In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the ...In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.展开更多
This paper discusses the effect of berm width and elevation of composite slope on irregular wave run-up. Based on the data obtained from model tests, the formula and distribution of irregular wave run-up on composite ...This paper discusses the effect of berm width and elevation of composite slope on irregular wave run-up. Based on the data obtained from model tests, the formula and distribution of irregular wave run-up on composite slope are derived. The changing of wind speed, width and elevation of the berm are considered comprehensively. The wave run-up with various exceedance probability can be es-timated utilizing the distribution curves of irregular wave run-up.展开更多
In the design of wind turbine foundations for offshore wind farms, the wave load and run-up slamming on the supporting structure are the quantities that need to be considered. Because of a special arc transition, the ...In the design of wind turbine foundations for offshore wind farms, the wave load and run-up slamming on the supporting structure are the quantities that need to be considered. Because of a special arc transition, the interaction between the wave field and the composite bucket foundation(CBF) becomes complicated. In this study, the hydrodynamic characteristics, including wave pressure, load, upwelling, and run-up, around the arc transition of a CBF influenced by regular waves are investigated through physical tests at Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China. The distributions of the wave pressures and upwelling ratios around the CBF are described, and the relationship between the wave load and the wave parameters is discussed. New formulae based on the velocity stagnation head theory with linear wave theory and the second-order Stokes wave theory for wave kinematics are proposed to estimate the wave run-up. Moreover, the multiple regression method with nonlinear technology is employed to deduce an empirical formula for predicting run-up heights. Results show that the non-dimensional wave load increases with the increase in the values of the wave scattering parameter and relative wave height. The wave upwelling height is high in front of the CBF and has the lowest value at an angle of 135? with the incoming wave direction. The performance of the new formulae proposed in this study is compared using statistical indices to demonstrate that a good fit is obtained by the multiple regression method and the analytical model based on the velocity stagnation head theory is underdeveloped.展开更多
An impedance analytical method （IAM） is developed to study the interaction of plane water wave with a slotted-wall caisson breakwater. The non-linear boundary condition at the slotted-wall is expressed in terms of f...An impedance analytical method （IAM） is developed to study the interaction of plane water wave with a slotted-wall caisson breakwater. The non-linear boundary condition at the slotted-wall is expressed in terms of flow resistance. A set of algebraic expressions are obtained for free surface elevation inside and outside chamber, and reflection coefficient. The prediction of the reflection coefficients shows that the relative widths of the chamber inducing the minimum reflection coefficient for a slotted-wall caisson breakwater are in a range of 0.10～0.20, which are smaller than that （0.15～0.25） for a perforated-wall caisson breakwater. The reflection coefficients and free surface elevation obtained by the present model are compared with that of laboratory experiments carried out by previous researchers.展开更多
Wave hydrodynamics over fringing reefs is largely controlled by the reef surface roughness and hydrodynamic forcing.It is believed that climate change will result in a net increase in the water depth over the reef fla...Wave hydrodynamics over fringing reefs is largely controlled by the reef surface roughness and hydrodynamic forcing.It is believed that climate change will result in a net increase in the water depth over the reef flat,a degrading of the surface roughness of coral reefs and changes in extreme incident wave heights.For an accurate assessment of how climate change affects the safety of reef-fringed coasts,a numerical study of the impact of climate change on irregular wave run-up over reef-fringed coasts was carried out based on a Boussinesq wave model,FUNWAVE-TVD.Validated with experimental data,the present model shows reasonable prediction of irregular wave evolution and run-up height over fringing reefs.Numerical experiments were then implemented based on the anticipated effects of climate change and carried out to investigate the effects of sea level rise,degrading of the reef surface roughness and increase of extreme incident wave height on the irregular wave run-up height over the backreef beach respectively.Variations of run-up components(i.e.,spectral characteristics of run-up and mean water level)were examined specifically and discussed to better understand the influencing mechanism of each climate change-related effect on the run-up.展开更多
