This study investigates the performance of dual curved-leg pontoon floating breakwaters in finite water depth under the assumption of linear wave theory. The analysis is carried out for four different models of curved...This study investigates the performance of dual curved-leg pontoon floating breakwaters in finite water depth under the assumption of linear wave theory. The analysis is carried out for four different models of curvedleg geometries, which are combinations of convex and concave shapes. The models are classified as follows. Model-1: Seaside and leeside face concave, Model-2: Seaside and leeside face convex, Model-3: Seaside face convex and leeside face concave, and Model-4: Seaside face concave and leeside face convex. The Boundary Element Method is utilized in order to find a solution to the associated boundary value problem. The numerical results are validated against existing analytical and experimental data. Further, the study examines the wave reflection, wave transmission, and the hydrodynamic forces acting on the structure for different values of waves and structural parameters. Overall, the different dual curved-leg pontoon breakwaters are more effective, reducing wave transmission by over 15% and increasing wave reflection by more than 5% compared to traditional models. The study shows that the wave reflected by Model 1 significantly increased and attenuated the wave transmission relative to other models. The study found that the height of the curved-leg of Model 1 plays a critical role in blocking waves and redirecting the flow. More precisely, the present analysis concludes that the hydrodynamic performance of Model-1 presents an optimized breakwater design that outperforms the proposed models.展开更多
Two asymmetric types of floating breakwaters integrated with a wave energy converter(WEC-FBs),a floating square box with a triangle(trapezoidal type)or a wave baffle(L type)attached to its rear side,have been proposed...Two asymmetric types of floating breakwaters integrated with a wave energy converter(WEC-FBs),a floating square box with a triangle(trapezoidal type)or a wave baffle(L type)attached to its rear side,have been proposed.In this research,the hydrodynamic performance,including capture width ratio(CWR),wave transmission coefficient,heave motion,and force coefficient,were studied and compared between the two types.A numerical simulation model based on the Navier-Stokes equation was employed.The effects of power take-off(PTO)damping coefficient,wave periods,and draft/displacement on the hydrodynamic performance of the two structure shapes were simulated and investigated.The results reveal that the L type performs better in shorter wave periods,and the trapezoidal type exhibits a higher CWR in intermediate wave periods.This study offers knowledge of the design and protection of the two WEC-FB types.展开更多
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 a...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.展开更多
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 considere...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.展开更多
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 e...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.展开更多
In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves...In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves and in the proximity of a vertical wall. Both single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with appropriate mixed type boundary conditions, and solved numerically using the ISBM. To model the permeability of the breakwaters fully absorbing boundary conditions are assumed. Numerical results are presented in terms of hydrodynamic quantities of the reflection coefficients. These are firstly validated against the results of a multi-domain boundary element method(BEM) developed independently for a previous study. The agreement between the results of the two methods is excellent. The coefficients of reflection are then computed and discussed for a variety of structural conditions including the breakwaters height, width, spacing, and absorbing permeability. Effects of the proximity of the vertical plane wall are also investigated. The breakwater's width is found to have only marginal effects compared with its height. Permeability tends to decrease the minimum reflections. These coefficients show periodic variations with the spacing relative to the wavelength. Trapezoidal breakwaters are found to be more cost-effective than the rectangular breakwaters. Dual breakwater systems are confirmed to perform much better than single structures.展开更多
This study examines wave interactions with multiple semi-immersed Jarlan-type perforated breakwaters. A numerical model based on linear wave theory and an eigenfunction expansion method has been developed to study the...This study examines wave interactions with multiple semi-immersed Jarlan-type perforated breakwaters. A numerical model based on linear wave theory and an eigenfunction expansion method has been developed to study the hydrodynamic characteristics of breakwaters. The numerical results show a good agreement with previous analytical results and experimental data for limiting cases of double partially immersed impermeable walls and double and triple Jarlan-type breakwaters. The wave transmission coefficient Cv; reflection coefficient CR, and energy dissipation coefficient CE coefficients and the horizontal wave force exerted on the front and rear walls are examined. The results show that CR reaches the maximum value when B/L = 0.46n while it is smallest when B/L=0.46n＋0.24 （n=0, 1, 2,...）. An economical triple semi-immersed Jarlan-type perforated breakwater can be designed with B/L = 0.25 and CR and CT ranging from 0.25 to 0.32 by choosing a relative draft d/h of 0.35 and a permeability parameter of the perforated front walls being 0.5 for an incident wave number kh nearly equal to 2.0. The triple semi-immersed Jarlan-type perforated breakwaters with significantly reduced CR, will enhance the structure＇s wave absorption ability, and lead to smaller wave forces compared with the double one. The proposed model may be used to predict the response of a structure in the preliminary design stage for practical engineering.展开更多
