In this paper, the truncated Painleve analysis and the consistent tanh expansion （CTE） method are developed for the （2＋1）-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction s...In this paper, the truncated Painleve analysis and the consistent tanh expansion （CTE） method are developed for the （2＋1）-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction solution of the equation is explicitly given, which is dimcult to be found by other traditional methods. When the value of the Jacobi elliptic function modulus rn = 1, the soliton-cnoidal wave interaction solution reduces back to the two-soliton solution. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.展开更多
We propose a systematic method to construct the Mel’nikov model of long–short wave interactions,which is a special case of the Kadomtsev–Petviashvili(KP)equation with self-consistent sources(KPSCS).We show details ...We propose a systematic method to construct the Mel’nikov model of long–short wave interactions,which is a special case of the Kadomtsev–Petviashvili(KP)equation with self-consistent sources(KPSCS).We show details how the Cauchy matrix approach applies to Mel’nikov’s model which is derived as a complex reduction of the KPSCS.As a new result wefind that in the dispersion relation of a 1-soliton there is an arbitrary time-dependent function that has previously not reported in the literature about the Mel’nikov model.This function brings time variant velocity for the long wave and also governs the short-wave packet.The variety of interactions of waves resulting from the time-freedom in the dispersion relation is illustrated.展开更多
The breakwaters have experienced many changes during their construction history.These changes have been considered to improve their performance,depending on their environmental conditions and applications.Numerical mo...The breakwaters have experienced many changes during their construction history.These changes have been considered to improve their performance,depending on their environmental conditions and applications.Numerical modelling was conducted using FLOW-3 D software.In this study,the wave overtopping from composite berm breakwater as new conceptual structure and the pressure imposed on the composite berm breakwater are considered and investigated.The results show a decrease of 84.01,70.88 and 61.42 percent of the wave overtopping in the composite berm breakwater,in comparison to the rubble mound breakwater,horizontally caisson breakwater and caisson breakwater,respectively.Also,the pressure applied to the composite berm breakwater with the pressure applied to the horizontally caisson breakwater was compared and evaluated.Composite berm breakwater compared with horizontally caisson breakwater in P1,the amount of the obtained pressure decreased by 52.09%,in P2 the amount of the obtained pressure decreased by 63.07%,in P3 decreased by 76.09%and in Pu,this pressure reduced by53.92%.For the composite berm breakwater,the impact of three types of berms,homogenous berm(Type 1),a berm consisting of armor-filter(Type 2)and multi-layer berm(Type 3)with the aim of optimizing the hydraulic responses and wave interaction on the caisson of the breakwater was examined and evaluated.In total,Type 3 will be recommended with a significant reduction in the overtopping values and maximum pressure.展开更多
New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangu...New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangular periodic wave solutions are obtained as well.展开更多
In this article,we study the exhaustive analysis of nonlinear wave interactions for a 2×2 homogeneous system of quasilinear hyperbolic partial differential equations(PDEs)governing the macroscopic production.We u...In this article,we study the exhaustive analysis of nonlinear wave interactions for a 2×2 homogeneous system of quasilinear hyperbolic partial differential equations(PDEs)governing the macroscopic production.We use the hodograph transformation and differential constraints technique to obtain the exact solution of governing equations.Furthermore,we study the interaction between simple waves in detail through exact solution of general initial value problem.Finally,we discuss the all possible interaction of elementary waves using the solution of Riemann problem.展开更多
Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis. For any given initial data with two pieces of constant states, the Riemann solutions are constructed as a c...Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis. For any given initial data with two pieces of constant states, the Riemann solutions are constructed as a combination of elementary waves. When the initial profile contains three pieces of constant states, the solution may be constructed from the Riemann solutions, with each two adjacent states connected by elementary waves. A new Riemann problem forms when these two waves collide. Through the exploration of these Riemann problems, the outcome of wave interactions may be classified in a suitable parametric space.展开更多
In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability ...In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability of the corresponding Riemann solutions under such small perturbations on the initial values. We find that the elementary wave interactions have a much more simple structure for Temple class than general systems of conservation laws. It is important to study the elementary waves interactions of the traffic flow system for the generalized Chaplygin gas not only because of their significance in practical applications in the traffic flow system, but also because of their basic role for the general mathematical theory.展开更多
