Kinematics of overturning solitary waves and their relations to breaker types

Numerical simulations using a full-nonlinear BIM (Boundary Integral Method) potential-theory wave model are carried out to study the internal velocity and acceleration fields of an solitary wave overturning on a reef with vertical face (submerged breakwater) and their relation to breaker type. The simulations make it clear that the jet size normalized by the incident wave height is uniquely governed by the crown height of the reef, while the jet shape is similar and independent of the size. Further, they reveal that the overall internal kinematics of overturning waves is clearly related to the jet size. As the jet size increases and the breaker type changes from spilling to plunging, the kinematics thus become increasingly different from those of steady waves. Water particles with the greatest velocities or accelerations within the wave converge towards the jet. After the breaking, both of the velocities and accelerations almost simultaneously reach extreme values near locations beneath the jet. Some of the extreme values are closely related to the breaker type and can be uniquely determined by substituting the breaker type index into the regression equations suggested here.     

直立堤浮托力的概率特征

本文基于1987和1988年夏季在古镇口港同步连续观测的波浪、波压力和浮托力资料,分析研究了浮托力的概率特征、浮托力沿堤底面的变化及其谱特征。结果表明,浮托力幅度和周期的累积分布实际上不随测点在堤底面上的位置变化,可用公式表示。浮托力沿堤底面宽度近似呈线性衰减,前趾浮托力最大,后趾不为零,呈梯形状。文中还给出了计算最大峰、谷总浮托力的方法。     

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.     

Numerical predictions of water–air wave slam using incompressible–compressible smoothed particle hydrodynamics

The high-speed impact between a body and water is an important practical problem, whether due to wave impact on a structural deck or wall, or due to a moving body such as a ship or aircraft hitting water. The very high pressures exerted are difficult to predict and the role of air may be significant. In this paper, numerical simulations are undertaken to investigate the impact of a rigid horizontal plate onto a wave crest and, in the limit, onto a flat water surface. A two-phase incompressible–compressible smoothed particle hydrodynamics (SPH) method for water and air, respectively, is applied where the water phase imposes kinematics on the air phase at the air–water interface and the air phase imposes pressures on the water at the interface. Results are compared with experimental measurements undertaken using a drop rig positioned over a wave flume so that a horizontal plate impacts the water surface in free flight. Numerical predictions of impact pressure are quite accurate; air is shown to have a significant cushioning effect for impact on to flat water and this reduces for waves as the ratio of wave height to wavelength increases.     

破碎波冲击直立桩柱的大比尺试验研究

波浪破碎是海洋中最常见的现象之一,其能够对海洋中的结构物产生巨大的波浪力作用。本文在大比尺波浪水槽通过聚焦波的方法生成了极端波浪和不同破碎阶段的破碎波浪,并对其冲击桩柱过程中的点压力进行了测量,进而采用连续小波变换的方法,对桩柱上点压力的分布及大小进行了细致分析。结果表明,多次重复试验下,相比非破碎极端波浪,破碎极端波浪产生的点压力离散性更强;波浪破碎程度越大,测点位置越靠近波峰,则点压力离散程度越大;破碎波的最大点压力出现在1.2倍的最大波面附近,且其大小可达3倍的最大静水压力;基于点压力小波谱,不同破碎阶段破碎波产生冲击作用不同,对于波浪作用桩柱前波浪已经发生破碎的情况,其冲击区域更大,点压力分布更复杂;而对于桩面破碎的情况,其造成的波浪总力更大。     

Scaling wave impact pressures on vertical walls

It is widely recognized that the use of Froude similarity for scaling up wave impact pressures recorded during physical model tests may lead to over-estimation of impact maxima. Based on reviewing historical work dating back to the 30s and further developments in the 60s and 80s, a general method is presented that is suitable for scaling up impact pressures and rise times measured during small scale physical model tests. The method accounts for the effect of air leakage and is applicable to most wave impact loads. The model is applied to scale wave impact pressures on vertical walls and similar structures, and consistent correction factors for the Froude scaling law are derived.     

大亚湾大鹏澳菱角石沿岸泥沙动态

本文根据大亚湾大鹏澳菱角石沿岸的波浪、潮流和泥沙资料,探讨了菱角石沿岸泥沙来源、泥沙活动水深和破波带,估算了破波带沿岸输沙率和非破波带底沙单宽输沙率,说明了沿岸泥沙运移以破波带沿岸输沙为主,验证了赵子丹提出的估算沿岸输沙率的关系曲线的可靠性。     

Dynamic analysis of a vertical plate exposed to breaking wave impact

From the experimental studies in recent years, it has become known that when a wave breaks directly on a vertical faced coastal structure, high magnitude impact pressures are produced. The theoretical and experimental studies show that the dynamic response of such structures under wave impact loading is closely dependent on the magnitude and duration of the load history. The dynamic analysis and design of a coastal structure can be succeeded provided the design load history for the wave impact is available. Since these types of data are very scarce, it is much more convenient to follow a method which is based on static analysis for the dynamic design procedure. Therefore, to facilitate the dynamic design of a vertical plate that is exposed to breaking wave impact, a multiplication factor called “dynamic magnification factor” is herein presented which is defined as the ratio of the maximum value of the dynamic response to that found by static analysis. The computational results of the present study show that the dynamic magnification factor is a useful ratio to transfer the results of static analysis to the dynamic design of a coastal plate for the maximum impact pressure conditions of p_max/γH₀≤18.     

