Parameterisation and transformation of wave asymmetries over a low-crested breakwater

This paper presents the results of an investigation of the transformation of wave skewness and asymmetry as waves propagate obliquely over low-crested breakwaters, (LCBs), based on an analysis of measurements collected in the DELOS project. Considering the effect of the local Ursell number on wave asymmetries, a set of practical empirical formulae were established using least squares regression for both smooth and rubble mound LCBs. Predictions are in good agreement with measurements. Wave skewness on both sides of LCBs is linearly correlated for rubble mound LCBs but weakly correlated for smooth LCBs. While wave asymmetry on both sides of LCBs has a weakly quadratic correlation. The effect of the relative freeboard on the relationships of wave asymmetries between both sides is significant for rubble mound LCBs, but the same does not hold for smooth LCBs. With the presence of LCBs, wave skewness retains a positive sign on both sides but asymmetry changes from negative on the incident side to positive on the transmission side. Bispectral analysis shows that positive skewness and negative asymmetry arises from self–self and sum interactions but positive asymmetry is due to difference interactions between frequencies. The findings provide improved understanding of changes in wave skewness and asymmetry in the vicinity of structures, which may help mitigate scour and improve the stability of breakwaters.     

Quantification of changes in current intensities induced by wave overtopping around low-crested structures

The phenomenon of overtopping is traditionally studied for well-emerged harbour structures and often focuses on safety and stability. In this paper laboratory tests are presented and analysed to sharpen the hypothesis that overtopping is capable of changing the horizontal circulation pattern around low-crested structures. A unique data set from laboratory experiments was acquired in the wave basin at Delft University of Technology. The experiments were performed using an emerged impermeable low-crested structure (three freeboards and three different wave conditions for each freeboard) and yielded nine different combinations of set-up and overtopping driving forces. Using this information it was possible to quantify the changes in cross-shore and longshore velocity induced by the overtopping and the set-up changes under the different freeboard and wave conditions described. It is found that overtopping enhances the outgoing flows (longshore velocities parallel to the structure) away from the lee side of the structure and dampens the water level gradient driven flow towards the structure.     

Transmission of obliquely incident waves at low-crested breakwaters: Theoretical interpretations of experimental observations

The paper presents a series of analytical and numerical investigations of oblique wave transmission at low-crested breakwaters. For a smooth breakwater, two important features of wave height and direction are analyzed to establish the generic nature of the wave transmission process at oblique incidence. The proposed framework of research is validated against laboratory data from the EU-sponsored project, DELOS. The numerical simulations exhibit a significant decrease of the transmission coefficient with increasingly oblique incidence at a smooth breakwater. The roles of wave-breaking, nonlinearity, wave-induced currents and set-up in determining the characteristics of oblique wave transmission are demonstrated in the paper. It is found that both the amplitude-dependent phase velocity and the decrease of mean wave period contribute to the change of mean wave direction on the transmission side. An attempt has also been made to qualitatively explain the different behaviour of oblique wave transmission at a rubble-mound breakwater.     

Analytical approximate wave form for asymmetric waves

A simple analytical formulation that reproduces a skewed, nonlinear near-bed wave orbital velocity is presented. It contains four free parameters, where two are solely related to the velocity and acceleration skewnesses. The equation is compared with other models and is validated against field and laboratory experiments. The results reveal that it can simulate a wide range of nonlinear wave shapes, reproducing satisfactorily the measured nonlinear wave particle velocity. Also, the new expression overcomes some limitations of the other models. The new formulation is therefore capable of being used in many engineering applications that require the use of representative wave forms.     

Transmission of wave energy at permeable low crested structures

This paper presents a conceptual model for the prediction of energy transmission in presence of emergent permeable low crested structures. The transmitted wave is reconstructed from the superposition of perturbations generated leeward the structure by filtration and overtopped volumes. The model requires only structure geometry and incident wave conditions (wave height, period). A fair agreement is obtained by comparing the predicted transmission coefficients and wave spectra with measurements performed in wave flume and wave basin.     