In this study, we examine the hydrodynamic characteristics of three rows of vertical slotted wall breakwaters in which the front and middle walls are permeable and partially immersed in a water channel of constant dep...In this study, we examine the hydrodynamic characteristics of three rows of vertical slotted wall breakwaters in which the front and middle walls are permeable and partially immersed in a water channel of constant depth, whereas the third wall is impermeable. The wave–structure interaction and flow behavior of this type of breakwater arrangement are complicated and must be analyzed before breakwaters can be appropriately designed. To study the hydrodynamic breakwater performance, we developed a mathematical model based on the eigenfunction expansion method and a least squares technique for predicting wave interaction with three rows of vertical slotted wall breakwaters. We theoretically examined the wave transmission, reflection, energy loss, wave runup, and wave force under normal regular waves. Comparisons with experimental measurements show that the mathematical model results adequately reproduce most of the important features. The results of this investigation provide a better understanding of the hydrodynamic performance of triple-row vertical slotted wall breakwaters.展开更多
An analytical method is developed to study wave diffraction on arc-shaped and bottom-mounted perforated breakwaters. The breakwater is assumed to be rigid, thin, vertical, immovable and located in water of constant de...An analytical method is developed to study wave diffraction on arc-shaped and bottom-mounted perforated breakwaters. The breakwater is assumed to be rigid, thin, vertical, immovable and located in water of constant depth. The fluid domain is divided into two regions by imaginary interface. The velocity potential in each region is expanded by eigenfunctions. By satisfying the continuity of pressure and normal velocity across the imaginary fluid interface, a set of linear algebraic equations can be obtained to determine the unknown coefficients of eigenfunctions. Numerical results, in the form of contour maps of the relative wave amplitude around the breakwater, are presented for a range of wave and breakwater parameters. Results show that the wave diffraction on the arc-shaped and bottom-mounted perforated breakwater is related to the incident wavelength and the porosity of the breakwater. The porosity of the perforated breakwater may have great effect on the diffracted field.展开更多
Extensive 3-D model tests have been performed to study the effects of wave obliquity and multi-directionality on the wave loads acting on vertical breakwaters. The variation of horizontal and uplift forces acting on a...Extensive 3-D model tests have been performed to study the effects of wave obliquity and multi-directionality on the wave loads acting on vertical breakwaters. The variation of horizontal and uplift forces acting on an unit length of a breakwater with wave direction, the longitudinal distribution of wave forces, as well as the longitudinal load reduction are analyzed. Some empirical formulae of the longitudinal distribution coefficient and the longitudinal load reduction factor are presented for practical use.展开更多
Fifteen formulae of wave transmission coefficient for submerged breakwaters obtained during last 3 decades are presented, compared, and analyzed in this paper. The dimensionless parameters mainly involved in this disc...Fifteen formulae of wave transmission coefficient for submerged breakwaters obtained during last 3 decades are presented, compared, and analyzed in this paper. The dimensionless parameters mainly involved in this discussion are the relative submerged depth Re/h, relative wave height Rc/Hi, relative rubble size B/D50, relative breakwater width B√ HiL0 and wave breaker index ξ. It indicates that there exist notable differences among the computed results, which mainly originate from the limited experimental conditions and different analytical methods, even though the major tendency keeps similar. It is necessary to conduct more systematic studies to obtain better understanding about the mechanism of wave transmission over submerged breakwaters.展开更多
This paper investigates the wave attenuation properties of the double trapezoidal submerged breakwaters on the flat-bed by conducting physical experiments subjected to linear and cnoidal incident waves.The method of G...This paper investigates the wave attenuation properties of the double trapezoidal submerged breakwaters on the flat-bed by conducting physical experiments subjected to linear and cnoidal incident waves.The method of Goda's two points is used to separate the heights of incident,reflected and transmitted waves based on the experimental data.The possible factors affecting the wave attenuation properties of the double trapezoidal submerged breakwaters(i.e.,the relative submerged water depth,relative breakwater spacing,wave steepness and relative wave height) are investigated with respect to the reflection and transmission coefficients.The results show that there is a range,within which the breakwater spacing has little impact on the reflection coefficient,and the transmission coefficient tends to be a constant.The influence of the wave steepness is reduced while the breakwater spacing is too large or too small.Within the range of the relative wave height tested in this study,the reflection and transmission coefficients increase and decrease with the relative wave height,respectively.The double trapezoidal submerged breakwaters model indicates a good attenuation effect for larger wave steepness,big relative wave height and within the range of the relative breakwater spacing between 12.5 and 14 according to linear and cnoidal waves.The changes of wave energy spectra between the double submerged breakwaters on the flat-bed are investigated by the fast Fourier transform(FFT) method,showing that wave energy dissipation can be reached more effectively when the relative breakwater spacing is 12.5.展开更多
