Layer thicknesses and velocities of wave overtopping flow at seadikes

Seadikes often fail due to wave overtopping and a failure of the landward slope. Therefore, these aspects have to be taken into account for the design of seadikes. In present design, the calculation of the crest height of seadikes is essentially based on using a design water level and the corresponding wave run-up height. An average overtopping rate is generally considered for wave overtopping which can not account for the stresses and other effects due to extreme individual overtopping events. Landward slope design is more or less based on experience. It can be concluded from failure analysis that dike failures on the landward slope are rather initiated by individual overtopping events, in particular by the related overtopping flow velocities and layer thicknesses which are relevant for the prediction of erosion, infiltration and slip failure. Therefore, overtopping flow velocities and layer thicknesses are required in addition to average overtopping rates as hydraulic boundary conditions for the geotechnical stability analysis of seadikes.The objective of the present paper is the theoretical and experimental determination of overtopping flow velocities and layer thicknesses on the seaward slope, the dike crest and the landward slope of a seadike. Overtopping parameters are derived on the basis of small scale model tests which are required for the design of the landward slope and to avoid dike failures by wave overtopping in the future. For the prediction of the layer thicknesses and the velocities of the overtopping flow on the seaward slope, the dike crest and the landward slope, a set of theoretical formulas is derived and validated by hydraulic scale model tests.     

Evolution of wave shape over a low-crested structure

This paper investigates the evolution of wave shape over a low-crested structure (LCS) using a 2-D RANS-VOF model. The model predictions of surface elevation and wave skewness and asymmetry are in good agreement with the recent measurements collected in a small scale wave channel at the University of Cantabria (UCA). The empirical formulae relating wave skewness and asymmetry to local Ursell number by Peng et al. (2009) have been extended to include the effect of wave reflection and the ramp in front of LCS and a wider range of Ursell number in the present study. In the presence of LCS, wave skewness decreases slightly above the seaward slope, then increases rapidly up to a maximum value above the structure crest, and decreases drastically above the leeward slope. Wave asymmetry decreases sharply above the seaward slope to a negative minimum value at the structure crest, and then increases rapidly to a positive value above the leeward slope. Our bispectral analysis indicates that sum interactions increase skewness and decrease asymmetry while difference interactions have opposite effects and that the former dominate above the seaward slope and on the structure crest but the latter dominate above the leeward slope of LCS. The observed wave shape evolution over a LCS can be attributed to the changes in the interplay of sum and difference interactions. We found that incident wave height and wave period, relative structure freeboard, structure crest width and structure porosity are the controlling factors for wave shape evolution over LCS. This study provides new insights on the role of wave skewness and asymmetry in the breakwaters stability and sediment transport around the structure and on the beaches behind it.     

A numerical model of wave overtopping on seadikes

This paper describes the development of a numerical model for wave overtopping on seadikes. The model is based on the flux-conservative form of the nonlinear shallow water equations (NLSW) solved with a high order total variation diminishing (TVD), Roe-type scheme. The goal is to reliably predict the hydrodynamics of wave overtopping on the dike crest and along the inner slope, necessary for the breach modelling of seadikes. Besides the mean overtopping rate, the capability of simulating individual overtopping events is also required. It is shown theoretically that the effect of wave breaking through the drastic motion of surface rollers in the surfzone is not sufficiently described by the conventional nonlinear shallow water equations, neglecting wave setup from the mean water level and thus markedly reducing the model predictive capacity for wave overtopping. This is significantly improved by including an additional source term associated with the roller energy dissipation in the depth-averaged momentum equation. The developed model has been validated against four existing laboratory datasets of wave overtopping on dikes. The first two sets are to validate the roller term performance in improving the model prediction of wave overtopping of breaking waves. The last two sets are to test the model performance under more complex but realistic hydraulic and slope geometric conditions. The results confirm the merit of the supplemented roller term and also demonstrate that the model is robust and reliable for the prediction of wave overtopping on seadikes.     