In this paper, we investigate the elementary wave interactions for the Suliciu relaxation system and construct uniquely the solution by the characteristic analysis method in the phase plane. We find that the elementar...In this paper, we investigate the elementary wave interactions for the Suliciu relaxation system and construct uniquely the solution by the characteristic analysis method in the phase plane. We find that the elementary wave interactions have a much simpler structure for the Temple class than the general systems of conservation laws. It is observed that the Riemann solutions of the Suliciu relaxation system are stable under the small perturbation on the Riemann initial data.展开更多
Cowl-induced incident Shock Wave/Boundary Layer Interactions (SWBLI) under the influence of gradual expansion waves are frequently observed in supersonic inlets. However, the analysis and prediction of interaction len...Cowl-induced incident Shock Wave/Boundary Layer Interactions (SWBLI) under the influence of gradual expansion waves are frequently observed in supersonic inlets. However, the analysis and prediction of interaction lengths have not been sufficiently investigated. First, this study presents a theoretical scaling analysis and validates it through wind tunnel experiments. It conducts detailed control volume analysis of mass conservation, considering the differences between inviscid and viscous cases. Then, three models for analysing interaction length under gradual expansion waves are derived. Related experiments using schlieren photography are conducted to validate the models in a Mach 2.73 flow. The interaction scales are captured at various relative distances between the shock impingement location and the expansion regions with wedge angles ranging from 12° to 15° and expansion angles of 9°, 12°, and 15°. Three trend lines are plotted based on different expansion angles to depict the relationship between normalised interaction length and normalised interaction strength metric. In addition, the relationship between the coefficients of the trend line and the expansion angles is introduced to predict the interaction length influenced by gradual expansion waves. Finally, the estimation of normalised interaction length is derived for various coefficients within a unified form.展开更多
Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for on...Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for one dimensional zero-pressure gas dynamics system.Here the first equation is the Burgers equation and the second one is the continuity equation.We consider the solution with initial data in the space of bounded Borel measures.First we prove a general existence result in the algebra of generalized functions of Colombeau.Then we study in detail special solutions withδ-measures as initial data.We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves.This gives an understanding of plane-wave interactions in the multidimensional case.We use the vanishing viscosity method in our analysis as this gives the physical solution.展开更多
Shock wave/boundary layer interaction in a 24°turning angle of the compression ramp at Mach number 2.9 controlled by steady microjet is investigated using direct numerical simulation.Three different jet spacings ...Shock wave/boundary layer interaction in a 24°turning angle of the compression ramp at Mach number 2.9 controlled by steady microjet is investigated using direct numerical simulation.Three different jet spacings which are termed as sparse,moderate and dense are considered,and the induced vortex system and shock structures are compared.A moderate jet spacing configuration is found to generate counter-rotating vortex pairs that transport high-momentum fluid towards the vicinity of wall and strengthen the boundary layer to resist separation,reducing the separation region.The dense jet spacing configuration creates a larger momentum deficit region,reducing the friction downstream of the corner.Analysis of pressure and pressure gradient reveals that dense jet spacing configuration reduces the intensity of separation shock.The impact of varying jet spacings on the turbulent kinetic energy transport mechanism is also investigated by decomposing the budget terms in the transport equation.Furthermore,the spectral characteristics of the separation region are studied using power spectral density and dynamic mode decomposition methods,revealing that moderate jet spacing configuration suppresses low-frequency fluctuations in the separation region.展开更多
Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper. For special ease of slope angle β = π/2, th...Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper. For special ease of slope angle β = π/2, this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves are also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoreti- cal autocorrelation and spectral density functions of the first and the second orders are derived. The boundary conditions for the determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated.展开更多
