Analytical Method for the Wave Diffraction of Asymmetrically Arranged Breakwaters

The layout forms of several breakwater structures can be generalized as asymmetrical arrangements in actual engineering.However,the problem of wave diffraction around asymmetrically arranged breakwaters has not been adequately investigated.In this study,we propose an analytical method of wave diffraction for regular waves passing through asymmetrically arranged breakwaters,and we use the Nyström method to obtain the analytical solution numerically.We compared the results of this method with those of previous analytical solutions and with numerical results to demonstrate the validity of our approach.We also provided diffraction coefficient diagrams of breakwaters with different layout forms.Moreover,we described the analytical expression for the problem of diffraction through long-wave incident breakwaters and presented an analysis of the relationship between the diffraction coefficients and the widths of breakwater gates.The analytical method presented in this study contributes to the limited literature on the theory of wave diffraction through asymmetrically arranged breakwaters.

Wave Reflection by Rectangular Breakwaters for Coastal Protection

In this study,we focus on the numerical modelling of the interaction between waves and submerged structures in the presence of a uniform flow current.Both the same and opposite senses of wave propagation are considered.The main objective is an understanding of the effect of the current and various geometrical parameters on the reflection coefficient.The wave used in the study is based on potential theory,and the submerged structures consist of two rectangular breakwaters positioned at a fixed distance from each other and attached to the bottom of a wave flume.The numerical modeling approach employed in this work relies on the Boundary Element Method(BEM).The results are compared with experimental data to validate the approach.The findings of the study demonstrate that the double rectangular breakwater configuration exhibits superior wave attenuation abilities if compared to a single rectangular breakwater,particularly at low wavenumbers.Furthermore,the study reveals that wave mitigation is more pronounced when the current and wave propagation are coplanar,whereas it is less effective in the case of opposing current.

Analytical and Experimental Research on Wave Scattering by an Open-Type Rectangular Breakwater with Horizontal Perforated Plates

This study proposes a novel open-type rectangular breakwater combined with horizontal perforated plates on both sides to enhance the sheltering effect of the rectangular box-type breakwaters against longer waves.The hydrodynamic characteristics of this breakwater are analyzed through analytical potential solutions and experimental tests.The quadratic pressure drop conditions are exerted on the horizontal perforated plates to facilitate assessing the effect of wave height on the dissipated wave energy of breakwater through the analytical solution.The hydrodynamic quantities of the breakwater,including the reflection,transmission,and energyloss coefficients,together with vertical and horizontal wave forces,are calculated using the velocity potential decomposition method as well as an iterative algorithm.Furthermore,the reflection and transmission coefficients of the breakwater are measured by conducting experimental tests at various wave periods,wave heights,and both porosities and widths of the horizontal perforated plates.The analytical predicted results demonstrate good agreement with the iterative boundary element method solution and measured data.The influences of variable incident waves and structure parameters on the hydrodynamic characteristics of the breakwater are investigated through further calculations based on analytical solutions.Results indicate that horizontal perforated plates placed on the water surface for both sides of the rectangular breakwater can enhance the wave dissipation ability of the breakwater while effectively decreasing the transmission and reflection coefficients.

Hydrodynamic Assessment of A New Nature-Based Armour Unit on Rubble Mound Breakwater for Coastal Protection

This research proposes a novel nature-based design of a new concrete armour unit for the cover layer of a rubblemoundbreakwater. Armour units are versatile with respect to shape, orientation, surface condition details, and porosity.Therefore, a detailed analysis is required to investigate the exact state of their hydraulic interactions and structuralresponses. In this regard, the performance results of several traditional armour units, including the Antifer cube,Tetrapod, X-block and natural stone, are considered for the first step of this study. Then, the related observed resultsare compared with those obtained for a newly designed (artificial coral) armour unit. The research methodology utilizesthe common wave flume test procedure. Furthermore, several verified numerical models in OpenFOAM code areused to gain the extra required data. The proposed armour is configured to provide an effective shore protection as anenvironmental-friendly coastal structure. Thus it is designed with a main trunk including deep grooves to imitate thetypical geometry of a coral type configuration, so as to attain desirable performance. The observed results and ananalytic hierarchy process (AHP) concept are used to compare the hydraulic performance of the studied traditionaland newly proposed (artificial coral) armour units. The results indicate that the artificial coral armour unit demonstratesacceptable performance. The widely used traditional armour units might be replaced by newer designs for betterwave energy dissipation, and more importantly, for fewer adverse effects on the marine environment.