Slotted breakwaters have been used to provide economical protection from waves in harbors where surface waves and currents may co-exist. In this paper, the effects of currents on the wave scattering by slotted breakwa...Slotted breakwaters have been used to provide economical protection from waves in harbors where surface waves and currents may co-exist. In this paper, the effects of currents on the wave scattering by slotted breakwaters are investigated by using a simple model. The model is based on a long wave approximation. The effects of wave height, barrier geometry and current strength on the reflection and transmission coefficients are examined by the model. The model results are compared with recent experimental data. It is found that both the wave-following and wave-opposing currents can increase the reflection coefficient and reduce the transmission coefficient. The model can be used to study the interaction between long waves and slotted breakwaters in coastal waters.展开更多
A series of 2D model tests were conducted to assess the foundation stability of composite vertical breakwaters. In this paper, the results from the experimental study are presented conjointly with a formula to estimat...A series of 2D model tests were conducted to assess the foundation stability of composite vertical breakwaters. In this paper, the results from the experimental study are presented conjointly with a formula to estimate the stability number of foundation, which is the most important parameter for evaluation of foundation stability of such structures. The influences of wave height, wave period and the berm width on the stability of compo^ite breakwaters with different armor stone sizes were investigated. Forty-five tests were performed to cover the influences of these parameters. According to the present research, berm width is a significant parameter concerning erosion of armor foundation. As the berm width increases, the amount of berm erosion decreases. Comparisons are made between results of present study and the estimated stability number proposed by Kimura et al. （1994）, which is extension of Tanimoto formula. Results show that the later formula underestimates the stability number. However, by applying an enhancement factor about 1.7 meters to Kimura et al. formula, results correlated with the present experimental results..展开更多
In this paper, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the hydrodynamic performance of bottom-standing submerged breakwaters in regular normally incident waves. ...In this paper, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the hydrodynamic performance of bottom-standing submerged breakwaters in regular normally incident waves. Both the single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. Only the impermeable breakwaters are considered in this study. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with the appropriate mixed-type boundary conditions, and it is solved numerically using the ISBM. The numerical results are presented in terms of the hydrodynamic quantities of reflection and transmission coefficients. The values are first validated against the data of previous studies, computed, and discussed for a variety of structural conditions, including the height, width, and spacing of breakwater submergence. An excellent agreement is observed between the ISBM results and those of other methods. The breakwater width is found to feature marginal effects compared with the height. The present method is shown to accurately predict the resonant conditions at which the maximum reflection and transmission occur. The trapezoidal breakwaters are found to generally present a wide spectrum of reflections, suggesting that they would function better than the rectangular breakwaters. The dual breakwater systems are confirmed to perform much better than single structures.展开更多
This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes seco...This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients （CR, Cr, and CE） for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.展开更多
First the scour and deposition patterns of the sandy seabed in front of a vertical breakwater under the action of irregular broken clapotis are investigated experimentally and classified into five types: scour typeⅠ,...First the scour and deposition patterns of the sandy seabed in front of a vertical breakwater under the action of irregular broken clapotis are investigated experimentally and classified into five types: scour typeⅠ, scour typeⅡ, scour type Ⅲ, deposition typeⅠ, and deposition typeⅡ. Secondly, the processes of formation of scour and deposition patterns are probed in comparison with those induced by regular broken clapotis and standing waves. Thirdly, the criteria for distinguishing scour and deposition patterns under irregular broken clapotis are presented.展开更多