In this paper,the focused wave groups with different parameters and their actions on a vertical cylinder are experimentally studied. The harmonic wave characteristics of the focusing waves are analyzed by the addition...In this paper,the focused wave groups with different parameters and their actions on a vertical cylinder are experimentally studied. The harmonic wave characteristics of the focusing waves are analyzed by the addition and subtraction of the crest and trough focusing waves. The analyzed results show that higher order harmonics can be generated because of the interaction of component waves. Nonlinearity increases with the inputted wave amplitude and the frequency width increment. Further, the wave run-up around the vertical circular cylinder is experimentally studied. It increases with the wave steepness and the relative cylinder diameter increase. However, the variations of wave run-up around the circular cylinder are different. The researches provide a reference for further numerical studies.展开更多
The run-up on offshore structures induced by the steep regular wave is a highly nonlinear flow with a free surface. This article focuses on the investigation of the steep regular wave run-up on a single vertical cylin...The run-up on offshore structures induced by the steep regular wave is a highly nonlinear flow with a free surface. This article focuses on the investigation of the steep regular wave run-up on a single vertical cylinder by solving the Navier-Stokes equations. A numerical wave tank is established based on the open-source package to simulate the wave scattering induced by a vertical cylinder. The VOF method is applied to capture the large deformation and breaking of the free surface. The numerical model is validated by experimental results. The relative wave run-ups on the front face and the back face along the centerline of a cylinder are analyzed. The changes of the relative run-ups with the wave steepness, the relative diameter and the relative depth are studied. It is found that the relative run-ups on the front face and the back face of the cylinder depend mainly on the wave steepness and the relative diameter, while the dependence on the relative depth is weak. The empirical formulae are proposed to calculate the relative run-ups in terms of the wave steepness of incident regular waves and the relative diameter of a cylinder.展开更多
This paper describes a plane regular wave interaction with a combined cylinder which consists of a solid inner column and a coaxial perforated outer cylinder. The outer perforated surface is a thin porous cylinder wit...This paper describes a plane regular wave interaction with a combined cylinder which consists of a solid inner column and a coaxial perforated outer cylinder. The outer perforated surface is a thin porous cylinder with an annular gap between it and the inner cylinder. The non-linear boundary condition at the perforated wall is a prime focus in the study; energy dissipation at the perforated wall occurs through the resistance to the fluid across the perforated wall. Explicit analytical formulae are presented to calculate the wave run-up on the outer and inner surfaces of the perforated cylinder and the surface of the inner column. The theoretical results of the wave run-up are compared with previous experimental data. Numerical results have also been obtained： when the ratio of the annular gap between the two cylinders to incident wavelength （b-a）/L≤0. 1, the wave run-up on the inner surface of the perforated cylinder and the surface of inner column can partially or completely exceed the incident wave height.展开更多
The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions a...The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.展开更多
This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x...This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x 1 , x ′ ） ∈ R n ＋ ：= R ＋ × R n 1 , u（0, x） = u 0 （x） → u ＋ , as x 1 → ＋ ∞ , u t （0, x） = u 1 （x）, u（t, 0, x ′ ） = u b , x ′ = （x 2 , x 3 , ··· , x n ） ∈ R n 1 . （I） For the non-degenerate case f ′ 1 （u ＋ ） 〈 0, it was shown in [10] that the above initialboundary value problem （I） admits a unique global solution u（t, x） which converges to the corresponding planar stationary wave φ（x 1 ） uniformly in x 1 ∈ R ＋ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u（t, x） for t → ＋ ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ （u） 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 （u b ） ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.展开更多
Submerged barriers are constructed in coastal zones for shoreline or harbor protection or to prevent the beach erosion. In the present study, the wave run-up on a vertical seawall protected by a submerged barrier is a...Submerged barriers are constructed in coastal zones for shoreline or harbor protection or to prevent the beach erosion. In the present study, the wave run-up on a vertical seawall protected by a submerged barrier is analyzed. The physical configurations include a rigid barrier and a long channel of finite depth. For linear water waves, by matching the velocity along the barrier and along the gap, the systems of linear equations about the velocity potentials are obtained. The wave rim-up is further analyzed for various settings of barrier height and distance between the barrier and the wall, i.e. the chamber length. For nonlinear waves and random sea waves, a numerical model is extended to investigate the effect parameters of the barrier on the wave rim-up against the seawall. Not only the numerical simulations, but also the analytical results illustrate that the wave run-up on the seawall depends very much on the distance between the barrier and the vertical seawall.展开更多
