Single Breakwater Research Articles

Derivation and analysis of lattice Boltzmann form of the mild slope equation

The present study investigates the performance of the Lattice Boltzmann Method (LBM) as an alternative numerical method for simulating wave propagation in coastal zones. While formulations like the Mild-Slope Equation (MSE) remain efficient for coastal engineering applications due to their simplicity, LBM offers an explicit numerical solver for partial differential equations (PDEs). LBM utilizes local operations, making it well-suited for Graphics Processing Unit (GPU) acceleration and consequently efficient simulations. This study examines LBM's performance in several benchmark cases, including wave propagation behind a single breakwater, harbor resonance, refraction of long waves over a parabolic shoal, and wave propagation over an elliptic shoal. The Chapman-Enskog multi-scale expansion was used within a popular 2D LBM scheme to derive the relaxation time and equilibrium distribution function. The results showed a good agreement between LBM predictions and benchmark data. Furthermore, LBM demonstrated efficiency in reducing the computation time, achieving a notable 30–50% decrease in CPU time and an 85% reduction when utilizing a GPU.

Modelling Turbulent Flows near Coastal Structures Using Various Turbulence Models

Introduction. The reduction in beach width due to erosion is a significant issue that can either be mitigated or exacerbated by coastal protection structures. Modelling breaking waves near the coast and around coastal structures can be used to determine their impact on the dynamics of the coastal zone. The objective of this study is to model and analyze the dynamics of turbulent structures around a single breakwater, obtained using two turbulence modelling schemes: RANS and LES.Materials and Methods. Turbulence induced by breaking waves was investigated. The modelling was based on bathymetric measurements conducted along the Azov Sea coast and a three-dimensional wave hydrodynamics model supplemented with various turbulence calculation configurations.Results. Modelling results of wave processes generating turbulent flows in the presence of coastal protection structures using different turbulence models were obtained. Results obtained based on Reynolds-averaged Navier-Stokes (RANS) equations are compared with the results of Large Eddy Simulation (LES) approach with Smagorinsky dynamic subgrid-scale model (DSM).Discussion and Conclusions. The results showed that wave heights simulated by LES were higher than those simulated by RANS in the front and leeward regions of the coastal protection structure and were lower in its upper part. Thus, according to LES, a greater amount of wave energy was preserved after passing over the breakwater. Velocity vectors of the water medium showed the formation of a vortex when LES was used, whereas no evidence of such turbulent vortices was detected in the case of RANS, confirming the better performance of LES for turbulence modelling in the coastal zone. According to the presented results, LES is the preferred tool for generating turbulence under incoming wave conditions in engineering practices.

Physical and Numerical Simulation of Wave Transmission Over Submerged Breakwater

Nowadays, the submerged breakwaters are becoming attractive to the coastal engineer because they have many advantages including keeping aesthetic value of coastal scenery and reasonable for wave energy reduction. However, on the other hand, their design is very complicated. So, it is very important to understand the characteristics and the impact of wave because of the submerged breakwaters. For this purpose, we developed both numerical and physical model for simulation of wave over submerged breakwaters. The numerical model was developed using CADMAS-SURF, which is widely used in a practice of business in Japan. Physical model studies were performed at the Coastal Engineering Research Laboratory, University of Miyazaki, Japan to assess the performance of submerged breakwaters under a wide range of design conditions. The tests include the use of single and double submerged breakwater, as well as the impact of interval between the breakwaters which will be useful references for submerged breakwater designing in the future. The results show that the transmission coefficients of the numerical simulation have a good agreement with the experiment result with the RMS error 0.14 and 0.19 for the single and double breakwater respectively. This study found that, the application of double breakwaters has no significant impact for reducing wave energy compared to the single breakwater for the wave steepness higher than 0.007 and 0.012 based on laboratory and numerical simulation respectively. The best relative breakwater spacings are 0.75, 0.4, 0.45 and 0.35 for any kind of wave with the period of 0.6, 0.8, 1.0 and 1.2 respectively. In those conditions, the transmission coefficients are on minimum value for each kind of wave, that means the double breakwaters have the good performance on energy reduction.

