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.     

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.     

Laboratory study of wave and turbulence velocities in a broad-banded irregular wave surf zone

The characteristics of wave and turbulence velocities created by a broad-banded irregular wave train breaking on a 1:35 slope were studied in a laboratory wave flume. Water particle velocities were measured simultaneously with wave elevations at three cross-shore locations inside the surf zone. The measured data were separated into low-frequency and high-frequency time series using a Fourier filter. The measured velocities were further separated into organized wave-induced velocities and turbulent velocity fluctuations by ensemble averaging. The broad-banded irregular waves created a wide surf zone that was dominated by spilling type breakers. A wave-by-wave analysis was carried out to obtain the probability distributions of individual wave heights, wave periods, peak wave velocities, and wave-averaged turbulent kinetic energies and Reynolds stresses. The results showed that there was a consistent increase in the kurtosis of the vertical velocity distribution from the surface to the bottom. The abnormally large downward velocities were produced by plunging breakers that occurred from time to time. It was found that the mean of the highest one-third wave-averaged turbulent kinetic energy values in the irregular waves was about the same as the time-averaged turbulent kinetic energy in a regular wave with similar deep-water wave height to wavelength ratio. It was also found that the correlation coefficient of the Reynolds stress varied strongly with turbulence intensity. Good correlation between u′ and w′ was obtained when the turbulence intensity was high; the correlation coefficient was about 0.3–0.5. The Reynolds stress correlation coefficient decreased over a wave cycle, and with distance from the water surface. Under the irregular breaking waves, turbulent kinetic energy was transported downward and landward by turbulent velocity fluctuations and wave velocities, and upward and seaward by the undertow. The undertow in the irregular waves was similar in vertical structure but lower in magnitude than in regular waves, and the horizontal velocity profiles under the low-frequency waves were approximately uniform.     

Random wave runup and overtopping a steep sea wall: Shallow-water and Boussinesq modelling with generalised breaking and wall impact algorithms validated against laboratory and field measurements

A semi-implicit shallow-water and Boussinesq model has been developed to account for random wave breaking, impact and overtopping of steep sea walls including recurves. At a given time breaking is said to occur if the wave height to water depth ratio for each individual wave exceeds a critical value of 0.6 and the Boussinesq terms are simply switched off. The example is presented of waves breaking over an offshore reef and then ceasing to break as they propagate inshore into deeper water and finally break as they run up a slope. This is not possible with the conventional criterion of a single onset of breaking based on rate of change of surface elevation which was also found to be less effective generally. The runup distribution on the slope inshore of the reef was well predicted. The model is tested against field data for overtopping available for Anchorsholme, Blackpool and corresponding 1:15 scale wave flume tests. Reflection of breaking waves impacting a steep sea wall is represented as a partial reversal of momentum flux with an empirically defined coefficient. Offshore to nearshore significant wave height variation was reasonably predicted although nearshore model spectra showed distinct differences from the experiments. The breaking wave shape described by a shape parameter was also not well represented as might be expected for such a simple model. Overtopping agreement between model, field and flume was generally good although repeatability of two nominally identical flume experiments was only within 25%. Different distributions of random phase between spectral components can cause overall overtopping rates to differ by up to a factor of two. Predictions of mean discharge by EurOtop methods were within a factor of two of experimental measurements.     

楔形体在波浪中自由入水的数值模拟

物体入水时波浪的影响不可忽略,基于流体力学模型采用VOF法,并利用自定义函数,模拟了楔形体的自由入水过程;同时结合推波板原理及海绵层消波理论实现了数值水槽的造消波,完成了波浪中楔形体自由入水的模拟,计算了楔形体入水时所受的水作用力、自由液面变化及物面压强分布等,研究了不同波高、周期以及在波浪不同位置入水时对楔形体的影响。结果表明:本文建立的数值模型可很好地模拟楔形体入水造成的射流及空泡的形成发展过程,波浪对楔形体入水的影响主要由波浪内部流场变化及表面波形决定,在波浪不同位置处入水对楔形体受力及入水形态均有较大影响。     