Based on the improved version of the meshless singular boundary method(ISBM)in multi domain(MD),a numerical method is proposed in this paper to study the interaction of submerged permeable breakwaters and regular wave...Based on the improved version of the meshless singular boundary method(ISBM)in multi domain(MD),a numerical method is proposed in this paper to study the interaction of submerged permeable breakwaters and regular waves at normal incidence.To account for fluid flow inside the porous breakwaters,the conventional model of Sollitt and Cross for porous media is adopted.Both single and dual trapezoidal breakwaters are examined.The physical problem is formulated in the context of the linear potential wave theory.The domain decomposition method(DDM)is employed,in which the full computational domain is decomposed into separate domains,that is,the fluid domain and the domains of the breakwaters.Respectively,appropriate mixed type boundary and continuity conditions are applied for each subdomain and at the interfaces between domains.The solution is approximated in each subdomain by the ISBM.The discretized algebraic equations are combined,resulting in an overdetermined full system that is solved using a least-square solution procedure.The numerical results are presented in terms of the hydrodynamic quantities of reflection,transmission,and wave-energy dissipation.The relevance of the results of the present numerical procedure is first validated against data of previous studies,and then selected computations are discussed for various structural conditions.The proposed method is demonstrated to be highly accurate and computationally efficient.展开更多
A numerical model is developed that can predict the interaction of regular waves normally incident upon a curtainwall-pile breakwater; the upper part of which is a vertical wall and the lower part consists of an array...A numerical model is developed that can predict the interaction of regular waves normally incident upon a curtainwall-pile breakwater; the upper part of which is a vertical wall and the lower part consists of an array of vertical piles. The numerical model is based on an eigenfunction expansion method, and utilizes a boundary condition nearby the vertical piles that accounts for wave energy dissipation. Numerical solution comprises a finite number of terms, which is a superposition of propagating waves and a series of evanescent waves. The modeling is validated by comparison with previous experimental studies and overall agreement between measurement and calculation is fairly good. The numerical results are related to reflection, transmission, and dissipation coefficient; wave nm-up, wave force, and wave overturning moment are also presented. Effect of porosity, relative draft, and relative water depth are discussed; the choice of suitable range of them is described. The relative draft is more effective for shallow water waves. Model shows decrease in relative draft and leads to reduction of relative wave force, overturning moment, and runup. It is shown that curtainwall- pile breakwaters can operate both effectively and efficiently in the range of relative draft between 0.15 and 0.75. The range 0.5 to 0.2 is also recommended for porosity.展开更多
Tetrapod, one of the well-known artificial concrete units, is frequently used as an armor unit on breakwaters. Two layers of tetrapod units are normmaly placed on the breakwaters with different placement methods. In t...Tetrapod, one of the well-known artificial concrete units, is frequently used as an armor unit on breakwaters. Two layers of tetrapod units are normmaly placed on the breakwaters with different placement methods. In this study, the stability of tetrapod units with two different regularly placement methods are investigated experimentally in irregular waves. Stability coefficients of tetrapod units for both placement methods are obtained. The important characteristic wave parameters of irregular waves causing the same damage ratio as those of the regular waves are also determined. It reveals that the average of one-tenth highest wave heights within the wave train （H1/lo） causes the similar damage as regular waves.展开更多
基金supported by Vellore Institute of Technology,Vellore,under a SEED grant(Sanction Order No.SG20230081)。
文摘This study investigates the performance of dual curved-leg pontoon floating breakwaters in finite water depth under the assumption of linear wave theory. The analysis is carried out for four different models of curvedleg geometries, which are combinations of convex and concave shapes. The models are classified as follows. Model-1: Seaside and leeside face concave, Model-2: Seaside and leeside face convex, Model-3: Seaside face convex and leeside face concave, and Model-4: Seaside face concave and leeside face convex. The Boundary Element Method is utilized in order to find a solution to the associated boundary value problem. The numerical results are validated against existing analytical and experimental data. Further, the study examines the wave reflection, wave transmission, and the hydrodynamic forces acting on the structure for different values of waves and structural parameters. Overall, the different dual curved-leg pontoon breakwaters are more effective, reducing wave transmission by over 15% and increasing wave reflection by more than 5% compared to traditional models. The study shows that the wave reflected by Model 1 significantly increased and attenuated the wave transmission relative to other models. The study found that the height of the curved-leg of Model 1 plays a critical role in blocking waves and redirecting the flow. More precisely, the present analysis concludes that the hydrodynamic performance of Model-1 presents an optimized breakwater design that outperforms the proposed models.