Performance of submerged semi-circular breakwater under solitary wave in consideration of porous media

Submerged breakwater as the main structure of coastal engineering to protect coast is widely laid on the seabed because of its significant wave-dissipation performance. To reveal the interaction mechanism between waves and submerged breakwater, the hydrodynamic characteristics of a wave passing over different solid breakwaters were numerically and experimentally studied. Compared with the previous research, considering breakwater made up of porous media and the effects of extreme waves generated by hurricanes or tsunamis, this paper systematically investigates the effects of the semi-circular porous medium breakwater on the breaking solitary wave run-up based on a numerical model with the immersed boundary (IB) method. The computational capability of this model is verified firstly. Then, depending on the model, a series of cases are carried out to research the effects of different breakwaters on the run-up of solitary waves. The results show that the influence of porous breakwater on wave propagation is more significant than that of the solid breakwater. With the increase of the gravel particle median diameter, the maximum run-up height and the horizontal hydrodynamic force on the breakwater decrease, while the vertical hydrodynamic force on the breakwater increases. Increasing the size of the breakwater is beneficial to reducing the wave run-up height and the forces on the sloping beach. Compared with the single breakwater, the impact of the tandem breakwater on the wave propagation is more significant.

Wave Interaction With a Pair of Submerged Floating Tunnels in the Presence of An Array of Submerged Porous Breakwaters

Abstract In this article, a coupled model is proposed for wave interaction with a pair of submerged floating tunnels in the presence of an array of bottom-standing trapezoidal porous breakwaters. The theory of Sollitt and Cross is adopted to govern the fluid flow inside the porous medium. For constant water-depth, the eigenfunction expansion method is employed, whereas for varying water-depth, the eigenfunction expansion method along with the mild-slope approximation is employed. The solutions, thus derived, are matched at the shared boundaries under defined physical conditions. First, the performance of a single breakwater of impermeable and permeable type in reducing wave forces on tunnels is analyzed. Next, the performance of two and three submerged breakwaters is studied. The reflection and transmission coefficients of waves are high in the absence of the submerged breakwater and in the presence of an impermeable breakwater. These coefficients significantly reduce in the presence of the submerged porous breakwater. As a result, the horizontal and vertical forces acting on bridges and tunnels are substantially subsided. Wave forces on tunnels reduce with an increase in the angle of incidence. Multiple porous breakwaters show better performance in mitigating wave forces on tunnels. Higher wave force on tunnels is noticed in intermediate water-depth. The findings can enhance the knowledge of submerged porous breakwaters’ performance in reducing wave loads on bridges and tunnels.

The production of the splash phenomenon, as a way of dissipating the energy of a gravitational wave

Investigations are aimed at revealing the conditions for the generation of a Splash wave phenomenon by a submerged breakwater, as having a particularly effective form of wave energy dissipation. On the basis of a wide range of well-known theoretical studies of wave transformation over bottom inhomogeneities, the expediency of laboratory experiments on physical models is shown as a method that allows taking into account the peculiarities of the influence of targeted turbolization of the water flow. Numerous experiments on physical models have shown the possibility of the occurrence of such a phenomenon over a system of bottom inhomogeneities and the rationality of further scientific search. However, the effect is achieved when certain parameters of many independent variables (significant and represented in a wide range of factors) are combined. This circumstance makes a positive solution of the problem rare in nature.In view of the multifactority of the hydrodynamic process under investigation, an analysis of the theoretical premises was carried out, which allowed us to concentrate on a new variant of the solution of the problem posed – a single breakwater with a special crest design. The version of a "box" type breakwater was taken.as a basis But part of the wave energy quenched in it is directed to quenching another part of the energy of the wave flow passing over the top of the breakwater. The task was to find the location, shape and size of the opening in the top. Two versions were investigated: in the form of a perforation and in the form of a slit located along the breakwater. The last version showed its superiority and this result allowed to proceed to the solution of the next problem, the search for the most effective of the of the breakwater cavity cross-section.shape. The obvious direction of the search was the effect of a curvilinear wave-breaking wall of the embankment. Instead of the vertical face under the "visor" (that is, under the horizontal plane of the top surface) previously accepted in the studies, two schemes for calculating the surface curves, differing from each other in radius and length, are studied. The size of the slit in the "visor" varied. The conditions and prospects for the development of Recommendations for the design of the submerged breakwater of this type are described.The urgency of the solution of the problem lies in the broad perspective of the use of submerged breakwaters in recreational zones.