Sediment flux and equilibrium slopes in a barred nearshore

Estimates of time-integrated values of total (ITVF) and net (INVF) sediment volume flux and the associated changes in bed elevation and local slope were determined for a crescentic outer nearshore bar in Kouchibouguac Bay, New Brunswick, Canada, for eight discrete storm events. A 100 × 150 m grid of depth-of-activity rods spaced at 10 m intervals was used to monitor sediment behaviour on the seaward slope, bar crest and landward slope during the storms, at which time winds, incident waves and near-bed oscillatory currents were measured. Comparisons between storm events and between these events and a longer-term synthetic wave climatology were facilitated using hindcast wave parameters. Strong positive correlations between storm-wave conditions (significant height and total cumulative energy) and total volume flux contrasted strongly with the zero correlation between storm-wave conditions and net volume flux. ITVF values ranged up to 1646 m³ for the experimental grid and were found to have power function relations with significant wave height (exponent 2) and cumulative wave wave energy (exponent 0.4); values of INVF ranged from 0 up to 100 m³ for the same grid indicating a balance of sediment volume in the bar form through time. Sediment reactivation increased linearly with decreasing depth across the seaward slope and bar crest reaching maxima of 20 cm for the two largest storms; bed elevation, and thus slope, changes were restricted to the bar crest and upper landward slope with near zero morphological change on the seaward slope. The latter represents a steady-state equilibrium with null net transport of sediment under shoaling waves. Measurements of the asymmetry of orbital velocities close to the bed show that the energetics approach to predicting beach slope of Inman and Bagnold (1963) is sound. Gradients predicted vary from 0.01 to 0.03 for a range of angles of internal friction appropriate to the local sediment (tan ø = 0.3–0.6). These compare favorably with the measured seaward slope of 0.015 formed under average maximum orbital velocities of 1.12 m s⁻¹ (landward) and 1.09 m s⁻¹ (seaward) recorded during the period of the largest storm waves.     

Analysis of overtopping flow on sea dikes in oblique and short-crested waves

Dike resilience against wave overtopping has gained more and more attention in recent years due to the effect of expected future climate changes. The overtopping flow velocities and flow depths on dikes have recently been studied in 2D small-scale experiments. This has led to semi-empirical formulae for the estimation of flow depths and flow velocities across a dike. The results have been coupled to the actual erosion of the landward dike slope determined by full-scale 2D tests using the so-called “Overtopping Simulator”. This paper describes the results from 96 small-scale tests carried out in a shallow water basin at Aalborg University to cover the so far unknown 3D effects from oblique long-crested and short-crested waves. Based on results from the laboratory tests, expansions are proposed to the existing 2D formulae so as to cover oblique and short-crested waves. The wave obliquity is seen to significantly reduce the overtopping flow velocities and flow depths on especially the landward slope of a sea dike. Moreover, the tests showed that the average flow directions on the dike crest from oblique long-crested and short-crested waves correspond approximately to the incident wave direction. Flow depths and the squared flow velocities on the dike are concluded to be Rayleigh-distributed in case of both long-crested and short-crested waves for all considered incident wave obliquities. Findings in the present paper are needed to obtain more realistic estimates of dike erosion caused by wave overtopping.     

Experimental study on mechanism of sea-dike failure due to wave overtopping

This work, which was largely a fruit of China's national marine hazard mitigation service, explicitly reveals the major mechanism of sea-dike failure during wave overtopping. A large group of wave-flume experiments were conducted for sea dikes with varying geometric characteristics and pavement types. The erosion and slide of the landward slope due to the combined effect of normal hit and great shear from overtopping flows was identified the major trigger of the destabilization of sea dikes. Once the intermittent hydrodynamic load and swash caused any deformation (bump or dent) of the pavement layer, pavement fractions (slabs or rubble) on the slope started to be initiated and removed by the water. The erosion of the landward slope was then gradually aggravated followed by entire failure within a couple of minutes. Hence, the competent velocity would be helpful evaluate the failure risk if as well accounted in standards or criteria. However, the dike top was measured experiencing the largest hydrodynamic pressure with a certain cap while the force on the wall increased rapidly as the overtopping intensity approached the dike-failure threshold. The faster increase of the force on the wall than on the landward slope yielded the sequencing of loads reaching hypothetic limits before failure as: dike top – top-mounted wall – landward slope. Therefore, beside the slide failure, the fatigue damage due to the instantaneous hydrodynamic impact might be another mechanism of the dike failure, which did not appear in the experiment but should be kept in mind. Instead of the widely adopted tolerable overtopping rate, a 0.117–0.424 m³/(m s) range of overtopping discharge and a 10 m/s overtopping velocity for the failure risk of typical sea dikes along China's coastlines were suggested, which enables the possible failure risk prediction through empirical calculations. The failure overtopping rate was identified strongly dependent on the pavement material, the landward slope and the dike-mounted wall but showed little variation with the width of the dike top. The flat concrete pavement and gentle landward slopes are suggested for the dike design and construction. For given configurations and hydrodynamic conditions in the experiment, the dike without the wall experienced less overtopping volume than those with the 1-m top-mounted wall. Meanwhile, the remove of the wall increased the failure overtopping rate, which means a certain increase of the failure criterion. Thus, care must be taken to conclude that the dike-mounted wall seems not an entirely appropriate reinforcement for the stability and safety of coastal protections. This should be further checked and discussed by researchers and engineers in the future.     