Fine structure of the turbulent atmospheric boundary layer over the water surface

In this paper, the results of a laboratory experiment on investigating the wind-velocity field over a water surface using the PIV method are described. The use of a rapid CCD-camera made it possible to perform a detailed study of the eddy structure of airflow. We have measured the velocity fields over a flat plate by wind waves and waves induced by a wave generator. The model of a turbulent boundary layer over a rough surface was directly verified. It has been shown that the wind-velocity profiles over waves obtained by averaging the instantaneous fields over the ensemble of samples and horizontal coordinate are satisfactorily consistent with the profiles calculated within the frameworks of the model of wind flow over rough water surface.     

The circulation of the western Mediterranean Sea in spring 2005 as inferred from observations and from model outputs

In situ observations and numerical model simulations have been used to study the circulation of the western Mediterranean Sea during April–May 2005. A hydrological survey and direct current measurements carried out in the western Mediterranean Sea are analyzed with an inverse box model. The model result is a mean circulation of the region during spring 2005 along with simultaneous evaluation of water fluxes through eight transects and associated uncertainties. In order to evaluate the consistency of the results and the weight of currents at shorter temporal and spatial scales, an inter-comparison of differently achieved results is performed. The inverse solution is evaluated against both instantaneous current measurements and simulated velocity fields from a General Circulation Model. The results obtained and the general agreement between the three approaches are encouraging and confirms that the inverse box model is a powerful instrument to investigate flow fields in wide areas of the sea. The picture coming out confirms the previous qualitative knowledge on the mean circulation at all levels, providing, in addition, robust quantitative estimations of the water masses fluxes throughout the western Mediterranean basin.     

Surf zone dynamics simulated by a Boussinesq type model. Part I. Model description and cross-shore motion of regular waves

This is the first of three papers on the modelling of various types of surf zone phenomena. In this first paper, part I, the model is presented and its basic features are studied for the case of regular waves. The model is based on two-dimensional equations of the Boussinesq type and it features improved linear dispersion characteristics, possibility of wave breaking, and a moving boundary at the shoreline. The moving shoreline is treated numerically by replacing the solid beach by a permeable beach characterized by an extremely small porosity. Run-up of nonbreaking waves is verified against the analytical solution for nonlinear shallow water waves. The inclusion of wave breaking is based on the surface roller concept for spilling breakers using a geometrical determination of the instantaneous roller thickness at each point and modelling the effect of wave breaking by an additional convective momentum term. This is a function of the local wave celerity, which is determined interactively. The model is applied to cross-shore motions of regular waves including various types of breaking on plane sloping beaches and over submerged bars. Model results comprise time series of surface elevations and the spatial variation of phase-averaged quantities such as the wave height, the crest and trough elevations, the mean water level, and the depth-averaged undertow. Comparisons with physical experiments are presented. The phaseaveraged balance of the individual terms in the momentum and energy equation is determined by time-integration and quantities such as the cross-sectional roller area, the radiation stress, the energy flux and the energy dissipation are studied and discussed with reference to conventional phase-averaged wave models. The companion papers present cross-shore motions of breaking irregular waves, swash oscillations and surf beats (part II) and nearshore circulations induced by breaking of unidirectional and multidirectional waves (part III).     

Turbulence and energy dissipations of surf-zone spilling breakers

A laboratory study on the turbulence and wave energy dissipations of spilling breakers in a surf zone is presented. Instantaneous velocity fields of propagating breaking waves on a 1/20 slope were measured using Particle Image Velocimetry (PIV). Due to the large region of the evolving wave breaking generated turbulent flow, seven PIV fields of view (FOVs) were mosaicked to form a continuous flow field in the surf zone. Mean and turbulence quantities were extracted by ensemble averaging 25 repeated instantaneous measurements at each FOV. New results for distribution and evolution of turbulent kinetic energy, mean flow energy, and total energy across the surf zone were obtained from analyzing the data. The turbulence dissipation rate was estimated based on several different approaches. It was found that the vertical distribution of the turbulence dissipation rate decays exponentially from the crest level to the bottom. The resulting energy budget and energy flux were also calculated. The calculated total energy dissipation rate was compared to that based on a bore approximation. It was found that the ratio of turbulence dissipation rate to total energy dissipation rate was about 0.01 in the outer surf zone and increased to about 0.1 after the breaking waves transformed into developed turbulent bores in the inner surf zone.     

