Wave height parameter for damage description of rubble-mound breakwaters

In this paper it will be shown that the wave height parameter H₅₀, defined as the average wave height of the 50 highest waves reaching a rubble-mound breakwater in its useful life, can describe the effect of the wave height on the history of the armor damage caused by the wave climate during the structure's usable life.Using Thompson and Shuttler (Thompson, D.M., Shuttler, R.M., 1975. Riprap design for wind wave attack: A laboratory study on random waves. HRS Wallingford, Report 61, UK) data it will be shown that H₅₀ is the wave parameter that best represents the damage evolution with the number of waves in a sea state. Using this H₅₀ parameter, formulae as van der Meer (van der Meer, J.W., 1988. Rock slopes and gravel beaches under wave attack. PhD Thesis. Technical University of Delft) and Losada and Giménez-Curto (Losada, M.A., Gimenez–Curto, L.A., 1979. The joint effect of the wave height and period on the stability of rubble mound breakwaters using Iribarren's number. Coastal Engineering, 3, 77–96) are transformed into sea-state damage evolution formulae. Using these H₅₀-transformed formulae for regular and irregular sea states it will be shown how damage predictions are independent of the sea state wave height distribution.To check the capability of these H₅₀-formulae to predict damage evolution of succession of sea states with different wave height distributions, some stability tests with regular and irregular waves have been carried out. After analysing the experimental results, it will be shown how H₅₀-formulae can predict the observed damage independently of the sea state wave height distribution or the succession of sea states.     

The stability of the antifer units used on breakwaters in case of irregular placement

The primary aim of the study is to experimentally investigate the stability performance of antifer units on the trunk section of breakwaters under the effect of regular and irregular waves in case of irregular placement. The stability performance tests were conducted for different slopes, i.e. cot α=1.25, 1.5, 2.0, 2.5, under irregular waves and for cot α=2.5 under regular waves. Hudson’s formula was employed in order to characterize the stability performance of antifer units for the irregular placement technique. Different representative wave height parameters, i.e. H_s, H_1/10 and H_max, were examined to determine the one best characterizing breakwater stability. Furthermore, the effects of wave period and wave steepness on the stability of the breakwater were explored.     

Dynamic pressures on inclined cylinders due to freak waves

The dynamic pressure distribution around a cylinder tilted along and against the principal wave direction is measured. The cylinder was exposed to the action of random waves in the presence and absence of extreme waves. Six inclinations from the vertical plane, three along and three against the wave direction, were considered. The cylinder in upright position was also studied. The variation of dimensionless peak pressure (pressure maximum/average highest one-third wave height, H_1/3) with the relative wave height (maximum wave height/H_1/3) for locations facing the wave and at the rear of the cylinder for different angles of inclinations of the cylinder are reported for the two kinds of waves mentioned earlier. The statistical properties of the different asymmetries in the pressure traces are also discussed.     

Movable bed roughness and current profiles in the presence of irregular waves with an arbitrary angle to currents

The bed roughness k_s and current velocity profiles in the presence of waves with an arbitrary angle θ to currents are studied. It is found that the movable bed roughness is affected by both the wave and the current and only slightly by the angle θ between the wave propagation and the current, and that existing formulae derived in purely oscillatory flows generally fail to predict k_s. In the present study, a new formula which takes account the effect of the wave and the current on the bed roughness is suggested to calculate k_s in combined wave-current flows. With the present formula, the current profiles calculated by the model of You agree satisfactorily with the laboratory data of van Kampen and Nap and Havinga, and the field measurements of Grant and Williams and Drake et al.     

On front slope stability of berm breakwaters

The short communication presents application of the conventional Van der Meer stability formula for low-crested breakwaters for the prediction of front slope erosion of statically stable berm breakwaters with relatively high berms. The method is verified (Burcharth, 2008) by comparison with the reshaping of a large Norwegian breakwater exposed to the North Sea waves. As a motivation for applying the Van der Meer formula a discussion of design parameters related to berm breakwater stability formulae is given. Comparisons of front erosion predicted by the use of the Van der Meer formula with model test results including tests presented in Sigurdarson and Van der Meer (2011) are discussed. A proposal is presented for performance of new model tests with the purpose of developing more accurate formulae for the prediction of front slope erosion as a function of front slope, relative berm height, relative berm width, method of armour stone placement, and hydraulic parameters. The formulae should cover the structure range from statically stable berm breakwaters to conventional double layer armoured breakwaters.     