Linear governing equations are formulated for the depth decay of the pressure and velocity variations associated with propagating surface gravity waves. These governing equations come from combining Bernoulli’s equat...Linear governing equations are formulated for the depth decay of the pressure and velocity variations associated with propagating surface gravity waves. These governing equations come from combining Bernoulli’s equation for steady frictionless flow along a streamline and the crossstream force balance involving gravity, the centrifugal force and a pressure gradient. Qualitative solutions show that the pressure decreases downward faster than the velocity does and at a rate that is probably not the normal exponential decrease, which does not agree with the classical result. The radius of curvature of the streamlines is a non-constant coefficient in these equations and it needs to be supplied, either from measurements or another theory, in order to complete the solution of the derived governing equations. There is no sensitivity of the solution to the exact path the radius of curvature takes between its minimum value at the surface of a crest and trough and infinity at great depth. In the future measurements, perhaps streak photographs, will be needed to distinguish between the new and old theories.展开更多
We consider a wave equation with nonlocal nonlinear damping and source terms.We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique.The main difficult is...We consider a wave equation with nonlocal nonlinear damping and source terms.We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique.The main difficult is how to handle with the nonlocal nonlinear damping term.Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso(Evolution Equation and Control Theory,2017(6):437-470)and Narciso(Evolution Equations and Control Theory,2020,9(2):487-508).展开更多
Coastal vegetation is capable of decreasing wave run-up.However,because of regrowth,decay or man-made damage,coastal vegetation is always distributed in patches,and its internal distribution is often non-uniform.This ...Coastal vegetation is capable of decreasing wave run-up.However,because of regrowth,decay or man-made damage,coastal vegetation is always distributed in patches,and its internal distribution is often non-uniform.This study investigates the effects of patchy vegetation on solitary wave run-up by using a numerical simulation.A numerical model based on fully nonlinear Boussinesq equations is established to simulate the wave propagation on a slope with patchy vegetation.By using the model,the process of solitary wave run-up attenuation due to patchy vegetation is numerically analysed.The numerical results reveal that patchy vegetation can considerably attenuate the wave run-up in an effective manner.In addition,high-density patched vegetation can attenuate the solitary wave run-up more effectively than low-density patched vegetation can.For the same density,patchy vegetation with a uniform distribution has a better attenuation effect on wave run-up compared to that of patchy vegetation with a non-uniform distribution.展开更多
The prediction of solitary wave run-up has important practical significance in coastal and ocean engineering, but the calculation precision is limited in the existing models. For improving the calculation precision, a...The prediction of solitary wave run-up has important practical significance in coastal and ocean engineering, but the calculation precision is limited in the existing models. For improving the calculation precision, a solitary wave run-up calculation model was established based on artificial neural networks in this study. A back-propagation （BP） network with one hidden layer was adopted and modified with the additional momentum method and the auto-adjusting learning factor. The model was applied to calculation of solitary wave run-up. The correlation coefficients between the neural network model results and the experimental values was 0.996 5. By comparison with the correlation coefficient of 0.963 5, between the Synolakis formula calculation results and the experimental values, it is concluded that the neural network model is an effective method for calculation and analysis of solitary wave ran-up.展开更多
This paper. details experiments undertaken in the UK Coastal Research Facility (CRF)at Hy draulies Research (HR), Wallingford, on transformation and run-up of wave trains. The purpose of these experiments is to provid...This paper. details experiments undertaken in the UK Coastal Research Facility (CRF)at Hy draulies Research (HR), Wallingford, on transformation and run-up of wave trains. The purpose of these experiments is to provide verification data for numerical models of wave transformation in shoaling. surf and swash zones. This is the kind of data ih:lt flume experiments are unable to provide, and is collected in the highly controlled environment of CRF where extrinsic factors present in the field are not an issue. The experiments concerning wave trains are undertaken by use of existing wave generation software, and the run-up measurements are made with large experimental run-up gauges.展开更多