Numerical investigations and optimizations of typical submerged box-type floating breakwaters using SPH

Box-type floating breakwaters have been studied extensively. However, the examinations of the performances of them with different shapes or different numbers of boxes are limited. In addition, if it is possible to optimize the floating breakwaters by combining the optimized parameters in separated testing groups is still unclear. Consequently, in this study, four typical box-type floating breakwaters, i.e., dual rectangular breakwater, single rectangular breakwater, dual circular breakwater, and single circular breakwater, are selected to do extensive investigations using SPH. The coupling between DualSPHysics and MoorDyn is implemented and verified, and the coupled code can be applied to simulate the interactions between waves and moored floating structures. A total of 88 cases are modeled, and the effects of the geometry parameters on wave-attenuation performances of the breakwaters are clarified. The numerical results show that the performances of the breakwaters are greatly sensitive to the immersion depth. In general, the larger and lighter the breakwaters, the better the performances will be. Meanwhile, the dual rectangular breakwater performs the best in wave attenuations, and its motions and forces are smaller than single breakwaters. Importantly, combining the optimized parameters in each separated testing group is found to be effective to optimize the floating breakwaters.

Hydrodynamic performance of a dual-floater hybrid system combining a floating breakwater and an oscillating-buoy type wave energy converter

The high cost of power generation impedes commercial-scale wave power operations. The objective of this work is to provide a cost-sharing solution by combining wave energy extraction and coastal protection. A two-dimensional numerical wave tank was developed using Star-CCM+ Computational Fluid Dynamics software to investigate the hydrodynamic performance of a dual-floater hybrid system consisting of a floating breakwater and an oscillating-buoy type wave energy converter (WEC), and was compared with published experimental results. The differences between the hydrodynamic performance of the hybrid system, a single WEC and a single breakwater were compared. Wave resonance in the WEC-breakwater gap has a significant impact on system performance, with the hybrid system demonstrating both better wave attenuation and wave energy extraction capabilities at low wave frequencies, i.e., wider effective frequency. Forces on the breakwater were generally reduced due to the WEC. Wave resonance in the narrow gap has an adverse effect on the energy efficiency of the hybrid system with an asymmetric WEC, while a beneficial effect with a symmetric WEC. The wave energy conversion efficiency of hybrid system can be improved by increasing the draft and width of the WEC and decreasing the distance between the WEC and the breakwater. The findings of this paper make wave energy economically competitive and commercial-scale wave power operations possible.

Environmental impacts of single and successive breakwaters along the Mediterranean coastline at Radès–Ezzahra, NE Tunisia

The coastline between Rades and Ezzahra, NE Tunisia, suffered from erosion during a strong storm in 1981. As a consequence, between 1985 and 1988 a single breakwater was constructed in Rades and two successive breakwaters in Ezzahra. The paper reports a study of the effectiveness of these structures and considers the other factors which influence the accretion/erosion of the shoreline.

Numerical Study of Effect of Wave Around Single Break-Water with the Swan Model

A new version of the Stimulating Wave Nearshore (SWAN) model (version 40.51) was used to stimulate the evolution of directional irregular wave near a single breakwater and the Wen spectrum was adopted as an input spectrum. The wave diffraction effect of irregular wave, which is the main improvement compared with the previous SWAN versions, was tested with the experimental data of single breakwater collected in the State Key Laboratory of Coastal and Offshore Engineering (SLCOE) at Dalian University of Technology (DUT) and the stimulated results of Wu Yan and JONSWAP spectrum as input data, respectively. By comparing the results in four cases, it is seen that the results stimulated by the SWAN model with the JONSWAP or Wen spectra are better than those with Wu's spectrum, and the results simulated with the Wen spectrum is little larger than those with the JONSWAP spectrum and more closely approximated to the measured data compared to the results with the JONSWAP spectrum. It is then concluded that the new SWAN model with the Wen spectrum can be well used to stimulate wave diffraction around a single breakwater.

