Dynamic Response Behaviors of Upright Breakwaters Under Breaking Wave Impact

The dynamic response behaviors of upright breakwaters under broken wave impact are analysed based on the mass-damper-spring dynamic system model. The effects of the mass, damping, stiffness, natural period, and impulse duration (or oscillation period) on the translation, rotation, sliding force, overturning moment, and corresponding dynamic amplifying factors are studied. It is concluded that the ampli-ying factors only depend on the ratio of the system natural period to impulse duration (or oscillation period) under a certain damping ratio. Moreover, the equivalent static approach to breakwater design is also discussed.

Physical Investigation of Directional Wave Focusing and Breaking Waves in Wave Basin

An experimental scheme for the generation of directional focusing waves in a wave basin is established in this paper. The effects of the directional range, frequency width and center frequency on the wave focusing are studied. The distribution of maximum amplitude and the evolution of time series and spectra during wave packet propagation and the variation of water surface parameters are extensively investigated. The results reveal that the characteristics of focusing waves are significantly influenced by wave directionality and that the breaking criteria for directional waves are distinctly different from those for unidirectional waves.

Experimental Study on Suspended Sediment Concentration and Its Vertical Distribution under Spilling Breaking Wave Actions in Silty Coast

In this paper, flume experiments are focused on sediment transport inside and outside the surf zone. According to the energy dissipation balance principle of sediment-laden flow and the similarity between energy dissipation of spilling breaking wave and hydraulic jump, formulas are proposed to predict time averaged suspended sediment concentration under both non-breaking and breaking waves. Assuming that the sediment diffusion coefficient, which is related with energy dissipation, is proportional to water depth, formulas are proposed to predict close-to-bed suspended sediment concentration and vertical distribution of suspended sediment under spilling breaking waves, and the prediction shows a good agreement with the measurement.

Vibrating-Rocking Motion of Caisson Breakwater Under Breaking Wave Impact

The possible motions of a caisson breakwater under dynamic load excitation include vibrating, vibrating-sliding and vibrating- rocking motions. The models of vibrating motion and vibrating-sliding motion have been proposed in an early paper. In this paper, a model of vibrating- rocking motion of caisson breakwaters under breaking wave impact is presented, which can be used to simulate the histories of vibrating-rocking motion of caisson breakwaters. The effect of rocking motion on the displacement, rotation, sliding force and overturning moment of breakwaters is investigated, In case the overturning moment exceeds the stability moment of a caisson, the caisson may only rock. The caisson overturns only in case the rocking angle exceeds the critical angle, It is shown that the sliding force and overturning moment of breakwaters can be reduced effectively due to the rocking motion, It is proposed that some rocking motion should be allowed in breakwater design.

Numerical Simulation of Breaking Wave Based on Higher-Order Mild Slope Equation

The 'surface roller' to simulate wave energy dissipation of wave breaking is introduced into the random wave model based on approximate parabolic mild slope equation in this paper to simulate the random wave transportation in chiding diffraction, refraction and breaking in nearshore areas. The roller breaking random wave higher-order approximate parabolic equation model has been verified by the existing experimental data for a plane slope beach and a circular shoal, and the numerical results of random wave breaking model agree with the experimental data very well, This model can be applied to calculate random wave propagation from deep to shallow water in large areas near the shore over natural topography.

A second order volume of fluid (VOF) scheme for numerical simulation of 2-D breaking waves

Among all environmental forces acting on ocean structures and marine vessels, those resulting from wave impacts are likely to yield the highest loads. Being highly nonlinear, transient and complex, a theoretical analysis of their impact would be impossible without numerical simulations. In this paper, a pressure-split two-stage numerical algorithm is proposed based on Volume Of Fluid （VOF） methodology. The algorithm is characterized by introduction of two pressures at each half and full cycle time step, and thus it is a second-order accurate algorithm in time. A simplified second-order Godunov-type solver is used for the continuity equations. The method is applied to simulation of breaking waves in a 2-D water tank, and a qualitative comparison with experimental photo observations is made. Quite consistent results are observed between simulations and experiments. Commercially available software and Boundary Integral Method （BIM） have also been used to simulate the same problem. The results from present code and BIM are in good agreement with respect to breaking location and timing, while the results obtained from the comrnercial software which is only first-order accurate in time has clearly showed a temporal and spatial lag, verifying the need to use a higher order numerical scheme.

