基于激波捕捉类Boussinesq模型对岛礁地形上波浪传播的数值模拟

为了探究激波捕捉类Boussinesq模型在模拟岛礁地形上规则波和不规则波传播的可行性,采用基于完全非线性Boussinesq方程并具有激波捕捉能力的数值模型Funwave-TVD对规则波和不规则波在岛礁地形上的传播进行了数值模拟,通过与试验数据对比,分析模型中空间步长的影响,验证模型在模拟波高、平均水位分布以及波谱空间演变的能力,结果表明:采用合适的空间步长,模型能较好地模拟规则波和不规则波在岛礁地形上的传播和演化过程。对于规则波,较小的空间步长可改善破碎点处波高峰值的预测,并能更好地预测波浪破碎后波高的空间分布,相比结合经验破碎的Boussinesq模型,Funwave-TVD能更好地模拟规则波在岛礁地形上的破碎,以及破碎以后行进涌波的再生成过程;对于不规则波,Funwave-TVD总体而言能较好地模拟涌浪有效波高、次重力波的生成及空间演化和平均水位,但会低估礁坪上次重力波波高,较粗的空间步长也会低估礁坪上涌浪有效波高。     

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.     

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.     

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.     

An evaluation of wave propagation simulations over a barred beach with a Boussinesq-type model

The FUNWAVE model is used for simulating simulation of monochromatic and irregular wave propagation in a channel with a bar-trough profile. FUNWAVE is based upon the extended Boussinesq equations. The study aims to analyze the model's performance when simulating shoaling, wave breaking and nonlinear interactions that are present in nearshore wave propagation. For that, high-order time domain statistics (root mean-square wave height, skewness, asymmetry and the kurtosis) of the model simulations and of the observations were compared along the whole channel. Also, a frequency domain analysis including standard spectral analysis and the bispectrum was carried out in selected points of the flume. The evaluation included the role of the wave breaking internal model parameters. The main conclusion is that, in general, the one-dimensional version of FUNWAVE simulates quite well the nonlinear transformation of a wave over a bottom with a bar-tough profile, for both regular and irregular wave conditions. The model reproduces the transformation of the wave shape, specially the increasing sharper wave crests and flatter troughs and also the lack of vertical symmetry with crests pitching forward, as it propagates along the domain. However, some differences persist after wave breaking, mainly due to the nature of the wave-breaking module. In this module, the energy dissipation is induced by the increase of viscosity, a rather simple mechanism, without the modification of the wave shape. Also, the energy dissipation develops in a smooth way which is appropriated for spilling breaking waves, but not for plunging breaking waves where the dissipation starts more abruptly.     

Effects of reef morphology variations on wave processes over fringing reefs

Many low-lying tropical and sub-tropical atolls fringed by coral reefs are susceptible to coastal inundation during extreme wave events. Previous studies have shown that the infragravity (IG) wave is the dominant component of shoreline run-up compared to the sea and swell (SS) wave and the wave-induced setup. To better understand both the SS and IG wave dynamics over a fringing reef with various morphologies, a series of laboratory experiments were conducted in a wave flume based on an idealized fringing reef profile. The shoreline responses of waves to different reef morphologies with/without the reef crest, the lagoon and the reef surface roughness were examined. IG wave resonance on the reef flat was identified by a spectral analysis of the shoreline wave records. Subsequently, a numerical model based on the Boussinesq equations was validated by the experimental data. The model was then applied to investigate the impacts of varying reef morphologic features (fore-reef slope, reef-crest width, lagoon width, and reef roughness coefficient) on the shoreline wave motions.     