Prediction of wave pressures on smooth impermeable seawalls

Simple prediction methods are proposed to estimate the wave induced pressures on smooth impermeable seawalls. Based on the physics of the wave structure interaction, the sloped seawall is divided into a total of five zones (zones 1, 2 and 3 during run-up (corresponding pressures are called as positive pressures) and zones 4 and 5 during run-down (corresponding pressures are called negative pressures)) (Fig. 1). Zone 1 (0<z<d−H_i/2), where the wave pressure is governed by the partial reflection and phase shift; Zone 2 (d−H_i/2<z<d), where the effect of wave breaking and turbulence is significant; Zone 3 (d<z<Run-up height), where the pressure is induced by the run-up water; Zone 4 (Run-down<z<d), where the wave pressure is caused by the run-down effect and Zone 5 (0<z<d-Run down), where the negative wave pressures are due to partial reflection and phase shift effects. Here d is the water depth at the toe of the seawall, H_i is the incident wave height and z is the vertical elevation with toe of the seawall as origin and z is positive upward. For wave pressure prediction in zones 1 and 5, the empirical formula proposed by Ahrens et al. (1993) to estimate the wave reflection and Sutherland and Donoghue's recommendations (1998) for the estimation of phase shift of the waves caused by the sloped structures are used. Multiple regression analysis is carried out on the measured pressure data and empirical formulas are proposed for zones 2, 3 and 4. The recommendations of Van der Meer and Breteler (1990) and Schüttrumpf et al. (1994) for the prediction of wave run-down are used for pressure prediction at zone 4. Comparison of the proposed prediction formulas with the experimental results reveal that the prediction methods are good enough for practical purposes. The present study also shows a strong relation between wave reflection, wave run-up, wave run-down and phase shift of waves on wave pressures on the seawalls.     

中国浙江和福建海域台风浪变化特征和趋势

基于非结构网格的海浪-海流耦合模式SWAN+ADCIRC(Simulating Waves Nearshore+Advanced Circulation model),模拟了1997—2016年共20年间所有影响浙江和福建海域台风过程期间的海浪过程。利用4个台风过程期间的海浪观测数据对模拟结果进行了验证,模拟结果和实测结果吻合较好。基于该长时间序列台风浪模拟结果,分别分析了浙江和福建海岸带台风浪有效波高极值以及台风浪有效波高大于1m和1.5m的持续时间。结果显示,在福建北部海岸带台风浪有效波高极值和台风浪有效波高大于1m的持续时间(tHs1)有显著增长的趋势。其中,台风浪高极值的增长趋势最大可达0.05m/a,tHs1的增长趋势位于0.54至1.72h/a之间。分析tHs1与ENSO指数的关系发现,福建省南部海域台风浪与ENSO指数有较显著的负相关,浙江省北部海域台风浪与ENSO指数有较显著的正相关,ENSO信号对这两个海域的台风浪有着较显著的影响。     

Effects of high-order nonlinear interactions on unidirectional wave trains

Numerical simulations of gravity waves with high-order nonlinearities in two-dimensional domain are performed by using the pseudo spectral method. High-order nonlinearities more than third order excite apparently chaotic evolutions of the Fourier energy in deep water random waves. The high-order nonlinearities increase kurtosis, wave height distribution and H_max/H_1/3 in deep water and decrease these wave statistics in shallow water. Moreover, they can generate a single extreme high wave with an outstanding crest height in deep water. High-order nonlinearities (more than third order) can be regarded as one cause of freak waves in deep water.     

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.     