Numerical Study on the Effect of Gap Diffraction on the Hydrodynamic Performance of A Floating Breakwater

Two-dimensional(2D)flume experiments are useful in investigating the performances of floating breakwaters(FBs),including hydrodynamic performances,motion responses,and mooring forces.Designing a reasonable gap between the flume wall and the FBs is a critical step in 2D flume tests.However,research on the effect of the gap on the accuracy of 2D FB experimental results is scarce.To address this issue,a numerical wave tank is developed using CFD to estimate the wave-FB interaction of a moored dual-cylindrical FB,and the results are compared to experimental data from a previously published work.There is good agreement between them,indicating that the numerical model is sufficiently accurate.The numerical model is then applied to explore the effect of gap diffraction on the performance of FBs in2D experiments.It was discovered that the nondimensional gap length L_(Gap)/W_(Pool)should be smaller than 7.5%to ensure that the relative error of the transmission coefficient is smaller than 3%.The influence of the gap is also related to the entering wave properties,such as the wave height and period.

Wave Force on the Crown Wall of Rubble Mound Breakwaters at Intermediate Depths

Rubble mound breakwaters with a crown wall are a common coastal engineering structure.The wave force on crown walls is an important parameter for the practice engineering design.Particularly,the wave force on crown walls under intermediate depths has been studied through physical model tests and numerical simulations.In this study,a three-dimensional numerical wave flume was developed to investigate monochromatic wave interactions in a rubble mound breakwater with a crown wall.Armor blocks were modeled in detail.The Navier-Stokes equations for two-phase incompressible flows,combined with shear stress transport k-ωturbulence model and volume of fluid method for tracking the free surface,were solved.A set of laboratory experiments were performed to validate the adopted model.Subsequently,a series of numerical simulations were implemented to examine the impacts of different hydrodynamic parameters(including wave height,incident wave period,and water depth)and the berm width on the wave force of the crown wall.Finally,a comparison of the experimental results and Martin method shows that the latter method is not suitable for this experimental scope.New empirical formulas are proposed to predict the wave force on crown walls under intermediate depth.The results can provide a basis for the design of crown wall of rubble mound breakwaters at intermediate depths.

Mathematical Modeling of Moored Ship Motion in Arbitrary Harbor utilizing the Porous Breakwater

The motion of the moored ship in the harbor is a classical hydrodynamics problem that still faces many challenges in naval operations,such as cargo transfer and ship pairings between a big transport ship and some small ships.A mathematical model is presented based on the Laplace equation utilizing the porous breakwater to investigate the moored ship motion in a partially absorbing/reflecting harbor.The motion of the moored ship is described with the hydrodynamic forces along the rotational motion(roll,pitch,and yaw)and translational motion(surge,sway,and heave).The efficiency of the numerical method is verified by comparing it with the analytical study of Yu and Chwang(1994)for the porous breakwater,and the moored ship motion is compared with the theoretical and experimental data obtained by Yoo(1998)and Takagi et al.(1993).Further,the current numerical scheme is implemented on the realistic Visakhapatnam Fishing port,India,in order to analyze the hydrodynamic forces on moored ship motion under resonance conditions.The model incorporates some essential strategies such as adding a porous breakwater and utilizing the wave absorber to reduce the port’s resonance.It has been observed that these tactics have a significant impact on the resonance inside the port for safe maritime navigation.Therefore,the current numerical model provides an efficient tool to reduce the resonance within the arbitrarily shaped ports for secure anchoring.