The boundary element method（BEM） is a main method for analyzing the interactions between the waves and the marine structures. As with the BEM, a set of linear equations are generated with a full matrix, the required...The boundary element method（BEM） is a main method for analyzing the interactions between the waves and the marine structures. As with the BEM, a set of linear equations are generated with a full matrix, the required calculations and storage increase rapidly with the increase of the structure scale. Thus, an accelerated method with a low storage is desirable for the wave interaction with a very large structure. A systematic review is given in this paper for the BEM for solving the problem of the wave interaction with a large scale structure. Various integral equations are derived based on different Green functions, the advantages and disadvantages of different discretization schemes of the integral equations by the constant panels, the higher order elements, and the spline functions are discussed. For the higher order element discretization method, the special concerns are given to the numerical calculations of the single-layer potential, the double layer potential and the solid angle coefficients. For a large scale computation problem such as the wave interaction with a very large structure or a large number of bodies, the BEMs with the FMM and p FFT accelerations are discussed, respectively, including the principles of the FMM and the p FFT, and their implementations in various integral equations with different Green functions. Finally, some potential applications of the acceleration methods for problems with large scale computations in the ocean and coastal engineering are introduced.展开更多
The consistent tanh expansion(CTE) method is employed to the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explic...The consistent tanh expansion(CTE) method is employed to the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters.展开更多
This work investigates the interactions among solitons and their consequences in the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and pos...This work investigates the interactions among solitons and their consequences in the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and positrons, and inertial non-relativistic helium ions. The extended Poincare′–Lighthill–Kuo（PLK） method is employed to derive the two-sided Korteweg–de Vries（KdV） equations with their corresponding phase shifts. The nonlinear Schrodinger equation（NLSE） is obtained from the modified Kd V（mKdV） equation, which allows one to study the properties of the rogue waves. It is found that the Fermi temperature and quantum mechanical effects become pronounced due to the quantum diffraction of electrons and positrons in the plasmas. The densities and temperatures of the helium ions, degenerate electrons and positrons, and quantum parameters strongly modify the electrostatic ion acoustic resonances and their corresponding phase shifts due to the interactions among solitons and produce rogue waves in the plasma.展开更多
In order to construct global solutions to two-dimensional(2 D for short)Riemann problems for nonlinear hyperbolic systems of conservation laws,it is important to study various types of wave interactions.This paper dea...In order to construct global solutions to two-dimensional(2 D for short)Riemann problems for nonlinear hyperbolic systems of conservation laws,it is important to study various types of wave interactions.This paper deals with two types of wave interactions for a 2 D nonlinear wave system with a nonconvex equation of state:Rarefaction wave interaction and shock-rarefaction composite wave interaction.In order to construct solutions to these wave interactions,the authors consider two types of Goursat problems,including standard Goursat problem and discontinuous Goursat problem,for a 2 D selfsimilar nonlinear wave system.Global classical solutions to these Goursat problems are obtained by the method of characteristics.The solutions constructed in the paper may be used as building blocks of solutions of 2 D Riemann problems.展开更多
A discrete three-dimensional three wave interaction equation with self-consistent sources is constructed using the source generation procedure. The algebraic structure of the resulting fully discrete system is clarifi...A discrete three-dimensional three wave interaction equation with self-consistent sources is constructed using the source generation procedure. The algebraic structure of the resulting fully discrete system is clarified by presenting its discrete Gram-type determinant solution. It is shown that the discrete three-dimensional three wave interaction equation with self-consistent sources has a continuum limit into the three-dimensional three wave interaction equation with self-consistent sources.展开更多
This paper investigates the hydrodynamic performance of a cylindrical-dual or rectangular-single pontoon floating breakwater using the numerical method and experimental study. The numerical simulation work is based on...This paper investigates the hydrodynamic performance of a cylindrical-dual or rectangular-single pontoon floating breakwater using the numerical method and experimental study. The numerical simulation work is based on the multi-physics computational fluid dynamics(CFD) code and an innovative full-structured dynamic grid method applied to update the three-degree-of-freedom(3-DOF) rigid structure motions. As a time-marching scheme, the trapezoid analogue integral method is used to update the time integration combined with remeshing at each time step.The application of full-structured mesh elements can prevent grids distortion or deformation caused by large-scale movement and improve the stability of calculation. In movable regions, each moving zone is specified with particular motion modes(sway, heave and roll). A series of experimental studies are carried out to validate the performance of the floating body and verify the accuracy of the proposed numerical model. The results are systematically assessed in terms of wave coefficients, mooring line forces, velocity streamlines and the 3-DOF motions of the floating breakwater. When compared with the wave coefficient solutions, excellent agreements are achieved between the computed and experimental data, except in the vicinity of resonant frequency. The velocity streamlines and wave profile movement in the fluid field can also be reproduced using this numerical model.展开更多
