Standing wave pressures due to regular and random waves on a vertical wall

The standing wave pressures due to laboratory-generated regular and random waves exerted on a vertical wall were measured in a wave flume. The standing wave pressures were measured at four relative depths of submergence on the test model. The regular wave test conditions ranged from intermediate to deep water conditions. The measured pressures due to regular waves were compared with results obtained using linear theory and third-order solution. In the case of random wave tests, the dynamic pressures due to the time histories of water surface elevation following the spectral characteristics of Pierson-Moskowitz and Bretschneider spectra were measured. These pressures are compared with simulated pressures obtained through the linear filter technique of Reid. The variation of pressure spectra along the depth are presented. In addition, comparison of spectral parameters, i.e. zeroth moment, spectral width parameter and narrowness parameter of measured and simulated pressure spectra, are reported and discussed. The behaviour of the coherence function between the wave elevation on the wall and the corresponding pressures is also discussed.     

Wave pressures on a vertical wall due to short-crested waves: fifth-order approximation

Non-linear wave pressure induced by short-crested waves on a vertical wall is an important factor to be considered in the design of coastal structures. The existing models to estimate the wave pressure in engineering design are limited to the third-order solution ([Hsu et al., 1979]). In this paper, an analytical solution up to the fifth-order is derived through perturbation approximation. This analytical closed-form solution is used to investigate the contributions of the higher-order components in short-crested waves. It is found that fifth-order components significantly affect the change of pressure, especially in shallow water and larger waves.     

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。     

Scour below pipelines and around vertical piles due to second-order random waves plus a current

This paper provides a method by which the scour depth below pipelines and around single vertical piles for combined random waves plus current including effects of second-order wave asymmetry can be derived. Here the empirical formulas proposed by Sumer and Fredsøe [1996. Scour below pipelines in combined waves and current. In: Proceedings of the 15th OMAE Conference, Florence, Italy. Vol. 5, ASME, New York, pp. 595–602] for pipelines, and by Sumer and Fredsøe [2002. The mechanics of scour in the marine environment. World Scientific, Singapore] for vertical piles are used together with Stokes second-order wave theory by assuming the basic harmonic wave motion to be a stationary Gaussian narrow-band random process. Comparisons are made with the Sumer and Fredsøe [1996. Scour below pipelines in combined waves and current. In: Proceedings of the 15th OMAE Conference, Florence, Italy. Vol. 5, ASME, New York, pp. 595–602; 2001. Scour around pile in combined waves and current. Journal of Hydraulic Engineering, 127(5), 403–411] data for linear random waves plus current. An example of calculation is also presented.     

Scour around vertical piles due to long-crested and short-crested nonlinear random waves plus a current

This paper provides a practical stochastic method by which the maximum equilibrium scour depth around a vertical pile exposed to long-crested (2D) and short-crested (3D) nonlinear random waves plus a current can be derived. The approach is based on assuming the waves to be a stationary narrow-band random process, adopting the Forristall (2000) wave crest height distribution representing both 2D and 3D nonlinear random waves, and using the empirical formulas for the scour depth by Sumer and Fredsøe (2002). Comparisons are made between the present approach and the Sumer and Fredsøe (2001) data for 2D random waves plus current. An example calculation is provided.     

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.     

An experimental investigation of hydrodynamic coefficients for a vertical truncated rectangular cylinder due to regular and random waves

The research into hydrodynamic loading on ocean structures has concentrated mostly on circular cross-section members and relatively limited work has been carried out on wave loading on other cross-sections such as rectangular sections. These find applications in many offshore structures as columns and pontoons in semi-submersibles and tension-leg platforms. The present investigation demonstrates the behaviour of rectangular cylinders subject to wave loading and also supplies the hydrodynamic coefficients for the design of these sections.This paper presents the results of wave forces acting on a surface piercing truncated rectangular cylinder set vertically in a towing tank. The experiments are carried out in a water depth of 2.2 m with regular and random waves for low Keulegan–Carpenter number up to 6. The rectangular cylinder is of 2 m length, 0.2 m breadth and 0.4 m width with a submergence depth of 1.45 m from still water level. Based on Morison equation, the relationship between inertia and drag coefficients are evaluated and are presented as a function of KC number for various values of frequency parameter β, for two aspect ratios of cylinders, equals to 1/2 and 2/1. Drag and inertia coefficients obtained through regular wave tests are used for the random wave analysis to compute the in-line force spectrum.The results of the experiments show the drag and inertia coefficients are strongly affected by the variation in the aspect ratios of the cylinder. The drag coefficients decreases and inertia coefficients increases with increase in Keulegan–Carpenter number up to the range of KC number tested. The random wave results show a good correlation between measured and computed force spectrums. The transverse forces in both regular and random waves are found to be small compared to in-line forces.     

不规则波远破波对直墙的作用

基于物模试验、理论推理、因次分析和工程实例验证等综合分析方法,就不规则波远破波对直墙作用力的计算方法进行了研究,用推荐的方法得到的结果与工程实例符合较好.     

Probability distribution of random wave forces in weakly nonlinear random waves

Based on the second-order random wave theory, the joint statistical distribution of the horizontal velocity and acceleration is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random wave forces are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. It is found that the distribution of wave forces depends solely on the frequency spectrum of sea waves associated with the first order approximation and the second order wave–wave interaction.     

