An experimental investigation of the velocity field under cnoidal waves over the asymmetric rippled bed

1 IntroductionIn coastal areas a ubiquitous phenomenon is theformation of ripples in the seabed. It is now widelyaccepted that the flow and sediment transport overseabed are vital in relation to erosion, surface wavedissipation and pollution dispersion et…     

Burial and scour around short cylinder under progressive shoaling waves

The results of a laboratory experimental program aimed at better understanding the scour around and burial of heavy cylindrical objects under oscillating flow on a sandy bed are described. This study was motivated by its application to the dynamics of isolated cobbles/mines on a sandy floor under nonlinear progressive waves, such as that occur in shallow coastal waters beyond the wave-breaking region. In the experiments, nonlinear progressive waves were generated in a long wave tank of rectangular cross-section with a bottom slope. Model mines (short cylinders) were placed on the sandy bottom and the temporal evolution of the bed profile and the velocity field in the near field of the object were observed. Experiments were conducted at relatively high Reynolds numbers for a range of flow conditions, which can be characterized by the Keulegan–Carpenter number and Shields parameter. Depending on the values of these parameters, four different scour regimes around the cylinder including periodical burial of cylinder under migrating sand ripples were observed; they were classified as: (i) no scour/burial, (ii) initial scour, (iii) expanded scour, and (iv) periodic burial cases. A scour regime diagram was developed and the demarcation criteria between different regimes were deduced. Semi-empirical formulae that permit estimation of the scour depth with time, the equilibrium maximum scour depth and length, and conditions necessary for the burial of the cylinder as a function of main external parameters are also proposed.     

Characteristics of coastal erosion geometry under regular and irregular waves

An experimental investigation of coastal erosion generated by the action of regular and irregular waves was carried out in laboratory channels. Natural beach sand, with medium diameter of 0.35 mm and specific gravity of 2.63, was used in this study. A 1:5 initial beach slope was selected for the model tests. Different wave groups were generated over the initially flat beach, and the characteristics of coastal erosion geometry such as erosion lengths, erosion depths, location of maximum erosion point, and total erosion areas were measured. The most important parameters governing coastal erosion were evaluated by using earlier investigations and experimental results. These parameters were expressed as a dimensionless group by using π theory. The empirical relationships between the geometric characteristics of coastal erosion and the dimensionless group are proposed through regression analysis for pure regular waves, pure irregular waves, and regular-irregular waves. The parameters, which were used to define geometric characteristics of coastal erosion, were evaluated and some ratios of these parameters gave a constant value.     

不规则波作用下沿岸流流速分布规律分析

基于MIKE21 PMS,对1/10、1/20、1/40、1/100四种不同坡度地形下不规则波浪产生的沿岸流进行数值模拟。将模拟得到的流速随着离开静水岸线距离的变化曲线进行无量纲化处理,并选用高斯分布函数对流速曲线进行拟合,进而得到高斯分布函数中流速最大值与其出现位置以及流速分布宽度等参数随着入射波浪要素和地形坡度的变化关系。研究结果表明,文中给出的高斯分布函数适用于描述不规则波浪作用生成的沿岸流流速分布规律。     

Laboratory measurements of large-scale near-bed turbulent flow structures under spilling regular waves

The instantaneous turbulent velocity field created by the breaking of spilling regular waves on a plane slope was measured in a plane running parallel to the slope using particle image velocimetry. The measurement plane was located at a height of about 1 mm above the bed. The measurement area encompassed the region where the large eddies generated at incipient wave breaking impinged on the bottom inside the surf zone. A total of 30 trials were conducted under identical experimental conditions. In each trial, six consecutive wave cycles were recorded. The measured velocity fields were separated into a mean flow and a turbulence component by ensemble averaging. The instantaneous turbulent velocity fields were analyzed to determine the occurrence frequency, location, geometry and evolution of the large eddies, and their contributions to instantaneous shear stresses, turbulent kinetic energy and turbulence energy fluxes. The motion of single glass spheres along the bed was also investigated. The two-phase flow measurements showed that the velocity and displacement of large solid particles on a smooth bed were significantly affected by the magnitude and direction of turbulence velocities. Overall, this study has examined the kinematic and dynamic properties of large eddies impinging on the bed and the interaction of these large-scale turbulent flow structures with the mean flow. The study has also highlighted the important role of large eddies in sediment transport.     

