat bottom. The water depth on the island varies in proportion to an arbitrary power, γ, of the radial distance. Separation of variables, Taylor series expansion, and Frobenius series are used to find the solutions, which are then validated by comparing them with previously developed analytical solutions. We also investigate how different wave periods, radii of the island toe, and γ values affect the solutions. For a circular island with a small value of γ (e.g. γ = 2/3, as in the equilibrium beach (Bruun, 1954)), the wave rays approaching near the island center reach the coastline, whereas the rays approaching away from the center bend away from the coastline, leading to smaller wave amplitudes along the coast. However, for a circular island with a large value of γ, e.g. γ = 2, all the rays on the island reach the coast, giving large coastline wave amplitudes. If the island domain is small compared to the wavelength, the wave amplitudes on the coastline do not increase significantly; however, when the island domain is not small, the wave amplitudes increase significantly. If γ is also large, the amplitudes can be so large as to cause a disaster on the island.     

A new approximation for ocean waves propagating over a beach with variable depth

In this paper, the phenomenon of ocean waves propagating over a beach with variable water depth is re-examined. Based on the assumption of shallow water, a linearised shallow water equation is solved with an arbitrary beach profile. These irregular beach profiles form a set of partial differential equation with variable coefficient as the governing equation, which is the main obstacle in obtaining analytical solutions. In this paper, two families of beach profile are used as examples. A parametric study is conducted to investigate the influence of the beach profiles on the water surface elevation (η) and velocities (u).