Numerical investigations of wave overtopping at coastal structures

Under the numerical modelling work package of the EU funded CLASH project, the time accurate, free surface capturing, incompressible Navier–Stokes solver AMAZON-SC has been applied to study impulsive wave overtopping at Samphire Hoe, near Dover in the United Kingdom. The simulations show that the overtopping process on this vertical, sheet pile, seawall is dominated by impulsive, aerated, near vertical overtopping jets. In order to perform the simulations AMAZON-SC has been extended to incorporate an isotropic porosity model and for validation purposes the solver has been applied to study overtopping of a low crested sea dike and a 10:1 battered wall. The results obtained for the battered wall and Samphire Hoe tests are in good agreement both with predicted overtopping discharges calculated using the UK overtopping manual and with available experimental results.     

孤立波低顶海堤越浪的数值模拟研究

灾害性波浪是中国沿海地区最具破坏性的自然灾害之一。采用开源程序OpenFOAM中interFoam求解器,对低顶海堤（在风暴潮和海平面上升情况下所面临的不利工况）的孤立波越浪特性开展数值模拟研究。通过孤立波冲击海堤的基准算例,验证模型在模拟波浪爬升和越浪过程中大变形波面以及剧烈波浪力方面的精度。基于验证的数值模型,对孤立波在低顶海堤上的越浪特征以及防浪墙高度对越浪的影响开展参数化研究。结果表明堤顶超高减小导致更为剧烈的越浪。针对尚无低顶海堤孤立波越浪量经验公式的问题,提出新的适用于堤顶超高小或为0的孤立波越浪量经验公式。此外,研究发现增加防浪墙高度可有效减少越浪,但防浪墙所受的波浪力也增大。综合考虑防浪墙减少越浪以及自身所受波浪力,针对文中研究采用的海堤截面和波浪条件,建议无量纲防浪墙高度取为1.00。     

Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations

A one-dimensional high-resolution finite volume model capable of simulating storm waves propagating in the coastal surf zone and overtopping a sea wall is presented. The model (AMAZON) is based on solving the non-linear shallow water (NLSW) equations. A modern upwind scheme of the Godunov-type using an HLL approximate Riemann solver is described which captures bore waves in both transcritical and supercritical flows. By employing a finite volume formulation, the method can be implemented on an irregular, structured, boundary-fitted computational mesh. The use of the NLSW equations to model wave overtopping is computationally efficient and practically flexible, though the detailed structure of wave breaking is of course ignored. It is shown that wave overtopping at a vertical wall may also be approximately modelled by representing the wall as a steep bed slope. The AMAZON model solutions have been compared with analytical solutions and laboratory data for wave overtopping at sloping and vertical seawalls and good agreement has been found. The model requires more verification tests for irregular waves before its application as a generic design tool.     

Quantification of changes in current intensities induced by wave overtopping around low-crested structures

The phenomenon of overtopping is traditionally studied for well-emerged harbour structures and often focuses on safety and stability. In this paper laboratory tests are presented and analysed to sharpen the hypothesis that overtopping is capable of changing the horizontal circulation pattern around low-crested structures. A unique data set from laboratory experiments was acquired in the wave basin at Delft University of Technology. The experiments were performed using an emerged impermeable low-crested structure (three freeboards and three different wave conditions for each freeboard) and yielded nine different combinations of set-up and overtopping driving forces. Using this information it was possible to quantify the changes in cross-shore and longshore velocity induced by the overtopping and the set-up changes under the different freeboard and wave conditions described. It is found that overtopping enhances the outgoing flows (longshore velocities parallel to the structure) away from the lee side of the structure and dampens the water level gradient driven flow towards the structure.     

Neural network modelling of wave overtopping at coastal structures

A method has been developed to estimate wave overtopping discharges for a wide range of coastal structures. The prediction method is based on Neural Network modelling. For this purpose use is made of a data set obtained from a large number of physical model tests (collected within the framework of the European project CLASH, see e.g. [Steendam, G.J., Van der Meer, J.W., Verhaeghe, H., Besley, P., Franco, L. and Van Gent, M.R.A. (2004). The international database on wave overtopping. World Scientific, Proc. 29th ICCE, vol. 4, pp. 4301–4313, Lisbon, Portugal.]). Moreover, a method was developed to obtain confidence intervals for the overtopping predictions of the neural network.     