Wave reflection characteristics of plane, dentated and serrated seawalls

The hydrodynamic performance of vertical and sloped plane, dentated and serrated seawalls were investigated using physical model studies. Regular and random waves of wide range of heights and periods were used. Tests were carried out for different inclinations of the seawall (i.e. θ=30, 40, 50, 60 and 90°) and for a constant water depth of 0.7 m. The wave reflection was measured to assess the dissipation character of the seawalls. It was observed that the serrated seawall was superior to the plane and dentated seawall in reducing the wave reflection. Even for the vertical case, the coefficient of reflection due to regular waves for dentated seawall ranged from 0.6–0.99 and for the vertical serrated seawall it was 0.45–0.98, whereas for the vertical plane wall, it was almost 1.0. It was found that the characteristic dimension of the seawall (i.e. L/W) and the relative water depth (i.e. d/L) were better influencing parameters compared to the conventionally used surf similarity parameter ‘ξ’ (ξ=tan θ/(H_i/L)^0.5) in predicting the reflection from the dentated and serrated seawall, where L is the local wave length, W the width of the dent along the length of the seawall slope, d the water depth at the toe and H_i is the incident wave height. A similar trend was observed for the random waves too. The reduction in the wave reflection due to random waves for the dentated seawall as compared to the plane seawall was about 18% and for the serrated seawall, it was 20%. It was observed that the reflection due to random waves was lesser for all the three different walls than the regular waves, due to the mutual interaction of random waves. Multiple regression analysis on the measured data points was carried out and predictive equations for the reflection coefficient were obtained for both regular and random waves. This study will be useful in the design of energy dissipating type vertical quay walls in ports and harbours, sloped seawalls for shore protection from erosion and sloped caisson as breakwaters. Comparison of predictive formulae with the experimental results revealed that the prediction methods were good enough for practical purposes.     

以海浪波要素表示的外频谱形式

孙孕等（１９９４）提出了外频谱的概念,并推导出外频谱的理论形式,但其控制参量是由内频谱导出的,不便于实际应用,通过对实测海浪数据的分析,得到了控制外频谱的３个和内频谱有关的参量与波浪要素之间的关系,进而将外频谱表示以有效波高和有效波周期作为控制参量的形式,应用实测资料将本文得到的外频谱形式与理论外频谱进行了比较,发现二者符合良好。     

General longshore transport model

In the present paper a general longshore transport (LT) model is proposed after a re-calibration of the model originally introduced by Lamberti and Tomasicchio (1997) based on a modified stability number, N_s^⁎⁎, for stone mobility at reshaping or berm breakwaters. N_s^⁎⁎ resembles the traditional stability number (Ahrens, 1987; van der Meer, 1988) taking into account the effects of a non-Rayleighian wave height distribution at shallow water (Klopman and Stive, 1989), wave steepness, wave obliquity, and nominal diameter of the units. Nine high-quality data sets from field and laboratory experiments have been considered to extend the validity of the original model for a wider mobility range of the units: from stones to sands. The predictive capability of the proposed model has been verified against the most popular formulae in literature for the LT estimation of not cohesive units at a coastal body. The comparison showed that the model gives a better agreement with the physical data with respect to the other investigated formulae.The proposed transport model presents a main advantage with respect to other formulae: it can represent an engineering tool suitable for a large range of conditions, from sandy beaches till reshaping breakwaters.     

随机波浪中畸形波在三维岛礁地形上的试验研究

在试验水池中,开展了波浪在岛礁地形上演化问题的研究。首先在实验水池中建立了西太平洋某岛礁地形的模型,然后采用改进的JONSWAP谱,由造波机产生不同周期、波高的随机波浪。试验中观察到了不同类型畸形波生成的过程及不同波面形态的畸形波。对偏度、峰度及水深与畸形波要素H_m/H_s（H_m表示波列中的最大波高, H_s为有效波高）的关系进行了详细的分析,同时,对畸形波波高H_fr与偏度的关也进行了分析。通过对试验结果分析,发现峰度与畸形波要素i>H_m/H_s呈正相关, H_fr增大时相应的偏度也会呈现增大的趋势。此外,水深的变化剧烈时（如斜坡、海山位置）有助于畸形波的发生。     

Structural stability of detached low crested breakwaters

The aim of the paper is to describe hydraulic stability of rock-armoured low-crested structures on the basis of new experimental tests and prototype observations.Rock armour stability results from earlier model tests under non-depth-limited long-crested head-on waves are reviewed.Results from new 2-D and 3-D model tests, carried out at Aalborg University, are presented. The tests were performed on detached low-crested breakwaters exposed to short-crested head-on and oblique waves, including depth-limited conditions. A formula that corresponds to initiation of hydraulic damage and allows determining armour stone size in shallow water conditions is given together with a rule of thumb for the required stone size in depth-limited design waves.Rock toe stability is discussed on the basis of prototype experience, hard bottom 2-D tests in depth-limited waves and an existing hydraulic stability formula. Toe damage predicted by the formula is in agreement with experimental results. In field sites, damage at the toe induced by scour or by sinking is observed and the volume of the berm is often insufficient to avoid regressive erosion of the armour layer.Stone sinking and settlement in selected sites, for which detailed information is available, are presented and discussed.     