Bispectrum and asymmetry of wave shape

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Effects of following and opposing vertical current shear on nonlinear wave interactions

A Navier-Stokes solver in OpenFOAM^® is combined with the Volume of Fluid (VOF) surface capturing method to investigate the wave interaction with depth-varying currents in intermediate and shallow waters. A special attention is paid to the separate effect of vertical current shear on near resonant triad wave interactions. It was found that in the presence of following vertical current shear, the wave exhibits a sharper crest and flatter trough, and the opposite is true in the presence of opposing vertical current shear. Our model results indicate that the wave steepness at which the current shear starts to affect the crest elevation is greater in deeper water than in shallower water. We found that adding vertical current shear to the uniform current further enhances the relative harmonic wave energy and the extent of triad interaction in the following current while weakens them in the opposing current. As a result, following and opposing current shear may cause wave to break at a lower and higher sea state respectively. Due to the increased wave nonlinearity in the presence of a following current shear, a linear superposition of the individual wave and current velocities is no longer adequate to represent the total horizontal velocity close to the free surface.     

A Boussinesq-type wave driver for a morphodynamical model to predict short-term morphology

The prediction of near-shore morphology on the time scale of a storm event and the length scale of a few surf zone widths is an active area of research. Intense wave breaking drives offshore-directed currents (undertow) carrying sediment seawards, resulting in offshore bar migration. In contrast, higher order nonlinear properties, such as wave asymmetry (velocity skewness) and velocity asymmetry, are drivers for shoreward transport. These wave processes are included in phase-resolving models such as Boussinesq-type wave models (e.g., TRITON). Short-wave averaging in the wave model yields wave-induced forces (e.g., radiation stress gradients) and a wave asymmetry term. The wave-induced forces are used in a hydrostatic model (e.g., Delft3D flow module) to drive the current and undertow, resulting in a 3D velocity profile. The wave model and hydrostatic model are coupled online with a morphodynamic model (e.g., Delft3D morphology module). The latter computes, based on the 3D flow profile and the wave asymmetry term, the sediment transport and performs the bathymetry updates. The updates are transferred directly back to the hydrodynamic models. The coupling of the wave model TRITON and the Delft3D modules is validated by comparing against extensive laboratory data sets (LIP and Boers) and a field case (Duck94), and show a good performance for the hydrodynamics and a reasonable/fair performance for the bar movements.     

Occurrence probability of a freak wave in a nonlinear wave field

The Edgeworth’s form of a cumulative expansion of the probability density function (PDF) of surface elevation expands the maximum wave height distribution to predict the occurrence probability of freak waves. This study investigated the enhancement of the occurrence probability of freak waves due to the fourth order moment of surface elevation, kurtosis, change and found that the nonlinear effects on the occurrence probability of a freak wave linearly depends on kurtosis for a small number of waves N=250. The statistical theory was compared with field data, and freak waves sometimes appear when not expected by the Rayleigh theory, but they were predicted by the proposed theory.     

Water wave interaction with a floating porous cylinder

The interaction of water waves with a freely floating circular cylinder possessing a side-wall that is porous over a portion of its draft is investigated theoretically. The porous side-wall region is bounded top and bottom by impermeable end caps thereby resulting in an enclosed fluid region within the structure. The problem is formulated based on potential flow and linear wave theory and assuming small-amplitude structural oscillations. An eigenfunction expansion approach is then used to obtain semi-analytical expressions for the hydrodynamic excitation and reaction loads on the structure. Numerical results are presented which illustrate the effects of the various wave and structural parameters on these quantities. It is found that the permeability, size and location of the porous region may have a significant influence on the horizontal components of the hydrodynamic excitation and reaction loads, while its influence on the vertical components in most cases is relatively minor.     

孤立波低顶海堤越浪的数值模拟研究

灾害性波浪是中国沿海地区最具破坏性的自然灾害之一。采用开源程序OpenFOAM中interFoam求解器,对低顶海堤（在风暴潮和海平面上升情况下所面临的不利工况）的孤立波越浪特性开展数值模拟研究。通过孤立波冲击海堤的基准算例,验证模型在模拟波浪爬升和越浪过程中大变形波面以及剧烈波浪力方面的精度。基于验证的数值模型,对孤立波在低顶海堤上的越浪特征以及防浪墙高度对越浪的影响开展参数化研究。结果表明堤顶超高减小导致更为剧烈的越浪。针对尚无低顶海堤孤立波越浪量经验公式的问题,提出新的适用于堤顶超高小或为0的孤立波越浪量经验公式。此外,研究发现增加防浪墙高度可有效减少越浪,但防浪墙所受的波浪力也增大。综合考虑防浪墙减少越浪以及自身所受波浪力,针对文中研究采用的海堤截面和波浪条件,建议无量纲防浪墙高度取为1.00。     