An experimental investigation of a vertical wall response to breaking wave impact

Laboratory experiments are conducted to measure the impact pressures and resulting deflections from breaking oscillatory waves on a vertical wall with 1/10 foreshore slope. The maximum impact pressure data on the wall are statistically analysed and the relationships between the magnitudes of impact pressures and forces, and their durations, are investigated. The maximum impact pressures, among the 90 wave impacts, are found to vary between 1.37 × 10⁴and 28.3 × 10⁴Pa. The maximum impact pressures are shown to reasonably satisfy the log-normal probability distribution and they occur most frequently slightly below the still-water level. The greatest wall deflection at the point of measurement is caused by an impact which has a maximum pressure of 3.6 × 10⁴Pa, corresponding to 50% probability in the log-normal distribution. It is found that the longer-lasting low impact forces are more effective in producing the larger wall deflections. In this respect, the maximum impact pressures in the range between 2.5 × 10⁴and 5 × 10⁴Pa obtained in this study are found to be the most effective. The upper limit of this range (when non-dimensionalised by the specific weight of water and deep-water wave steepness) is suggested as a design value for vertical walls.     

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.     

Extreme wave run-up and pressure on a vertical seawall

The performance of coastal vertical seawalls in extreme weather events is studied numerically, aiming to provide guidance in designing and reassessing coastal structures with vertical wall. The extreme wave run-up and the pressure on the vertical seawall are investigated extensively. A time-domain higher-order boundary element method (HOBEM) is coupled with a mixed Eulerian-Lagrangian technique as a time marching technique. Focused wave groups are generated by a piston wave-maker in the numerical wave tank using a wave focusing technique for accurately reproducing extreme sea states. An acceleration-potential scheme is used to calculate the transient wave loads. Comparisons with experimental data show that the extended numerical model is able to accurately predict extreme wave run-ups and pressures on a vertical seawall. The effects of the wave spectrum bandwidth, the wall position and the wave nonlinearity on the wave run-up and the maximum wave load on the vertical seawall are investigated by doing parametric studies.     

Wave induced forces around buried pipelines

This work refers to an experimental investigation carried out to analyze wave induced pressures on a pipeline buried in a permeable seabed. In this investigation, the model tests were performed on a pipeline buried in the soil test bed. The wave flume used was 30 m long, 2 m wide and 1.7 m deep, 96 number of tests were conducted with waves generated for different wave heights. A pipeline 200 mm in diameter was buried in the sandy bed at different burial depth ratios. The pipeline was laid perpendicular to the wave direction, pressure was measured with 12 transducers along the outer circumference of the pipeline. The results show that wave induced pressures are significantly controlled by the wave period analyzed in terms of the scattering parameter (ka). Higher pressures were recorded at the top and the lower pressures were recorded at the bottom.     

Impact pressure of breaking waves on vertical and sloping walls

Laboratory tests are conducted to measure the impact pressures of breaking waves on vertical, 5° forward, and 5, 10, 20, 30, and 45° backward sloping walls. The base structure of the wall has a foreshore slope of . Regular waves are used throughout the experiments for all wall angles. The maximum impact pressures on the wall are shown to satisfy the log-normal probability distribution. It is found from the present experiments that the impact pressures and resulting forces on sloping walls can be greater than those on a vertical wall. On the seven different walls tested, the maximum impact pressures occur most frequently slightly below the still-water level. The pattern of the impact pressure history does not change with the slope of the wall, and as the probability of maximum impact pressure decreases, the pressures around the peak pressure region of the impact pressure histories remain longer.     

Impulse modelling of wave impact pressures on vertical wall

Breaking waves on coastal structures cause high magnitude impact pressures which may be important for the structural stability. In estimating the impact pressure distribution on the wall, there have been a lot of theoretical and experimental work. The present study is concerned with a theoretical approach which is based on the pressure impulse, to find the impact pressures on vertical wall. The numerical solution of the governing equation is carried out using the boundary element method. The theoretical impact pressures are determined using the experimental values of impact pressure rising time. The computational results of the impact pressures from the pressure impulse model are found to agree well with the experimental data of an earlier study.     