Experimental Study of Pore Water Pressure and Bed Profile Change Under Regular Breaking Waves

There lies a close relationship between the seabed destruction and the distribution of pore water pressure under the action of breaking wave. The experiments were carried out in a wave flume with a 1：30 sloping sandy seabed to study regular breaking wave induced pore water pressure. A wide range of measurements from the regular wave runs were reported, including time series of wave heights, pore pressures. The video records were analysed to measure the time development of the seabed form and the characteristics of the orbital motion of the sand in the wave breaking region. The pore water pressure in the breaker zone showed the time variation depending on the wave phases including wave breaking and bore propagation. The time-averaged pore water pressure was higher near the seabed surface. The peak values of pore water pressure increase significantly at the breaking point. The direction of pore water pressure difference forces in the breaker zone is of fundamental importance for a correct description of the sediment dynamics. The upwards- directed pressure differences may increase sand transport by reducing the effective weight of the sediment, thereby increasing the bed form evolution. The seabed configuration changed greatly at the wave breaking zone and a sand bar was generated remarkably. The amplitude of the pore water pressure changed with the seabed surface. The results are to improve the understanding of sand transport mechanisms and seabed responses due to breaking regular waves over a sloping sandy bed.

Vibrating-Sliding Motion of Caisson Breakwaters Under Various Breaking Wave Impact Forces

Sliding is one of the principal failure types of caisson breakwaters and is an essential content of stability examination in caisson breakwater design. Herein, the mass-spring-dashpot model of caisson-base system is used to simulate the vibrating-sliding motion of the caisson under various types of breaking wave impact forces, i.e., single peak impact force, double peak impact force, and shock-damping oscillation impact force. The effects of various breaking wave impacts and the sliding motion on the dynamic response behaviors of caisson breakwaters are investigated and the calculation of relevant system parameters is discussed. It is shown that the dynamic responses of the caisson are significantly different under different types of breaking wave impact forces even when the amplitudes of impact forces are equal. The amplitude of dynamic response of the caisson is lower under single peak impact excitation than that under double peak impact or shock-damping oscillation impact excitation. Though the displacement of the caisson is large due to sliding, the rotation, the sliding force and the overturning moment of the caisson are significantly reduced.

Study on the Set-up and Set-down Induced by Breaking Waves Over A Reef

This paper proposes an equation to calculate breaking wave induced wave set-up and set-down along reef flat. The mathematical equation was derived based on the theory of radiation stress and the conservation of wave energy. The equation is primarily determined by several physical variables including the breaking wave index, the stable wave index, the attenuation coefficient of wave energy flux, and the flow velocity in the re-stabilization zone. A series of laboratory experiments were carried out to calibrate the theoretical equations. Specifically, the breaking wave index,the stable wave index, and the velocity over the reef flat were measured in the laboratory. The attenuation coefficient of wave energy flux in our theoretical equation was determined by calibration by comparing with the laboratory measured wave height. Furthermore, it has been put forward that the velocity based on cnoidal wave theory could be used to determine the velocity over the reef flat if there is no velocity measurement available. Overall, the proposed equation can provide satisfactory prediction of wave set-up and set-down along the reef flat.

Modeling Loads Caused by Breaking Waves Striking Vertical Walls

Breaking waves can have tremendous destructive impact on vertical walls, yet they are poorly understood. By using particle imaging velocimetry （PIV） technology and high-precision pressure transducers, actual breaking wave loads on vertical walls were studied. By simultaneously comparing the flow field structure and wave pressure, the mechanisms of breaking wave pressure could be analyzed. The probability distribution of the peak value of the first impact of a breaking wave was investigated. The results showed that the impact pressure p is mainly distributed in the range of 0.25-2.75 pv2, with the greatest possible probability at p/pv2 = 0.75.

