AN EXPERIMENTAL OBSERVATION OF A SOLITARY WAVE IMPINGE-MENT,RUN-UP AND OVERTOPPING ON A SEAWALL

A sequence of laboratory experiments using solitary waves was performed to model the effect of leading form of three types of tsunamis(a bore,an impinging wave and an overtopping wave)on a seawall on a sloping beach.The wave evolution process,impinging pressure along the seawall surface,total overtopping discharge behind the seawall and the maximum run-up height on the rear slope were measured and compared.Laboratory data were employed to re-examine relevant empirical formulae in the literature.The effect of the presence of the seawall in reducing maximum run-up height using the present setup was briefly discussed.The present data can be used for calibrating numerical and mathematical models.     

THE VOF METHOD FOR STUDY OF WAVE RUN-UP AND BREAKING ON A SLOPING STRUCTURE

The volume of fluid method(VOF method)for numerical simulations describing wave run-up on a sloping structure including the overturning,breaking and.merging phenomena is presented.The flow motions are governed by the classical,two-dimen-sional Navier-Stokes equation for incompressible fluid.Computational results concerning the time evolution of the free surface and pressure distribution along water bed and slope boundary are given,showing how an initial solitary wave undergoes run-up,overturning,breaking and merging on the slope.It is found that most of the wave energy is lost after the wave breaking and merging.     

PROPAGATION AND BREAKING OF WAVES ON SLOPING BEACH

In this paper the propagation and breaking of the solitary wave,the sinusoidalwave and the second Stokes wave on a slope of 1/30 are discussed based upon the TUMMACmethod,and the velocity fields of breaking waves on the slope are obtained by using the tracingmethod.The.numerical results for wave deformation are in good agreement with experimentaldata,and the breaker indexes depending on the kinetic criterion agree approximately with previ-ous results.Furthermore,compared with the experimental results measured by Iwagaki and bythe authors,the tendency of velocity distribution of breaking waves computed by this numericalmethod is also satisfactory.     

A PRACTICAL MODEL FOR THE DECAY OF RANDOM WAVES ON MUDDY BEACHES

A practical model has been developed for the propagation and decay of random waves on muddy beaches. In the model, an irregular wave train is characterized by its root-mean-squared wave height, mean wave frequency and mean wave direction. It is also assumed that the wave spectrum is narrow-banded in terms of both frequency and direction. Transformation of root-mean-squared wave height is derived from the conservation of energy flux for individual wave components. Energy dissipation is considered due to both wave breaking and the dynamics response of muddy seabed. The model is applied to waves on the muddy beach at Hangzhou Bay, and the numerical results obtained are shown to be acceptably accurate as comparing with available field data.     

Application of CLEAR-VOF method to wave and flow simulations

A two-dimensional numerical model based on the Navier-Stokes equations and computational Lagrangian-Eulerian advection remap-volume of fluid (CLEAR-VOF) method was developed to simulate wave and flow problems. The Navier-Stokes equations were discretized with a three-step finite element method that has a third-order accuracy. In the CLEAR-VOF method, the VOF function F was calculated in the Lagrangian manner and allowed the complicated free surface to be accurately captured. The propagation of regular waves and solitary waves over a flat bottom, and shoaling and breaking of solitary waves on two different slopes were simulated with this model, and the numerical results agreed with experimental data and theoretical solutions. A benchmark test of dam-collapse flow was also simulated with an unstructured mesh, and the capability of the present model for wave and flow simulations with unstructured meshes, was verified. The results show that the model is effective for numerical simulation of wave and flow problems with both structured and unstructured meshes.     

An experimental study of impact loading on deck of shore-connecting jetties exposed to oblique waves and current

The impact pressure from waves is an important issue to be considered in the design of coastal structures. In this paper, the waves acting on the deck of a shore-connecting jetty on a slope exposed to oblique waves and in the presence of current are examined based on laboratory experiments. The impact pressures are measured on a 1：50 scale model of a jetty head with down-standing beams and berthing members. The relations of the impact pressure with the incident wave angle and the current velocity are examined. It is shown that the impact pressure is sensitive to the wave angle and the current velocity. A computational model for the impact load on the deck of shore-connecting jetties exposed to oblique waves and current is developed.     

INTERNAL SOLITARY WAVE IN TWO-LAYER FLUID SYSTEM TOWARDS SHELF

The propagation of an interracial solitary wave in a two-layer fluid system with fixed upper surface to shelf isdiscussed.The numerical results of the Boussincsq model show the fission of the solitary wave,the reflected wavesby the slope and their dependence on the shelf height and slope.It is shown that the amplitude of the first transmit-ted solitary wave fully developed is esscentially independent of the bottom slope.     

