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Keywords = porous breakwater

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19 pages, 10986 KiB  
Article
A Study on the Effects of Morphological Changes Due to the Construction of Multiple Coastal Structures
by Kyu-Tae Shim and Kyu-Han Kim
J. Mar. Sci. Eng. 2024, 12(12), 2174; https://doi.org/10.3390/jmse12122174 - 28 Nov 2024
Cited by 2 | Viewed by 1288
Abstract
The study area was Anin Beach, where a 1.48-km-long breakwater, consisting of a non-porous caisson, was constructed over 16 months. During this process, significant erosion occurred over a wide area behind the coast, with a maximum reduction in the beach width of 36 [...] Read more.
The study area was Anin Beach, where a 1.48-km-long breakwater, consisting of a non-porous caisson, was constructed over 16 months. During this process, significant erosion occurred over a wide area behind the coast, with a maximum reduction in the beach width of 36 m observed in the central part of the coastline. As a countermeasure to prevent erosion, a submerged breakwater was installed that consisted of concrete blocks and had a length of 600 m. Following the implementation of this submerged breakwater, the beach behind it increased in width by 64 m, in proportion to the installation length, while erosion phenomena, such as the loss of coastal roads, were observed at both ends of the structure. In this study, the topographical changes caused by waves and currents were analyzed to identify their causes and establish countermeasures. Additionally, the planned measures, established before structure installation, were closely examined against the actual occurrences observed onsite through a coastline survey. Full article
(This article belongs to the Special Issue Coastal Evolution and Erosion under Climate Change)
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13 pages, 4339 KiB  
Article
Experimental Investigation on Wave Dissipation of Perforated Pipe Breakwater Under Regular Wave Conditions
by Shaopeng Yang, Lipeng Yang, Bing Shi, Jing Na and Yakun Guo
J. Mar. Sci. Eng. 2024, 12(12), 2137; https://doi.org/10.3390/jmse12122137 - 23 Nov 2024
Viewed by 1209
Abstract
The permeable breakwater is an innovative, eco-friendly coastal protection structure that reduces wave impact while minimizing “dead water” and environmental harm. This study introduces a perforated pipe breakwater design with an increasing pipe diameter from top to bottom, evaluated through physical model tests [...] Read more.
The permeable breakwater is an innovative, eco-friendly coastal protection structure that reduces wave impact while minimizing “dead water” and environmental harm. This study introduces a perforated pipe breakwater design with an increasing pipe diameter from top to bottom, evaluated through physical model tests using transmission coefficient Kt and reflection coefficient Kr serving as the primary parameters. The results indicate that Kt decreases as the relative width (B/L), wave steepness (H/L), and relative water depth (h/L) increase, but rises with a steeper breakwater slope. When B/L exceeds 0.3, H/L surpasses 0.06, or the h/L ratio is greater than 0.3, Kt gradually declines until reaching a stable state, resulting in a more pronounced wave reduction. As B/L and H/L increase, the coefficient Kr initially drops, then rises. The slope ratio of 1:1.5 demonstrates the most effective wave energy dissipation, with primary dissipation occurring on the front slope. The mixed pipe diameter design shows superior wave absorption over a uniform diameter. Compared to a porous horizontal plate, the perforated pipe breakwater exhibits better wave absorption. These findings offer valuable guidance for designing eco-friendly coastal protection projects. Full article
(This article belongs to the Section Ocean Engineering)
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18 pages, 52176 KiB  
Article
Design and Deployment of a Floating Porous Screen Breakwater in a Mesotidal Environment
by Brandon Lieberthal, Richard Perry, Elisabeth Younce, Liam Hanley, Mary Bryant and Kimberly Huguenard
J. Mar. Sci. Eng. 2024, 12(9), 1684; https://doi.org/10.3390/jmse12091684 - 23 Sep 2024
Viewed by 2379
Abstract
The performance of an intermediate-scale modular, permeable, floating breakwater comprised of an array of vertical screens is optimized and tested. A distinctive attribute of this breakwater design is its adaptive capacity to fluctuating water levels owing to its floating configuration, thereby preserving its [...] Read more.