Static wave setup with emphasis on damping effects by vegetation and bottom friction

Wave setup can contribute significantly to elevated water levels during severe storms. In Florida we have found that wave setup can be 30% to 60% of the total 100-year storm surge. In areas with relatively narrow continental shelves, such as many locations along the Pacific Coast of the United States, wave setup can be an even larger proportionate contributor of anomalous water levels during major storms. Wave setup can be considered as comprising two components, with the first being the well-known static wave setup resulting from the transfer of breaking wave momentum to the water column. The second, oscillating component, is a result of nonlinear transfer of energy and momentum from the primary (linear) spectrum to waves with length and time scales on the order of the wave groups.Static wave setup is the focus of this paper with emphasis on effects due to internal or surface forces that act on the wave system and cause both dissipation of wave energy and transfer of momentum. In particular, the effects of wave damping by vegetation and bottom friction are considered. Linear wave theory is applied to illustrate these effects and, for shallow water waves, the setup is reduced by two-thirds the amount that would occur if the same amount of energy dissipation occurred in the absence of forces. Effects of nonlinear waves are then considered and it is found, for a shallow water wave of approximately one-half breaking height, that a wave setdown rather than setup occurs due to damping by vegetation and bottom friction.The problem of wave setup as waves propagate through vegetation was stimulated by studies to establish hazard zones associated with 100-year storm events along the shorelines of the United States. These storms can generate elevated water levels exceeding 4 to 6 m and can result in overland wave propagation. As these waves propagate through vegetation and damp, the question arose as to the contribution of this process to elevated mean water levels through additional wave setup.     

Modeling wave�Ccurrent bottom boundary layers beneath shoaling and breaking waves

The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth. In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and morphology evolution.     

T型防波堤与波浪相互作用数值研究

针对T型透空式防波堤,通过浪高仪采集防波堤前后不同位置波面变化曲线,使用声学多普勒流速仪(NDV)测量不同位置流速随时间的变化,并分析了其相位平均流速的分布。基于VOF法的二维波浪数值水槽,对规则波作用下T型防波堤附近的动力特性进行了计算,水槽模型试验结果和数值模拟结果对比表明,数值计算结果与实验值吻合较好。采用该模型进一步对T型防波堤附近波浪场、流线、紊动动能、紊动动能耗散率变化以及不同尺寸的防波堤消浪效果进行模拟计算,重点分析了入射波高、防波堤入水深度和防波堤宽度变化的影响。     

Solitary wave propagation influenced by submerged breakwater

The form of Boussinesq equation derived by Nwogu （1993） using velocity at an arbitrary distance and surface elevation as variables is used to simulate wave surface elevation changes. In the numerical experiment, water depth was divided into five layers with six layer interfaces to simulate velocity at each layer interface. Besides, a physical experiment was carried out to validate numerical model and study solitary wave propagation.“Water column collapsing”method （WCCM） was used to generate solitary wave. A series of wave gauges around an impervious breakwater were set-up in the flume to measure the solitary wave shoaling, run-up, and breaking processes. The results show that the measured data and simulated data are in good agreement. Moreover, simulated and measured surface elevations were analyzed by the wavelet transform method. It shows that different wave frequencies stratified in the wavelet amplitude spectrum. Finally, horizontal and vertical velocities of each layer interface were analyzed in the process of solitary wave propagation through submerged breakwater.     