NUMERICAL SIMULATION OF PROPAGATION AND BREAKING PROCESSES OF A FOCUSED WAVES GROUP

A two-dimensional numerical wave flume is developed to study the focused waves group propagation and the consequent breaking processes. The numerical model is based on the Reynolds-Averaged Navier-Stokes (RANS) equations, with the standard k-ε turbulence model to simulate the turbulence effects. To track the complicated and broken free-surface, the Volume Of Fluid (VOF) method is employed. The numerical model combines the "Partial Cell Treatment (PCT)" method with the "Locally Relative Stationary (LRS)" concept to treat the moving wave paddle so that various waves can be generated directly in a fixed Cartesian grid system. The theoretical results of the linear and nonlinear waves are used to validate the numerical wave flume firstly, and then a plunging breaking wave created by a focused waves group is simulated. The numerical results are compared to the experimental data and other simulation results, with very good agreements. The turbulence intensity, the flow field and the energy dissipation in the breaking processes are analyzed based on the numerical results. It is shown that the present numerical model is efficient and accurate for studying the waves group generation, the waves packet propagation, and the wave breaking processes.     

A NOVEL ADAPTIVE σ COORDINATE MODEL AND ITS APPLICA- TIONS TO WAVE AND STRUCTURE INTERACTION

In this paper, a novel adaptive mesh σ coordinate model is proposed for the studies of Wave and Structure Interaction (WSI). The model is validated by using the case of a solitary wave movement in an open channel with constant water depth and the case of nonbreaking solitary wave propagating over a step. Numerical results agree well with the analytical solutions obtained based on the Boussinesq theory, the laboratory data and other numerical model results. The proposed model is then used to study a solitary wave interacting with a suspended fixed structure.     

NUMERICAL SIMULATION OF TWO-DIMENSIONAL OVERTOPPING AGAINST SEAWALLS ARMORED WITH ARTIFICIAL UNITS IN REGULAR WAVES

A new mathematical model for the overtopping against seawalls armored with artificial units in regular waves was established. The 2-D numerical wave flume, based on the Reynolds Averaged Navier-Stokes (RANS) equations and the standard k-ε turbulence model, was developed to simulate the turbulent flows with the free surface, in which the Volume Of Fluid (VOF) method was used to handle the large deformation of the free surface and the relaxation approach of combined wave generation and absorbing was implemented. In order to consider the effects of energy dissipation due to the armors on a slope seawall, a porous media model was proposed and implemented in the numerical wave flume. A series of physical model experiments were carried out in the same condition of the numerical simulation to determine the drag coefficient in the porous media model in terms of the overtopping discharge. Compared the computational value of overtopping over the seawall with the experimental data, the values of the effective drag coefficient was calibrated for the layers of blocks at different locations along the seawalls.     

非淹没刚性植被影响下孤立波在岸滩上的爬高

为探究海岸刚性植被对海啸波的削弱效应,通过物理模型试验和数值模拟研究了孤立波与不同坡度岸滩上非淹没刚性植被的相互作用问题。物理模型试验在波浪槽中进行,测试了不同的入射波波高、植被密度和岸滩坡度对孤立波爬高的影响,并运用物理模型试验数据校核改进后的Boussinesq方程,得到植被的拖曳力系数。结果表明:拖曳力系数随植被密度的增大而增大,随坡度增大而减小;植被后的无量纲透射波高和无量纲岸滩爬高随着无量纲的入射波高的增大而减小,随着植被密度的增大而减小;当岸滩坡度增大时,无量纲透射波高增大而无量纲爬高并无显著差异。最后根据回归分析得出了岸滩爬高与相对入射波高、植被密度和岸滩坡度的幂函数型经验关系式。     

Run-up of non-breaking double solitary waves with equal wave heights on a plane beach

The evolution and run-up of double solitary waves on a plane beach were studied numerically using the nonlinear shallow water equations(NSWEs) and the Godunov scheme. The numerical model was validated through comparing the present numerical results with analytical solutions and laboratory measurements available for propagation and run-up of single solitary wave. Two successive solitary waves with equal wave heights and variable separation distance of two crests were used as the incoming wave on the open boundary at the toe of a slope beach. The run-ups of the first wave and the second wave with different separation distances were investigated. It is found that the run-up of the first wave does not change with the separation distance and the run-up of the second wave is affected slightly by the separation distance when the separation distance is gradually shortening. The ratio of the maximum run-up of the second wave to one of the first wave is related to the separation distance as well as wave height and slope. The run-ups of double solitary waves were compared with the linearly superposed results of two individual solitary-wave run-ups. The comparison reveals that linear superposition gives reasonable prediction when the separation distance is large, but it may overestimate the actual run-up when two waves are close.     