A series of hydraulic model tests are carried out to investigate random wave run-up and overtopping on smooth, impermeable single slope and composite slope. Based on the analysis of the influences of wave steepness, s...A series of hydraulic model tests are carried out to investigate random wave run-up and overtopping on smooth, impermeable single slope and composite slope. Based on the analysis of the influences of wave steepness, structure slope, incident wave angle, width of the berm and water depth on the berm and the wave run-up, empirical formulas for wave run-up on dike are proposed. Moreover, empirical formula on estimating the wave run-up on composite slope with multiple berms is presented for practical application of complex dike cross-section. The present study shows that the influence factors for wave overtopping are almost the same as those for wave run-up and the trend of the wave overtopping variation with main influence parameters is also similar to that for wave run-up. The trend of the wave overtopping variations can be well described by two main factors, i.e. the wave run-up and the crest freeboard of the structure. A new prediction method for wave overtopping is proposed for random waves. The proposed prediction formulas are applied to case study of over forty cases and the results show that the prediction methods are good enough for practical design purposes.展开更多
-The effect of wave group on wave run-up on a slope dike is mainly discussed in this paper. Two simulating methods of wave group and their applications in laboratory are introduced. Synthesizing the research results o...-The effect of wave group on wave run-up on a slope dike is mainly discussed in this paper. Two simulating methods of wave group and their applications in laboratory are introduced. Synthesizing the research results of wave run-up on a slope dike, the effect of wave group on wave run-up on a slope dike in coastal protection engineering is studied as the main point.展开更多
The parametric decay instabilities （PDIs） of ion Bernstein wave with different input power levels are investigated via particle-in-cell simulation. It is found that the number of decay channels increases with the in...The parametric decay instabilities （PDIs） of ion Bernstein wave with different input power levels are investigated via particle-in-cell simulation. It is found that the number of decay channels increases with the input power. Resonant mode-mode couplings dominate for a low input power. With increasing the input power, the nonresonant PDIs appear to dissipate the energy of the injected wave and give rise to edge ion heating. The generated child waves couple with each other as well as the injected wave and /or act as a pump wave to excite new decay channels. As a result, the frequency spectrum is broadened with the increase of the input power.展开更多
Foaming issues are encountered at the stages in crude oil production, transportation, processing, especially in chemical flooding enhanced oil recovery(EOR) oilfields. These accumulated foams would cause a lot of trou...Foaming issues are encountered at the stages in crude oil production, transportation, processing, especially in chemical flooding enhanced oil recovery(EOR) oilfields. These accumulated foams would cause a lot of trouble for downstream operation. The destruction of foams under ultrasonic has been increasingly paying attention in the background of green oilfield development. This study focuses on the decay kinetic characteristics of alkaline-surfactant-polymer-strengthened foams under the ultrasonic standing wave.The performance of the diverse foams was characterized. A decay kinetic model incorporating the energy correlation was developed and validated. The factors that affect the decay kinetic characteristics were discussed. The results indicated that the collapse rate and the collapse volume fraction decreased when the foam size decreased, the gas-liquid ratio decreased and the surface tension increased. Ultrasonic standing wave parameters have a significant impact on the decay behavior of the foam. Both the ultrasonic frequency and ultrasonic amplitude were increased by 50%, the collapse volume fraction of foams increased by about 1.25 times in the identical irradiation time. The relative deviation between the measured results and the model prediction was less than 10%. The potential collapse mechanism was also explained using the principle of energy correlation of foam surface. This study is not only beneficial to provide a robust and rigorous way to defoam of produced liquid in the alkaline/surfactant/polymer(ASP)flooding EOR process but also meaningful to well understand the decay process of oil-based foams.展开更多
文摘In this paper,we establish global classical solutions of semilinear wave equations with small compact supported initial data posed on the product space R^(3)×T.The semilinear nonlinearity is assumed to be of the cubic form.The main ingredient here is the establishment of the L^(2)-L^(∞)decay estimates and the energy estimates for the linear problem,which are adapted to the wave equation on the product space.The proof is based on the Fourier mode decomposition of the solution with respect to the periodic direction,the scaling technique,and the combination of the decay estimates and the energy estimates.
文摘This paper discusses the effect of berm width and elevation of composite slope on irregular wave run-up. Based on the data obtained from model tests, the formula and distribution of irregular wave run-up on composite slope are derived. The changing of wind speed, width and elevation of the berm are considered comprehensively. The wave run-up with various exceedance probability can be es-timated utilizing the distribution curves of irregular wave run-up.