Linear irregular wave generation in a numerical wave tank

In the design of any floating or fixed marine structure, it is vital to test models in order to understand the fluid/structure interaction involved. A relatively inexpensive method, compared to physical model testing, of achieving this is to numerically model the structure and the wave conditions in a numerical wave tank. In this paper, a methodology for accurately replicating measured ocean waves in a numerical model at full scale is detailed. A Fourier analysis of the measured record allows the wave to be defined as a summation of linear waves and, therefore, Airy's linear wave theory may be used to input the wave elevation and associated water particle velocities. Furthermore, a structure is introduced into the model to display the ability of the model to accurately predict wave–structure interaction. A case study of three individual measured waves, which are recorded at the Atlantic marine energy test site, off the west coast of Ireland, is also presented. The accuracy of the model to replicate the measured waves and perform wave–structure interaction is found to be very high. Additionally, the absolute water particle velocity profile below the wave from the numerical model is compared to a filtered analytical approximation of the measured wave at a number of time-steps and is in very good agreement.     

Bragg resonant reflection of carrier waves composing wave groups

Numerical analyses for the Bragg resonant reflection of carrier waves associated long waves due to sinusoidally varying seabeds are performed by using a set of coupled ordinary differential equations derived from the Boussinesq equations. The Boussinesq equations are firstly approximated with the Fourier decomposition. The coupled governing equations are then derived and used to simulate evolution of both short and long wave components. It is also found that wave groups are generated by two carrier waves with slightly different frequencies. The wave energy of the initial wave components is transferred to other harmonic components during propagation over a long distance. Evolution and reflection of both short and long waves were largely affected by nonlinearity.     

Short-crested wave interaction with a concentric porous cylindrical structure

In this paper, theoretical study is carried out to investigate the general 3D short-crested wave interaction with a concentric two-cylinder system. The interior cylinder is impermeable and the exterior cylinder is thin in thickness and porous to protect the interior cylinder. Both cylinders are surface-piercing and bottom mounted. Analytical solution is derived based on the linear potential theory. The effects of the wide range wave parameters and structure configuration including porosity of the exterior cylinder and the annular spacing on the wave forces, surface elevations and the diffracted wave contours are examined.     

大糙率珊瑚礁附近规则波非线性特征实验研究

通过波浪水槽实验对大糙率礁面存在下珊瑚礁海岸附近规则波非线性特征参数(偏度、不对称度和厄塞尔数)的变化规律进行了研究。实验采用圆柱体阵列来模拟礁面的粗糙度,测试了一系列规则波工况。结果表明:偏度、不对称度和厄塞尔数的幅值分别在珊瑚礁破碎带结束位置、破碎带内和破碎带开始位置达到最大。3个参数的幅值均随着入射波波高的增大而增大;偏度值随着波浪周期的增大而减小,不对称度幅值和厄塞尔数随着周期的增大而增大;偏度值随着礁坪水深的增大而增大,不对称度幅值和厄塞尔数随着礁坪水深的增大而减小。深水厄塞尔数可以用来描述礁坪上波浪非线性参数的变化,最后给出了用其预测礁坪上3个非线性特征参数的经验关系式。     

Analytical and experimental study of wave setup over permeable coral reef

An analytical solution is proposed to predict the wave set-up over permeable reef flat based on porous flow model and momentum conservation. A laboratory experiment is carried out to verify the analytical solution. Good agreement is obtained by comparing the analytical results and the experimental data. Both the analytical results and the experimental data show the wave setup increases with the increase of the incident wave height and the decrease of the submergence water depth. The influences of the porous properties of the coral reef on wave set-up are discussed based on the analytical solution and experiment results. The wave set-up on the reef flat is found to decrease with the increasing particle size of porous media layer. The increase of the porosity and the height of porous media layer can lead to significant reduction in the wave set-up on the reef flat.     