基金Supported by Shandong Provincial Natural Science Foundation,China(ZR2020ME259)Open Fund of Shandong Key Laboratory of Civil Engineering Disaster Prevention and Mitigation(CDPM2021KF21).
文摘Two asymmetric types of floating breakwaters integrated with a wave energy converter(WEC-FBs),a floating square box with a triangle(trapezoidal type)or a wave baffle(L type)attached to its rear side,have been proposed.In this research,the hydrodynamic performance,including capture width ratio(CWR),wave transmission coefficient,heave motion,and force coefficient,were studied and compared between the two types.A numerical simulation model based on the Navier-Stokes equation was employed.The effects of power take-off(PTO)damping coefficient,wave periods,and draft/displacement on the hydrodynamic performance of the two structure shapes were simulated and investigated.The results reveal that the L type performs better in shorter wave periods,and the trapezoidal type exhibits a higher CWR in intermediate wave periods.This study offers knowledge of the design and protection of the two WEC-FB types.
基金supported by the National Natural Science Foundation of China(Grant No.51679132)the Science and Technology Commission of Shanghai Municipality(Grant No.21ZR1427000)Shanghai Frontiers Science Center of“Full Penetration”Far-Reaching Offshore Ocean Energy and Power.
文摘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.
文摘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.
基金by Joint Fund of the National Natural Science Foundation of China the Hong Kong Science Research Bureau (49910161985)+1 种基金the National Natural Science Foundation of China (50025924,50179004)the Research Fund for the Development of harbor engineeri
文摘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.
基金financially supported by the Direction Général des Enseignements et de la Formation Supérieure of Algeria(Grant CNEPRU No.G0301920140029)
文摘In the present work, the improved version of the meshless singular boundary method(ISBM) is developed for analyzing the performance of bottom standing submerged permeable breakwaters in regular normally incident waves and in the proximity of a vertical wall. Both single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with appropriate mixed type boundary conditions, and solved numerically using the ISBM. To model the permeability of the breakwaters fully absorbing boundary conditions are assumed. Numerical results are presented in terms of hydrodynamic quantities of the reflection coefficients. These are firstly validated against the results of a multi-domain boundary element method(BEM) developed independently for a previous study. The agreement between the results of the two methods is excellent. The coefficients of reflection are then computed and discussed for a variety of structural conditions including the breakwaters height, width, spacing, and absorbing permeability. Effects of the proximity of the vertical plane wall are also investigated. The breakwater's width is found to have only marginal effects compared with its height. Permeability tends to decrease the minimum reflections. These coefficients show periodic variations with the spacing relative to the wavelength. Trapezoidal breakwaters are found to be more cost-effective than the rectangular breakwaters. Dual breakwater systems are confirmed to perform much better than single structures.
