On the evolution and run-up of breaking solitary waves on a mild sloping beach

This paper presents new laboratory experiments carried out in a supertank (300 m × 5 m × 5.2 m) of breaking solitary waves evolution on a 1:60 plane beach. The measured data are employed to re-examine existing formulae that include breaking criterion, amplitude evolution and run-up height. The properties of shoreline motion, underwater particle velocity and scale effect on run-up height are briefly discussed. Based on our analyses, it is evidently found that there exist five zones during a wave amplitude evolution course on the present mild slope. A simple formula which is capable of predicting maximum run-up height for a breaking solitary wave on a uniform beach with a wide range of beach slope (1:15–1:60) is also proposed. The calculated results from the present model agree favorably with available laboratory data, indicating that our method is compatible with other predictive models.     

Interaction of non-breaking regular waves with a periodic array of artificial porous bars

A computational model is developed to investigate the wave damping characteristics of a periodic array of porous bars. The transmission and reflection coefficients as well as the wave energy dissipation are evaluated relating to the physical properties and geometric factors of bars. It is shown that the porosity, number, width and height of bars all play important roles in the wave damping characteristics, compared to other factors such as the intrinsic permeability. It is observed that like impermeable bars, permeable bars display Bragg phenomenon. However, Bragg reflection produced by permeable bars is smaller than that by impermeable bars. Permeable bars reflect smaller waves, transmit smaller waves and dissipate more wave energy. It is indicated that if the porosity increases, both the reflection and transmission coefficients decrease and more wave energy is dissipated. Further, it is found that the porosity controls the magnitude, but not the oscillation frequency of the reflection coefficient, which depends only on the number of bars.     

关于波浪破碎特性的研究

有关波浪破碎问题的研究是海岸工程界十分关注的课题。本文列举了前人有关波浪破碎特性方面的研究成果；分析了波浪破碎前后波高的变化规律，作出了适当的假定；并考虑了动床海滩坡度、底摩擦以及紊动对波浪破碎特性的影响。应用波动能量耗散率理论，并结合孤立波理论的有关公式，作者推导了计算动床海滩上破碎指标ｒ_ｂ的公式，并进而给出破碎水深ｈ_ｂ与破碎波高Ｈ_ｂ的计算公式。通过不同规模实验水槽的资料验证表明，这组计算式具有广泛的实用性。     

A wave-flume study of scour at a pile breakwater: Solitary waves

Understanding the sediment transport and the resulting scour around coastal structures such as pile breakwaters under local extreme wave conditions is important for the foundation safety of various coastal structures. This study reports a wave-flume experiment investigating the scour induced by solitary waves at a pile breakwater, which consists of a row of closely spaced large piles. A wave blacking gate with a simple operation procedure in the experiment was designed to eliminate possible multiple reflections of the solitary wave inside the flume. An underwater laser scanner and a point probe were used in combination to provide high-resolution data of the bed profile around the pile breakwater. Effects of incident wave height and local water depth on the maximum scour depth, the maximum deposition height and the total scour and deposition volumes were examined. An existing empirical formula describing the evolution of the scour at a single pile in current or waves was extended to describe the scour at the pile breakwater under the action of multiple solitary waves, and new empirical coefficients were obtained by fitting the formula to the new experimental data to estimate the equilibrium scour depth. It appears that the maximum scour depth and the total scour volume are two reliable quantities for validation of numerical models developed for the scour around pile breakwaters under highly nonlinear wave conditions.     

驱动非线性浅水波的行波特征研究

采用带有外界强迫效应的浅水动力学模式研究非线性波动、获得了依赖于外界输入形式的驱动水波的行波解。研究结果表明,驱动水波仍具有非线性波动的一般性质,而当外界强迫波速与水波固有速度一致时,水波出现共振效应,并且外界强迫孤立子将导致驱动水波孤立子产生。     

Incompressible SPH flow model for wave interactions with porous media

The paper presents an Incompressible Smoothed Particle Hydrodynamics (ISPH) method to simulate wave interactions with a porous medium. The SPH method is a mesh free particle modeling approach that is capable of tracking the large deformation of free surfaces in an easy and accurate manner. The ISPH method employs a strict incompressible hydrodynamic formulation to solve the fluid pressure and the numerical solution is obtained by using a two-step semi-implicit scheme. The ISPH flow model solves the unsteady 2D Navier–Stokes (NS) equations for the flows outside the porous media and the NS type model equations for the flows inside the porous media. The presence of porous media is considered by including additional friction forces into the equations. The developed ISPH model is first validated by the solitary and regular waves damping over a porous bed and the solitary wave interacting with a submerged porous breakwater. The convergence of the method and the sensitivity of relevant model parameters are discussed. Then the model is applied to the breaking wave interacting with a breakwater covered with a layer of porous materials. The computational results demonstrate that the ISPH flow model could provide a promising simulation tool in coastal hydrodynamic applications.     