Effects of Breaking Waves on Composite Backscattering from Ship-Ocean Scene

The existence of the sea surface is bound to affect the electromagnetic （EM） scattering from marine targets. When dealing with the composite scattering from targets over a sea surface by applying high-frequency EM theories, the total scattering field can be decomposed into three parts in low sea states, namely, the direct scattering from the sea surface, the direct scattering from targets and the coupling scattering between the sea surface and targets. With regard to high sea states, breaking waves make the direct scattering from the sea surface and the coupling scattering more complicated. To solve this issue, a scattering model is proposed to analyze the composite scattering from a ship over a rough sea surface under high sea states. To consider the effect of breaking waves, a three dimensional geometric model is adopted together with Ufimtsev＇s theory of edge waves for the scattering from a breaker. In addition, the coupling scattering between targets and breaking waves is taken into account by considering all possible scattering paths. The simulated results indicate that the influence of breaking waves on the scattering field from the sea surface and on the coupling field is non-negligible, and the numerical results also show the effectiveness of the proposed scattering model.

Microwave backscattering from the sea surface with breaking waves

Based on the effective medium approximation theory of composites, the whitecap-covered sea surface is treated as a medium layer of dense seawater droplets and air. Two electromagnetic scattering models of randomly rough surface are applied to the investigation of microwave backscattering of breaking waves driven by strong wind. The shapes of seawater droplets are considered by calculating the effective dielectric constant of the whitecap layer. The responses of seawater droplets shapes, such as sphere and ellipsoid, to the backscattering coefficient are discussed. Numerical results of the models are in good agreement with the experimental measurements of horizontally and vertically polarized backscattering at microwave frequency 13.9GHz and different incidence angles.

One-Dimensional Horizontal Boussinesq Model Enhanced for Non-Breaking and Breaking Waves

Based on a set of fully nonlinear Boussinesq equations up to the order of O（μ^2, ε^3μ^2） （where ε is the ratio of wave amplitude to water depth and ,μ is the ratio of water depth to wave length） a numerical wave model is formulated. The model＇s linear dispersion is acceptably accurate to μ ≌ 1.0, which is confirmed by comparisons between the simulat- ed and measured time series of the regular waves propagating on a submerged bar. The moving shoreline is treated numer- ically by replacing the solid beach with a permeable beach. Run-up of nonbreaking waves is verified against the analytical solution for nonlinear shallow water waves. The inclusion of wave breaking is fulfilled by introducing an eddy term in the momentum equation to serve as the breaking wave force term to dissipate wave energy in the surf zone. The model is applied to cross-shore motions of regular waves including various types of breaking on plane sloping beaches. Comparisons of the model test results comprising spatial distribution of wave height and mean water level with experimental data are presented.

A VOF-based numerical model for breaking waves in surf zone

This paper introduces a numerical model for studying the evolution of a periodic wave train, shoaling, and breaking in surf zone. The model can solve the Reynolds averaged Navier-Stokes （RANS） equations for a mean flow, and the k-ε equations for turbulence kinetic energy k and turbulence dissipation rate ε. To track a free surface, the volume of fluid （VOF） function, satisfying the advection equation was introduced. In the numerical treatment, third-order upwind difference scheme was applied to the convection terms of the RANS equations in order to reduce the effect of numerical viscosity. The shoaling and breaking processes of a periodic wave train on gently sloping beaches were modeled. The computed wave heights of a sloping beach and the distribution of breaking wave pressure on a vertical wall were compared with laboratory data.

Numerical Simulation of Breaking Wave Generated Sediment Suspension and Transport Process Based on CLSVOF Algorithm

The sediment suspension and transport process under complex breaking wave situation is investigated using large eddy simulation (abbreviated as LES hereafter) method. The coupled level set (LS) and volume of fluid (VOF) method is used to accurately capture the evolution of air-water interface. The wall effect at the bottom is modeled based on the wave friction term while the complicate bottom boundary condition for sediment is tackled using Chou and Fringer's sediment erosion and deposition flux method. A simulation is carried out to study the sediment suspension and transport process under periodic plunging breaking waves. The comparison between the results by CLSVOF method and those obtained by the LS method is given. It shows that the latter performs as well as the CLSVOF method in the pre-breaking weak-surface deformation situation. However, a serious mass conservation problem in the later stages of wave breaking makes it inappropriate for this study by use of the LS method and thus the CLSVOF method is suggested. The flow field and the distribution of suspended sediment concentration are then analyzed in detail. At the early stage of breaking, the sediment is mainly concentrated near the bottom area. During the wave breaking process, when the entrapped large-scale air bubble travels downward to approach the bottom, strong shear is induced and the sediment is highly entrained.