文摘This study examines wave interactions with multiple semi-immersed Jarlan-type perforated breakwaters. A numerical model based on linear wave theory and an eigenfunction expansion method has been developed to study the hydrodynamic characteristics of breakwaters. The numerical results show a good agreement with previous analytical results and experimental data for limiting cases of double partially immersed impermeable walls and double and triple Jarlan-type breakwaters. The wave transmission coefficient Cv; reflection coefficient CR, and energy dissipation coefficient CE coefficients and the horizontal wave force exerted on the front and rear walls are examined. The results show that CR reaches the maximum value when B/L = 0.46n while it is smallest when B/L=0.46n＋0.24 （n=0, 1, 2,...）. An economical triple semi-immersed Jarlan-type perforated breakwater can be designed with B/L = 0.25 and CR and CT ranging from 0.25 to 0.32 by choosing a relative draft d/h of 0.35 and a permeability parameter of the perforated front walls being 0.5 for an incident wave number kh nearly equal to 2.0. The triple semi-immersed Jarlan-type perforated breakwaters with significantly reduced CR, will enhance the structure＇s wave absorption ability, and lead to smaller wave forces compared with the double one. The proposed model may be used to predict the response of a structure in the preliminary design stage for practical engineering.
基金King Abdul-Aziz City for Science and Technology,General Directorate of Research Grants Programs(LGP-35-287)
文摘In this study, we examine the hydrodynamic characteristics of three rows of vertical slotted wall breakwaters in which the front and middle walls are permeable and partially immersed in a water channel of constant depth, whereas the third wall is impermeable. The wave–structure interaction and flow behavior of this type of breakwater arrangement are complicated and must be analyzed before breakwaters can be appropriately designed. To study the hydrodynamic breakwater performance, we developed a mathematical model based on the eigenfunction expansion method and a least squares technique for predicting wave interaction with three rows of vertical slotted wall breakwaters. We theoretically examined the wave transmission, reflection, energy loss, wave runup, and wave force under normal regular waves. Comparisons with experimental measurements show that the mathematical model results adequately reproduce most of the important features. The results of this investigation provide a better understanding of the hydrodynamic performance of triple-row vertical slotted wall breakwaters.
基金This project was supported by the Natural Science Foundation of Jiangsu Province (Grant NoBk2006013)
文摘An analytical method is developed to study wave diffraction on arc-shaped and bottom-mounted perforated breakwaters. The breakwater is assumed to be rigid, thin, vertical, immovable and located in water of constant depth. The fluid domain is divided into two regions by imaginary interface. The velocity potential in each region is expanded by eigenfunctions. By satisfying the continuity of pressure and normal velocity across the imaginary fluid interface, a set of linear algebraic equations can be obtained to determine the unknown coefficients of eigenfunctions. Numerical results, in the form of contour maps of the relative wave amplitude around the breakwater, are presented for a range of wave and breakwater parameters. Results show that the wave diffraction on the arc-shaped and bottom-mounted perforated breakwater is related to the incident wavelength and the porosity of the breakwater. The porosity of the perforated breakwater may have great effect on the diffracted field.
文摘Extensive 3-D model tests have been performed to study the effects of wave obliquity and multi-directionality on the wave loads acting on vertical breakwaters. The variation of horizontal and uplift forces acting on an unit length of a breakwater with wave direction, the longitudinal distribution of wave forces, as well as the longitudinal load reduction are analyzed. Some empirical formulae of the longitudinal distribution coefficient and the longitudinal load reduction factor are presented for practical use.
文摘Fifteen formulae of wave transmission coefficient for submerged breakwaters obtained during last 3 decades are presented, compared, and analyzed in this paper. The dimensionless parameters mainly involved in this discussion are the relative submerged depth Re/h, relative wave height Rc/Hi, relative rubble size B/D50, relative breakwater width B√ HiL0 and wave breaker index ξ. It indicates that there exist notable differences among the computed results, which mainly originate from the limited experimental conditions and different analytical methods, even though the major tendency keeps similar. It is necessary to conduct more systematic studies to obtain better understanding about the mechanism of wave transmission over submerged breakwaters.