南沙群岛礁概化地形上拍岸浪数值模拟与统计分析

南沙群岛珊瑚岛礁众多,大多数岛礁具有向海坡陡峭、外礁坪比较平缓的特征。将南沙群岛岛礁的迎浪向地形概化为陡坡和缓坡组成的双斜坡,采用FUNWAVE-TVD模式数值模拟概化地形上的波浪,根据模拟的破碎波高分析其拍岸浪特征。对拍岸浪数值模拟结果进行比较分析,向海坡的坡度对拍岸浪影响不大,外礁坪上拍岸浪高随地形坡度增大而略有增大;向海坡和外礁坪交界位置(即坡折点)水深对拍岸浪有比较明显的影响,拍岸浪高随坡折点水深增大而减小;拍岸浪高随入射波高和波周期增大而增大。利用大量的拍岸浪数值模拟数据对国内外5种统计模型进行检验,并且基于拍岸浪数值模拟数据建立了3种南沙群岛岛礁拍岸浪统计模型,计算结果显示这些模型适用性较好。     

Examination of empirical formulas for wave shoaling and breaking on steep slopes

Estimation of the wave height transformation of shoaling and breaking is essential for the nearshore hydrodynamics and the design of coastal structures. Many empirical formulas have been well recognized to the wave height transformation, but most of them were only applicable for gentle slopes. This paper reports the experimental results of wave shoaling and breaking over the steep slopes to examine the applicability of the previous empirical formulas. Two steep bottom slopes of 1/3 and 1/5, and one gentle slope of 1/10 were conducted in the present experiments. Experimental results show that the shoaling distance of steep slopes become short and the surface waves may be partially reflected from the steep bottom, thus the estimation of wave shoaling using the well-known previous formula did not conform completely to the experimental results. The previous empirical formulas for the wave breaking criteria were also examined, and the modified equations to the steep beaches were proposed in this work. A numerical model was finally adopted to calculate the wave height transformation in the surf zone by introducing the modified breaking index.     

One-dimensional modelling of individual waves and wave-induced longshore currents in the surf zone

A probabilistic model ( -model) was developed to describe the propagation and transformation of individual waves (wave by wave approach). The individual waves shoal until an empirical criterion for breaking is satisfied. Wave height decay after breaking is modelled by using an energy dissipation method. Wave-induced set-up and set-down and breaking-associated longshore currents are also modelled. Laboratory and field data were used to calibrate and verify the model. The model was calibrated by adjusting the wave breaking coefficient (as a function of local wave steepness and bottom slope) to obtain optimum agreement between measured and computed wave height. Four tests carried out in the large Delta flume of Delft Hydraulics were considered. Generally, the measured H_1/3-wave heights are reasonably well represented by the model in all zones from deep water to the shallow surf zone. The fraction of breaking waves was reasonably well represented by the model in the upsloping zones of the bottom profile. Verification of the model results with respect to wave-induced longshore current velocities was not extensive, because of a lack of data. In case of a barred profile the measured longshore velocities showed a relatively uniform distribution in the (trough) zone between the bar crest and the shoreline, which could to some extent be modelled by including space-averaging of the radiation force gradient, horizontal mixing and longshore water surface gradients related to variations in set-up. In case of a monotonically upsloping profile the cross-shore distribution of the longshore current velocities is reasonably well represented.     

Non-hydrostatic finite element model for coastal wave processes

This paper presents the application of the depth-integrated non-hydrostatic finite element model, CCHE2D-NHWAVE (Wei and Jia, 2014), for simulating several types of coastal wave processes. Specifically, the model is applied to (1) predict the swash zone hydrodynamics involving wave bore propagation, (2) resolve wave propagation, breaking, and overtopping in fringing reef environments, (3) study the vegetation effect on wave height reduction through both submerged and emergent vegetation zones using the drag force term technique, and (4) simulate tsunami wave breaking in the nearshore zone and inundation in the coastal area. Satisfactory agreement between numerical results and benchmark data shows that the non-hydrostatic model is capable of modeling a wide range of coastal wave processes. Furthermore, thanks to its simple numerical formulation, the non-hydrostatic model also demonstrates a better computation efficiency when comparing with other numerical models.     

珊瑚礁地形上破碎波高试验研究

破碎波高是珊瑚礁地形上波浪演化的重要参数之一,对工程安全和海岸变形具有重要影响。通过二维波浪水槽,对珊瑚礁地形上破碎波高进行试验研究,分析破碎波高随波陡、礁坪水深以及礁前斜坡坡度的变化。研究表明,相对破碎波高随相对礁坪水深的增大而增大,随入射波陡的增大而减小,但礁前斜坡坡度对相对破碎波高的影响并不明显。通过引入相对礁坪水深,将经典的破碎波高计算公式拓展至珊瑚礁地形上破碎波高的计算。该公式计算值与前人的试验值进行对比验证,吻合较好。研究成果可为工程实践和数值模拟提供参考与借鉴。     

基于破碎临界区的新型拍岸浪统计计算模型研究

When waves propagate from deep water to shallow water, wave heights and steepness increase and then waves roll back and break. This phenomenon is called surf. Currently, the present statistical calcula...     