基金financially supported by the funds for the National Natural Science Foundation of China (Nos. 51509230 and 52071304)the Primary Research&Development Plan of Shandong Province (No. 2019GHY 112044)。
文摘In the design of wind turbine foundations for offshore wind farms, the wave load and run-up slamming on the supporting structure are the quantities that need to be considered. Because of a special arc transition, the interaction between the wave field and the composite bucket foundation(CBF) becomes complicated. In this study, the hydrodynamic characteristics, including wave pressure, load, upwelling, and run-up, around the arc transition of a CBF influenced by regular waves are investigated through physical tests at Shandong Provincial Key Laboratory of Ocean Engineering, Ocean University of China. The distributions of the wave pressures and upwelling ratios around the CBF are described, and the relationship between the wave load and the wave parameters is discussed. New formulae based on the velocity stagnation head theory with linear wave theory and the second-order Stokes wave theory for wave kinematics are proposed to estimate the wave run-up. Moreover, the multiple regression method with nonlinear technology is employed to deduce an empirical formula for predicting run-up heights. Results show that the non-dimensional wave load increases with the increase in the values of the wave scattering parameter and relative wave height. The wave upwelling height is high in front of the CBF and has the lowest value at an angle of 135? with the incoming wave direction. The performance of the new formulae proposed in this study is compared using statistical indices to demonstrate that a good fit is obtained by the multiple regression method and the analytical model based on the velocity stagnation head theory is underdeveloped.
文摘An impedance analytical method （IAM） is developed to study the interaction of plane water wave with a slotted-wall caisson breakwater. The non-linear boundary condition at the slotted-wall is expressed in terms of flow resistance. A set of algebraic expressions are obtained for free surface elevation inside and outside chamber, and reflection coefficient. The prediction of the reflection coefficients shows that the relative widths of the chamber inducing the minimum reflection coefficient for a slotted-wall caisson breakwater are in a range of 0.10～0.20, which are smaller than that （0.15～0.25） for a perforated-wall caisson breakwater. The reflection coefficients and free surface elevation obtained by the present model are compared with that of laboratory experiments carried out by previous researchers.
基金the National Natural Science Foundation of China(Grant Nos.51679212 and 51809234)the Key Laboratory of Port,Waterway and Sedimentation Engineering,Ministry of Communications,China(Grant No.Yn918002)the Tang Scholar
文摘Wave hydrodynamics over fringing reefs is largely controlled by the reef surface roughness and hydrodynamic forcing.It is believed that climate change will result in a net increase in the water depth over the reef flat,a degrading of the surface roughness of coral reefs and changes in extreme incident wave heights.For an accurate assessment of how climate change affects the safety of reef-fringed coasts,a numerical study of the impact of climate change on irregular wave run-up over reef-fringed coasts was carried out based on a Boussinesq wave model,FUNWAVE-TVD.Validated with experimental data,the present model shows reasonable prediction of irregular wave evolution and run-up height over fringing reefs.Numerical experiments were then implemented based on the anticipated effects of climate change and carried out to investigate the effects of sea level rise,degrading of the reef surface roughness and increase of extreme incident wave height on the irregular wave run-up height over the backreef beach respectively.Variations of run-up components(i.e.,spectral characteristics of run-up and mean water level)were examined specifically and discussed to better understand the influencing mechanism of each climate change-related effect on the run-up.
