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。     

Theoretical and Experimental Study of Breaking Wave on Sloping Bottoms

This paper studies the continuous evolution of breaking wave for the surface water waves propagating on a sloping beach. A Lagrangian asymptotic solution is derived. According to the solution coupled with the wave breaking criteria and the equations of water particles motion, the wave deformation and the continuous wave breaking processes for the progressive water waves propagating on a sloping bottom can be derived. A series of experiments are also conducted to compare with the theoretical solution. The results show that the present solution can reasonably describe the plunging or spilling wave breaking phenomenon.     

Energy budget of surface waves in the global ocean

Mechanical energy input from atmosphere and losses from wave-breaking dissipation of sea surface waves are estimated by a direct scheme. This scheme is based on the integration in the wavenumber space of the wind input and breaking dissipation source functions of the MASNUM wave model. The global amount of wind energy input, averaged in 2005, is about 57 TW, and the wave-breaking dissipation summed in deep-water is about 33 TW, over a half of the wind energy input. The residual may be dissipated by beach processes. Global distributions of the energy input and breaking dissipation concentrate in the westerlies of the Southern Hemisphere.     

Improvement of sand activation depth prediction under conditions of oblique wave breaking

This study presents sand activation depth (SAD) measurements recently obtained on two contrasting beaches located along the Atlantic coast of France: the gently sloping, high-energy St Trojan beach where wave incidence is usually weak, and the steep, low-energy Arçay Sandspit beach where waves break at highly oblique angles. Comparisons between field measurements and predictions from existing formulae show good agreement for St Trojan beach but underestimate the SAD on the Arçay Sandspit beach by 40–60%. Such differences suggest a strong influence of wave obliquity on SAD. To verify this hypothesis, the relative influence of wave parameters was investigated by means of numerical modelling. A quasi-linear increase of SAD with wave height was confirmed for shore-normal and slightly oblique wave conditions, and a quasi-linear increase in SAD with wave obliquity was also revealed. Combining the numerical results with previously published relations, both a new semi-empirical and an empirical formula for the prediction of SAD were developed which showed good SAD predictions under conditions of oblique wave breaking. The new empirical formula for the prediction of SAD (Z ₀) takes into account the significant wave height (H _s), the beach face slope (β) and the wave angle at breaking (α), and is of the form $ Z_{0} = 1.6\tan {\left( \beta \right)}H^{{0.5}}_{{\text{s}}} {\sqrt {1 + \sin {\left( {2\alpha } \right)}} } This study presents sand activation depth (SAD) measurements recently obtained on two contrasting beaches located along the Atlantic coast of France: the gently sloping, high-energy St Trojan beach where wave incidence is usually weak, and the steep, low-energy Ar?ay Sandspit beach where waves break at highly oblique angles. Comparisons between field measurements and predictions from existing formulae show good agreement for St Trojan beach but underestimate the SAD on the Ar?ay Sandspit beach by 40–60%. Such differences suggest a strong influence of wave obliquity on SAD. To verify this hypothesis, the relative influence of wave parameters was investigated by means of numerical modelling. A quasi-linear increase of SAD with wave height was confirmed for shore-normal and slightly oblique wave conditions, and a quasi-linear increase in SAD with wave obliquity was also revealed. Combining the numerical results with previously published relations, both a new semi-empirical and an empirical formula for the prediction of SAD were developed which showed good SAD predictions under conditions of oblique wave breaking. The new empirical formula for the prediction of SAD (Z ₀) takes into account the significant wave height (H _s), the beach face slope (β) and the wave angle at breaking (α), and is of the form . The use of a dataset from the literature demonstrates the predictive skill of these new formulae for a wide range of wave heights, wave incidence and beach gradients.     