LABORATORY STUDIES ON THE STABILITY OF TANDEM BREAKWATER

ABSTRACT Tandem Breakwater consists of a submerged reef breakwater constructed at some distance in front of a conventional non-overtopping rubble mound breakwater. The submerged reef breakwater breaks the high waves and the stilling basin between two breakwaters attenuates them. Hence, smaller waves approach the non-overtopping rubble mound breakwater and break on it. Therefore, the non-overtopping rubble mound breakwater may be designed for smaller waves, resulting in relatively lighter armour stones. In the model studies, it has been found that for a relative breakwater spacing X/d varying from 3.33 to 4.29 between the breakwaters, the damage of a tandem Breakwater is 20% to 60% less as compared with a single breakwater for similar operating criteria.

Numerical simulation of wave effects around compound coastal structures

A new three-dimensional potential flow numerical method has been developed to study wave diffraction around compound coastal structures. This new method is based on a multi-block finite-analytic scheme. A chimera domain decomposition technique is used to model complex geometry and to connect overlapped grids by interpolating information across block boundaries. Calculations were performed for three examples, including a harbor entrance, a single breakwater, and a combined breakwater and large floating platform, to illustrate the flexibility and effectiveness of the present method.

Oblique-Wave Diffraction by Noncollinear Segmented Offshore Breakwaters

A theoretical solution is presented for oblique-wave diffraction by a segmented offshore breakwater system consisting of an infinite array of equally spaced vertical barriers oriented at an arbitrary angle to the line joining their centers. The solution is obtained by a Green's function approach. The geometrical periodicity of the breakwater system reduces the problem to that of a singular integral equation for the potential difference across a single breakwater element. Zero-order reflection and transmission coefficients are defined in terms of the amplitudes of the asymptotic (propagating) diffracted waves traveling in the opposite direction to or the same direction as the incident waves, respectively. Numerical values of these coefficients are presented for a range of angles of wave incidence and breakwater orientation, for various breakwater geometric configurations. For certain parameter combinations, significant wave reflection can be achieved using this type of breakwater system.

Wave regime in the water area of a port with a single breakwater under the effect of long waves

The investigations established that the wave regime in the water area of a port with a single breakwater occurring under the effect of a long wave represents a complex picture of interaction of the incident wave and system of reflected waves.

Accretion Behind Single Offshore Breakwater

This study notes that the main variables in evaluating apex postion of a salient behind a single breakwater parallel to the shore with waves normal to both are its length and distance offshore. Because the shape of the salient is related to wave diffraction patterns, the apex distance from the breakwater on its centerline, its radial distance, and angle from the tip of the breakwater are all useful measurements when related to the two main variables mentioned. It is also noted that values of breakwater length to distance offshore have been established for the limting conditions of tombolo and zero salient formation. Between these two extremities, the extent of salient accumulation in equilibrium state can be determined quantitatively for designing a single offshore breakwater.

GENERALIZED WAVE DIFFRACTION DIAGRAMS

Wave diffraction is the phenomenon in which water waves are propagated into a sheltered region formed by a breakwater or similar barrier which interrupts a portion of a regular wave train (Fig. 1). The principles of diffraction have considerable practical application in connection with the design of breakwaters as discussed by Dunham (1951) at the Long Beach Conference. The phenomenon is analogous to the diffraction of light, sound, and electromagnetic waves. Two general types of diffraction problems usually are encountered: one, the passage of waves around the end of a semi-infinite impermeable breakwater (Putnam and Arthur, 1948), and, second, the passage of waves through a gap in a breakwater (Blue and Johnson, 1949t Carr and Stelzriede, 1951). In general, the theoretical solutions have been found to apply with conservative results, that is, the predicted wave heights in the lee of a breakwater are found to be slightly larger than the height of waves that may be expected under actual conditions. The use of the diffraction theory in breakwater design is made convenient when summarized in the form of diagrams with curves of equal values of diffraction coefficients on a coordinate system in which the origin of the Bystem is at the tip of a single breakwater (Figs. 2a-2b, and 3) or at the center of a gap (Figs. 2c, and 4-6). The diffraction coefficient in this instance is defined as the ratio of the diffracted wave height to the incident wave height and usually is designated by the symbol K». The procedure in preparing diffraction diagrams appears elsewhere (Johnson, 1950). The purpose of this paper is to present diffraction diagrams to supplement the material of Dunham (1951). For complete details on the application of diffraction diagrams to typical harbor problems the reader is referred to this latter paper.