The performance of an intermediate-scale modular, permeable, floating breakwater comprised of an array of vertical screens is optimized and tested. A distinctive attribute of this breakwater design is its adaptive capacity to fluctuating water levels owing to its floating configuration, thereby preserving its efficacy during high tide and storm tide scenarios—an advancement over conventional bottom-mounted structures. The initial validation of the concept was tested in a laboratory wave basin in regular waves, which demonstrated promising results for three porous panels. Next, the breakwater’s design parameters were optimized using a finite difference computational fluid dynamics software, (FLOW-3D version 2023R2), considering porosity, spacing, and panel count. A scaled prototype, representative of a 1:2 ratio was then deployed during the summer of 2022 along the coast of Castine, ME, within a mesotidal, semi-sheltered system characterized by tidal currents and waves. Notably, the breakwater succeeded in attenuating half of the wave energy for periods shorter than 4 s, evidenced by transmission coefficients below 0.5, making this technology suitable for locally generated waves with shorter periods. During storm events, instantaneous transmission coefficients decreased to as low as 0.25, coinciding with significant wave heights exceeding 0.8 m. Additionally, the efficacy of wave attenuation improved slightly over time as biofoulants adhered to the structure, thereby enhancing drag and mass. Full article
(This article belongs to the Section Ocean Engineering)
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19 pages, 3877 KiB  
Article
Scattering Study of a Composite Breakwater Placed in Front of an Impermeable Back Wall under the Action of Water Waves
by Jiaxiu Cao, Chao Wang and Zeping Wang
J. Mar. Sci. Eng. 2023, 11(10), 1878; https://doi.org/10.3390/jmse11101878 - 27 Sep 2023
Viewed by 1373
Abstract
Based on the assumption of linear potential flow theory, the scattering problem of a composite breakwater placed in front of an impermeable back wall is theoretically investigated. The velocity potential in each subregion is found using the eigenfunction expansion method. The boundary conditions [...] Read more.
Based on the assumption of linear potential flow theory, the scattering problem of a composite breakwater placed in front of an impermeable back wall is theoretically investigated. The velocity potential in each subregion is found using the eigenfunction expansion method. The boundary conditions of the porous region are treated using Darcy’s law. The semi-analytical solution of a composite breakwater placed in front of an impermeable back wall is then obtained based on the matching conditions of the boundaries of the different regions. The effects of different parameters on the wave loads and wave amplitudes are investigated. In addition, to better understand the performance of the composite breakwater, the scattering problem of the composite breakwater without considering an impermeable back wall is also investigated. The correctness of this theoretical model is verified by comparing the results with previous work. Based on the results of hydrodynamic calculations and analysis of various aspects of a composite breakwater placed in front of an impermeable back wall, the study of the effect of a composite breakwater placed in front of an impermeable back wall allows us to propose a long-term and cost-effective solution for the protection of various marine facilities from wave attacks. Full article
(This article belongs to the Special Issue The 10th International Conference on Coastal and Ocean Engineering)
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18 pages, 7586 KiB  
Article
Wave Characteristics over a Dual Porous Submerged Breakwater Using a Fully Nonlinear Numerical Wave Tank with a Porous Domain
by Eun-Hong Min, Weoncheol Koo and Moo-Hyun Kim
J. Mar. Sci. Eng. 2023, 11(9), 1648; https://doi.org/10.3390/jmse11091648 - 23 Aug 2023
Cited by 2 | Viewed by 2034
Abstract
This study developed a two-dimensional fully nonlinear numerical wave tank (FN-NWT) to examine the nonlinear interaction between waves and dual submerged porous structures. Using the FN-NWT, not only reflection and transmission coefficients, but also wave deformation/force depending on porosity were investigated. The FN-NWT [...] Read more.
This study developed a two-dimensional fully nonlinear numerical wave tank (FN-NWT) to examine the nonlinear interaction between waves and dual submerged porous structures. Using the FN-NWT, not only reflection and transmission coefficients, but also wave deformation/force depending on porosity were investigated. The FN-NWT was developed using the boundary element method (BEM), and consisted of a fluid domain and a porous medium domain. Darcy’s law or the non-Darcy (Forchheimer) flow equation were applied to the flow passing through the porous domain. The wave reflection coefficient of the porous submerged structures agreed well with the given experimental data when using Forchheimer flow boundary conditions. Excessive attenuation of the transmitted wave occurred when Darcy’s condition was employed. The difference in each coefficient due to the spacing of the submerged structure was reduced in the porous structure compared with the non-porous structure. The difference according to the incident wave height was clearly revealed in the transmission coefficient. The developed dual-domain FN-NWT can be applied to investigate the nonlinear interaction between waves and porous structures as a first-cut design tool. Full article
(This article belongs to the Special Issue Advances in Marine Applications of Computational Fluid Dynamics)
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10 pages, 769 KiB  
Technical Note
Influence of Van Gent Parameters on the Overtopping Discharge of a Rubble Mound Breakwater
by Federico Castiglione, Martina Stagnitti, Rosaria Ester Musumeci and Enrico Foti
J. Mar. Sci. Eng. 2023, 11(8), 1600; https://doi.org/10.3390/jmse11081600 - 16 Aug 2023
Cited by 2 | Viewed by 1225
Abstract
The choice of the values of the friction parameters may strongly influence the numerical modeling of the interaction between waves and porous media. Here, an assessment of such an influence is carried out using the OpenFOAM solver IhFoamV1 to simulate the response of [...] Read more.