基金supported bythe National Natural Science Foundation of China (Grant Nos.50379002 and 50921001)the New Century Excellent Talents in University (Grant No.NCET-05-0282)
文摘In this paper,the focused wave groups with different parameters and their actions on a vertical cylinder are experimentally studied. The harmonic wave characteristics of the focusing waves are analyzed by the addition and subtraction of the crest and trough focusing waves. The analyzed results show that higher order harmonics can be generated because of the interaction of component waves. Nonlinearity increases with the inputted wave amplitude and the frequency width increment. Further, the wave run-up around the vertical circular cylinder is experimentally studied. It increases with the wave steepness and the relative cylinder diameter increase. However, the variations of wave run-up around the circular cylinder are different. The researches provide a reference for further numerical studies.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.11632012 and 41861144024)the National Basic Research Program of China(973 Program,Grant No.2014CB046203)
文摘The run-up on offshore structures induced by the steep regular wave is a highly nonlinear flow with a free surface. This article focuses on the investigation of the steep regular wave run-up on a single vertical cylinder by solving the Navier-Stokes equations. A numerical wave tank is established based on the open-source package to simulate the wave scattering induced by a vertical cylinder. The VOF method is applied to capture the large deformation and breaking of the free surface. The numerical model is validated by experimental results. The relative wave run-ups on the front face and the back face along the centerline of a cylinder are analyzed. The changes of the relative run-ups with the wave steepness, the relative diameter and the relative depth are studied. It is found that the relative run-ups on the front face and the back face of the cylinder depend mainly on the wave steepness and the relative diameter, while the dependence on the relative depth is weak. The empirical formulae are proposed to calculate the relative run-ups in terms of the wave steepness of incident regular waves and the relative diameter of a cylinder.
文摘This paper describes a plane regular wave interaction with a combined cylinder which consists of a solid inner column and a coaxial perforated outer cylinder. The outer perforated surface is a thin porous cylinder with an annular gap between it and the inner cylinder. The non-linear boundary condition at the perforated wall is a prime focus in the study; energy dissipation at the perforated wall occurs through the resistance to the fluid across the perforated wall. Explicit analytical formulae are presented to calculate the wave run-up on the outer and inner surfaces of the perforated cylinder and the surface of the inner column. The theoretical results of the wave run-up are compared with previous experimental data. Numerical results have also been obtained： when the ratio of the annular gap between the two cylinders to incident wavelength （b-a）/L≤0. 1, the wave run-up on the inner surface of the perforated cylinder and the surface of inner column can partially or completely exceed the incident wave height.
基金The National Natural Science Foundation of China(No.10771032)
文摘The Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│）-1 and a nonlinearity │u│p-1u is studied.The total energy decay estimates of the global solutions are obtained by using multiplier techniques to establish identity ddtE（t）＋F（t）=0 and skillfully selecting f（t）,g（t）,h（t）when the initial data have a compact support.Using the similar method,the Cauchy problem for the nonlinear wave equation with a critical potential type of damping coefficient（1＋│x│＋t）-1 and a nonlinearity │u│p-1u is studied,similar solutions are obtained when the initial data have a compact support.
基金The research of Fan Lili was supported by two grants from the National Natural Science Foundation of China (10871151 10925103)+1 种基金the research of Liu Hongxia was supported by National Natural Science Foundation of China (10871082)the research of Yin Hui was supported by National Natural Sciences Foundation of China (10901064)
文摘This paper is concerned with the initial-boundary value problem for damped wave equations with a nonlinear convection term in the multi-dimensional half space R n ＋ ： u tt u ＋ u t ＋ divf （u） = 0, t 〉 0, x = （x 1 , x ′ ） ∈ R n ＋ ：= R ＋ × R n 1 , u（0, x） = u 0 （x） → u ＋ , as x 1 → ＋ ∞ , u t （0, x） = u 1 （x）, u（t, 0, x ′ ） = u b , x ′ = （x 2 , x 3 , ··· , x n ） ∈ R n 1 . （I） For the non-degenerate case f ′ 1 （u ＋ ） 〈 0, it was shown in [10] that the above initialboundary value problem （I） admits a unique global solution u（t, x） which converges to the corresponding planar stationary wave φ（x 1 ） uniformly in x 1 ∈ R ＋ as time tends to infinity provided that the initial perturbation and/or the strength of the stationary wave are sufficiently small. And in [10] Ueda, Nakamura, and Kawashima proved the algebraic decay estimates of the tangential derivatives of the solution u（t, x） for t → ＋ ∞ by using the space-time weighted energy method initiated by Kawashima and Matsumura [5] and improved by Nishihkawa [7]. Moreover, by using the same weighted energy method, an additional algebraic convergence rate in the normal direction was obtained by assuming that the initial perturbation decays algebraically. We note, however, that the analysis in [10] relies heavily on the assumption that f ′ （u） 〈 0. The main purpose of this paper isdevoted to discussing the case of f ′ 1 （u b ） ≥ 0 and we show that similar results still hold for such a case. Our analysis is based on some delicate energy estimates.