Surf zone dynamics simulated by a Boussinesq type model. Part II: surf beat and swash oscillations for wave groups and irregular waves

This is the second of three papers on the modelling of various types of surf zone phenomena. In the first paper the general model was described and it was applied to study cross-shore motion of regular waves in the surf zone. In this paper, part II, we consider the cross-shore motion of wave groups and irregular waves with emphasis on shoaling, breaking and runup as well as the generation of surf beats. These phenomena are investigated numerically by using a time-domain Boussinesq type model, which resolves the primary wave motion as well as the long waves. As compared with the classical Boussinesq equations, the equations adopted here allow for improved linear dispersion characteristics and wave breaking is modelled by using a roller concept for spilling breakers. The swash zone is included by incorporating a moving shoreline boundary condition and radiation of short and long period waves from the offshore boundary is allowed by the use of absorbing sponge layers. Mutual interaction between short waves and long waves is inherent in the model. This allows, for example, for a general exchange of energy between triads rather than a simple one-way forcing of bound waves and for a substantial modification of bore celerities in the swash zone due to the presence of long waves. The model study is based mainly on incident bichromatic wave groups considering a range of mean frequencies, group frequencies, modulation rates, sea bed slopes and surf similarity parameters. Additionally, two cases of incident irregular waves are studied. The model results presented include transformation of surface elevations during shoaling, breaking and runup and the resulting shoreline oscillations. The low frequency motion induced by the primary-wave groups is determined at the shoreline and outside the surf zone by low-pass filtering and subsequent division into incident bound and free components and reflected free components. The model results are compared with laboratory experiments from the literature and the agreement is generally found to be very good. Finally the paper includes special details from the breaker model: time and space trajectories of surface rollers revealing the breakpoint oscillation and the speed of bores; envelopes of low-pass filtered radiation stress and surface elevation; sensitivity of surf beat to group frequency, modulation rate and bottom slope is investigated. Part III of this work (Sørensen et al., 1998) presents nearshore circulations induced by the breaking of unidirectional and multi-directional waves.     

浅滩地形上波浪破碎对低频波能放大的影响

低频长波对港湾共振、泥沙输运、波浪爬高与越浪等过程有重要影响。采用非静压模型SWASH模拟了不规则波在浅滩上的传播及破碎过程,重点探讨了滩顶短波破碎程度对低频波能演变的影响。模拟结果显示,当滩顶短波处于临界破碎状态时,低频波能流沿浅滩持续增长,浅滩对低频长波的放大效应（滩后与滩前低频波能流之比）显著;当滩顶短波轻微破碎、破波仅发生在外破波区时,低频波能流的沿滩增长率进一步变大;当滩顶短波剧烈破碎、破波延续到内破波区时,低频波能流沿滩先增长而后转为衰减,滩后放大率较临界破碎时明显减小。研究结果表明,浅滩顶部水深改变了短波破碎程度,进而影响低频长波的演化过程,浅滩上长波总体增长率随滩顶水深的减小呈现先增大后减小的规律,在短波轻微破碎时最大。     

Numerical study of combined overflow and wave overtopping over a smooth impermeable seawall

A numerical wave flume is used to investigate the discharge characteristics of combined overflow and wave overtopping of impermeable seawalls. The numerical procedure computes solutions to the Reynolds-averaged Navier–Stokes equations and includes the generation of an irregular train of waves, the simulation of wave breaking and interaction with a sloping, impermeable wall. The numerical model is first tested against published experimental observations, approximate analytical solutions and empirical design formulae for the cases of pure overflow and pure overtopping. A sequence of numerical experiments simulating combined overflow and overtopping are described. The results are used to determine empirical discharge formulae of the form used in current practice.     

