This paper proposes an equation to calculate breaking wave induced wave set-up and set-down along reef flat. The mathematical equation was derived based on the theory of radiation stress and the conservation of wave e...This paper proposes an equation to calculate breaking wave induced wave set-up and set-down along reef flat. The mathematical equation was derived based on the theory of radiation stress and the conservation of wave energy. The equation is primarily determined by several physical variables including the breaking wave index, the stable wave index, the attenuation coefficient of wave energy flux, and the flow velocity in the re-stabilization zone. A series of laboratory experiments were carried out to calibrate the theoretical equations. Specifically, the breaking wave index,the stable wave index, and the velocity over the reef flat were measured in the laboratory. The attenuation coefficient of wave energy flux in our theoretical equation was determined by calibration by comparing with the laboratory measured wave height. Furthermore, it has been put forward that the velocity based on cnoidal wave theory could be used to determine the velocity over the reef flat if there is no velocity measurement available. Overall, the proposed equation can provide satisfactory prediction of wave set-up and set-down along the reef flat.展开更多
Storm surge along the China's Zhe-Min coast is addressed using the tightly coupled surge model ofADCIRC+SWAN. In this study, we primarily focus on the effects of surge-tide interaction and waveset-up/set-down. And t...Storm surge along the China's Zhe-Min coast is addressed using the tightly coupled surge model ofADCIRC+SWAN. In this study, we primarily focus on the effects of surge-tide interaction and waveset-up/set-down. And the influences of intensity and landing moment of tropical cyclone (TC) arealso presented. The results show that: water elevation without considering tide-surge interactiontends to be underestimated/overestimated when TC lands during astronomical low/high tide;tide-surge coupling effect is more pronounced north of TC track (more than 0.7 m in our cases);irrelevant to TC's intensity, wave set-up south of TC track is negligible because the depth-relatedwave breaking doesn't occur in water body blown towards open seas.展开更多
This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave fo...This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.展开更多
Based on the time dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation, and the...Based on the time dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation, and then a practical method for the simulation of wave height and wave set- up in nearshore regions is presented. The variation of the complex wave amplitude is numerically simulated by use of the parabolic mild slope equation including the effect of wave energy dissipation due to wave breaking. The components of wave radiation stress are calculated subsequently by new expressions for them according to the obtained complex wave amplitude, and then the depth-averaged equation is applied to the calculation of wave set-up due to wave breaking. Numerical results are in good agreement with experimental data, showing that the expression for the energy dissipation factor is reasonable and that the new method is effective for the simulation of wave set-up due to wave breaking in nearshore regions.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
The dynamic analysis of a Tension Leg Platform (TLP) in random wave is investigated by considering the set-down of a floating body. The nonlinear restoring stiffness is derived with the set-down motion of a floating...The dynamic analysis of a Tension Leg Platform (TLP) in random wave is investigated by considering the set-down of a floating body. The nonlinear restoring stiffness is derived with the set-down motion of a floating body and the coupled motion of the tension leg and platform and the differential equations of the motion are established. The study focuses on the influence of the set-down motion on the nonlinear response of the platform. By considering different significant wave heights and currents, motion responses of the platform are calculated and compared. The analysis shows that the set-down motion significantly increases the heave motion with low frequency and the equilibrium position of the heave motion with the set-down motion is much lower than that without set-down motion. The results in this paper indicate that the set-down motion has a major impact on the safety of the platform inproduction operation, and it is also a threat to the strength of tension legs and risers.展开更多
For the simulation of the three-dimensional(3D)nearshore circulation,a 3D hydrodynamic model is developed by taking into account the depth-dependent radiation stresses.Expressions for depth-dependent radiation stres...For the simulation of the three-dimensional(3D)nearshore circulation,a 3D hydrodynamic model is developed by taking into account the depth-dependent radiation stresses.Expressions for depth-dependent radiation stresses in the Cartesian coordinates are introduced on the basis of the linear wave theory,and then vertical variations of depth-dependent radiation stresses are discussed.The 3D hydrodynamic model of ELCIRC(Eulerian-Lagrangian CIRCulation)is extended by adding the terms of the depth-dependent or depth-averaged radiation stresses in the momentum equations.The wave set-up,set-down and undertow are simulated by the extended ELCIRC model based on the wave fields provided by the experiment or the REF/DIF wave model.The simulated results with the depth-dependent and depth-averaged radiation stresses both show good agreement with the experimental data for wave set-up and set-down.The undertow profiles predicted by the model with the depth-dependent radiation stresses are also consistent with the experimental results,while the model with the depth-averaged radiation stresses can not reflect the vertical distribution of undertow.展开更多