Harmonic generation past a submerged porous step

Experiments were conducted in a wave flume to study the differences between harmonic evolution of monochromatic waves as they propagate over a submerged impermeable or porous step under non-breaking conditions. Results are used as a preliminary analysis to establish some engineering design criteria on harmonic generation on submerged porous structures. The root-mean-squared wave height evolution is also studied and compared to linear models as a first approximation. It is shown that porous structure increases the effective relative depth and decreases the relative wave height, resulting in a lower Ursell number and a lower chance to generate harmonics. The effective water depth over a step as defined in the paper, provides information to evaluate the potential harmonic generation.     

Propagation of a solitary wave over rigid porous beds

The unsteady two-dimensional Navier–Stokes equations and Navier–Stokes type model equations for porous flows were solved numerically to simulate the propagation of a solitary wave over porous beds. The free surface boundary conditions and the interfacial boundary conditions between the water region and the porous bed are in complete form. The incoming waves were generated using a piston type wavemaker set up in the computational domain. Accuracy of the numerical model was verified by comparing the numerical results with the theoretical solutions. The main characteristics of the flow fields in both the water region and the porous bed were discussed by specifying the velocity fields. Behaviors of boundary layer flows in both fluid and porous bed regions were also revealed. Effects of different parameters on the wave height attenuation were studied and discussed. The results of this numerical model indicate that for the investigated incident wave as the ratio of the porous bed depth to the fluid depth exceeds 10, any further increase of the porous bed depth has no effect on wave height attenuation.     

On the wave damping due to a permeable seabed

Laboratory experiments were performed to study the wave damping induced by a porous bed. During the propagation of waves over a porous medium the wave characteristics change: a significant wave height attenuation of about 20–30% is observed and, in almost all cases, an increase in wavelength. The wave decay is found to depend on the wave characteristics like the wave height, the wavelength and the wave shape. We have also studied the influence of the geometric properties of the porous bed (i.e. thickness and length) on the wave dissipation. It is found that the attenuation of the wave height increases with the permeable bed thickness and that there is a maximum wave dissipation for a length of the porous seabed equal to 2.0–2.5 times the wavelength. A comparison is also made of our findings with available literature results. A parametric study of the wave damping has been performed by varying the values of the resistance coefficients derived by both literature and experiments. Literature analytical models have been applied by using the resistance coefficients that better describe our flow conditions. All models in use underpredict the observed wave attenuation for any sensible values of the resistance coefficients.     

NWF: Propagation of Tsunami and its Interaction with Continental Shelf and Vertical Wall

In this article, tsunamis represented as solitary waves was simulated using the fully nonlinear free surface waves based on Finite Element method developed by Sriram et al. (2006). The split up of solitary wave while it propagates over the uneven bottom topography is successfully established. Wave transmission and reflection over a vertical step introduced in the bottom topography is in good agreement with the experimental results from Seabra-Santos et al. (1987). The wave transformation over a continental shelf with different smooth slopes reveals that the solitary wave reflection increases while the continental slope varies from flat to steep. The interaction of the solitary wave with a vertical wall for different wave steepness has been analysed. The reflected shape of the profile is in good agreement with the observation made by Fenton and Rienecker (1982) and an increase in wave celerity is observed.     

Evolution of Interface Soliton over Topography

Several ray-type 1D and 2D KdV equations for two-layer stratified ocean with topographic effect are derived in detail in the present study.A simplified version of these equations,ray type 1D KdV equation,is used to calculate numerically the disintegration of initial interface soliton from the deep sea to the continental shelf.At the same time,a laboratory experiment is carried out in a 2D stratified flow and internal wave tank to examine the numerical results.A comparison of the numerical results with the experimental results shows that they are in good agreement.The numerical results also show that the ray-type KdV equation has high accuracy in describing the evolution of initial interface waves in shelf/slope regions.Form these results,it can be concluded that the fission process is a dominant generating mechanism of interface soliton packets on the continental shelf.     