A scale comparison of waves breaking on a beach

A measurement programme, conducted in a small-scale wave flume, which comprised the breaking of periodic and random waves on a gently sloping beach, was partly repeated in a large-scale wave flume. The results are used here to make a scale comparison. The quantities considered in the comparison are wave heights, set-up and vertical profiles of maximum seaward, maximum shoreward and time-mean horizontal velocities. It appears that, both qualitatively and quantitatively, scale effects in these quantities are virtually absent in the wave height range of 0.1 m to 1.5 m.     

一维全非线性Green-Naghdi水波方程数值模型

建立了求解一维全非线性Green-Naghdi水波方程的中心有限体积/有限差分混合数值格式。采用结构化网格对守恒形式的控制方程进行离散和积分,界面数值通量采用有限体积法计算,剩余项则采用中心有限差分格式求解。其中,采用中心迎风有限体积格式计算控制体界面数值通量,并结合界面变量的线性重构方法,使其在空间上具有四阶精度,通过引入静压重构技术和波浪破碎指标使模型具备处理海岸水-陆动边界及波浪破碎的能力。时间积分则采用具有总时间变差减小(Total Variation Diminishing,TVD)性质的三阶龙格-库塔法进行。应用该模型对孤立波在常水深和斜坡海岸上的传播过程及规则波跨越潜堤传播的实验进行了数值模型研究,数值计算同解析解及实验数据吻合良好。     

Energy dissipation in waves breaking on gentle slopes

The flow field of waves breaking on a gently sloping beach is shown to closely resemble that of hydraulic jumps. This supports the use of the hydraulic jump formulation for the breaking wave energy dissipation. A correction to this formulation, which takes into account the effects of turbulent flow, is found to explain the observed discrepancies between the classical theoretical result and the experiments satisfactorily. These findings are used to propose a simple, semi-empirical model for the wave height decay which includes the set-up. The model is generalized to a wider range of wave conditions by analyzing published data.     

植被斜坡岸滩海啸波消减数值模拟研究

An explicit one-dimensional model based on the shallow water equations(SWEs) was established in this work to simulate tsunami wave propagation on a vegetated beach. This model adopted the finite-volume method(FVM)for maintaining the mass balance of these equations. The resistance force caused by vegetation was taken into account as a source term in the momentum equation. The Harten–Lax–van Leer(HLL) approximate Riemann solver was applied to evaluate the interface fluxes for tracing the wet/dry transition boundary. This proposed model was used to simulate solitary wave run-up and long-periodic wave propagation on a sloping beach. The calibration process suitably compared the calculated results with the measured data. The tsunami waves were also simulated to discuss the water depth, tsunami force, as well as the current speed in absence of and in presence of forest domain. The results indicated that forest growth at the beach reduced wave energy loss caused by tsunamis. A series of sensitivity analyses were conducted with respect to variable parameters(such as vegetation densities, wave heights, wave periods, bed resistance, and beach slopes) to identify important influences on mitigating tsunami damage on coastal forest beach.     

A two-point method for estimating wave reflection over a sloping beach

This work presents a frequency-domain method for estimating incident and reflected waves when normally incident waves’ propagating over a sloping beach in a wave flume is considered. Linear wave shoaling is applied to determine changes of the wave amplitude and phase due to variations of the bathymetry. The wave reflection coefficient is estimated using wave heights measured at two fixed wave gauges with a distance. The present model demonstrates a high capacity of estimating reflection and shoaling coefficients from synthetic wave-amplitude data. Sensitivity tests for the present model due to measurement errors of wave amplitudes and distance of two probes can more accurately predict the reflection coefficients. The measurement error of wave amplitude affects more significantly than measurement error of distance of two probes on calculating reflection coefficient of waves over a sloping bed.     