SCOURS IN FRONT OF A BREAKWATER BY BROKEN WAVES AND THEIR SIMILARITY LAW

The sea bottom in front of a breakwater is scoured under the action of broken waves,and this will affect the stability of the breakwater.In this paper,the scours of sandy seabed in front of a breakwater under the action of broken waves are investigated experimentally.The depth and range of the scouring trough at the foot of a breakwater are studied,and the influence of open foundation-bed on scouring and depositing is also discussed.In order to apply the research results to practical projects,the scale of model sediment and the scale of scours and depositions are suggested.

Reflection of Oblique Incident Waves by Breakwaters with Partially-Perforated Wall

The reflection of oblique incident waves from breakwaters with a partially-perforated front wall is investigated. The fluid domain is divided into two sub-domains and the eigenfunction expansion method is applied to expand velocity potentials in each domain. In the eigen-expansion of the velocity potential, evanescent waves are included. Numerical results of the present model are compared with experimental data. The effect of porosity, the relative chamber width, the relative water depth in the wave absorbing chamber and the water depth in front of the structure are discussed.

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.

Numerical Simulation on Hydraulic Performances of Quarter Circular Breakwater

Quarter circular breakwater （QCB） is a new-type breakwater developed from senti-circular breakwater （SCB）. The superstructure of QCB is composed of a quarter circular front wall, a horizontal base slab and a vertical rear wall. The width of QCB＇ s base slab is about half that of SCB, which makes QCB suitable to be used on relatively finn soil foundation. The numerical wave flume based on the Reynolds averaged Navier-Stokes equations for impressible viscosity fluid is adopted in this paper to simulate the hydraulic performances of QCB. Since the geometry of both breakwaters is similar and SCB has been studied in depth, the hydraulic performances of QCB are given in comparison with those of SCB.

Effect of Under Connected Plates on the Hydrodynamic Efficiency of the Floating Breakwater

In this paper, the hydrodynamic efficiency of a floating breakwater system is experimentally studied by use of physical models. Regular waves with wide ranges of wave heights and periods are tested. The efficiency of the breakwater is presented as a function of the wave transmission, reflection, and energy dissipation coefficients. Different parameters affecting the breakwater efficiency are investigated, e.g. the number of the under connected vertical plates, the length of the mooring wire, and the wave length. It is found that, the transmission coefficient kt decreases with the increase of the relative breakwater width B/L, the number of plates n and the relative wire length l/h, while the reflection coefficient kr takes the opposite trend. Therefore, it is possible to achieve kt values smaller than 0.25 and kr values larger than 0.80 when B/L is larger than 0.25 for the case of l/h-1.5 and n=4. In addition, empirical equations used for estimating the transmission and reflection coefficients are developed by using the dimensionless analysis, regression analysis and measured data and verified by different theoretical and experimental results.

Wave Forces on Submerged Semi-Circular Breakwater and Similar Structures

The results of design and experiment of a submerged semi-circular breakwater at the Yangtze estuary show that the submerged structure will be unsafe when the general empirical wave force formula for semi-circular breakwater is used in design. Therefore, a new calculation method for the wave forces acting on a submerged semi-circular structure is given in this paper, in which the wave force acting on the inside circumference of semi-circular arch is included, and the phase modification coefficient in the general empirical formula is adjusted as well. The new wave force calculation method has been Verified by the results of seven related physical model tests and adopted in the design of the south esturary jetty of the first stage project of Deep Channel Improvement Project of the Yangtze River Estuary, the total jetty length being 17.5 km.

Transmitted and Reflected Coefficients for Horizontal or Vertical Plate Type Breakwater

Surface or submerged horizontal or vertical plate can be considered as a new concept breakwater. This paper investigates the wave-plate interaction of this type of breakwater by use of the boundary element method. The relationships of wave transmitted and reflected among plate thickness, submergence and length are carefully studied by numerical simulation. It is shown that： （1） The transmitted coefficients of submerged horizontal plate or vertical plate will become larger with the increase of plate thickness and reduce rapidly with the decrease of plate submergence. （2） Both surface horizontal and vertical plate are efficient for intermediate and short wave elimination, but vertical plate is more effective. （3） Submerged horizontal plate can act more effectively than submerged vertical plate does. With all wave frequencies, the vertical plate almost has no wave elimination effect.