基金supported by the National Natural Science Foundation of China (Grant No.10702042)the Scientific Reseasch Startup Foundation of Shanghai Jiao Tong University (Grant No. A2823B) the Shanghai Leading Academic Discipline Project (Grant No.B206)
文摘Submerged barriers are constructed in coastal zones for shoreline or harbor protection or to prevent the beach erosion. In the present study, the wave run-up on a vertical seawall protected by a submerged barrier is analyzed. The physical configurations include a rigid barrier and a long channel of finite depth. For linear water waves, by matching the velocity along the barrier and along the gap, the systems of linear equations about the velocity potentials are obtained. The wave rim-up is further analyzed for various settings of barrier height and distance between the barrier and the wall, i.e. the chamber length. For nonlinear waves and random sea waves, a numerical model is extended to investigate the effect parameters of the barrier on the wave rim-up against the seawall. Not only the numerical simulations, but also the analytical results illustrate that the wave run-up on the seawall depends very much on the distance between the barrier and the vertical seawall.
文摘Linear governing equations are formulated for the depth decay of the pressure and velocity variations associated with propagating surface gravity waves. These governing equations come from combining Bernoulli’s equation for steady frictionless flow along a streamline and the crossstream force balance involving gravity, the centrifugal force and a pressure gradient. Qualitative solutions show that the pressure decreases downward faster than the velocity does and at a rate that is probably not the normal exponential decrease, which does not agree with the classical result. The radius of curvature of the streamlines is a non-constant coefficient in these equations and it needs to be supplied, either from measurements or another theory, in order to complete the solution of the derived governing equations. There is no sensitivity of the solution to the exact path the radius of curvature takes between its minimum value at the surface of a crest and trough and infinity at great depth. In the future measurements, perhaps streak photographs, will be needed to distinguish between the new and old theories.
基金Supported by National Natural Science Foundation of China(11601122,11801145)。
文摘We consider a wave equation with nonlocal nonlinear damping and source terms.We prove a general energy decay property for solutions by constructing a stable set and using the multiplier technique.The main difficult is how to handle with the nonlocal nonlinear damping term.Our result extends and improves the result in the literature such as the work by Jorge Silva and Narciso(Evolution Equation and Control Theory,2017(6):437-470)and Narciso(Evolution Equations and Control Theory,2020,9(2):487-508).
基金The National Natural Science Foundation of China under contract Nos 51579036 and 51779039the Fundamental Research Funds for the Central Universities of China under contract No.DUT19LAB13。
文摘Coastal vegetation is capable of decreasing wave run-up.However,because of regrowth,decay or man-made damage,coastal vegetation is always distributed in patches,and its internal distribution is often non-uniform.This study investigates the effects of patchy vegetation on solitary wave run-up by using a numerical simulation.A numerical model based on fully nonlinear Boussinesq equations is established to simulate the wave propagation on a slope with patchy vegetation.By using the model,the process of solitary wave run-up attenuation due to patchy vegetation is numerically analysed.The numerical results reveal that patchy vegetation can considerably attenuate the wave run-up in an effective manner.In addition,high-density patched vegetation can attenuate the solitary wave run-up more effectively than low-density patched vegetation can.For the same density,patchy vegetation with a uniform distribution has a better attenuation effect on wave run-up compared to that of patchy vegetation with a non-uniform distribution.
基金supported by State Key Development Program of Basic Research of China (Grant No.2010CB429001)
文摘The prediction of solitary wave run-up has important practical significance in coastal and ocean engineering, but the calculation precision is limited in the existing models. For improving the calculation precision, a solitary wave run-up calculation model was established based on artificial neural networks in this study. A back-propagation （BP） network with one hidden layer was adopted and modified with the additional momentum method and the auto-adjusting learning factor. The model was applied to calculation of solitary wave run-up. The correlation coefficients between the neural network model results and the experimental values was 0.996 5. By comparison with the correlation coefficient of 0.963 5, between the Synolakis formula calculation results and the experimental values, it is concluded that the neural network model is an effective method for calculation and analysis of solitary wave ran-up.