斜坡上波浪破碎与越浪非静压数值模拟

为合理确定防浪建筑物的越浪量,基于含非静水压力梯度项的非线性浅水方程建立了近岸波浪越浪数值模型。通过采用域内造波、消波并结合波前静压假定的破碎模型,模拟了规则波和不规则波在斜坡上的波浪传播变形,并在此基础上进行了越浪量数值计算。数值计算结果与物理模型实验结果表明,非静压模型可合理地描述波浪破碎点位置、破碎后的波高、增减水以及斜坡上的堤后越浪量。数值模型具有较高的计算精度和计算效率,可为实际工程防浪建筑物越浪以及堤顶高程的设计提供一种新的数值研究手段。     

Study of irregular wave run-up over fringing reefs based on a shock-capturing Boussinesq model

This paper presents the results of a parametric study of irregular wave run-up over fringing reefs using the shock-capturing Boussinesq wave model Funwave-TVD to better understand the role of fringing reefs in the mitigation of wave-driven flooding. Laboratory experiments were newly performed with a typical fringing reef profile and typical hydrodynamic conditions to validate the model. Experimental data shows irregular wave run-ups are dominated by the low-frequency motions and confirms the run-up resonant phenomenon over the back-reef slope, which has been revealed in previous numerical studies. It is demonstrated that irregular wave evolution and run-up over fringing reefs are reasonably reproduced by the present model with a proper grid size. However, the infragravity run-up height and highest 2% run-up height over the back-reef slope are under-predicted due to the underestimation of the infragravity wave height over the reef flat. The validated model was then utilized to model irregular wave transformations and run-ups under different conditions. Through a series of numerical experiments, the effects of key hydrodynamic and reef geometry parameters, including the reef flat width, water depth over the reef flat, fore-reef slope angle and back-reef slope angle, on the irregular wave run-up were investigated. Variations of spectral components of irregular wave run-ups were examined to better understand the physical process underlying the effect of each parameter.     

Spatial distribution of wave overtopping water behind coastal structures

Spatial distribution of random wave overtopping water behind coastal structures was investigated using a numerical model based on Reynolds-Averaged Navier-Stokes solver (RANS) and Volume of Fluid (VOF) surface capturing scheme (RANS-VOF). The computed spatial distributions of wave overtopping water behind the structure agree well with the measurements by Pullen et al (2008) for a vertical wall and Lykke Andersen and Burcharth (2006) for a 1:2 sea dike. A semi-analytical model was derived to relate spatial distribution of wave overtopping water behind coastal structures to landward ground level, velocity and layer thickness on the crest. This semi-analytical model agrees reasonably well with both numerical model results and measurements close to coastal structures. Our numerical model results suggest that the proportion of wave overtopping water passing a landward location increases with a seaward slope when it is less than 1:3 and decreases with a seaward slope when it gets steeper. The proportion of wave overtopping water passing a landward location increases with landward ground level and overtopping discharge. It also increases with the product of incident wave height and wavelength, but decreases with increasing relative structure freeboard and crest width. We also found that the extent of hazard area due to wave overtopping is significantly reduced by using a permeable structure crown. Findings in this study will enable engineers to establish the extent of hazard zones due to wave overtopping behind coastal structures.     

Numerical study for vegetation effects on coastal wave propagation by using nonlinear Boussinesq model

The vegetation has important impacts on coastal wave propagation. In the paper, the sensitivities of coastal wave attenuation due to vegetation to incident wave height, wave period and water depth, as well as vegetation configurations are numerically studied by using the fully nonlinear Boussinesq model. The model is based on the implementation of drag resistances due to vegetation in the fully nonlinear Boussinesq equation where the drag resistance is provided by the Morison’s formulation for rigid structure induced drag stresses. The model is firstly validated by comparing with the experimental results for wave propagation in vegetation zones. Subsequently, the model is used to simulate waves with different height, period propagating on vegetation zones with different water depth and vegetation configurations. The sensitivities of wave attenuation to incident wave height, wave period, water depth, as well as vegetation configurations are investigated based on the numerical results. The numerical results indicate that wave height attenuation due to vegetation is sensitive to incident wave height, wave period, water depth, as well as vegetation configurations, and attenuation ratio of wave height is increased monotonically with increases of incident wave height and decreases of water depth, while it is complex for wave period. Moreover, more vegetation segments can strengthen the interaction of vegetation and wave in a certain range.     