Numerical Simulation of Waves Interaction with A Submerged Horizontal Twin-Plate Breakwater

The numerical investigation of regular waves interacting with a submerged horizontal twin-plate breakwater is pre- sented in this paper. A numerical model with an absorbing wave-maker is established based on the VOF method. The validity of the model is verified by experimental results. Comparisons between the numerical and experimental results show that beth the water surface profiles and the wave-induced pressures can be modeled accurately. Wave deformation over the breakwater, water particle velocities around the breakwater, and the wave-induced pressures on the structure are nu- merically investigated. Tile pressure amplitudes of the fundamental and second harmonies on the model surface are exanl- ined in various water depths. The computed and experimental results have revealed that the higher frequency components are generated at the onshore side of the breakwater. Furthermore, the computed results demonstrate a circulating flow formed at the onshore side of the breakwater.

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 Study of A Pile-Restrained Floating Breakwater Constructed of Pontoon and Plates

A pile-restrained pontoon-plate floating breakwater is proposed in this paper. The laboratory physical-model tests are conducted to investigate the wave-dissipation property and heave-motion response of a model. The influence of the model＇s geometric parameters including relative pontoon width, plate width, number of plates and pontoon draft on wavedissipation performance and heave-motion response are discussed, as well as the correlation between these two factors. The result indicates that wave-dissipation performance of the proposed structure is better than the pontoon structure： its transmission coefficient and heave-motion height are reduced by 0.2 and 0.3, respectively, in comparison with those of the pile-restrained pontoon model at a relative pontoon width of 0.2.

Reliability Index of Caisson Breakwaters for Load Variables Correlated

In order to suit the condition that the wave uplift is correlated with the horizontal wave load acting on a vertical breakwater, a generally used method for determining the reliability index β of the breakwater, i.e. the Hasofer-Lind method, is extended in a generalized stochastic space for correlative variables. The computational results for a caisson breakwater indicate that the value of β for the case of correlated variables is obviously smaller than that for the case of independent variables.

Interaction Between Waves and A Comb-Type Breakwater

The characteristics of wave transmission, reflection and energy dissipation of comb-type caisson breakwaters are studied through laboratory physical model tests. Regular and irregular waves, with a wide range of wave heights and periods and a constant water depth, are considered. Different dimensions of each portion of the comb-type caisson breakwater are tested. Empirical formulae for calculating the reduction coefficient k, which is the ratio of horizontal wave force on unit length of the comb-type breakwater to that on unit length of the vertical wall breakwater, and for calculating the reflection coefficient of waves k, are obtained from the measurements. The comb-type caisson breakwater has been found to be very efficient in dissipating incident wave energy and in reducing wave reflection, and has already been used for the construction of an island breakwater in the Dayao Bay of Dalian Port, Liaoning Province, China. Compared with the cost of a common caisson breakwater, about 24.5% of the investment has been saved owing to the use of this comb-type breakwater.

Risk Assessment of Vertical Breakwaters -A Case Study in Turkey

In the reliability-risk assessment, the second order reliability index (βⅡ ) method and the Conditional Expectation Monte Carlo (CEMC) simulation are interrelated as a new Level Ⅲ approach for the analysis of the safety level of the Dalaman yacht harbor vertical wall breakwater in Turkey. The missing wave data of the Dalaman measurement station are hindcasted by use of multi-layer feed-forward neural networks with the steepest descent and conjugate gradient algorithms. The structural failure probabilities of sliding and overturning failure modes are forecasted by approximation of the failure sur-face with a second-degree polynomial of an equal curvature at the design point. in the new approach, for each randomly generated load and tide combination, the joint failure probability reflects both the occurrence probability of loading condition and the structural failure risk at the limit state. The approach can be applied to risk assessment of vertical breakwaters in short CPU durations of portable computers.