In this paper, the tropical air-sea interaction is discussed by using a simple air-sea coupled model, in which the inertia-gravity waves are filtered off and only the equatorial Rossby waves are reserved in both the a...In this paper, the tropical air-sea interaction is discussed by using a simple air-sea coupled model, in which the inertia-gravity waves are filtered off and only the equatorial Rossby waves are reserved in both the atmosphere and the ocean. There exist two kinds of air-sea interaction waves in the coupled model, that is, the high-frequency fast waves and the low-frequency slow waves. The phase speed of the fast waves is westward and the frequencies are close to those of the equatorial Rossby waves in the atmosphere. The slow waves propagate westward in the part of short wavelengths and eastward in that of long wavelengths. There exist instabilities for both the westward and eastward propagating slow waves. If the fast waves are filtered off, there is little effect on the slow waves which have great influence on the long range process in the tropical air-sea coupled system. According to the tropical air-sea interaction waves we obtain here, a possible explanation to the propagating process of ENSO events is given.展开更多
Wave and longshore current interaction was examined based on the numerical models.In these models,water waves in the presence of longshore currents were modeled by parabolic mild slope equation,and wave breaking induc...Wave and longshore current interaction was examined based on the numerical models.In these models,water waves in the presence of longshore currents were modeled by parabolic mild slope equation,and wave breaking induced longshore currents were modeled by shallow water equation.Water wave provided the radiation stress gradients to drive current.Wave and longshore current interactions were considered by cycling the wave and longshore current models to a steady state.The experiments for regular and irregular breaking wave induced longshore currents by Hamilton and Ebersole (2001) and Reniers and Battjes (1997) were simulated.The numerical results indicate that the present models are effective for simulating the interaction of wave and breaking wave induced longshore currents,and the numerically simulated longshore current at wave breaking point considering wave and longshore current interaction show some disagreement with those neglecting the wave-current interaction,and the breaking wave induced longshore current effect on wave transformation is not obvious.展开更多
基金Supported by National Natural Science Foundation of China under Grant Nos.11271211,11275072,11435005K.C.Wong Magna Fund in Ningbo University
文摘In this paper, the truncated Painleve analysis and the consistent tanh expansion （CTE） method are developed for the （2＋1）-dimensional breaking soliton equation. As a result, the soliton-cnoidal wave interaction solution of the equation is explicitly given, which is dimcult to be found by other traditional methods. When the value of the Jacobi elliptic function modulus rn = 1, the soliton-cnoidal wave interaction solution reduces back to the two-soliton solution. The method can also be extended to other types of nonlinear evolution equations in mathematical physics.
基金supported by the NSF of China(Nos.11875040 and 11631007)。
文摘We propose a systematic method to construct the Mel’nikov model of long–short wave interactions,which is a special case of the Kadomtsev–Petviashvili(KP)equation with self-consistent sources(KPSCS).We show details how the Cauchy matrix approach applies to Mel’nikov’s model which is derived as a complex reduction of the KPSCS.As a new result wefind that in the dispersion relation of a 1-soliton there is an arbitrary time-dependent function that has previously not reported in the literature about the Mel’nikov model.This function brings time variant velocity for the long wave and also governs the short-wave packet.The variety of interactions of waves resulting from the time-freedom in the dispersion relation is illustrated.
文摘The breakwaters have experienced many changes during their construction history.These changes have been considered to improve their performance,depending on their environmental conditions and applications.Numerical modelling was conducted using FLOW-3 D software.In this study,the wave overtopping from composite berm breakwater as new conceptual structure and the pressure imposed on the composite berm breakwater are considered and investigated.The results show a decrease of 84.01,70.88 and 61.42 percent of the wave overtopping in the composite berm breakwater,in comparison to the rubble mound breakwater,horizontally caisson breakwater and caisson breakwater,respectively.Also,the pressure applied to the composite berm breakwater with the pressure applied to the horizontally caisson breakwater was compared and evaluated.Composite berm breakwater compared with horizontally caisson breakwater in P1,the amount of the obtained pressure decreased by 52.09%,in P2 the amount of the obtained pressure decreased by 63.07%,in P3 decreased by 76.09%and in Pu,this pressure reduced by53.92%.For the composite berm breakwater,the impact of three types of berms,homogenous berm(Type 1),a berm consisting of armor-filter(Type 2)and multi-layer berm(Type 3)with the aim of optimizing the hydraulic responses and wave interaction on the caisson of the breakwater was examined and evaluated.In total,Type 3 will be recommended with a significant reduction in the overtopping values and maximum pressure.
文摘New exact solutions expressed by the Jacobi elliptic functions are obtained to the long-short wave interaction equations by using the modified F-expansion method. In the limit case, solitary wave solutions and triangular periodic wave solutions are obtained as well.