规则波在浅水中运动及破碎的数值计算

利用一维Boussinesq方程描述了在浅水中的波浪运动以及破碎情况。在方程中引入了表面翻滚的概念，认为翻滚的水体是以波速运动的，翻滚的作用表现在水平速度的垂直分布上，产生了附加迁移动量项。通过对Airy波在浅水中运动以及破碎情况的研究，得出的一些结论与Schaeffer和合田的成果吻合良好。     

Study on Energy Spectrum Instability in the Processes of Propagating and Breaking of Focusing Waves

Based on phase focusing theory, focusing waves with different spectral types and breaking severities were generated in a wave flume. The time series of surface elevation fluctuation along the flume were obtained by utilizing 22 wave probes mounted along the mid-stream of the flume. Based on the wave spectrum obtained using fast Fourier transform(FFT), the instability characteristics of the energy spectrum were reported in this paper. By analyzing the variation of total spectral energy, the total spectral energy after wave breaking was found to clearly decrease, and the loss value and ratio gradually increased and tended to stabilize with the enhancement of breaking severity for different spectral types. When wave breaking occurred, the energy loss was primarily in a high-frequency range of f/fp1.0, and energy gain was primarily in a low-frequency range of f/fp1.0. As the breaking severity increased, the energy gain-loss ratio decreased gradually, which demonstrates that the energy was mostly dissipated. For plunging waves, the energy gain-loss ratio reached 24% for the constant wave steepness(CWS) spectrum, and was slightly larger at approximately 30% for the constant wave amplitude(CWA) spectrum, and was the largest at approximately 42% for the Pierson-Moskowitz(PM) spectrum.     

基于破碎临界区的新型拍岸浪统计计算模型研究

When waves propagate from deep water to shallow water, wave heights and steepness increase and then waves roll back and break. This phenomenon is called surf. Currently, the present statistical calcula...     

Modelling of waves and currents around submerged breakwaters

Recent experimental data collected during the DELOS project are used to validate two approaches for simulating waves and currents in the vicinity of submerged breakwaters.The first approach is a phase-averaged method in which a wave model is used to simulate wave transformation and calculate radiation stresses, while a flow model (2-dimensional depth averaged or quasi-3D) is used to calculate the resulting wave driven currents. The second approach is a phase resolving method in which a high order 2DH-Boussinesq-type model is used to calculate the waves and flow.The models predict wave heights that are comparable to measurements if the wave breaking sub-model is properly tuned for dissipation over the submerged breakwater. It is shown that the simulated flow pattern using both approaches is qualitatively similar to that observed in the experiments. Furthermore, the phase-resolving model shows good agreement between measured and simulated instantaneous surface elevations in wave flume tests.     

Propagation of solitary waves over a submerged permeable breakwater

We study the interactions between a non-breaking solitary wave and a submerged permeable breakwater experimentally and numerically. The particle image velocimetry (PIV) technique is employed to measure instantaneous free surface displacements and velocity fields in the vicinity of a porous dike. The porous medium, consisting of uniform glass spheres, is mounted on the seafloor. Due to the limited size of each field of view (FOV) for high spatial resolution purposes, four FOVs are set in order to form a continuous flow field around the structure. Quantitative mean properties are obtained by ensemble averaging 30 repeated instantaneous measurements. The Reynolds decomposition method is then adopted to separate the velocity fluctuations for each trial to estimate the turbulent kinetic energy. In addition, a highly accurate two-dimensional model with the volume of fluid interface tracking technique is used to simulate an idealized volume-averaged porous medium. The model is based on the Volume-Averaged Reynolds Averaged Navier–Stokes equations coupled with the non-linear k–ε turbulence closure solver. Comparisons are performed between measurements and numerical results for the time histories of the free surface elevation recorded by wave gauges and the spatial distributions of free surface displacement with the corresponding velocity and turbulent kinetic energy around the permeable object imaged by the PIV system. Fairly good agreements are obtained. It is found that the measured and modeled turbulent intensities on the weather side are much larger than those on the lee side of the object, and that the magnitude of the turbulent intensity increases with increasing wave height of a solitary wave at a constant water depth. The verified numerical model is then used to estimate the energy reflection, transmission and dissipation using the energy integral method by varying the aspect ratio and the grain size of the permeable obstacle.