Modelling the effect of wave overtopping on nearshore hydrodynamics and morphodynamics around shore-parallel breakwaters

Wave overtopping nearshore coastal structures, such as shore-parallel breakwaters, can significantly alter the current circulation and sediment transport patterns around the structures, which in turn affects the formation of tombolos and salients in the nearshore area. This paper describes the implementation of a wave overtopping module into an existing depth-averaged coastal morphological mode: COAST2D and model applications to investigate the effect of wave overtopping on the hydrodynamics and morphodynamics around a group of shore-parallel breakwaters. The hydrodynamic aspects of the model were validated against a series of laboratory conditions. The model was then applied to a study site at Sea Palling, Norfolk, UK, where 9 shore-parallel segmented breakwaters including 4 surface-piercing and 5 low-crested breakwaters are present, for the storm conditions in Nov 2006. The model results were compared with laboratory data and field measurements, showing a good agreement on both hydrodynamics and morphological changes. Further analysis of wave overtopping effect on the nearshore hydrodynamics and morphodynamics reveals that wave overtopping has significant impacts on the nearshore circulation, sediment transport and the resulting morphological changes within such a complex breakwater scheme under the storm and macro-tide conditions. The results indicate the importance of including the wave overtopping in modelling nearshore morphodynamics with the presence of coastal structures.     

Numerical study of combined overflow and wave overtopping over a smooth impermeable seawall

A numerical wave flume is used to investigate the discharge characteristics of combined overflow and wave overtopping of impermeable seawalls. The numerical procedure computes solutions to the Reynolds-averaged Navier–Stokes equations and includes the generation of an irregular train of waves, the simulation of wave breaking and interaction with a sloping, impermeable wall. The numerical model is first tested against published experimental observations, approximate analytical solutions and empirical design formulae for the cases of pure overflow and pure overtopping. A sequence of numerical experiments simulating combined overflow and overtopping are described. The results are used to determine empirical discharge formulae of the form used in current practice.     

Evolution of waves and currents over a submerged laboratory shoal

The vertically-integrated effect of interaction between waves and wave-induced currents on wave transformation over a submerged elliptic shoal was investigated based on numerical simulations of the Vincent and Briggs experiment [Vincent, C.L., Briggs, M.J., 1989. Refraction- diffraction of irregular waves over a mound. Journal of Waterway, Port, Coastal and Ocean Engineering, 115(2), pp. 269–284.]. The numerical simulations were performed using two numerical wave-current model systems: one, a combination of the wave model SWAN and the current model SHORECIRC, and the other, a combination of the wave model REF/DIF and the same current model. A time-dependent, phase-resolving wave and current model, FUNWAVE, was also utilized to simulate the experiment. In the simulations, the developed wave-induced currents defocused waves behind the shoal and brought on a wave shadow zone that showed relatively low wave height distributions. For the breaking case of monochromatic waves, the wave heights computed using FUNWAVE showed good agreement with the measurements and the resulting wave-induced currents showed a jet-like velocity distribution in transverse direction. And the computed results of the two model combinations agreed better with the measurements than the computed results obtained by neglecting wave-current interaction. However, it was found that for the case in which transverse interference pattern caused by refracted waves was strong, REF/DIF-SHORECIRC did not correctly evaluate radiation stresses, the gradients of which generate wave-induced currents. SWAN-SHORECIRC, which cannot deal with the interference patterns, predicted a jet-like wave-induced current. For breaking random wave cases, the computed results of the two model combinations and FUNWAVE agreed well with the measurements. The agreements indicate that it is necessary to take into account the effect of wave-induced current on wave refraction when wave breaking occurs over a submerged shoal.     

Experimental study of unidirectional irregular wave slamming on the three-dimensional structure in the splash zone

The experimental investigation of unidirectional random wave slamming on the three-dimensional structure in the splash zone is presented. The experiment is conducted in the marine environment channel in the State Key Laboratory of Coastal and Offshore Engineering, Dalian University of Technology. The test wave is unidirectional irregular wave. The experiments are carried out with perpendicular random waves (β=0°) and oblique random waves (β=15°, 30°, 45°), the significant wave heights H_1/3 ranging from 7.5 to 20 cm with 2.5 cm increment, the peak wave periods T_p ranging from 0.75 to 2.0 s with 0.25 s increment, and the clearance of the model with respect to the significant wave height s/H_1/3 ranging from 0.0 to 0.5 with 0.1 increment. The statistical analysis results of different test cases are presented. The statistical distribution characteristics of the perpendicular irregular wave impact pressures are compared with that of the oblique irregular wave on the underside of the structure. The effect of the wave direction β on the wave impact forces on the underside of the structure is determined. The relation between the impact forces and the parameters such as the significant wave height, the relative structure width and the relative clearance of the structure is also discussed.