The choice of the values of the friction parameters may strongly influence the numerical modeling of the interaction between waves and porous media. Here, an assessment of such an influence is carried out using the OpenFOAM solver IhFoamV1 to simulate the response of the Catania harbor breakwater under extreme wave attack. The numerical model was validated by comparison with an experimental dataset, and a sensitivity analysis of the overtopping discharge estimate to van Gent parameter β was carried out testing values suggested by previous studies. A discussion on the importance of a careful estimate of such a parameter when dealing with the numerical modeling of porous coastal structures is presented. Indeed, variations in the non-dimensional overtopping discharge higher than 150% were observed as a consequence of a small variation (1020%) in the absolute value of β. Full article
(This article belongs to the Special Issue Advanced Studies in Breakwaters and Coastal Protection)
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19 pages, 2814 KiB  
Article
Wave Transmission over Rubble-Mound Submerged Breakwaters
by Elpidoforos Repousis, Ioannis Roupas and Constantine Memos
J. Mar. Sci. Eng. 2023, 11(7), 1346; https://doi.org/10.3390/jmse11071346 - 1 Jul 2023
Cited by 5 | Viewed by 2108
Abstract
This study focuses on the prediction of technical efficiency of narrow-crested submerged permeable rubble-mound breakwaters, in terms of wave attenuation. A number of existing formulae for estimating wave transmission coefficient for submerged breakwaters can be found in the literature, whereas in this work [...] Read more.
This study focuses on the prediction of technical efficiency of narrow-crested submerged permeable rubble-mound breakwaters, in terms of wave attenuation. A number of existing formulae for estimating wave transmission coefficient for submerged breakwaters can be found in the literature, whereas in this work further improvement for that estimation has been achieved mainly through physical modelling. A series of 2D experiments under scale were conducted for regular and random waves providing data on wave transmission coefficient and respective wave breaking characteristics. A Boussinesq-type wave model capable of simulating wave propagation for regular waves over porous submerged breakwaters was also used in order to provide additional wave transmission information. Data analysis showed that wave breaking mechanism significantly affects wave energy dissipation and, therefore, wave breaking occurrence and type can be directly linked to wave transmission coefficient for a given structure’s geometry and sea state. The result of this work is the proposal of a set of simple semi-empirical equations for predicting wave transmission coefficient over small profile porous submerged breakwaters in relevance to the parameterization of the expected dominant wave breaking mechanism. Full article
(This article belongs to the Special Issue Advanced Studies in Breakwaters and Coastal Protection)
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20 pages, 13612 KiB  
Article
A Laboratory Scale of the Physical Model for Inclined and Porous Breakwaters on the Coastline of Soc Trang Province (Mekong Delta)
by Chuong Thanh Le, Duong Van Do, Duong Binh Nguyen and Ping Wang
Water 2023, 15(7), 1366; https://doi.org/10.3390/w15071366 - 1 Apr 2023
Cited by 2 | Viewed by 2486
Abstract
In the last few decades, the Mekong Delta coastlines have suffered serious erosion. Strong waves during the Northeast Monsoon are one of the main reasons for this. Many types of breakwaters with different structural components have been designed and built to mitigate coastline [...] Read more.