This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and de...This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and determining the Fourier coefficients by solving a set of nonlinear algebraic equations through the Taylor expansion and perturbation method. The universal solution is expressed upon the still water depth with the still water level as datum and retains a global perturbation parameter. The wave set-up term generated by the self-interaction of oscillatory waves is explicitly included in the free surface function. With the use of different definitions for the wave celerity, different water levels as the datum, different non-dimensional variables as the perturbation parameter, and different treatments for the total head, the universal solution can be reduced to the existing various Stokes solutions, thus explaining the reasons and the physical significance of different non-periodic terms in them, such as the positive or negative constant term in the free surface expression and the time-or space-proportional term in the potential function.展开更多
The wave transformation over the deep-sea coral reefs is an essential issue in the analysis of the reef ecosystem and the design of large reef-top structures.Extensive wave flume experiments are conducted to investiga...The wave transformation over the deep-sea coral reefs is an essential issue in the analysis of the reef ecosystem and the design of large reef-top structures.Extensive wave flume experiments are conducted to investigate the wave transformation processes over an idealized reef model.Detailed measurements of the wave height,the wave set-up and the wave-generated flow on the reef-top are made with and without the reef-top structure at various submerged depths and under different wave conditions.It is found that the reef-top structure has a significant influence on the wave breaking,the wave set-up and the wave-generated flow.The wave set-up increases with the increasing wave height and the decreasing submergence depth.However,the relationship between the wave set-up and the wave period is complex,influenced by the reef-top structure.展开更多
Previous studies have shown that high-frequency(HF)waves,low-frequency(LF)waves and wave set-up coexist on shallow coral reef-flat and jointly contribute to potential floods and subsequent damages of infrastructures a...Previous studies have shown that high-frequency(HF)waves,low-frequency(LF)waves and wave set-up coexist on shallow coral reef-flat and jointly contribute to potential floods and subsequent damages of infrastructures and islands on it.To better understand the reef-flat wave dynamics with incident waves and still water level,a wave-flume experiment was performed based on an idealized platform reef composed of a steep reef-face(1:4),a relatively mild reef-rim(1:14)and a horizontal reef-flat.Also,the non-hydrostatic phase-resolving model SWASH was validated against the experiment and then applied to further numerically investigate the effects of reef-rim topographic features on the reef-flat wave motions.The results show that incident waves of a larger wave height and a longer wave period can generate larger LF waves and wave set-up,thereby inducing greater HF waves on the reef-flat.Higher still water level can lead to larger HF waves but result in smaller wave set-up.In contrast to HF waves and wave set-up,LF waves are minimally affected by the still water level.A rim of milder slope and larger edge depth will induce smaller HF and LF waves and set-up on the reef-flat,and thus provide better protection for the reef-flat region.Furthermore,on the reef-flat,the ratio of HF significant wave height to water depth H_(s_h)/(h_(r)+η^(-))is approximately constant;the dimensionless LF significant wave height Hs_l/H_(s0) and the dimensionless wave set-upη^(-)/[T_(p)(gH_(s0))1/2]can be related to the inverse wave steepness parameter gT_(p)^(2)/H_(s0) and the relative reef-flat submergence(h_(r)+η^(-))/H_(s0) respectively.展开更多
基金jointly supported by the National Key R&D Program of China (Grant No. 2018YFC0407503)the National Natural Science Foundation of China (Grant No. 51779149)+2 种基金the Scientific Research Project of Yangtze-to-Huaihe Water Diversion Project (Grant No. YJJHYJJC-ZX-20191106220)the Nanjing Hydraulic Research Institute Special Fund for Basic Scientific Research of Central Public Research Institutes(Grant Nos. Y220002, Y219012 and Y220013)the Water Conservancy Science and Technology Project of Jiangsu Province (Grant No. 2019009)。
文摘This paper proposes an equation to calculate breaking wave induced wave set-up and set-down along reef flat. The mathematical equation was derived based on the theory of radiation stress and the conservation of wave energy. The equation is primarily determined by several physical variables including the breaking wave index, the stable wave index, the attenuation coefficient of wave energy flux, and the flow velocity in the re-stabilization zone. A series of laboratory experiments were carried out to calibrate the theoretical equations. Specifically, the breaking wave index,the stable wave index, and the velocity over the reef flat were measured in the laboratory. The attenuation coefficient of wave energy flux in our theoretical equation was determined by calibration by comparing with the laboratory measured wave height. Furthermore, it has been put forward that the velocity based on cnoidal wave theory could be used to determine the velocity over the reef flat if there is no velocity measurement available. Overall, the proposed equation can provide satisfactory prediction of wave set-up and set-down along the reef flat.