基金Ministry of Human Resource Development,Government of India,for the institute fellowship(grant no.IIT/ACAD/PGS&R/F.II/2/14MA90J08)from IIT KharagpurSERB,DST,India(Ref.No.MTR/2019/001210)for its financial support through MATRICS grant。
文摘In this article,we study the exhaustive analysis of nonlinear wave interactions for a 2×2 homogeneous system of quasilinear hyperbolic partial differential equations(PDEs)governing the macroscopic production.We use the hodograph transformation and differential constraints technique to obtain the exact solution of governing equations.Furthermore,we study the interaction between simple waves in detail through exact solution of general initial value problem.Finally,we discuss the all possible interaction of elementary waves using the solution of Riemann problem.
基金Project supported by the Major State Basic Research Development Program("Nonlinear Science")of China(No.G2000077305)the National Natural Science Foundation of China(Nos.10002002and 90407021)
文摘Elementary waves in Suliciu model for dynamic phase transitions are obtained through traveling wave analysis. For any given initial data with two pieces of constant states, the Riemann solutions are constructed as a combination of elementary waves. When the initial profile contains three pieces of constant states, the solution may be constructed from the Riemann solutions, with each two adjacent states connected by elementary waves. A new Riemann problem forms when these two waves collide. Through the exploration of these Riemann problems, the outcome of wave interactions may be classified in a suitable parametric space.
文摘In this paper, we investigate the elementary wave interactions of the Aw-Rascle model for the generalized Chaplygin gas. We construct the unique solution by the characteristic analysis method and obtain the stability of the corresponding Riemann solutions under such small perturbations on the initial values. We find that the elementary wave interactions have a much more simple structure for Temple class than general systems of conservation laws. It is important to study the elementary waves interactions of the traffic flow system for the generalized Chaplygin gas not only because of their significance in practical applications in the traffic flow system, but also because of their basic role for the general mathematical theory.
文摘In this paper, we investigate the elementary wave interactions for the Suliciu relaxation system and construct uniquely the solution by the characteristic analysis method in the phase plane. We find that the elementary wave interactions have a much simpler structure for the Temple class than the general systems of conservation laws. It is observed that the Riemann solutions of the Suliciu relaxation system are stable under the small perturbation on the Riemann initial data.
基金co-supported by the National Natural Science Foundation of China (No. 12172175)the National Science and Technology Major Project, China (No. J2019-II0014-0035)the Science Center for Gas Turbine Project, China (Nos. P2022-C-II-002-001, P2022-A-II-002-001)
文摘Cowl-induced incident Shock Wave/Boundary Layer Interactions (SWBLI) under the influence of gradual expansion waves are frequently observed in supersonic inlets. However, the analysis and prediction of interaction lengths have not been sufficiently investigated. First, this study presents a theoretical scaling analysis and validates it through wind tunnel experiments. It conducts detailed control volume analysis of mass conservation, considering the differences between inviscid and viscous cases. Then, three models for analysing interaction length under gradual expansion waves are derived. Related experiments using schlieren photography are conducted to validate the models in a Mach 2.73 flow. The interaction scales are captured at various relative distances between the shock impingement location and the expansion regions with wedge angles ranging from 12° to 15° and expansion angles of 9°, 12°, and 15°. Three trend lines are plotted based on different expansion angles to depict the relationship between normalised interaction length and normalised interaction strength metric. In addition, the relationship between the coefficients of the trend line and the expansion angles is introduced to predict the interaction length influenced by gradual expansion waves. Finally, the estimation of normalised interaction length is derived for various coefficients within a unified form.
基金supported by the TIFR-CAM Doctoral Fellowshipthe NISER Postdoctoral Fellowship (through the project “Basic research in physics and multidisciplinary sciences” with identification # RIN4001) during the preparation of this papersupported by the Raja Ramanna Fellowship
文摘Evolution and interaction of plane waves of the multidimensional zero-pressure gas dynamics system leads to the study of the corresponding one dimensional system.In this paper,we study the initial value problem for one dimensional zero-pressure gas dynamics system.Here the first equation is the Burgers equation and the second one is the continuity equation.We consider the solution with initial data in the space of bounded Borel measures.First we prove a general existence result in the algebra of generalized functions of Colombeau.Then we study in detail special solutions withδ-measures as initial data.We study interaction of waves originating from initial data concentrated on two point sources and interaction with classical shock/rarefaction waves.This gives an understanding of plane-wave interactions in the multidimensional case.We use the vanishing viscosity method in our analysis as this gives the physical solution.
基金Supported by the National Natural Science Foundation of China(Nos.11972064,92052104)the Key Laboratory of Computational Aerodynamics,AVIC Aerodynamics Research Institute,China(No.YL2022XFX0405)the Fundamental Research Funds for the Central Universities,China.