Wave run-up and overtopping on smooth and rough slopes of coastal structures

A series of hydraulic model tests has been carried out in a glass wave flume to investigate the influences of wave height, wave period, wave steepness, surf similarity parameter, roughness, layer thickness and porosity on wave run-up and overtopping of 1:2 sloped impermeable and permeable breakwaters fronted by a 1:10 gentle, smooth beach slope. The analysis of results involves the correlation between the overtopping energy transfer with the relative wall height and the relationship between wave run-up and overtopping rate. Further, measured wave run-up and overtopping rates are compared with the results given in the Shore Protection Manual (1984), Automated Coastal Engineering System (1992)and results of other investigators.     

礁坪上波浪传播的数值模拟

本文基于具备间断捕捉能力的二阶全非线性Boussinesq数值模型,对规则波和随机波在礁坪地形上的传播变形进行了数值模拟。该模型采用高阶有限体积法和有限差分方法求解守恒格式的控制方程,将波浪破碎视为间断,同时采用静态重构技术处理了海岸动边界问题。重点针对礁坪上波浪传播过程中的波高空间分布和沿程衰减,礁坪上的平均水位变化,以及波浪能量频谱的移动和空间差异等典型水动力现象开展数值计算。将数值结果与实验结果对比,两者吻合情况良好,验证了模型具有良好的稳定性,具备模拟破碎波浪和海-岸动边界的能力,能较为准确地模拟波浪在礁坪地形上的传播过程中发生的各种水动力现象。     

Wave transmission by overtopping due to random waves

Experimental studies of wave transmission by overtopping for a smooth impermeable breakwater with 1:1.5 slope under both regular and random waves were conducted. A resulting relationship between the transmission coefficient (determined by wave height and wave period) and a breakwater height above mean water level normalized with the height of wave run-up measured directly by capacity wave meter is reported. Meanwhile, their discrepancies in both regular and random waves are also discussed in this study. The authors find also that the transmitted significant wave period by overtopping of random waves may be much longer than those of the incoming wave. This characteristic is especially prominent and probably creates the oscillation phenomenon in the wave basin at the back of breakwater when the breakwater height (above mean water level) to water depth ratio is greater than 0.23 and the incoming wave period is longer than 8 sec.     

Laboratory study of wave and turbulence characteristics in narrow-band irregular breaking waves

Wave elevations and water particle velocities were measured in a laboratory surf zone created by the breaking of a narrow-band irregular wave train on a 1/35 plane slope. The incident waves form wave groups that are strongly modulated. It is found that the waves that break close to the shoreline generally have larger wave-height-to-water-depth ratios before breaking than the waves that break farther offshore. After breaking, the wave-height-to-water-depth ratio for the individual waves approaches a constant value in the inner surf zone, while the standard deviation of the wave period increases as the still water depth decreases. In the outer surf zone, the distribution of the period-averaged turbulent kinetic energy is closely correlated to the initial wave heights, and has a wider variation for narrow-band waves than for broad-band waves. In the inner surf zone, the distribution of the period-averaged turbulent kinetic energy is similar for narrow-band waves and broad-band waves. It is found that the wave elevation and turbulent kinetic energy time histories for the individual waves in a wave group are qualitatively similar to those found in a spilling regular wave. The time-averaged transport of turbulent kinetic energy by the ensemble-averaged velocity and turbulence velocity under the irregular breaking waves are also consistent with the measurements obtained in regular breaking waves. The experimental results indicate that the shape of the incident wave spectrum has a significant effect on the temporal and spatial variability of wave breaking and the distribution of turbulent kinetic energy in the outer surf zone. In the inner surf zone, however, the distribution of turbulent kinetic energy is relatively insensitive to the shape of the incident wave spectrum, and the important parameters are the significant wave height and period of the incident waves, and the beach slope.     

Laboratory experiments on wave transmission by overtopping

Laboratory experiments with regular waves were used to investigate wave transmission by overtopping for a smooth, impermeable breakwater with a 1-in-4 slope.A resulting relationship between the transmission coefficient and a breakwater height above mean sea level normalized with a theoretical wave run-up height is reported in this paper.