In this study, characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical two-dimensional model are Rey...In this study, characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical two-dimensional model are Reynolds Averaged Navier Stokes equations. The Reynolds stress terms are closed by a nonlinear k - ε turbulence transportation model. The free surface is traced through the PILC-VOF method. The proposed numerical model is verified with experimental results. The numerical result shows that the wave profile may become more asymmetrical when wave propagates over breakwater. When wave crest propagates over breakwater, the anticlockwise vortex may generate. On the contrary, when wave hollow propagates over breakwater, the clockwise vortex may generate. Meanwhile, the influenced zone of vortex created by wave crest is larger than that created by wave hollow. All the maximum values of the turbulent kinetic energy, turbulent dissipation and eddy viscosity occur on the top of breakwater. Both the turbulent dissipation and eddy viscosity increase as the turbulent kinetic energy increases. Wave energy may rapidly decrease near the breakwater because turbulent dissipation increases and energy in lower harmonics is transferred into higher harmonics.展开更多
The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique combining the advantage of the finite element method (FEM) and the boundary element method (BEM) with its unique properties....The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique combining the advantage of the finite element method (FEM) and the boundary element method (BEM) with its unique properties. In this paper, the SBFEM is used for computing wave passing submerged breakwaters, and the reflection coeffcient and transmission coefficient are given for the case of wave passing by a rectangular submerged breakwater, a rigid submerged barrier breakwater and a trapezium submerged breakwater in a constant water depth. The results are compared with the analytical solution and experimental results. Good agreement is obtained. Through comparison with the results using the dual boundary element method (DBEM), it is found that the SBFEM can obtain higher accuracy with fewer elements. Many submerged breakwaters with different dimensions are computed by the SBFEM, and the changing character of the reflection coeffcient and the transmission coefficient are given in the current study.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
Experiments are carried out to study the characteristics of active bubbles entrained by breaking waves as these propagate over an abruptly topographical change or a submerged breakwater. Underwater sounds generated by...Experiments are carried out to study the characteristics of active bubbles entrained by breaking waves as these propagate over an abruptly topographical change or a submerged breakwater. Underwater sounds generated by the entrained air bubbles are detected by a hydrophone connected to a charge amplifier and a data acquisition system. The size distribution of the bubbles is then determined inversely from the received sound frequencies. The sound signals are converted from time domain to time-frequency domain by applying Gabor transform. The number of bubbles with different sizes are counted from the signal peaks in the time-frequency domain. The characteristics of the bubbles are in terms of bubble size spectra, which account for the variation in bubble probability density related to the bubble radius r. The experimental data demonstrate that the bubble probability density function shows a - 2.39 power-law sealing with radius for r 〉 0. 8 mm, and a- 1.11 power law for r 〈0.8 mm.展开更多
The form of Boussinesq equation derived by Nwogu (1993) using velocity at an arbitrary distance and surface elevation as variables is used to simulate wave surface elevation changes. In the numerical experiment, wat...The form of Boussinesq equation derived by Nwogu (1993) using velocity at an arbitrary distance and surface elevation as variables is used to simulate wave surface elevation changes. In the numerical experiment, water depth was divided into five layers with six layer interfaces to simulate velocity at each layer interface. Besides, a physical experiment was carried out to validate numerical model and study solitary wave propagation.“Water column collapsing”method (WCCM) was used to generate solitary wave. A series of wave gauges around an impervious breakwater were set-up in the flume to measure the solitary wave shoaling, run-up, and breaking processes. The results show that the measured data and simulated data are in good agreement. Moreover, simulated and measured surface elevations were analyzed by the wavelet transform method. It shows that different wave frequencies stratified in the wavelet amplitude spectrum. Finally, horizontal and vertical velocities of each layer interface were analyzed in the process of solitary wave propagation through submerged breakwater.展开更多