Geometrical properties of perfect breaking waves on composite breakwaters

The experimental results have so far shown that when a wave breaks on a vertical wall with an almost vertical front face at the instant of impact that is called perfect breaking or perfect impact, the greatest impact forces are produced on the wall. Therefore, the configuration of breaking waves is important in the design considerations of coastal structures. The present study is concerned with determining the geometrical properties of oscillatory waves that break perfectly on the vertical wall of composite-type breakwaters. The laboratory tests for perfect breaking waves on composite breakwaters are conducted with base slopes of 1/2, 1/4 and 1/6, and with berm widths of 0.00, 0.10, 0.20, 0.30 and 0.40 m. The shape and the dimensions of waves at the instant of perfect breaking on the wall are determined using a video camera. The experimental results for the geometrical properties of the breakers are presented non-dimensionally. Within the range of present experimental conditions, it is found that the dimensionless breaker crest height, h_b/d_w, and dimensionless breaker height, H_b/d_w, decrease; and, dimensionless breaker depth, d_w/H₀, increases with increasing relative berm width, B/D. The breaker height index, H_b/H₀, is almost unaffected by B/D. The deep-water wave steepness and the base slope of the breakwater do not seem to influence the geometrical properties of the breakers at wall systematically.     

黄渤海海域波浪时空变化特征分析

本文利用欧洲中期预报中心(ECMWF)第五代再分析数据集(ECMWF Reanalysis v5,ERA5),对中国黄渤海海域2000—2019年的波浪进行了统计分析.得到如下的结论:1)黄渤海海区波浪具有明显的季节性,渤海区域有效波高呈现出周边小,中间大的特点;黄海海域有效波高呈现由南向北降低的趋势;研究区域冬季有效...     

Some properties of surf-beats

Long ocean waves with periods of several minutes (surf-beats) were observed at a marine observation tower. We have analysed time series data of an envelope of incident swell, long period current velocity and surface elevation fluctuations. Current velocity was measued by an electromagnetic flow meter. Surf-beats amplitudeH ^(l) is shown to be proportional to 3/2 power of incident swell amplitudeH ^(s), and decreases with increase of depthh in proportional toh ^–1/2 such thatH ^(l) H ^(s) (H ^(s)/h)^1/2. Frequency energy density functionP _LL (f) of surface elevation had two dominant peaks whose frequencies were highly stable through the entire observational period. Cross-spectral analysis suggested that those peaks correspond to traveling edge waves caused by the excess momentum and mass flux in the surf zone. The forced long ocean waves predicted byLonguet-Higgins andStewart (1964) was ditected. Phase-shift and wave height of the wave with respect to those of incident swell envelope are shown to be in remarkable agreement with the predictions. However the forced long wave is only a minor component in the total energy of surf-beats. Current fields are shown to be largely composed of non-surface modes.     

Placement Effect on the Stability of Tetrapod Armor Unit on Breakwaters in Irregular Waves

Tetrapod, one of the well-known artificial concrete units, is frequently used as an armor unit on breakwaters. Two layers of tetrapod units are normmaly placed on the breakwaters with different placement methods. In this study, the stability of tetrapod units with two different regularly placement methods are investigated experimentally in irregular waves. Stability coefficients of tetrapod units for both placement methods are obtained. The important characteristic wave parameters of irregular waves causing the same damage ratio as those of the regular waves are also determined. It reveals that the average of one-tenth highest wave heights within the wave train (H_1/10) causes the similar damage as regular waves.     

南海灾害性波浪基本特征研究

本文基于1991-2016年全球卫星高度计融合数据对南海灾害性波浪基本特征进行了分析,根据灾害性波浪诱发天气类型不同,将其分为"台风浪"和"非台风浪"。依此主线,对两类波浪在南海不同海域的特征进行了研究,并提出了用于定量研究两类波浪强度关系的台风浪权重系数（W）,得到了两类波浪在南海相对强弱关系的分布规律,量化研究了南海灾害性波浪的特征。本文以卫星高度计波高数据为样本进行了极值分析,得到了南海重现期波浪要素整体分布规律,研究发现W值大小与广义极值曲线类型显著相关。