Validation of a new generation system for bottom boundary layer beneath solitary wave

Understanding of sea bottom boundary layer characteristics, especially bottom shear stress acting on the sea bed, is an important step needed in sediment transport modeling for practical application purposes. In the present study, a new generation system for bottom boundary layer under solitary wave is proposed. Applicability of this system is examined by comparing measured and numerical solution velocities. Moreover, transitional behavior from laminar to turbulence was investigated. It is concluded that the critical Reynolds number in the experiments shows good agreement with DNS result of Vittori and Blondeaux (2008) and laboratory data of Sumer et al. (2010), indicating validity of the generation system. Since the present generation system enables continuous measurement to obtain ensemble averaged quantities, it can be effectively utilized for future experimental studies on solitary wave boundary layers, including sediment transport experiments with movable bed.     

内孤立波过山脊地形演化实验研究

通过模型实验,研究了下沉型内孤立波通过山脊地形演化特征。实验以三角形障碍物模拟海底山脊地形,采用两种密度的分层水,对上层流体和下层流体的高度比、密度等进行了量化处理。实验研究表明:KdV理论波形可较好模拟本次实验内孤立波波形,但随着内孤立波振幅的增大,误差增加;在内孤立波与障碍物微量作用、中度作用和破波作用三种程度的相互作用中,内孤立波过障碍物具有不同的波形变化和主波能量衰减率。     

二阶Boussinesq方程的孤立波解

基于同量阶迭代法，在保留同阶面的前提下，对林建国等（1998a)得到的二阶Boussinesq类方程进行了求解，得到了与其量阶相对应的取立波解，并春与Euler方程的二阶孤立波解进行了比较，结果显示，本文解比传统Boussinesq方程的孤立波解有明显的改善，扩大了孤立的适用范围。     

Study of interaction between intense internal wave solitons in the context of the Choi-Camassa model

Based on the approximated theory developed by the authors to describe the interaction of complex solitons that are formed by kinks, i.e., drops of fields of different polarity, the features of the dynamics of intense internal wave solitons are studied in the context of nonintegrable Choi-Camassa equations. These equations describe the evolution of long internal waves with arbitrary amplitudes in a two-layer fluid. Making allowance for the complex character of the limiting amplitude solitons made it possible to study the dynamics of their interaction as longitudinal (not pointlike) formations for the first time. A series of the features of soliton interaction caused by the complexity of their structure is discovered and explained. These include the appearance of solitary waves with opposite polarity in the collision process, anomalously large phase shifts, etc. The existence of these features is verified by numerical experiments in the context of internal wave models permitting the existence of complex solitons.     

Internal solitary waves shoaling onto a shelf: Comparisons of weakly-nonlinear and fully nonlinear models for hyperbolic-tangent stratifications

In this study the evolution of internal solitary waves shoaling onto a shelf is considered. The results of high resolution two-dimensional numerical simulations of the incompressible Euler equations are compared with the predictions of several weakly-nonlinear shoaling models of the Korteweg–de Vries family including the Gardner equation and the cubic regularized long wave (or Benjamin–Bona–Mahoney) equation. Wave models in both physical x–t space and in s–x space are considered where s is a commonly used characteristic time variable. The effects of rotation, background currents and damping are ignored. The Boussinesq and rigid lid approximations are also used. The shoaling internal solitary waves generally fission into several waves. Reflected waves are negligible in the cases considered here. Several hyperbolic tangent stratifications are considered with and without a critical point. Among the equations in x–t space the cubic regularized long wave equation gives the best predictions. The Gardner equation in s–x space gives the best predictions of the shape of the leading waves on the shelf, but for many stratifications it predicts a propagation speed that is too large.     

Wave height transformation and set-up between a submerged permeable breakwater and a seawall

In this study,we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall.Modified time-dependent mild-slope equations,which involve parameters of the porous medium,were used to calculate the wave height transformation and the mean water level change around a submerged breakwater.The numerical solution is verified with experimental data.The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall.In contrast to cases without a seawall,the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall.Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater.We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.     

The influence of beach porosity on wave uprush and backwash

Packwood, A.R., 1983. The influence of beach porosity on wave uprush and backwash. Coastal Eng., 7: 29–40.A numerical model is described to calculate the influence of a porous bed on the run-up of a bore on a gently sloping sandy beach. It is shown that fine-medium grade sands have very little effect in the run-up phase. Significant differences between impermeable and porous bed solutions are found in the backwash which might explain certain sand erosion and deposition phenomena.