Breaking wave impact on vertical and sloping coastal structures

The results of laboratory experiments on the maximum and bottom impact pressures from waves breaking directly on vertical and sloping faced coastal structures are presented. Direct wave breaking on a wall is classified as early, late, and perfect breaking. Although the present study is aimed at dealing with the type of impact resulting from the perfect breaking, to some extent the occurrence of early and late breaking are unavoidable. The wave impact pressures, therefore, have a random nature of variation from impact-to-impact under the same conditions. The maximum and bottom impact pressures on walls are treated statistically. The effects of the wall angle and foreshore slope on these two quantities are examined. The results show that for practical applications, the still-water level can be taken as the acting place for the maximum impact pressure on the wall. Simultaneous impact pressure distribution below and above still-water level may be approximated as parabolic and linear, respectively. Finally, using a wall deflection criterion, a water depth region in front of the wall is defined, where the breaking wave forces may reach a critical level.     

Implementation and evaluation of alternative wave breaking formulas in a coastal spectral wave model

This paper describes methods and results of research for incorporating four different parameterized wave breaking and dissipation formulas in a coastal wave prediction model. Two formulations assume the breaking energy dissipation to be limited by the Rayleigh distribution, whereas the other two represent the breaking wave energy by a bore model. These four formulations have been implemented in WABED, a directional spectral wave model based on the wave action balance equation with diffraction, reflection, and wave–current interaction capabilities. Four parameterized wave breaking formulations are evaluated in the present study using two high-quality laboratory data sets. The first data set is from a wave transformation experiment at an idealized inlet entrance, representing four incident irregular waves in a slack tide and two steady-state ebb current conditions. The second data set is from a laboratory study of wave propagation over a complex bathymetry with strong wave-induced currents. Numerical simulation results show that with a proper breaking formulation the wave model can reproduce laboratory data for waves propagating over idealized or complicated bathymetries with ambient currents. The extended Goda wave breaking formulation with a truncated Rayleigh distribution, and the Battjes and Janssen formulation with a bore model produced the best agreement between model and data.     

Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone

In this paper, a hybrid finite volume-finite difference scheme is applied to study surf zone dynamics. The numerical model solves the 2DH extended Boussinesq equations proposed by Madsen and Sørensen (1992) where nonlinear and dispersive effects are both relevant whereas it solves NSWE equations where nonlinearity prevails. The shock-capturing features of the finite volume method allow an intrinsic representation of wave breaking and runup; therefore no empirical (calibration) parameters are necessary. Comparison with laboratory measurements demonstrates that the proposed model can accurately predict wave height decay and mean water level setup, for both regular and solitary wave breaking on a sloping beach. The model is also applied to reproduce two-dimensional wave transformation and breaking over a submerged circular shoal, showing good agreement with experimental data.     

Calculations of wave transformation across the surf zone

The accuracy of predicting wave transformation in the nearshore is very important to wave hydrodynamics, sediment transport and design of coastal structures. An efficient numerical model based on the time-dependent mild-slope equation is presented in this paper for the estimation of wave deformation across the surf zone. This model incorporates an approximate nonlinear shoaling formula and an energy dissipation factor due to wave breaking to improve the accuracy of the calculation of wave height deformation prior to wave breaking and also in the surf zone. The model also computes the location of first wave breaking, wave recovery and second wave breaking, if physical condition permits. Good agreement is found upon comparison with experimental data over several one-dimensional beach profiles, including uniform slope, bar and step profiles.     

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.     

Longshore sorting on a beach under wave action

Sorting of sediment on a beach under wave action takes several forms. Stratified layers of finer and coarser sediment, which depend on wave climate, grain size and beach slope are formed. This complex problem can be simplified by defining the cross-shore and longshore sorting according to the angle between the breaking wave and the coast. In the present study, longshore distribution of sediment as well as corresponding beach profiles was measured in a wave basin. Three-dimensional hydraulic model experiments were performed with regular waves. Eighteen sets of experiments performed in longshore sorting mechanism using two different sand beds. The sorting of the bed material and the formation of armour coats along the beach were defined by grain size distributions and dimensionless parameters for sandy beaches.The rate of sediment transport with grain size sorting was measured in a wave basin. A method introduced sorting process was presented in this study. The sediment rate based on sorting mechanism was also discussed with known methods. It has been found that the non-uniformity of the grain size and hence sorting of the beaches play a very important role in the sand transport due to wave motion in a similar way to the case of steady flow in alluvial channels.     