基金This project was supported by the Flood and Coastal Defense Commission of UK(FD0204)the National Natural Science Foundation of China(59809001)
文摘This paper. details experiments undertaken in the UK Coastal Research Facility (CRF)at Hy draulies Research (HR), Wallingford, on transformation and run-up of wave trains. The purpose of these experiments is to provide verification data for numerical models of wave transformation in shoaling. surf and swash zones. This is the kind of data ih:lt flume experiments are unable to provide, and is collected in the highly controlled environment of CRF where extrinsic factors present in the field are not an issue. The experiments concerning wave trains are undertaken by use of existing wave generation software, and the run-up measurements are made with large experimental run-up gauges.
文摘A series of hydraulic model tests are carried out to investigate random wave run-up and overtopping on smooth, impermeable single slope and composite slope. Based on the analysis of the influences of wave steepness, structure slope, incident wave angle, width of the berm and water depth on the berm and the wave run-up, empirical formulas for wave run-up on dike are proposed. Moreover, empirical formula on estimating the wave run-up on composite slope with multiple berms is presented for practical application of complex dike cross-section. The present study shows that the influence factors for wave overtopping are almost the same as those for wave run-up and the trend of the wave overtopping variation with main influence parameters is also similar to that for wave run-up. The trend of the wave overtopping variations can be well described by two main factors, i.e. the wave run-up and the crest freeboard of the structure. A new prediction method for wave overtopping is proposed for random waves. The proposed prediction formulas are applied to case study of over forty cases and the results show that the prediction methods are good enough for practical design purposes.
文摘-The effect of wave group on wave run-up on a slope dike is mainly discussed in this paper. Two simulating methods of wave group and their applications in laboratory are introduced. Synthesizing the research results of wave run-up on a slope dike, the effect of wave group on wave run-up on a slope dike in coastal protection engineering is studied as the main point.
基金Supported by the JSPS-NRF-NSFC A3 Foresight Program in the Field of Plasma Physics(NSFC No 11261140328 and NRF No 2012K2A2A6000443)the National Magnetic Confinement Fusion Science Program of China under Grant No 2013GB111002+1 种基金the National Natural Science Foundation of China under Grant Nos 11175212 and 11475220the Program of Fusion Reactor Physics and Digital Tokamak with the Chinese Academy of Sciences 'One-Three-Five' Strategic Planning
文摘The parametric decay instabilities （PDIs） of ion Bernstein wave with different input power levels are investigated via particle-in-cell simulation. It is found that the number of decay channels increases with the input power. Resonant mode-mode couplings dominate for a low input power. With increasing the input power, the nonresonant PDIs appear to dissipate the energy of the injected wave and give rise to edge ion heating. The generated child waves couple with each other as well as the injected wave and /or act as a pump wave to excite new decay channels. As a result, the frequency spectrum is broadened with the increase of the input power.
基金financially supported by the National Natural Science Foundation of China (Grant No.52174060)the PetroChina Innovation Foundation (Grant No.2019D-5007-0501)The Postdoctoral Scientific Foundation of Heilongjiang Province in China (Grant No. LBH-Q20012)。
文摘Foaming issues are encountered at the stages in crude oil production, transportation, processing, especially in chemical flooding enhanced oil recovery(EOR) oilfields. These accumulated foams would cause a lot of trouble for downstream operation. The destruction of foams under ultrasonic has been increasingly paying attention in the background of green oilfield development. This study focuses on the decay kinetic characteristics of alkaline-surfactant-polymer-strengthened foams under the ultrasonic standing wave.The performance of the diverse foams was characterized. A decay kinetic model incorporating the energy correlation was developed and validated. The factors that affect the decay kinetic characteristics were discussed. The results indicated that the collapse rate and the collapse volume fraction decreased when the foam size decreased, the gas-liquid ratio decreased and the surface tension increased. Ultrasonic standing wave parameters have a significant impact on the decay behavior of the foam. Both the ultrasonic frequency and ultrasonic amplitude were increased by 50%, the collapse volume fraction of foams increased by about 1.25 times in the identical irradiation time. The relative deviation between the measured results and the model prediction was less than 10%. The potential collapse mechanism was also explained using the principle of energy correlation of foam surface. This study is not only beneficial to provide a robust and rigorous way to defoam of produced liquid in the alkaline/surfactant/polymer(ASP)flooding EOR process but also meaningful to well understand the decay process of oil-based foams.