基金the support of National Natural Science Foundation of China (11772339)the Strategic Priority Research Programs (Category B) of the Chinese Academy of Sciences (XDB22040203)
文摘Storm surge along the China's Zhe-Min coast is addressed using the tightly coupled surge model ofADCIRC+SWAN. In this study, we primarily focus on the effects of surge-tide interaction and waveset-up/set-down. And the influences of intensity and landing moment of tropical cyclone (TC) arealso presented. The results show that: water elevation without considering tide-surge interactiontends to be underestimated/overestimated when TC lands during astronomical low/high tide;tide-surge coupling effect is more pronounced north of TC track (more than 0.7 m in our cases);irrelevant to TC's intensity, wave set-up south of TC track is negligible because the depth-relatedwave breaking doesn't occur in water body blown towards open seas.
基金supported by the National Natural Science Foundation of China(Nos.51239008 and 51279130)
文摘This paper presents a study on the motion response of a tension-leg platform(TLP) under first-and second-order wave forces, including the mean-drift force, difference and sum-frequency forces. The second-order wave force is calculated using the full-field quadratic transfer function(QTF). The coupled effect of the horizontal motions, such as surge, sway and yaw motions, and the set-down motion are taken into consideration by the nonlinear restoring matrix. The time-domain analysis with 50-yr random sea state is performed. A comparison of the results of different case studies is made to assess the influence of second-order wave force on the motions of the platform. The analysis shows that the second-order wave force has a major impact on motions of the TLP. The second-order difference-frequency wave force has an obvious influence on the low-frequency motions of surge and sway, and also will induce a large set-down motion which is an important part of heave motion. Besides, the second-order sum-frequency force will induce a set of high-frequency motions of roll and pitch. However, little influence of second-order wave force is found on the yaw motion.
基金This subject was financially supported by the National Natural Science Foundation of China (Grant No. 59839330 and No. 59979025)
文摘Based on the time dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation, and then a practical method for the simulation of wave height and wave set- up in nearshore regions is presented. The variation of the complex wave amplitude is numerically simulated by use of the parabolic mild slope equation including the effect of wave energy dissipation due to wave breaking. The components of wave radiation stress are calculated subsequently by new expressions for them according to the obtained complex wave amplitude, and then the depth-averaged equation is applied to the calculation of wave set-up due to wave breaking. Numerical results are in good agreement with experimental data, showing that the expression for the energy dissipation factor is reasonable and that the new method is effective for the simulation of wave set-up due to wave breaking in nearshore regions.
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financially supported by the National Natural Science Foundation of China(Grant Nos.51239008 and 51279130)
文摘The dynamic analysis of a Tension Leg Platform (TLP) in random wave is investigated by considering the set-down of a floating body. The nonlinear restoring stiffness is derived with the set-down motion of a floating body and the coupled motion of the tension leg and platform and the differential equations of the motion are established. The study focuses on the influence of the set-down motion on the nonlinear response of the platform. By considering different significant wave heights and currents, motion responses of the platform are calculated and compared. The analysis shows that the set-down motion significantly increases the heave motion with low frequency and the equilibrium position of the heave motion with the set-down motion is much lower than that without set-down motion. The results in this paper indicate that the set-down motion has a major impact on the safety of the platform inproduction operation, and it is also a threat to the strength of tension legs and risers.