The purpose of this paper is to develop a functional method for designing a series of submerged breakwaters on practical topography. The method is used to verify the feasibility and effectiveness of Bragg breakwaters ...The purpose of this paper is to develop a functional method for designing a series of submerged breakwaters on practical topography. The method is used to verify the feasibility and effectiveness of Bragg breakwaters for coastal protection by using field topography. The first part of this paper provides definitions and procedures needed in the design process for applying the mechanism of Bragg reflection. Next, Bragg breakwaters are designed on the basis of the cross-sectional topography and then on the plane topography of the Mi-Tuo coast by following the proposed process and procedure. Numerical modeling (Hsu et al., 2003; Wen and Tsai, 2008) was used as a design and assessment tool. Finally, the effectiveness and feasibility of a Bragg breakwater was assessed by practical cases. Based on the mechanism of Bragg reflection, an optimum layout for a series of submerged breakwaters is proposed to protect the Mi-Tuo coast. The results indicate that the proper layout of a series of submerged creakwaters can achieve the objective of beach protection.展开更多
The wave motion over a submerged larlan-type breakwater consisting of a perforated front wall and a solid rear wall was investigated analytically and experimentally. An analytical solution was developed using matched ...The wave motion over a submerged larlan-type breakwater consisting of a perforated front wall and a solid rear wall was investigated analytically and experimentally. An analytical solution was developed using matched eigenfunction expansions. The analytical solution was confirmed by previously known solutions for single and double submerged solid vertical plates, a multidomain boundary element method solution, and experimental data. The calculated results by the analytical solution showed that compared with double submerged vertical plates, the submerged Jarlan-type perforated breakwater had better wave-absorbing performance and lower wave forces. For engineering designs, the optimum values of the front wall porosity, relative submerged depth of the breakwater, and relative chamber width between front and rear walls were 0.1-0.2, 0.1-0.2, and 0.3-0.4, respectively. Interchanging the perforated front wall and solid rear wail may have no effect on the transmission coefficient. However, the present breakwater with a seaside perforated wall had a lower reflection coefficient.展开更多
In this paper a series of numerical simulations are performed to investigate the vortex shedding mechanism for a solitary wave propagating over a submerged breakwater by use of Reynolds averaged Navier-Stokes (RAINS...In this paper a series of numerical simulations are performed to investigate the vortex shedding mechanism for a solitary wave propagating over a submerged breakwater by use of Reynolds averaged Navier-Stokes (RAINS) model combined with a k-ε model. Flows of different Reynolds numbers up to Re = 1.4 × 10^5 corresponding to varying incident wave heights are considered in which the characteristic fluid velocity is represented by the maximum horizontal velocity above the submerged breakwater. For the verification of the accuracy of the numerical model, the incident waves and the velocity field in the vicinity of the breakwater are compared with experimental data. The result shows that the model is capable of describing vortex shedding for a solitary wave propagating over a rectangular submerged breakwater. Key features of vortex generation, evolution and dissipation are investigated. It is found that the vortex shedding and their evolution due to separated boundary layer over the breakwater are strongly related to the Reynolds number. A considerable number of vortices and complicated vortex pattern are observed as the Reynolds number increases.展开更多
The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a ReynoldsAveraged Navier–Stokes(RANS) flow solver with a Volume of Fluid(VOF) surface capturing scheme(RANSVOF) model...The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a ReynoldsAveraged Navier–Stokes(RANS) flow solver with a Volume of Fluid(VOF) surface capturing scheme(RANSVOF) model. The vertical variation of the instantaneous velocity indicates that flow separation occurs at the boundary layer near the breakwater. The temporal evolution of the velocity and vorticity fields demonstrates vortex generation and shedding around the submerged quartercircular breakwater due to the flow separation. An empirical relationship between the vortex intensity and a few hydrodynamic parameters is proposed based on parametric analysis. In addition, the instantaneous and time-averaged vorticity fields reveal a pair of vortices of opposite signs at the breakwater which are expected to have significant effect on sediment entrainment, suspension, and transportation,therefore, scour on the leeside of the breakwater.展开更多