In the last few decades, the Mekong Delta coastlines have suffered serious erosion. Strong waves during the Northeast Monsoon are one of the main reasons for this. Many types of breakwaters with different structural components have been designed and built to mitigate coastline erosion. Vertical seawalls have been widely used, but they create reflection waves, which can generate water particle kinematics in front of the structure and increase the toe scour. In this study, an innovative block of inclined and porous breakwaters was studied by conducting laboratory-scale experiments. The experimental results show that inclined and porous breakwaters can considerably reduce wave energy due to transmission, reflection, and diffraction compared to inclined breakwaters. The porosity on the front and back sides of the structures has also been studied. Letting sediment-laden seawaters penetrate inside the sheltered zones, porous breakwaters promote accretion and facilitate the forestation of mangrove belts. Full article
(This article belongs to the Special Issue Estuarine and Coastal Hydrodynamics)
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21 pages, 13436 KiB  
Article
Numerical Study on the Effects of the Multiple Porous Medium Breakwaters on the Propagation of the Solitary Wave
by Kui Zhu, Runxiang Jiang, Zhaolong Sun, Hao Qin, Zeqi Cheng, Yang Wang and Enjin Zhao
J. Mar. Sci. Eng. 2023, 11(3), 565; https://doi.org/10.3390/jmse11030565 - 7 Mar 2023
Cited by 5 | Viewed by 2338
Abstract
Submerged breakwater, as an important marine engineering structure, can effectively absorb wave energy and is widely used in marine engineering protection. As a new type of breakwater, porous medium breakwater has a certain influence on wave propagation. However, the influence of multiple porous [...] Read more.
Submerged breakwater, as an important marine engineering structure, can effectively absorb wave energy and is widely used in marine engineering protection. As a new type of breakwater, porous medium breakwater has a certain influence on wave propagation. However, the influence of multiple porous medium submerged breakwaters on extreme waves remains to be studied. In the study, considering effects of extreme waves generated by hurricanes or tsunamis, the influence of the solitary wave on the multiple semi-circle porous medium breakwater is systematically investigated. According to the computational fluid dynamics theory, a numerical tank is established, in which the porous medium module is coupled. The computational capability of this model is verified first. Then, depending on the model, a series of cases are carried out to study the effects of different porous medium breakwaters on the propagation of the solitary wave. The results show that when the porosity is 0.8, the force on the submerged breakwaters is the smallest, and the water level and the velocity decrease seriously. With the increase in the diameter of the submerged breakwater, the wave profile gradually becomes flat. The higher the wave height, the more serious the wave deformation after passing through the submerged breakwater. Full article
(This article belongs to the Special Issue Coastal Engineering: Sustainability and New Technologies)
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18 pages, 7340 KiB  
Article
Efficiency and Wave Run-Up of Porous Breakwater with Sloping Deck
by Mengmeng Han and Chien Ming Wang
J. Mar. Sci. Eng. 2022, 10(12), 1896; https://doi.org/10.3390/jmse10121896 - 5 Dec 2022
Cited by 4 | Viewed by 2641
Abstract
In order to protect fragile shoreline and coastal assets during extreme storms, a combined floating breakwater-windbreak has been proposed to reduce both wind and wave energies in the sheltered area. The 1 km-long breakwater has a porous hull with internal tubes to allow [...] Read more.
In order to protect fragile shoreline and coastal assets during extreme storms, a combined floating breakwater-windbreak has been proposed to reduce both wind and wave energies in the sheltered area. The 1 km-long breakwater has a porous hull with internal tubes to allow free passage of water; thereby further dissipating wave energy. The deck of the structure is designed to have a slope of 25 degrees facing the upstream side, and arrays of cylindrical tubes are placed on the sloping deck to form a windbreak. A reduced-scale (1:50) model test was carried out in a wave flume to examine wave sheltering performance under significant wave heights Hs = 3.0 m to 7.5 m and peak wave periods Tp = 9.4 s to 14 s sea states. Both regular and random wave conditions with different wave heights were considered. It is found that transmission coefficients ranging from 0.4 to 0.6 can be achieved under tested wave conditions. Porous breakwater hull increases the wave dissipation coefficients and is effective in reducing the wave reflection at the upstream side. The wave run-up length is dependent on the Iribarren number if the reduction induced by vertical freeboard is considered. Based on experimental data, empirical formulae have been proposed to predict the wave run-up responses in regular waves, probability of non-zero wave run-up occurrence, modified Weibull distribution of the wave run-up peaks and extreme wave run-up in random waves. Full article
(This article belongs to the Special Issue Recent Advances in Floating Structures)
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26 pages, 18346 KiB  
Article
Wave Motion and Seabed Response around a Vertical Structure Sheltered by Submerged Breakwaters with Fabry–Pérot Resonance
by Lai Jiang, Jisheng Zhang, Linlong Tong, Yakun Guo, Rui He and Ke Sun
J. Mar. Sci. Eng. 2022, 10(11), 1797; https://doi.org/10.3390/jmse10111797 - 21 Nov 2022
Cited by 8 | Viewed by 2759
Abstract
This paper presents the results from a numerical simulation study to investigate wave trapping by a series of trapezoidal porous submerged breakwaters near a vertical breakwater, as well as the seabed response around the vertical breakwater. An integrated model, based on the volume-averaged [...] Read more.