Determination of wave energy dissipation factor and numerical simulation of wave height in the surf zone

Based on the time-dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation. The wave height of regular and irregular waves is numerically simulated by use of the parabolic mild slope equation considering the energy dissipation due to wave breaking. Comparison of numerical results with experimental data shows that the expression for the energy dissipation factor is reasonable. The effects of the wave breaking coefficient on the breaking point and the distribution of wave height after breaking are discussed through the study of a specific experimental topography.     

Transformation model of wave height distribution on planar beaches

A new probability density function (pdf) for the transformation of depth-limited wave height distributions is presented. Assuming the bore approach for modeling the energy dissipation in the inner surf zone to be valid, an analytical expression for the transformation of wave height distribution including shoaling and breaking on a planar beach is obtained. The resulting expression for the pdf is formulated with a single function and only one shape parameter, which is calibrated as a function of the local root-mean-square (rms) wave height-to-water depth ratio and the local Iribarren number. The transformed pdf is able to reproduce the shape of field and laboratory measured wave height histograms and the sharp change in the shape of the wave height distribution in depth-limited breaking conditions for low exceedance probability. Results show that the theory is appropriate to represent wave height distribution transformation over shallow foreshores or in the surf zone. Alternatively, a combination of the new model with existing state-of-the-art wave energy propagation models allows the complete definition of the wave height distribution transformation on a planar beach.     

The impact of various methods of wave transfers from deep water to nearshore when determining extreme beach erosion

Several levels of increasing complexity of transferring wave information from offshore to nearshore have been studied to quantify their influence on extreme beach erosion estimates. Beach profiles which have been monitored since 1976 were used to estimate extreme beach erosion and compared to predictions. Examination of the wave propagation assumptions revolves around two types of offshore to nearshore transfer: excluding or including wave breaking and bottom friction. A second complication is whether still water level variations (ocean tide plus storm surge) are included.The inclusion of various combinations of wave propagation processes other than shoaling and refraction in the wave transfer function changes on the extreme erosion distribution tail through lowering estimates above one year return period. This brings the predicted tails closer to the observations, but does not capture the upper limit of storm demand implied by the extensive beach profile data set. Including wave breaking has a marked effect on probabilistic estimates of beach erosion. The inclusion of bottom friction is less significant. The inclusion of still water level variability in the wave transfer calculation had minimal impact on results for the case study site, where waves were transferred from offshore to water at 20 m depth. These changes were put into perspective by comparing them to changes resulting from limiting beach erosion by adjusting the statistical distributions of peak wave height and storm duration to have maximum limits. We conclude that the proposed improvements on wave transformation methods are as significant as limiting wave erosion potential and worth including.     

The influence of beach porosity on wave uprush and backwash

Packwood, A.R., 1983. The influence of beach porosity on wave uprush and backwash. Coastal Eng., 7: 29–40.A numerical model is described to calculate the influence of a porous bed on the run-up of a bore on a gently sloping sandy beach. It is shown that fine-medium grade sands have very little effect in the run-up phase. Significant differences between impermeable and porous bed solutions are found in the backwash which might explain certain sand erosion and deposition phenomena.     

A three-point method for estimating wave reflection of obliquely incident waves over a sloping bottom

A three-point method for estimating wave reflection is proposed to account for monochromatic oblique incident waves propagating over a sloping beach. The amplitudes of reflected wave and incident wave are separated using wave amplitudes measured at three fixed wave gauges with a distance. The applicability of the theory is verified by comparing the simulated results with the available theoretical, numerical and experimental results for the estimation of wave reflection. The sensitivity is also tested to provide a more accurate prediction of the reflection coefficient.