This paper discusses some previous, and presents some new experimental results on wave transmission over submerged breakwaters. The objective of this study is to evaluate wave transmission coefficient and develop a tw...This paper discusses some previous, and presents some new experimental results on wave transmission over submerged breakwaters. The objective of this study is to evaluate wave transmission coefficient and develop a two-dimensional (2D) model as an improvement to the existing wave transmission coefficient models. Factors which affect wave transmission over stbmerged breakwaters are discussed through a series of laboratory experiments. Basic recommendations for evaluation and design of submerged rubble-monud breakwaters are presented. From the test results, a calculation formula of wave transmission coefficient is proposed.展开更多
In this study, we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall. Modified time-dependent mild-slope equations, which involve parameters of the porous medium, w...In this study, we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall. Modified time-dependent mild-slope equations, which involve parameters of the porous medium, were used to calculate the wave height transformation and the mean water level change around a submerged breakwater. The numerical solution is verified with experimental data. The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall. In contrast to cases without a seawall, the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall. Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater. We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.展开更多
This study investigates the hydrodynamic performance of a submerged two layer horizontal plate breakwater. The plate thickness is considered as non-zero in the study. In the context of linear potential theory, an anal...This study investigates the hydrodynamic performance of a submerged two layer horizontal plate breakwater. The plate thickness is considered as non-zero in the study. In the context of linear potential theory, an analytical solution for interaction of water waves with the plates is obtained using the matched eigenfunction expansion method. The solution consists of a symmetric part and an antisymmetric part. Its validity is confirmed by comparing the numerical results of reflection and transmission coefficients for limiting cases with previous predictions. Numerical examples are given to examine the major factors that affect the reflection and transmission coefficients of the plates. Some useful results are presented for engineering design.展开更多
基金The National Natural Science Foundation of China under contract Nos 50979008 and 50909009Program for Hunan Province Key Laboratory of WaterSediment Sciences & Flood Hazard Prevention and Open Research Fund Program of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering,Hohai University No.2008490911
文摘In this study, characteristics of flow field and wave propagation near submerged breakwater on a sloping bed are investigated with numerical model. The governing equations of the vertical two-dimensional model are Reynolds Averaged Navier Stokes equations. The Reynolds stress terms are closed by a nonlinear k - ε turbulence transportation model. The free surface is traced through the PILC-VOF method. The proposed numerical model is verified with experimental results. The numerical result shows that the wave profile may become more asymmetrical when wave propagates over breakwater. When wave crest propagates over breakwater, the anticlockwise vortex may generate. On the contrary, when wave hollow propagates over breakwater, the clockwise vortex may generate. Meanwhile, the influenced zone of vortex created by wave crest is larger than that created by wave hollow. All the maximum values of the turbulent kinetic energy, turbulent dissipation and eddy viscosity occur on the top of breakwater. Both the turbulent dissipation and eddy viscosity increase as the turbulent kinetic energy increases. Wave energy may rapidly decrease near the breakwater because turbulent dissipation increases and energy in lower harmonics is transferred into higher harmonics.
基金This research wasfinanciallysupported bythe National Natural Science Foundation of China(Grant No.50639030)a Programfor Changjiang ScholarsInnovative Research Teamin Dalian University of Technology(Grant No.IRTO420)
文摘The scaled boundary finite element method (SBFEM) is a novel semi-analytical technique combining the advantage of the finite element method (FEM) and the boundary element method (BEM) with its unique properties. In this paper, the SBFEM is used for computing wave passing submerged breakwaters, and the reflection coeffcient and transmission coefficient are given for the case of wave passing by a rectangular submerged breakwater, a rigid submerged barrier breakwater and a trapezium submerged breakwater in a constant water depth. The results are compared with the analytical solution and experimental results. Good agreement is obtained. Through comparison with the results using the dual boundary element method (DBEM), it is found that the SBFEM can obtain higher accuracy with fewer elements. Many submerged breakwaters with different dimensions are computed by the SBFEM, and the changing character of the reflection coeffcient and the transmission coefficient are given in the current study.