Violent breaking wave impacts. Part 1: Results from large-scale regular wave tests on vertical and sloping walls

As part of an investigation into the detailed characteristics of wave impacts, experimental data are presented for the impact pressures and forces generated by waves up to 1.7 m high breaking onto a vertical wall and a wall inclined at 27° to the vertical. Particular attention is given to the influence of entrained and entrapped air and, by selecting regular wave conditions that produce impacts, trends are identified for highly variable phenomena that could easily be missed when masked by the even greater variability associated with irregular waves.     

Wave impacts on structures with rectangular geometries: Part 2 decks,baffles and seawalls with impermeable or porous surfaces

This paper considers wave impacts on baffles, on baffles or decks adjacent to a vertical wall, and on porous seawalls and/or sea beds. For seawalls and vertical baffles, impacts can occur in steep waves, whilst a deck can be struck from below by a rising wave crest either in open sea or in a tank with standing waves (sloshing). A simple analytical model for the pressure impulse, P, due to a wave of idealized geometry and dynamics is developed and applied to the following geometries with impermeable surfaces:

• •horizontal wave impact onto a vertical wall with a deck at the waterline,
• •vertical wave impact under a deck in the same configuration (equivalent to vertical water impact of a horizontal plate),
• •horizontal wave impact onto a surface-piercing vertical baffle in open sea,
• •as for 3. but with the baffle in front of a wall,
• •as for 4. but with a deck extending from the vertical wall to the baffle,
• •bottom-mounted baffle in front of a wall with impact occurring on the wall.

We also consider cases that complement part 1 of this paper to include the effect on impacts on a seawall with a porous sea bed and/or sea wall with/without a berm. Finally we reconsider case 3) above but with a porous baffle.The method uses eigenfunction expansions in each of the rectangular regions that satisfy some of the impermeable or porous surface conditions, and a simplified free-surface condition. Their unknown coefficients are determined from the impact boundary condition, impermeable or porous boundary conditions and by matching the solutions, in any two neighbouring rectangles, along their common boundary. Although the fluid motion is treated rather crudely, the method yields the pressure impulse throughout the entire region. Impulses, I, and moment impulses, M, on all or parts of the structure are also presented.     

Experiments on full-scale wave impact pressures

Measurements of full-scale wave impact pressures on seawalls have been made over a period of four years, up to and including the winter of 1980/1981, on seawalls in the South and West of England. This investigation is the first of its kind to be carried out in the U.K. using modern measuring and recording techniques and has produced significantly more wave impact pressure data than all previous full-scale investigations.Poor correlation was found between the semi-empirical equations at present used to estimate wave impact pressures and the prototype data obtained during this investigation. A rational expression for the estimation of wave impact pressures on coastal structures has thus been derived based on the local wave parameters at impact and includes a coefficient related to the percentage of air entrained in the incident wave.     

Prediction of geometrical properties of perfect breaking waves on composite breakwaters

Breaking wave loads on coastal structures depend primarily on the type of wave breaking at the instant of impact. When a wave breaks on a vertical wall with an almost vertical front face called the “perfect breaking”, the greatest impact forces are produced. The correct prediction of impact forces from perfect breaking of waves on seawalls and breakwaters is closely dependent on the accurate determination of their configurations at breaking. The present study is concerned with the determination of the geometrical properties of perfect breaking waves on composite-type breakwaters by employing artificial neural networks. Using a set of laboratory data, the breaker crest height, h_b, breaker height, H_b, and water depth in front of the wall, d_w, from perfect breaking of waves on composite breakwaters are predicted using the artificial neural network technique and the results are compared with those obtained from linear and multi-linear regression models. The comparisons of the predicted results from the present models with measured data show that the h_b, H_b and d_w values, which represent the geometry of waves breaking directly on composite breakwaters, can be predicted more accurately by artificial neural networks compared to linear and multi-linear regressions.     

An experimental investigation of plunging breaker boundary layers in the transformation zone

Experimental investigation is made on the boundary layers of the transformation zone (i.e. the region between the last symmetrical wave profile depth and the breaking point) of plunging breakers propagating on a smooth beach with 1/12 uniform slope. Using a laser anemometer, the particle velocities are measured at four verticals along the transformation zone for three different steepnesses of waves within the plunging breaker range. The boundary layer flow in the transformation zone is found mostly of turbulent character and vertical distribution of particle velocities does not seem to conform to the classical law of the wall distribution given for steady-flow boundary layers. The results show that free-stream particle velocities, in the boundary layer of the breaker under the crest phase, increase considerably as the wave progresses towards the breaking point. The boundary layer thickness, defined as the velocity-affected region, remains constant throughout the transformation zone but it decreases with increasing deep-water wave steepness for the particular beach slope tested.