基金supported bythe National Natural Science Foundation of China(Grant No.50279029)
文摘For the simulation of the three-dimensional(3D)nearshore circulation,a 3D hydrodynamic model is developed by taking into account the depth-dependent radiation stresses.Expressions for depth-dependent radiation stresses in the Cartesian coordinates are introduced on the basis of the linear wave theory,and then vertical variations of depth-dependent radiation stresses are discussed.The 3D hydrodynamic model of ELCIRC(Eulerian-Lagrangian CIRCulation)is extended by adding the terms of the depth-dependent or depth-averaged radiation stresses in the momentum equations.The wave set-up,set-down and undertow are simulated by the extended ELCIRC model based on the wave fields provided by the experiment or the REF/DIF wave model.The simulated results with the depth-dependent and depth-averaged radiation stresses both show good agreement with the experimental data for wave set-up and set-down.The undertow profiles predicted by the model with the depth-dependent radiation stresses are also consistent with the experimental results,while the model with the depth-averaged radiation stresses can not reflect the vertical distribution of undertow.
基金supported by Fundamental Research Funds for the Central Universities (Grant No. 2010B02614)Natural Science Foundation of Hohai University (Grant No. 2009423511)+1 种基金National Natural Science Foundation of China (Grant No. 4176008)Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and determining the Fourier coefficients by solving a set of nonlinear algebraic equations through the Taylor expansion and perturbation method. The universal solution is expressed upon the still water depth with the still water level as datum and retains a global perturbation parameter. The wave set-up term generated by the self-interaction of oscillatory waves is explicitly included in the free surface function. With the use of different definitions for the wave celerity, different water levels as the datum, different non-dimensional variables as the perturbation parameter, and different treatments for the total head, the universal solution can be reduced to the existing various Stokes solutions, thus explaining the reasons and the physical significance of different non-periodic terms in them, such as the positive or negative constant term in the free surface expression and the time-or space-proportional term in the potential function.
基金Supported by the National Natural Science Foundation of China(Grant No.51679032).
文摘The wave transformation over the deep-sea coral reefs is an essential issue in the analysis of the reef ecosystem and the design of large reef-top structures.Extensive wave flume experiments are conducted to investigate the wave transformation processes over an idealized reef model.Detailed measurements of the wave height,the wave set-up and the wave-generated flow on the reef-top are made with and without the reef-top structure at various submerged depths and under different wave conditions.It is found that the reef-top structure has a significant influence on the wave breaking,the wave set-up and the wave-generated flow.The wave set-up increases with the increasing wave height and the decreasing submergence depth.However,the relationship between the wave set-up and the wave period is complex,influenced by the reef-top structure.
基金supported by the Fundamental Research Funds for the Central Universities(Grant No.2018B13314)the Science and Technology Project on Transportation Construction(Grant No.2015328521280).
文摘Previous studies have shown that high-frequency(HF)waves,low-frequency(LF)waves and wave set-up coexist on shallow coral reef-flat and jointly contribute to potential floods and subsequent damages of infrastructures and islands on it.To better understand the reef-flat wave dynamics with incident waves and still water level,a wave-flume experiment was performed based on an idealized platform reef composed of a steep reef-face(1:4),a relatively mild reef-rim(1:14)and a horizontal reef-flat.Also,the non-hydrostatic phase-resolving model SWASH was validated against the experiment and then applied to further numerically investigate the effects of reef-rim topographic features on the reef-flat wave motions.The results show that incident waves of a larger wave height and a longer wave period can generate larger LF waves and wave set-up,thereby inducing greater HF waves on the reef-flat.Higher still water level can lead to larger HF waves but result in smaller wave set-up.In contrast to HF waves and wave set-up,LF waves are minimally affected by the still water level.A rim of milder slope and larger edge depth will induce smaller HF and LF waves and set-up on the reef-flat,and thus provide better protection for the reef-flat region.Furthermore,on the reef-flat,the ratio of HF significant wave height to water depth H_(s_h)/(h_(r)+η^(-))is approximately constant;the dimensionless LF significant wave height Hs_l/H_(s0) and the dimensionless wave set-upη^(-)/[T_(p)(gH_(s0))1/2]can be related to the inverse wave steepness parameter gT_(p)^(2)/H_(s0) and the relative reef-flat submergence(h_(r)+η^(-))/H_(s0) respectively.