海堤上波浪爬高与越浪计算分析

基于线性波理论,采用VOF法、RNG k-ε的湍流模型,通过FLUENT软件平台的二次开发功能实现了质量源造波。利用多孔介质模型,在动量方程里添加多孔介质源项,对斜坡堤上铺设异型块体时的爬高与越浪进行了数值模拟,并通过模拟爬高值率定出FLUENT中多孔阻力系数与多种异形块体糙渗系数之间的关系,进而建立了可供实际应用的海堤上波浪爬高与越浪数值模型。     

Numerical simulation of irregular wave overtopping against a smooth sea dike

Based on the filtered Navier-Stokes equations and Smagorinsky turbulence model,a numerical wave flume is developed to investigate the overtopping process of irregular waves over smooth sea dikes.Simulations of fully nonlinear standing wave and regular wave’s run-up on a sea dike are carried out to validate the implementation of the numerical wave flume with wave generation and absorbing modules.To model stationary ergodic stochastic processes,several cases with different random seeds are computed for each specified irregular wave spectrum.It turns out that the statistical mean overtopping discharge shows good agreement with empirical formulas,other numerical results and experimental data.     

斜坡堤波浪爬高和越浪数值模拟

基于FLUENT软件,采用k-ε湍流模型和VOF方法追踪自由表面,由连续性方程和动量方程推导出源函数,根据数值水槽各个区段的功能设置,借助其UDF二次开发功能,实现无反射的源造波,在验证水槽两端消波有效性的基础上,数值模拟规则波在不可渗透斜坡堤上的波浪爬高和越浪。通过与物模试验研究成果相对比,表明建立的数值水槽具有高效性和较高精度,可供实际工程参考应用。     

An application of Boussinesq modeling to Hurricane wave overtopping and inundation

Wave and combined wave-and-surge overtopping was significant across a large portion of the hurricane protection system of New Orleans during Hurricane Katrina. In particular, along the east-facing levees of the Mississippi River-Gulf Outlet (MRGO), the overtopping caused numerous levee breaches. This paper will focus on the MRGO levees, and will attempt to recreate the hydrodynamic conditions during Katrina to provide an estimate of the experienced overtopping rates. Due to the irregular beach profiles leading up to the levees and the general hydrodynamic complexity of the overtopping in this area, a Boussinesq wave model is employed. This model is shown to be accurate for the prediction of waves shoaling and breaking over irregular beach profiles, as well as for the overtopping of levees. With surge levels provided by ADCIRC and nearshore wave heights by STWAVE, the Boussinesq model is used to predict conditions at the MRGO levees for 10 h near the peak of Katrina. The peak simulated overtopping rates correlate well with expected levee damage thresholds and observations of damage in the levee system. Finally, the predicted overtopping rates are utilized to estimate a volumetric flooding rate as a function of time for the entire 20 km stretch of east-facing MRGO levees.     

Simulation of wave overtopping by an incompressible SPH model

The paper presents an incompressible Smoothed Particle Hydrodynamics (SPH) model to investigate the wave overtopping of coastal structures. The SPH method is a grid-less Lagrangian approach which is capable of tracking the large deformations of the free surface with good accuracy. The incompressible algorithm of the model is implemented by enforcing the constant particle density in the pressure projection. The SPH model is employed to reproduce a transient wave overtopping over a fixed horizontal deck and the regular/irregular waves overtopping of a sloping seawall. The computations are validated against the experimental and numerical data and a good agreement is observed. The SPH modelling is shown to provide a promising tool to predict the overtopping characteristics of different waves. The present model is expected to be of practical purpose if further improvement in the spatial resolution and CPU time can be adequately made.     

波浪增减水的实用数学模型及其数值模拟

提出了一种模拟近岸区波浪增减水的实用数学模型.首先采用考虑波能损失的抛物型缓坡方程数值模拟波浪破碎引起的波浪复振幅变化,接着根据计算得到的波浪复振幅,采用一种新的辐射应力公式计算辐射应力分量,然后采用深度平均方程计算波浪破碎产生的增减水.采用该模型对规则波和不规则波破碎引起的增减水进行了数值模拟,数值模拟结果与实验结果吻合良好,表明该模型可有效模拟近岸区由于波浪破碎引起的增减水.     