基金Supported by the General Program of National Natural Science Foundation of China(No.50979066 and No.50979008)Ph.D.Programs Foundation of Ministry of Education of China(No.20094316110002)Scientific Research Fund of Department of Education, Hunan Province(No.10A006)
文摘This paper investigates the wave attenuation properties of the double trapezoidal submerged breakwaters on the flat-bed by conducting physical experiments subjected to linear and cnoidal incident waves.The method of Goda's two points is used to separate the heights of incident,reflected and transmitted waves based on the experimental data.The possible factors affecting the wave attenuation properties of the double trapezoidal submerged breakwaters(i.e.,the relative submerged water depth,relative breakwater spacing,wave steepness and relative wave height) are investigated with respect to the reflection and transmission coefficients.The results show that there is a range,within which the breakwater spacing has little impact on the reflection coefficient,and the transmission coefficient tends to be a constant.The influence of the wave steepness is reduced while the breakwater spacing is too large or too small.Within the range of the relative wave height tested in this study,the reflection and transmission coefficients increase and decrease with the relative wave height,respectively.The double trapezoidal submerged breakwaters model indicates a good attenuation effect for larger wave steepness,big relative wave height and within the range of the relative breakwater spacing between 12.5 and 14 according to linear and cnoidal waves.The changes of wave energy spectra between the double submerged breakwaters on the flat-bed are investigated by the fast Fourier transform(FFT) method,showing that wave energy dissipation can be reached more effectively when the relative breakwater spacing is 12.5.
基金The project partially supported by the Hong Kong Research Grant Council under Grant NoHKUST-DAG03/04.EG39 and HKUST6227/04E.
文摘Slotted breakwaters have been used to provide economical protection from waves in harbors where surface waves and currents may co-exist. In this paper, the effects of currents on the wave scattering by slotted breakwaters are investigated by using a simple model. The model is based on a long wave approximation. The effects of wave height, barrier geometry and current strength on the reflection and transmission coefficients are examined by the model. The model results are compared with recent experimental data. It is found that both the wave-following and wave-opposing currents can increase the reflection coefficient and reduce the transmission coefficient. The model can be used to study the interaction between long waves and slotted breakwaters in coastal waters.
文摘A series of 2D model tests were conducted to assess the foundation stability of composite vertical breakwaters. In this paper, the results from the experimental study are presented conjointly with a formula to estimate the stability number of foundation, which is the most important parameter for evaluation of foundation stability of such structures. The influences of wave height, wave period and the berm width on the stability of compo^ite breakwaters with different armor stone sizes were investigated. Forty-five tests were performed to cover the influences of these parameters. According to the present research, berm width is a significant parameter concerning erosion of armor foundation. As the berm width increases, the amount of berm erosion decreases. Comparisons are made between results of present study and the estimated stability number proposed by Kimura et al. （1994）, which is extension of Tanimoto formula. Results show that the later formula underestimates the stability number. However, by applying an enhancement factor about 1.7 meters to Kimura et al. formula, results correlated with the present experimental results..
基金supported by the Direction Général des Enseignements et de la Formation Supérieure of Algeria under Grant CNEPRU number G0301920140029
文摘In this paper, the improved version of the meshless singular boundary method (ISBM) is developed for analyzing the hydrodynamic performance of bottom-standing submerged breakwaters in regular normally incident waves. Both the single and dual prismatic breakwaters of rectangular and trapezoidal forms are examined. Only the impermeable breakwaters are considered in this study. The physical problem is cast in terms of the Laplace equation governing an irrotational flow and incompressible fluid motion with the appropriate mixed-type boundary conditions, and it is solved numerically using the ISBM. The numerical results are presented in terms of the hydrodynamic quantities of reflection and transmission coefficients. The values are first validated against the data of previous studies, computed, and discussed for a variety of structural conditions, including the height, width, and spacing of breakwater submergence. An excellent agreement is observed between the ISBM results and those of other methods. The breakwater width is found to feature marginal effects compared with the height. The present method is shown to accurately predict the resonant conditions at which the maximum reflection and transmission occur. The trapezoidal breakwaters are found to generally present a wide spectrum of reflections, suggesting that they would function better than the rectangular breakwaters. The dual breakwater systems are confirmed to perform much better than single structures.