孤立波翻越防波堤流动的湍流数值模拟

应用湍流数学模型和流体体积法模拟孤立波翻越防波堤的流动和自由表面变化。数模成功地再现了波浪涌顶和喷射、射流入水、自由表面破碎和漩涡产生等复杂流动过程,并获得了孤立波翻越防波堤时的压力分布。     

数值模拟波浪翻越直立方柱

本文应用ＶＯＦ方法研究了孤立波翻越直立方柱流动的全过程。用人工压缩法和差分法求解二维Ｎａｖｉｅｒ－Ｓｔｏｋｅｓ方程，用施主－受主法求解流体体积函数控制方程。通过数值计算得到了孤立波翻越直立方柱的流场和压力值，并成功地模拟出波浪涌顶，水柱喷射，冲击和界面破碎的过程。     

基于RANS方程的海堤越浪数值模拟

基于FLUENT商业化软件,以RANS方程为控制方程,基于有限体积法,采用k-epsilon湍流模型,运用一种“解析松弛”方法实现了适用于VOF方法的数值源造波技术。在该数值波浪水槽中对规则波在不可渗透简单斜坡堤上越浪过程进行了数值模拟,将越浪量计算值同物理实验结果及基于非线性浅水方程的数值结果进行了比对。结果表明：该数值模型能够较好地复演海堤越浪过程,同基于非线性浅水方程的数值结果相比,能更有效地模拟含有强烈卷吸、射流和破碎的海堤越浪问题。     

内河航道中船行波在岸坡爬高的数值模拟

该文基于RANS方程、RNG k-ε湍流模型建立数值波浪水池,用VOF法追踪自由面的位置,并模拟了内河航道中船行波的生成、传播、爬高和岸壁反射过程,且与典型断面航道中船行波在岸坡最大爬高和回落的现场测量值进行了比较,验证了数值模型的有效性。通过对航道中船行波进行数值模拟,获得了船行波的波形及其在岸坡上爬高与回落的最大值。分析了船舶吃水、航速和航道岸坡倾角对特征波高以及最大爬高与回落的影响。最后建立了计算船行波特征波高、爬高和回落的经验公式。     

波流共同作用下细沙粉沙质海岸复合沿岸输沙率计算

应用能量原理建立波浪作用下沿岸输沙率公式时,通常采用波浪的“载沙量”与沿岸流的乘积推导而得.对于一般的沙质海岸,由于岸滩坡度较陡,波浪破碎带较窄,破波带内潮流流速与破波产生的沿岸流相比较小,常可忽略.而对于细沙粉沙质海岸,岸滩坡度相对较缓,风暴潮期间,近岸波浪较大,破波水深较深,破波带较宽,近岸潮流流速也较大.因此,细沙粉沙质海岸风暴潮期间波浪和潮流共同作用下的复合沿岸输沙率计算应当考虑波浪和潮流的共同作用.在以往波浪作用下沙质海岸沿岸输沙率研究的基础上,通过波浪潮流共同作用下近岸水流特性和沿岸输沙率特性港池试验研究,得出了波流共同作用下复合沿岸流计算公式,据此,将能量输沙原理导出的沿岸输沙率计算公式推广应用到波流共同作用下的复合沿岸输沙率计算,经与模型试验结果和现场实测资料对比,吻合良好.该公式可以有条件地推广应用到细沙粉沙质海岸波浪潮流共同作用下复合沿岸输沙率计算.     

Wave runup simulations using Lagrangian blocks on Eulerian mesh

The runup of breaking and non-breaking solitary waves on a plane beach has been simulated using the shallow-water equations and a Lagrangian blocks on Eulerian mesh (LBEM) method. The results obtained for the entire range of wave steepness are compared with the experimental data, the nonlinear theory, and the finite-difference method. The LBEM simulation agrees with the nonlinear theory when the amplitude of the wave is small. On the whole, it produces a better result in agreement with the experimental data when friction is included in the simulation. The simulation also produced better result than the finite-difference simulation.