This paper presents the results from a numerical simulation study to investigate wave trapping by a series of trapezoidal porous submerged breakwaters near a vertical breakwater, as well as the seabed response around the vertical breakwater. An integrated model, based on the volume-averaged Reynolds-averaged Navier–Stokes (VARANS) equations is developed to simulate the flow field, while the dynamic Biot’s equations are used for simulating the wave-induced seabed response. The reflection of the wave energy over the submerged breakwaters, caused by the vertical breakwater, can be reserved, indicating that the existence of the submerged breakwaters in the front of the vertical breakwater can either provide shelter or worsen the hazards to the vertical breakwater. Numerical examples show two different modes under the Fabry–Pérot (F–P) resonance condition of the wave transformation, namely the wave reflection (Mode 1) and the wave trapping (Mode 2). The distance between the submerged breakwaters and the vertical breakwater, is a key parameter dominating the local hydrodynamic process and the resultant dynamic stresses around the vertical breakwater. The numerical results indicated that more submerged breakwaters and a higher porosity of submerged breakwaters will obviously dissipate more wave energy, and hence induce a smaller wave force on the rear vertical breakwater and liquefaction area around the vertical breakwater. Full article
(This article belongs to the Special Issue Wave Interactions with Coastal Structures II)
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17 pages, 2285 KiB  
Article
Numerical Model of Constrained Wave Energy Hyperbaric Converter under Full-Scale Sea Wave Conditions
by Moisés Brito, Francisco Bernardo, Maria G. Neves, Diogo R. C. B. Neves, Alejandro J. C. Crespo and José M. Domínguez
J. Mar. Sci. Eng. 2022, 10(10), 1489; https://doi.org/10.3390/jmse10101489 - 14 Oct 2022
Cited by 10 | Viewed by 3097
Abstract
A 2D numerical investigation of the power absorption of a constrained wave energy hyperbaric converter (WEHC) under full-scale sea wave conditions is presented. A fully non-linear numerical model DualSPHysics, based on the coupling of a smoothed particle hydrodynamics (SPH) fluid solver with a [...] Read more.
A 2D numerical investigation of the power absorption of a constrained wave energy hyperbaric converter (WEHC) under full-scale sea wave conditions is presented. A fully non-linear numerical model DualSPHysics, based on the coupling of a smoothed particle hydrodynamics (SPH) fluid solver with a multibody dynamics solver, is used to model the interaction between wave and WEHC sub-systems. The numerical model was first validated against experimental data for a similar device, with a good accordance between PTO position and velocity. The model is then employed to study the hydrodynamics of a constrained WEHC considering several sea states, different hydraulic power take-off (PTO) damping and breakwater geometries. It is observed that the capture width ratio (CWR) is particularly sensitive to variations in the PTO damping, although the CWR absolute maximum is less sensitive considering mild variations applied to the PTO damping. Both wave height and wave period have an important effect on the CWR. The breakwater geometry is also essential for the performance of the WEHC, with a decrease in maximum CWR of about 15% for porous breakwater. These results are necessary to understand the full-scale behaviour of WEHC. Full article
(This article belongs to the Special Issue Coastal Engineering: Sustainability and New Technologies)
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29 pages, 19567 KiB  
Article
Validation and Comparisons of Methodologies Implemented in a RANS-VoF Numerical Model for Applications to Coastal Structures
by Eric Didier and Paulo R. F. Teixeira
J. Mar. Sci. Eng. 2022, 10(9), 1298; https://doi.org/10.3390/jmse10091298 - 14 Sep 2022
Cited by 9 | Viewed by 2351
Abstract
Methodologies to be used in numerical models based on Reynolds-averaged Navier–Stokes (RANS) equations and the volume of fluid (VoF) to deal with waves over coastal structures, which involve wave breaking and overtopping and porous structures, are shown in this manuscript. Two turbulence models, [...] Read more.