Performance of solid and perforated U-type breakwaters under regular and irregular waves

An experimental investigation of U-type breakwaters was carried out in a laboratory channel. Both regular and irregular waves were used during testing. Two types of breakwaters such as solid and perforated were studied to analyse the porosity effect of structures. In order to investigate performance of these breakwaters for different immersion depths, four depths of immersions of the solid and perforated breakwaters were selected. Different wave groups were generated over these breakwaters, and the transmission, reflection and energy dissipation characteristics of each breakwater were determined. Three coefficients such as transmission, reflection and energy dissipation coefficients, which were named as C_t, C_r, and C_l, respectively, were used during the evaluation of the test results. The most important parameters governing performance of these breakwaters were determined by using earlier investigations and experimental results. These parameters were expressed as a dimensionless group by using π theory. Based on the test results, empirical expressions were formulated to describe the C_t, C_r, and C_l for different immersion depths of solid and perforated breakwaters under regular and irregular waves.     

Static stability of submerged partial revetment structures under regular and irregular waves

Physical models of submerged partial revetment structures were built on natural beach sand with a diameter of 0.35 mm and specific gravity of 2.63. The armor units, the diameter and specific gravity of which varied in the range of 8.5–67.95 mm and 1.81–2.77 respectively, were placed only on wave breaking areas. A series of experiments has been conducted on the conditions of different armor units and different wave characteristics using regular waves and irregular waves. Based on the experimental data, the effects of wave height, wave period, diameter and specific gravity of armor units, water depth in the channel, and wave types on static damage of given structures are assessed. Some empirical formulas have been suggested through regression analysis to describe static stability and stability number of submerged partial revetment structures under pure regular waves, pure irregular waves, and regular–irregular waves. The suggested formulas compared with Van der Meer’s (1988) formulas and some differences have occurred because of differences among revetment types and test conditions; therefore, proposed formulas give reasonable results for the test conditions used.     

Investigation of Π-type breakwaters performance under regular and irregular waves

In this paper, performance of solid and perforated Π-type breakwaters was investigated experimentally. Both regular and irregular waves were used during testing. Four depths of immersions were selected for each breakwater and wave type. Different wave groups were generated over these breakwaters, and the transmission, reflection and energy-dissipation characteristics were determined. The results of the experimental study were evaluated and some empirical expressions based on the results were suggested to define the transmission, reflection and energy-dissipation coefficients for different immersion depths of solid and perforated breakwaters under regular and irregular waves. Moreover, performance of solid and perforated Π-type breakwaters were compared with that of solid and perforated U-type breakwaters investigated by Günaydın and Kabdaşlı [2006. Performance of solid and perforated U-type breakwaters under regular and irregular waves. Ocean Engineering 31, 1377–1405]. These comparisons showed that the most reasonable model and wave type are selected to determine requiring performance parameters.     

含砂量变化影响海底沉积物压缩波速度的分析研究

本文通过对南海海底沉积物样品的声学物理参数和沉积粒度特征统计分析,发现了高、低含砂量沉积物的声学物理特征存在明显差异,建立了海底沉积物的含砂量与压缩波速度、孔隙度、含水量和密度等经验公式,分析了含砂量变化与沉积物的体积压缩模量和密度变化的关系,从声速理论基础上阐明了含砂量变化引起沉积物压缩波速度变化的内在原因是含砂量变化引起了体积压缩模量和密度发生了变化,说明了含砂量增大引起沉积物压缩波速度增大的内在原因是含砂量增大引起了体积压缩模量变化量大于密度变化量,从而在数据统计和理论分析结合基础上,论证了含砂量是影响海底沉积物压缩波速度的重要因素之一。这一研究对声学方法反演海底沉积物粒度参数和沉积物类型、地声参数转换模型的建立,以及对水声反演海底和海底资源勘探等方面都具有重要理论意义和应用价值。     

Experimental researches on reflective and transmitting performances of quarter circular breakwater under regular and irregular waves

A series of regular and irregular wave experiments are conducted to study the reflective and transmitting performances of quarter circular breakwater (QCB) in comparison with those of semi-circular breakwater (SCB). Based on regular wave tests, the reflection and transmission characteristics of QCB are analyzed and a few influencing factors are investigated. Then, the wave energy dissipation as wave passing over the breakwater is discussed based on the hydraulic coefficients of QCB and SCB. In irregular wave experiments, the reflection coefficients of QCB and their spectrums are studied. Finally, the comparisons between the experimental results and numerical simulations for QCB under regular and irregular wave conditions are presented.     

Experimental investigation on the dynamic response of a moored wave energy device under regular sea waves

This paper attempts to provide a better understanding of the hydrodynamic behaviour of a floating multi-resonant oscillating column wave energy device which combines the concept of a floating breakwater and a wave energy device. Experiments were conducted on a 1:20 scale model of the floating wave energy device moored by six mooring lines to study the dynamics of the device under regular waves for various scopes. The effect of non-dimensionalized wave frequency parameter on the motion response and mooring force are reported and discussed in detail in this paper.     

of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core

The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction method. Numerical results of the present model are compared with the experimental data of different researchers. Numerical examples are given to examine the effect of rock fill on the reflection coefficient. The differences between regular and irregular waves are also investigated by means of theoretical and experimental results. It is found that the minimum reflection coefficient of irregular waves is larger than that of corresponding regular waves, but the contrary is the case for the maximum reflection coefficient.     

Reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core

The reflection of regular and irregular waves from a partially perforated caisson breakwater with a rock-filled core is examined. The present mathematical model is developed by means of the matched eigenfunction method. Numerical results of the present model are compared with the experimental data of different researchers. Numerical examples are given to examine the effect of rock fill on the reflection coefficient. The differences between regular and irregular waves are also investigated by means of theoretical and experimental results. It is found that the minimum reflection coefficient of irregular waves is larger than that of corresponding regular waves, but the contrary is the case for the maximum reflection coefficient.     

Dynamics of a moored barge under regular and random waves

Developments in the study of wave forces and construction techniques in deep water by the offshore oil industry have increased the use of marine terminals at deep water locations. A thorough understanding of moored ship dynamics when subjected to waves, wind and current combined with the use of flexible mooring lines would help to design berthing terminals for exposed areas. In this paper, the three dimensional problem of wave interactions with a barge moored to a single point is dealt with, based on the finite element method. The effect of flexibility of the mooring line and the point of mooring on the response of the barge as well as the mooring line tension is investigated. The paper compares the numerical results with model tests carried out on a barge moored to a fixed support under regular and random waves in head sea. The effect of stiffness of the mooring line on the barge response for different mooring points is discussed, which would be useful for the designers. The effect of viscous damping is also considered. The analytical results are in good agreement with the experimental results in both regular and random waves.     

Laboratory study of the nonlinear transformation of irregular waves over a mild slope

This paper considers the nonlinear transformation of irregular waves propagating over a mild slope （1：40）. Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this purpose. The results indicate that the wave heights obey the Rayleigh distribution at the offshore location; however, in the shoaling region, the heights of the largest waves are underestimated by the theoretical distributions. In the surf zone, the wave heights can be approximated by the composite Weibull distribution. In addition, the nonlinear phase coupling within the irregular waves is investigated by the wavelet-based bicoherence. The bicoherence spectra reflect that the number of frequency modes participating in the phase coupling increases with the decreasing water depth, as does the degree of phase coupling. After the incipient breaking, even though the degree of phase coupling decreases, a great number of higher harmonic wave modes are also involved in nonlinear interactions. Moreover, the summed bicoherence indicates that the frequency mode related to the strongest local nonlinear interactions shifts to higher harmonics with the decreasing water depth.     

The reffection of regular and irregular waves by a partially perforated caisson breakwater on a step bed

This study examines the reffection of regular and irregular waves from a partially perforated caisson breakwater located on a step bed. The step bed is treated as an idealized rubble mound foundation. Based on the linear potential theory, an analytical solution is developed to calculate the reffection coefficient of the structure subjected to regular waves. The matched eigenfunction expansion method is used for the solution. The regular wave method is also extended to irregular waves using a linear transfer...     

The reflection of regular and irregular waves by a partially perforated caisson breakwater on a step bed

This study examines the reflection of regular and irregular waves from a partially perforated caisson breakwater located on a step bed. The step bed is treated as an idealized rubble mound foundation. Based on the linear potential theory, an analytical solution is developed to calculate the reflection coefficient of the structure subjected to regular waves. The matched eigenfunction expansion method is used for the solution. The regular wave method is also extended to irregular waves using a linear transfer function. The calculated results obtained for limiting cases are exactly the same as corresponding results given by the previous researchers. The present predictions also agree well with experimental data in the published literatures. Numerical experiments are conducted to examine the variations of the reflection coefficient versus its main effect factors, and some interesting results are presented.     

Forces and moment on a horizontal plate due to regular and irregular waves in the presence of current

This work presents an experimental study of a submerged plate used as a breakwater for coastal areas protection. Questions addressed concern the influence of current on the reflective power of the plate, and its influence on the hydrodynamic loads exerted on it. Results concern both monochromatic and irregular waves. Generally speaking, an influence of the current is found, changing the reflecting power of the structure up to 50%. A homogenized behavior of the loads and moments is found in the presence of currents, meaning that the load values become less sensitive to the frequency. Furthermore, the influence of waves reflected by the wave absorber, representing partially reflective conditions at the shore, is found to be of same order in the absence of current. In any case, the linear behavior of the breakwater is emphasized through the irregular waves approach.     

On energy transport and group velocity of water waves

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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.