Predictions on Irregular Wave run-up and Overtopping

A series of hydraulic model tests are carried out to investigate random wave run-up and overtopping on smooth, impermeable single slope and composite slope. Based on analysis of the influences of wave steepness, structure slope, incident wave angle, width of the berm and water depth on the berm and the wave run-up, empirical formulas for wave run-up on dike are proposed. Moreover, empirical formula on estimating the wave run-up on composite slope with multiple berms is presented for practical application of complex dike cross-section. The present study shows that the influence factors for wave overtopping are almost the same as those for wave run-up and the trend of the wave overtopping variation with main influence parameters is also similar to that for wave run-up. The trend of the wave overtopping discharge variations can be well described by two main factors, i.e. the wave run-up and the crest freeboard of the structure. A new prediction method for wave overtopping discharge is proposed for random waves. The proposed prediction formulas are applied to case study of over forty cases and the results show that the prediction methods are good enough for practical design purposes.     

Appraisal of storm beach buffer width for cyclonic waves

The loss of beach sand from berm and dune due to high waves and surge is a universal phenomenon associated with sporadic storm activities. To protect the development in a coastal hazard zone, hard structures or coastal setback have been established in many countries around the world. In this paper, the requirement of a storm beach buffer, being a lesser extent landward comparing with the coastal setback to ensure the safety of infrastructures, is numerically assessed using the SBEACH model for three categories of wave conditions in terms of storm return period, median sand grain size, berm width, and design water level. Two of the key outputs from the numerical calculations, berm retreat and bar formation offshore, are then analysed, as well as beach profile change. After having performed a series of numerical studies on selected large wave tank (LWT) test results with monochromatic waves using SBEACH, we may conclude that: (1) Berm erosion increases and submerged bar develops further offshore as the storm return period increases for beach with a specific sand grain size, or as the sand grain reduces on a beach under the action of identical wave condition; (2) Higher storm waves yield a large bar to form quicker and subsequently cause wave breaking on the bar crest, which can reduce the wave energy and limit the extent of the eroding berm; (3) A larger buffer width is required for a beach comprising small sand grain, in order to effectively absorb storm wave energy; and (4) Empirical relationships can be tentatively proposed to estimate the storm beach buffer width, from the input of wave conditions and sediment grain size. These results would benefit a beach nourishment project for shore protection or design of a recreational beach.     

磨刀门河口枯季波生流场数值模拟研究

本文建立曲线坐标系下的双曲型缓坡方程波浪模型和考虑波浪辐射应力影响的深度平均2D潮流数学模型,首次研究了磨刀门河口2011年地形条件下的枯季波生流场。受波浪作用影响,落潮阶段,波浪作用方向与流向相反,在波浪顶托效应下拦门沙沙脊及外坡处流速普遍减小,形成两个主要回流区,口门外东西两侧浅滩处流速也减小,东西两汊及横洲深槽流速增大;涨潮阶段,波浪作用方向与流向相同,拦门沙沙脊及外坡处流速增大,沙脊处出现冲越流,口门两侧浅滩处流速增大,横洲深槽流速减小。     

The applicability of the shallow water equations for modelling violent wave overtopping

The shallow water equations (SWE) have been used to model a series of experiments examining violent wave overtopping of a near-vertical sloping structure with impacting wave conditions. A finite volume scheme was used to solve the shallow water equations. A monotonic reconstruction method was applied to eliminate spurious oscillations and ensure proper treatment of bed slope terms. Both the numerical results and physical observations of the water surface closely followed the relevant Rayleigh probability distributions. However, the numerical model overestimated the wave heights and suffered from the lack of dispersion within the shallow water equations. Comparisons made on dimensionless parameters for the overtopping discharge and percentage of waves overtopping between the numerical model and the experimental observations indicated that for the lesser impacting waves, the shallow water equations perform satisfactorily and provide a good alternative to computationally more expensive methods.     