Dynamic pressures and run-up on semicircular breakwaters due to random waves

The dynamic pressures due to random waves of predefined spectral characteristics exerted on a semicircular breakwater model at five different elevations along the depth are measured. In addition, the wave run-up on the model and its reflection characteristics are measured. The results on the variation of the frequency pressure spectra along the depth and the run-up spectra are reported in this paper. The average spectral characteristics as well as statistical properties of the above two parameters are presented. The average reflection coefficient is reported as a function of the wave steepness, described as the ratio of the significant wave height to the square of the peak period.     

The irregular broken wave forces on vertical wall

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Theoretical and experimental investigation of a vertical wall response to wave impact

The laboratory and field experiments so far have shown that when a wave breaks directly on a vertical faced coastal structure, the resulting impact pressures may become very severe in magnitude and short in duration. Some experimental evidence in the literature suggests that the structural response to the extremely high magnitude impact forces is only limited. This study is mainly concerned with the comparison of the theoretical and experimental results of a vertical wall response under the wave impact loading. In the dynamic analysis of the wall the classical elastic plate theory is used and the numerical results for the dynamic values of the transverse displacement are obtained by employing the method of finite elements. In the theoretical analyses the experimental pressure histories are used and the theoretical wall deflection histories are compared with the experimental results. The computational and experimental deflection histories exhibit similar patterns. The theoretical maximum wall deflections are mostly found to be slightly smaller than the experimental values.     

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.     

In-line response of vertical cylinders in regular and random waves

The in-line response of a vertical flexibly mounted cylinder in regular and random waves is reported.Both theoretical analyses and experimental measurements have been performed.The theoretical predictions are based on the Morison equation which is solved by the incremental harmonic balance method.Experiments are then performed in a wave flume to determine the accuracy of the Morison equation in predicting the in-line response of the cylinder in regular and random waves.The interaction between waves and vibrating cylinders are investigated.     

Scour below pipelines and around vertical piles in random waves

An approach by which the scour depth and scour width below a fixed pipeline and scour depth around a circular vertical pile in random waves can be derived is presented. Here, the scour depth formulas by Sumer and Fredsøe [ASCE J. Waterw., Port, Coastal Ocean Eng. 116 (1990) 307] for pipelines and Sumer et al. [ASCE J. Waterw., Port, Coastal Ocean Eng. 114 (1992) 599] for vertical piles as well as the scour width formula by Sumer and Fredsøe [The Mechanics of Scour in the Marine Environment, World Scientific, Singapore, 2002] for pipelines combined with describing the waves as a stationary Gaussian narrow-band random process are used to derive the cumulative distribution functions of the scour depths and width. Comparisons are made between the present approach and random wave scour data. Tentative approaches to related random wave scour cases are also suggested.     

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.     

Wave interaction with a submarine pipeline in clayey soil due to random waves

The wave pressure and uplift force due to random waves on a submarine pipeline (resting on bed, partially buried and fully buried) in clayey soil are measured. The influence of various parameters viz., wave period, wave height, water depth, burial depth and consistency index of the soil on wave pressures around and uplift force on the submarine pipeline was investigated. The wave pressures were measured at three locations around the submarine pipeline (each at 120° to the adjacent one). It is found that the wave pressure and uplift force spectrum at high consistency index of the soil is smaller compared to that of low consistency index. Just burying the pipeline (e/D=1.0) in clayey soil reduces the uplift force to less than 60% of the force experienced by a pipeline resting on the seabed (e/D=0.0) for I_c=0.33.     

Observations of freak waves in random wave field in 2D experimental wave flume

Long time series of wave field are experimentally simulated by JONSWAP spectra with random phases in a 2D wave flume. Statistic properties of wave surface, such as significant wave height, skewness and kurtosis, are analyzed, and the freak wave occurrence probability and its relations with Benjamin-Feir index （BFI） are also investigated. The results show that the skewness and the kurtosis are significantly dependent on the wave steepness, and the kurtosis increases along the flume when BFI is large. The freak waves are observed in random wave groups. They occur more frequently than expected, especially for the wave groups with large BFI.     

斜向不规则波对直墙作用的实验研究

通过长峰不规则波和方向波谱对直墙作用的实验研究 ,分别给出了每延米斜向不规则波波浪力与正向力之比 ,方向波谱波浪力与斜向长峰不规则波波浪力之间的关系 ,通过与规则波实验结果的比较给出了斜向规则波与不规则波波浪力之间的相对关系 ;并对斜向不规则波的反射系数与正向波时的变化作出了分析     

Revisiting the complete wave transmission and reflection due to an array of 2-D surface-piercing truncated vertical plates fixed in regular incident waves

When two 2-D vertical surface-piercing plates are fixed with a certain distance in incident regular waves, it is known that complete wave transmission and reflection could take place, at least in a linear wave theory, depending on the wave period of the incident waves. This paper revisits the same subject from the viewpoint of the hydrodynamic interaction between the two plates induced by the waves transmitted and reflected due to the plates, which is enabled by accounting for the hydrodynamic interactions between the two plates while decomposing the waves into component waves. In doing so, some new insight into the mechanism of the complete transmission and the complete reflection has been obtained.