文摘This study examines the hydrodynamic performance of multiple-row vertical slotted breakwaters. We developed a mathematical model based on an eigenfunction expansion method and a least squares technique for Stokes second-order waves. The numerical results obtained for limiting cases of double-row and triple-row walls are in good agreement with results of previous studies and experimental results. Comparisons with experimental measurements of the reflection, transmission, and dissipation coefficients （CR, Cr, and CE） for double-row walls show that the proposed mathematical model adequately reproduces most of the important features. We found that for double-row walls, the CR increases with increasing wave number, kd, and with a decreasing permeable wall part, din. The Cr follows the opposite trend. The CE slowly increases with an increasing kd for lower kd values, reaches a maximum, and then decreases again. In addition, an increasing porosity of dm would significantly decrease the CR while increasing the Cr. At lower values of kd, a decreasing porosity increases the CE, but for high values of kd, a decreasing porosity reduces the Ce. The numerical results indicate that, for triple-row walls, the effect of the arrangement of the chamber widths on hydrodynamic characteristics is not significant, except when kd〈0.5 Double-row slotted breakwaters may exhibit a good wave-absorbing performance at kd〉0.5, where by the horizontal wave force may be smaller than that of a single wall. On the other hand, the difference between double-row and triple-row vertical slotted breakwaters is marginal.
文摘First the scour and deposition patterns of the sandy seabed in front of a vertical breakwater under the action of irregular broken clapotis are investigated experimentally and classified into five types: scour typeⅠ, scour typeⅡ, scour type Ⅲ, deposition typeⅠ, and deposition typeⅡ. Secondly, the processes of formation of scour and deposition patterns are probed in comparison with those induced by regular broken clapotis and standing waves. Thirdly, the criteria for distinguishing scour and deposition patterns under irregular broken clapotis are presented.
基金the Ministry of Higher Edu-cation and Scientific Research of Algeria(grant PRFU number A01L06UN310220200002).
文摘Based on the improved version of the meshless singular boundary method(ISBM)in multi domain(MD),a numerical method is proposed in this paper to study the interaction of submerged permeable breakwaters and regular waves at normal incidence.To account for fluid flow inside the porous breakwaters,the conventional model of Sollitt and Cross for porous media is adopted.Both single and dual trapezoidal breakwaters are examined.The physical problem is formulated in the context of the linear potential wave theory.The domain decomposition method(DDM)is employed,in which the full computational domain is decomposed into separate domains,that is,the fluid domain and the domains of the breakwaters.Respectively,appropriate mixed type boundary and continuity conditions are applied for each subdomain and at the interfaces between domains.The solution is approximated in each subdomain by the ISBM.The discretized algebraic equations are combined,resulting in an overdetermined full system that is solved using a least-square solution procedure.The numerical results are presented in terms of the hydrodynamic quantities of reflection,transmission,and wave-energy dissipation.The relevance of the results of the present numerical procedure is first validated against data of previous studies,and then selected computations are discussed for various structural conditions.The proposed method is demonstrated to be highly accurate and computationally efficient.
文摘A numerical model is developed that can predict the interaction of regular waves normally incident upon a curtainwall-pile breakwater; the upper part of which is a vertical wall and the lower part consists of an array of vertical piles. The numerical model is based on an eigenfunction expansion method, and utilizes a boundary condition nearby the vertical piles that accounts for wave energy dissipation. Numerical solution comprises a finite number of terms, which is a superposition of propagating waves and a series of evanescent waves. The modeling is validated by comparison with previous experimental studies and overall agreement between measurement and calculation is fairly good. The numerical results are related to reflection, transmission, and dissipation coefficient; wave nm-up, wave force, and wave overturning moment are also presented. Effect of porosity, relative draft, and relative water depth are discussed; the choice of suitable range of them is described. The relative draft is more effective for shallow water waves. Model shows decrease in relative draft and leads to reduction of relative wave force, overturning moment, and runup. It is shown that curtainwall- pile breakwaters can operate both effectively and efficiently in the range of relative draft between 0.15 and 0.75. The range 0.5 to 0.2 is also recommended for porosity.
基金the Research Foundation of Yildiz Technical University for their financial support
文摘Tetrapod, one of the well-known artificial concrete units, is frequently used as an armor unit on breakwaters. Two layers of tetrapod units are normmaly placed on the breakwaters with different placement methods. In this study, the stability of tetrapod units with two different regularly placement methods are investigated experimentally in irregular waves. Stability coefficients of tetrapod units for both placement methods are obtained. The important characteristic wave parameters of irregular waves causing the same damage ratio as those of the regular waves are also determined. It reveals that the average of one-tenth highest wave heights within the wave train （H1/lo） causes the similar damage as regular waves.