Energy dissipation through wind-generated breaking waves

Wave breaking is an important process that controls turbulence properties and fluxes of heat and mass in the upper oceanic layer.A model is described for energy dissipation per unit area at the ocean surface attributed to wind-generated breaking waves,in terms of ratio of energy dissipation to energy input,windgenerated wave spectrum,and wave growth rate.Also advanced is a vertical distribution model of turbulent kinetic energy,based on an exponential distribution method.The result shows that energy dissipation rate depends heavily on wind speed and sea state.Our results agree well with predictions of previous works.

Theoretical and Experimental Study of Breaking Wave on Sloping Bottoms

This paper studies the continuous evolution of breaking wave for the surface water waves propagating on a sloping beach. A Lagrangian asymptotic solution is derived. According to the solution coupled with the wave breaking criteria and the equations of water particles motion, the wave deformation and the continuous wave breaking processes for the progressive water waves propagating on a sloping bottom can be derived. A series of experiments are also conducted to compare with the theoretical solution. The results show that the present solution can reasonably describe the plunging or spilling wave breaking phenomenon.

Detection of Breaking Waves Using X-Band Pulse Radar in the Nearshore Region

An X-band pulsed Doppler microwave radar has been used to determine the characteristics of breaking waves. Field experiments were conducted at the Shuang-Si estuary in the north of Taiwan in the winter of 2005. Analyses on maxima radar cross section and Doppler frequency shift are done to characterize wave breaking zones. Based on observations of breaking waves, the wave breaking zones are shown to be located at water depths of 1.8 to 2.2 m in the experimental site. In general, the results indicate that a radar system has the potential to delineate the spatial variation of breaking waves clearly and that this is sufficient to achieve a measurement operation for near-shore air-sea interaction events.

A novel synthetic aperture radar scattering model for sea surface with breaking waves

In this study a novel synthetic aperture radar(SAR)scattering model for sea surface with breaking waves is proposed.Compared with existing models,the proposed model considers an empirical relationship between wind speed and wave breaking scattering to present the contribution of wave breaking.Moreover,the scattering weight factor p,and wave breaking rate q,are performed to present the contribution of the quasi-specular scattering term,Bragg scattering term,and wave breaking scattering term to the total scattering from the sea surface.To explore the modeling accuracy of sea-surface scattering,a simulated normalized radar cross-section(NRCS)and measured NRCS are compared.The proposed model generated the simulated NRCS and a matching GF-3 dataset was used for the measured NRCS.It was revealed that the performance of the VV polarization of our model was much better than that of HH polarization,with a correlation of 0.91,bias of-0.14 dB,root mean square error(RMSE)of 1.26 dB,and scattering index(SI)of-0.11.In addition,the novel model is explored and compared with the geophysical model of CMODs and satellite-measured NRCS from GF-3 SAR wave mode imagery.For an incidence angle 40°–41°,the relationship between the NRCS and wind speed,relative wind direction is proposed.As with the SAR-measured NRCS,the performance of VV polarization was much better than HH polarization,with a correlation of 0.99,bias of-0.25 dB,RMSE of 0.64 dB,and SI of-0.04.

Flow characteristics and bubble statistics during the fragmentation process of the ingested main cavity in plunging breaking waves

Plunging breaking waves play an important role in the exchange of heat,momentum,and mass between the atmosphere and ocean.In this paper,a series of direct numerical simulations is conducted to investigate the fragmentation process of the ingested main cavity in plunging breaking waves.The two-phase Navier-Stokes equations are solved using the finite-volume method based on adaptive refinement meshes.The free surface is captured using a geometrical volume of fluid method.Both 2-D,3-D simulations are conducted.Instantaneous flow fields at different stages of wave breaking are presented and quantitative analysis for bubbles is performed.The 2-D instantaneous vorticity field and local velocity field are visualized to discuss the general flow characteristics during the fragmentation process.Then a 2-D parametric study is conducted to investigate the differences in the flow characteristics during the fragmentation process under different wave parameters including initial wave steepness(ε),Bond number(Bo),and Reynolds number(Re).3-D vortex structures are shown to further investigate the mechanisms behind the differences in the flow characteristics.The bubble size distributions under two different initial wave steepness are also discussed with their relationship to the fragmentation process of the ingested main cavity.This research offers a significant understanding of the distinct procedures and fundamental dynamics involved in wave breaking,enhancing our comprehension of this intricate event.