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.
文摘Experiments are carried out to study the characteristics of active bubbles entrained by breaking waves as these propagate over an abruptly topographical change or a submerged breakwater. Underwater sounds generated by the entrained air bubbles are detected by a hydrophone connected to a charge amplifier and a data acquisition system. The size distribution of the bubbles is then determined inversely from the received sound frequencies. The sound signals are converted from time domain to time-frequency domain by applying Gabor transform. The number of bubbles with different sizes are counted from the signal peaks in the time-frequency domain. The characteristics of the bubbles are in terms of bubble size spectra, which account for the variation in bubble probability density related to the bubble radius r. The experimental data demonstrate that the bubble probability density function shows a - 2.39 power-law sealing with radius for r 〉 0. 8 mm, and a- 1.11 power law for r 〈0.8 mm.
基金supported by the foundation"China Seawall Safety Risk Zoning and Storm Surge Envelope Diagram"(Grant No.200101061)by the Ministry of Water Resources,China
文摘The form of Boussinesq equation derived by Nwogu (1993) using velocity at an arbitrary distance and surface elevation as variables is used to simulate wave surface elevation changes. In the numerical experiment, water depth was divided into five layers with six layer interfaces to simulate velocity at each layer interface. Besides, a physical experiment was carried out to validate numerical model and study solitary wave propagation.“Water column collapsing”method (WCCM) was used to generate solitary wave. A series of wave gauges around an impervious breakwater were set-up in the flume to measure the solitary wave shoaling, run-up, and breaking processes. The results show that the measured data and simulated data are in good agreement. Moreover, simulated and measured surface elevations were analyzed by the wavelet transform method. It shows that different wave frequencies stratified in the wavelet amplitude spectrum. Finally, horizontal and vertical velocities of each layer interface were analyzed in the process of solitary wave propagation through submerged breakwater.
文摘The purpose of this paper is to develop a functional method for designing a series of submerged breakwaters on practical topography. The method is used to verify the feasibility and effectiveness of Bragg breakwaters for coastal protection by using field topography. The first part of this paper provides definitions and procedures needed in the design process for applying the mechanism of Bragg reflection. Next, Bragg breakwaters are designed on the basis of the cross-sectional topography and then on the plane topography of the Mi-Tuo coast by following the proposed process and procedure. Numerical modeling (Hsu et al., 2003; Wen and Tsai, 2008) was used as a design and assessment tool. Finally, the effectiveness and feasibility of a Bragg breakwater was assessed by practical cases. Based on the mechanism of Bragg reflection, an optimum layout for a series of submerged breakwaters is proposed to protect the Mi-Tuo coast. The results indicate that the proper layout of a series of submerged creakwaters can achieve the objective of beach protection.
基金The National Natural Science Foundation of China under contract Nos 51322903,51279224 and 51010009
文摘The wave motion over a submerged larlan-type breakwater consisting of a perforated front wall and a solid rear wall was investigated analytically and experimentally. An analytical solution was developed using matched eigenfunction expansions. The analytical solution was confirmed by previously known solutions for single and double submerged solid vertical plates, a multidomain boundary element method solution, and experimental data. The calculated results by the analytical solution showed that compared with double submerged vertical plates, the submerged Jarlan-type perforated breakwater had better wave-absorbing performance and lower wave forces. For engineering designs, the optimum values of the front wall porosity, relative submerged depth of the breakwater, and relative chamber width between front and rear walls were 0.1-0.2, 0.1-0.2, and 0.3-0.4, respectively. Interchanging the perforated front wall and solid rear wail may have no effect on the transmission coefficient. However, the present breakwater with a seaside perforated wall had a lower reflection coefficient.