大气-海浪耦合模式对台风“碧利斯”的数值模拟

本文将海表粗糙度作为耦合大气、海浪模式的重要因子,实现中尺度大气模式MM5(V3)和第三代海浪模式WAVEWATCHⅢ的双向耦合,建立充分考虑大气、海浪相互作用的大气.海浪耦合模式.将该大气-海浪耦合模式应用于对0604次台风"碧利斯"的数值模拟,在耦合模式中引入Smith92海表粗糙度参数化方案,探讨其对台风和台风浪的影响.研究结果表明,大气-海浪耦合模式能够抓住台风过程的总体特征.Smith92海表粗糙度参数化方案对台风路径影响不大.但在台风系统强度的模拟上影响明显,采用Smith92方案使得台风系统强度显著增强,对台风系统强度的模拟有明显改善.同样,大气-海浪耦合模式能够很好的模拟台风过程中海浪的传播和演变.采用Smith92方案使得海面有效波高明显增高,对海面有效波高的模拟有一定程度改善.因此,在大气-海浪耦合模式中恰当的选择海表粗糙度参数化对改进大气-海浪耦合模式的模拟效果是很有意义的.     

Wave transmission and reflection at low-crested structures: Design formulae,oblique wave attack and spectral change

A part of the DELOS research focused on wave transformation at low-crested structures, called LCS. This paper gives a summary of all results. Wave transmission on rubble mound structures has been subject for more flume tests in the DELOS programme and simultaneously an existing database has been increased extensively by receiving data from other researchers in the world. This new database consists of more than 2300 tests and has been used to come up with the best 2D wave transmission formula for rubble mound LCS, although not necessarily new as existing ones have been evaluated. Oblique wave attack on LCS was a second objective within DELOS. Results were analysed leading to new empirical transmission formulae for smooth LCS and to conclusions on 3D effects for both rubble mound and smooth LCS. The spectral shape changes due to wave transmission and this change has been subject of analysis for all new test data described above. Although analysis has not been finished completely, former assumptions on spectral change were more or less confirmed. Finally, some analysis was performed on reflection at LCS and a first formula was derived to take into account the effect that wave overtopping or transmission reduces reflection and must be dependent on the crest height of the structure.     

完全非线性波浪破碎模型沿岸流数值模拟

探讨一种基于完全非线性Boussinesq方程的波浪破碎模型在沿岸流计算中的应用问题。针对控制方程中的完全非线性项对沿岸流成长过程的影响进行了深入讨论。数学模型计算结果表明,完全非线性项有使平均流局部化的作用;通过数模实验还发现,垂向高阶涡度项可以有效抑制破波区外回流;运用Visser的实验室沿岸流实测资料从沿岸流速度、波高和平均水位几方面对所提模型进行了验证,并给出了紊动参数的计算结果。     

长江口横沙东滩典型海堤越浪量现场和试验研究

越浪量是允许越浪海堤设计的重要参数。在对以往相关研究成果进行回顾和分析基础上,结合长江口横沙东滩促淤圈围五期工程现场波浪和越浪量实测资料,通过对横沙东滩典型断面型式进行整体和断面物理模型试验,研究结构各参数对越浪量的影响,进而提出适合长江口海堤的越浪量计算公式。公式计算结果与试验数据吻合良好,与Van der Meer公式相比具有较好的一致性。     

基于格子Boltzmann方法的斜坡堤越浪数值模拟研究

准确确定越浪量对于斜坡堤设计有重要意义。利用格子Boltzmann方法(LBM),并采用主动吸收式速度入口造波、出流边界消波、VOF方法追踪自由表面以及静态Smagorinsky模型模拟紊流运动,建立二维数值波浪水槽,对光滑斜坡堤上规则波与不规则波越浪进行数值模拟。模拟结果与试验值及其他数值模型结果比较表明,二维LBM数值波浪水槽具有模拟斜坡堤越浪的能力,但对于破碎较为剧烈的越浪过程模拟,该模型还存在一定的不足,未来可从提高自由表面模型精度等方面进一步改善其性能。