Exceedance probability for wave overtopping on a fixed deck

Detailed laboratory measurements were made of the instantaneous free surface elevation in front of a fixed deck and the instantaneous free surface elevation, velocity, and overtopping rate at the leading edge of the deck. The study showed that the exceedance probabilities for the normalized maximum instantaneous overtopping rate and the normalized overtopping volume were predicted by a simple exponential curve. The measured exceedance probability seaward of the deck compared well with the nonlinear theory of Kriebel and Dawson (Kriebel D.L., Dawson T.H., 1993. Nonlinearity in wave crest statistics. In: Proceedings Ocean Wave Measurement and Analysis. American Society of Civil Engineers, pp. 61–75). Conditional sampling of the crest heights seaward of the deck gave a normalized probability distribution similar to that of the maximum water level measured on the deck for each overtopping event. However, the values used to normalize each distribution were not the same.     

非淹没刚性植物对海啸作用下海堤水动力特性影响数值模拟研究

基于非静压单相流模型NHWAVE建立了高精度数值波浪水槽。通过设计不同的计算工况,系统研究了非淹没刚性植物对海啸作用下海堤周围水动力特性的影响。着重分析了不同入射波高、不同植物分布密度以及不同植物分布宽度条件下海啸波沿程波形特征以及海堤堤顶越浪流空间分布特征。结果表明:不同入射波高、植物分布密度以及植物宽度条件下,堤顶流厚度和水体流速具有明显单调的变化趋势,并且随着植物分布密度和宽度增大,波能衰减增大;随着入射波非线性增强,植物分布密度和分布宽度对堤顶前段水流厚度的影响也随之增强,而对堤顶后段水流厚度的影响则减弱,且堤顶后缘水流厚度约为堤顶前缘厚度的二分之一;在波浪非线性较大情况下,植物的存在对堤顶流速度的空间分布趋势几乎没有影响,但相对堤顶流速度增加程度均大于无植物情况,且堤顶后缘水流速度约为堤顶前缘的1.6倍。     

Wave overtopping and induced currents at emergent low crested structures

This paper deals with wave overtopping associated to low emergent detached breakwaters. It starts presenting the various mechanisms which define the functional behaviour of detached breakwaters which are frequently overtopped. The emphasis is on the role played by overtopping and how this contributes to the wave pumping in the area around the structure. The paper then reviews the available formulations for predicting overtopping, considering the sensitivity of various equations to climatic drivers and their suitability for low crested coastal structures. The paper then analyzes nearshore circulation models and how overtopping discharges can be included. This is illustrated with a sample Q-3D model by analyzing the differences obtained with/without overtopping. The emphasis is on the implications for the functional design of the structure and its morpho-hydrodynamic impact. The main conclusion is the sensitivity of the functional design of such structures to the underlying hydrodynamics processes and the importance to explicitly include overtopping for numerical simulations of the morpho-hydrodynamic behaviour of low crested breakwaters.     

基于FLUENT的波浪溢流水动力数值模拟

波浪溢流现象使得海堤受到了越浪和溢流的联合作用,复杂的水动力过程会引起海堤后坡产生严重的侵蚀破坏。基于FLUENT软件建立了二维数值波浪溢流水槽模型,该模型运用UDF速度边界造波法分析在不同超高条件下海堤后坡流量和水流厚度的水力学特性。结果表明数值模拟结果与前人物理模型试验结果吻合,该模型可以真实地模拟出海堤波浪溢流现象。在此基础上进一步研究了波浪溢流中越浪和溢流在不同相对超高条件下的主导性作用,而后建立了十分准确的波浪溢流海堤后坡稳定水流厚度计算公式。     

Prototype measurements and small-scale model tests of wave overtopping at shallow rubble-mound breakwaters: the Ostia-Rome yacht harbour case