基金supported by the Science Council and Top University of NCKU(Grant Nos .NSC96-2221-E-127-006-MY3 and A0162)
文摘In this paper a series of numerical simulations are performed to investigate the vortex shedding mechanism for a solitary wave propagating over a submerged breakwater by use of Reynolds averaged Navier-Stokes (RAINS) model combined with a k-ε model. Flows of different Reynolds numbers up to Re = 1.4 × 10^5 corresponding to varying incident wave heights are considered in which the characteristic fluid velocity is represented by the maximum horizontal velocity above the submerged breakwater. For the verification of the accuracy of the numerical model, the incident waves and the velocity field in the vicinity of the breakwater are compared with experimental data. The result shows that the model is capable of describing vortex shedding for a solitary wave propagating over a rectangular submerged breakwater. Key features of vortex generation, evolution and dissipation are investigated. It is found that the vortex shedding and their evolution due to separated boundary layer over the breakwater are strongly related to the Reynolds number. A considerable number of vortices and complicated vortex pattern are observed as the Reynolds number increases.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51509178 and 51509177)the Natural Science Foundation of Tianjin City(Grant No.14JCYBJC22100)the Natural Science Foundation of Tianjin Education Commission(Grant No.2017KJ046)
文摘The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a ReynoldsAveraged Navier–Stokes(RANS) flow solver with a Volume of Fluid(VOF) surface capturing scheme(RANSVOF) model. The vertical variation of the instantaneous velocity indicates that flow separation occurs at the boundary layer near the breakwater. The temporal evolution of the velocity and vorticity fields demonstrates vortex generation and shedding around the submerged quartercircular breakwater due to the flow separation. An empirical relationship between the vortex intensity and a few hydrodynamic parameters is proposed based on parametric analysis. In addition, the instantaneous and time-averaged vorticity fields reveal a pair of vortices of opposite signs at the breakwater which are expected to have significant effect on sediment entrainment, suspension, and transportation,therefore, scour on the leeside of the breakwater.
文摘This paper discusses some previous, and presents some new experimental results on wave transmission over submerged breakwaters. The objective of this study is to evaluate wave transmission coefficient and develop a two-dimensional (2D) model as an improvement to the existing wave transmission coefficient models. Factors which affect wave transmission over stbmerged breakwaters are discussed through a series of laboratory experiments. Basic recommendations for evaluation and design of submerged rubble-monud breakwaters are presented. From the test results, a calculation formula of wave transmission coefficient is proposed.
基金supported by The Science Council of Taiwan under Grant No. 95-2221-E-005-154
文摘In this study, we investigated wave transformation and wave set-up between a submerged permeable breakwater and a seawall. Modified time-dependent mild-slope equations, which involve parameters of the porous medium, were used to calculate the wave height transformation and the mean water level change around a submerged breakwater. The numerical solution is verified with experimental data. The simulated results show that modulations of the wave profile and wave set-up are clearly observed between the submerged breakwater and the seawall. In contrast to cases without a seawall, the node or pseudo-node of wave height evolution can be found between the submerged breakwater and the seawall. Higher wave set-up occurs if the nodal or pseudo-nodal point appears near the submerged breakwater. We also examined the influence of the porosity and friction factor of the submerged permeable breakwater on wave transformation and set-up.
基金supported by the National Natural Science Foundation of China (Grant Nos.50739004, 50609001)the Natural Science Foundation of Shandong Province (Grant No.Q2008F01)the specialized Research Fund for the Doctoral Program of High Education (Grant No. 200804231006)
文摘This study investigates the hydrodynamic performance of a submerged two layer horizontal plate breakwater. The plate thickness is considered as non-zero in the study. In the context of linear potential theory, an analytical solution for interaction of water waves with the plates is obtained using the matched eigenfunction expansion method. The solution consists of a symmetric part and an antisymmetric part. Its validity is confirmed by comparing the numerical results of reflection and transmission coefficients for limiting cases with previous predictions. Numerical examples are given to examine the major factors that affect the reflection and transmission coefficients of the plates. Some useful results are presented for engineering design.