Methodologies to be used in numerical models based on Reynolds-averaged Navier–Stokes (RANS) equations and the volume of fluid (VoF) to deal with waves over coastal structures, which involve wave breaking and overtopping and porous structures, are shown in this manuscript. Two turbulence models, k-ε NLS (non-linear Reynolds stress tensor) and k-ε SCM (stabilized closure model), that are used to avoid the growth of the eddy viscosity, are implemented in the FLUENT® numerical model. Additionally, equations of momentum and turbulence models are adapted to simulate porous media of coastal structures. Comparisons of performance of k-ε NLS, k-ε SCM and standards k-ε and k-ω SST models in several classical cases of regular and random waves on coastal structures are carried out. It was noticed that the standard k-ε turbulence model, and k-ω SST with less intensity, over-predicted eddy viscosity, caused the decay of the free surface elevation and under-estimated wave overtopping discharge. k-ε NLS and k-ε SCM turbulence models have similar performance, with slightly better results of k-ε NLS, showing good agreement with experimental ones. Full article
(This article belongs to the Special Issue Coastal Engineering: Sustainability and New Technologies)
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14 pages, 7863 KiB  
Article
Experimental Investigation on Bragg Resonant Reflection of Waves by Porous Submerged Breakwaters on a Horizontal Seabed
by Wei Xu, Chun Chen, Min Han Htet, Mohammad Saydul Islam Sarkar, Aifeng Tao, Zhen Wang, Jun Fan and Degang Jiang
Water 2022, 14(17), 2682; https://doi.org/10.3390/w14172682 - 29 Aug 2022
Cited by 6 | Viewed by 2960
Abstract
Submerged breakwaters based on Bragg resonance could be one of the measures used for mitigating marine disasters and coastal erosion in nearshore areas. Here, flume experiments were conducted to investigate the Bragg resonant reflection of waves propagating over porous submerged breakwaters. Furthermore, the [...] Read more.
Submerged breakwaters based on Bragg resonance could be one of the measures used for mitigating marine disasters and coastal erosion in nearshore areas. Here, flume experiments were conducted to investigate the Bragg resonant reflection of waves propagating over porous submerged breakwaters. Furthermore, the influence of permeability, relative width, relative height, and section shapes of submerged breakwaters on Bragg resonant reflection were considered. This revealed that the Bragg resonant reflection coefficient increased with the decrease in permeability and increase in the relative height of submerged breakwaters. However, a slowing trend occurred when the Bragg resonant reflection coefficient peak decreased with the increase in permeability and increased with the increase in relative height. Moreover, the primary peak Bragg resonance increased with the increase in the relative width of submerged breakwaters in the range of 0.1–0.3. This was consistent with the numerical results of Ni and Teng (2021), to a certain extent, as the reflection coefficient first increased and then decreased with the relative bar width. In addition, rectangular submerged breakwaters demonstrated a better reflection effect than the trapezoidal submerged breakwaters, and the triangular submerged breakwaters demonstrated a poor reflection effect. Full article
(This article belongs to the Special Issue Research on the Interaction of Water Waves and Ocean Structures)
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27 pages, 6556 KiB  
Article
Wave Forces on a Partially Reflecting Wall by Oblique Bragg Scattering with Porous Breakwaters over Uneven Bottoms
by Jen-Yi Chang and Chia-Cheng Tsai
J. Mar. Sci. Eng. 2022, 10(3), 409; https://doi.org/10.3390/jmse10030409 - 11 Mar 2022
Cited by 7 | Viewed by 2597
Abstract
In this study, the scattering of oblique water waves by multiple variable porous breakwaters near a partially reflecting wall over uneven bottoms are investigated using the eigenfunction matching method (EMM). In the solution procedure, the variable breakwaters and bottom profiles are sliced into [...] Read more.
In this study, the scattering of oblique water waves by multiple variable porous breakwaters near a partially reflecting wall over uneven bottoms are investigated using the eigenfunction matching method (EMM). In the solution procedure, the variable breakwaters and bottom profiles are sliced into shelves separated steps and the solutions on the shelves are composed of eigenfunctions with unknown coefficients representing the wave amplitudes. Using the conservations of mass and momentum as well as the condition for the partially reflecting sidewall, a system of linear equations is resulted that can be solved by a sparse-matrix solver. The proposed EMM is validated by comparing its results with those in the literature. Then, the EMM is applied for studying oblique Bragg scattering by periodic porous breakwaters near a partially reflecting wall over uneven bottoms. The constructive and destructive Bragg scattering are discussed. Numerical results suggest that the partially reflecting wall should be separated from the last breakwater by half wavelength of the periodic breakwaters to migrate the wave force on the vertical wall. Full article
(This article belongs to the Special Issue Feature Papers in Ocean Engineering)
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