The paper presents the comparison between the results of small-scale model tests and prototype measurements of wave overtopping at a rubble-mound breakwater. The specific structure investigated is the west breakwater of the yacht harbour of Rome at Ostia (Italy) and is characterized by a gentle seaward slope (1/4) and by a long, shallow foreshore. The laboratory tests firstly aimed at carefully reproducing two measured storms in which overtopping occurred and was measured. The tests have been carried out in two independent laboratories, in a wave flume and in a wave basin, hence using a two-dimensional (2-D) and a three-dimensional (3-D) setup. In the 2-D laboratory tests no overtopping occurred during the storm reproductions; in the 3-D case discharges five to ten times smaller than those observed in prototype have been measured. This indicates the existence of model and scale effects. These effects have been discussed on the basis of the results of several parametric tests, which have been carried out in both laboratories, in addition to the storm reproductions, varying wave and water level characteristics. Final comparison of all the performed tests with 86 prototype measurements still suggests the existence of scale and model effects that induce strong underestimation of overtopping discharge at small scale. The scale reproduction of wave breaking on the foreshore, together with the 3-D features of the prototype conditions and the absence of wind stress in the laboratory measurements, have been individuated as the main sources of scale and model effects. The paper also provides a comparison between the data and a largely used formula for wave overtopping discharges in the presence of structures similar to the one at hand. The suitable value of a roughness factor that appears in that formula is investigated and good agreement is found with other recent researches on rubble-mound breakwaters.     

Laboratory study of combined wave overtopping and storm surge overflow of a levee

Combined wave overtopping and storm surge overflow of a levee with a trapezoidal cross section was studied in a two-dimensional laboratory wave/flow flume at a nominal prototype-to-model length scale of 25-to-1. The goal of this study was to develop design guidance in the aftermath of Hurricane Katrina. Time series of water depth at two locations on the levee crown and flow thickness at five locations on the landward-side slope were measured along with horizontal velocity near the landward edge of the crown. New equations are presented for average overtopping discharge, distribution of instantaneous discharge, and distribution of individual wave volumes. Equations are also given for mean flow thickness, RMS wave height, mean velocity, and velocity of the wave front down the landward-side slope.     

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 experimental model application of wavescreen: Dynamic pressure, water particle velocity, and wave measurements

This paper analyses the results of an application of a piled wavescreen. Experimental measurements were undertaken in the laboratory conditions for a given structural configuration under the attack of regular and irregular waves. Dynamic pressure distribution along and around the inclined piles was obtained employing pressure transducers. Using these data, in-line dynamic wave forces acting on piles were also determined. Water particle (orbital) velocities were measured at seaward and landward of the wavescreen using two acoustic Doppler velocimeters (ADV) simultaneously. Furthermore, wave data were collected using resistance type wave gauges at the seaward and landward of the structure. Based on those data, wave attenuation performance of the wavescreen was explored for two different depth values. Findings showed that piled wavescreen can provide effective shore protection as an environmentally friendly coastal structure.     

Structure of the Sunda Trench lower slope off sumatra from multichannel seismic reflection data

Multichannel seismic reflection profiles across the Sunda Trench slope off central Sumatra reveal details of subduction zone structure. Normal faults formed on the outer ridge of the trench offset deep strate and the oceanic crust, but die out upsection under the trench sediments. At the base of the inner trench slope, shallow reflectors are tilted seaward, while deeper reflectors dip landward parallel to the underlying oceanic crustal reflector. Intermediate depth reflectors can be traced landward through a seaward-dipping monocline. We interpret this fold as the shallow expression of a landward-dipping thrust fault at depth. Landward of this flexure, relatively undeformed strata have been stripped off the oceanic plate, uplifted 700 meters, and accreted to the base of the slope. The oceanic crust is not involved in the deformation at the toe of the slope, and it can be observed dipping landward about 25 km under the toe of the accretionary prism.The middle portion of the trench slope is underlain by deformed accreted strata. Shallow reflectors define anticlinal structures, but coherent deep reflectors are lacking. Reflectors 45 to 55 km landward of the base of the slope dip 4°-5° landward beneath a steep slope, suggesting structural imbrication.A significant sediment apron is absent from the trench slope. Instead, slope basins are developed in 375–1500 m water depths, with an especially large one at about 1500 m water depth that is filled with more than 1.1 seconds of relatively undeformed sediments. The seaward flank of the basin has recently been uplifted, as indicated by shallow landward-dipping reflectors. Earlier periods of uplift also appear to have coincided with sedimentation in this basin, as indicated by numerous angular unconformities in the basin strata.Contribution of the Scripps Institution of Oceanography, new series.