文摘Shock wave/boundary layer interaction in a 24°turning angle of the compression ramp at Mach number 2.9 controlled by steady microjet is investigated using direct numerical simulation.Three different jet spacings which are termed as sparse,moderate and dense are considered,and the induced vortex system and shock structures are compared.A moderate jet spacing configuration is found to generate counter-rotating vortex pairs that transport high-momentum fluid towards the vicinity of wall and strengthen the boundary layer to resist separation,reducing the separation region.The dense jet spacing configuration creates a larger momentum deficit region,reducing the friction downstream of the corner.Analysis of pressure and pressure gradient reveals that dense jet spacing configuration reduces the intensity of separation shock.The impact of varying jet spacings on the turbulent kinetic energy transport mechanism is also investigated by decomposing the budget terms in the transport equation.Furthermore,the spectral characteristics of the separation region are studied using power spectral density and dynamic mode decomposition methods,revealing that moderate jet spacing configuration suppresses low-frequency fluctuations in the separation region.
文摘Based on the full water-wave equation, a second-order analytic solution for nonlinear interaction of short edge waves on a plane sloping bottom is presented in this paper. For special ease of slope angle β = π/2, this solution can reduced to the same order solution of deep water gravity surface waves traveling along parallel coastline. Interactions between two edge waves including progressive, standing and partially reflected standing waves are also discussed. The unified analytic expressions with transfer functions for kinematic-dynamic elements of edge waves are also given. The random model of the unified wave motion processes for linear and nonlinear irregular edge waves is formulated, and the corresponding theoreti- cal autocorrelation and spectral density functions of the first and the second orders are derived. The boundary conditions for the determination of the parameters of short edge wave are suggested, that may be seen as one special simple edge wave excitation mechanism and an extension to the sea wave refraction theory. Finally some computation results are demonstrated.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.51379032,51490672 and 51479026)
文摘The boundary element method（BEM） is a main method for analyzing the interactions between the waves and the marine structures. As with the BEM, a set of linear equations are generated with a full matrix, the required calculations and storage increase rapidly with the increase of the structure scale. Thus, an accelerated method with a low storage is desirable for the wave interaction with a very large structure. A systematic review is given in this paper for the BEM for solving the problem of the wave interaction with a large scale structure. Various integral equations are derived based on different Green functions, the advantages and disadvantages of different discretization schemes of the integral equations by the constant panels, the higher order elements, and the spline functions are discussed. For the higher order element discretization method, the special concerns are given to the numerical calculations of the single-layer potential, the double layer potential and the solid angle coefficients. For a large scale computation problem such as the wave interaction with a very large structure or a large number of bodies, the BEMs with the FMM and p FFT accelerations are discussed, respectively, including the principles of the FMM and the p FFT, and their implementations in various integral equations with different Green functions. Finally, some potential applications of the acceleration methods for problems with large scale computations in the ocean and coastal engineering are introduced.
基金Supported by the National Natural Science Foundation of China under Grant No.11505154the Zhejiang Provincial Natural Science Foundation of China under Grant No.LQ16A010003the Scientific Research Foundation for Doctoral Program of Zhejiang Ocean University under Grant No.Q1511
文摘The consistent tanh expansion(CTE) method is employed to the(2+1)-dimensional Caudrey–Dodd–Gibbon–Kotera–Sawada(CDGKS) equation. The interaction solutions between solitons and the cnoidal periodic waves are explicitly obtained. Concretely, we discuss a special kind of interaction solution in the form of tanh functions and Jacobian elliptic functions in both analytical and graphical ways. The results show that the profiles of the soliton-cnoidal periodic wave interaction solutions can be designed by choosing different values of wave parameters.
文摘This work investigates the interactions among solitons and their consequences in the production of rogue waves in an unmagnetized plasmas composing non-relativistic as well as relativistic degenerate electrons and positrons, and inertial non-relativistic helium ions. The extended Poincare′–Lighthill–Kuo（PLK） method is employed to derive the two-sided Korteweg–de Vries（KdV） equations with their corresponding phase shifts. The nonlinear Schrodinger equation（NLSE） is obtained from the modified Kd V（mKdV） equation, which allows one to study the properties of the rogue waves. It is found that the Fermi temperature and quantum mechanical effects become pronounced due to the quantum diffraction of electrons and positrons in the plasmas. The densities and temperatures of the helium ions, degenerate electrons and positrons, and quantum parameters strongly modify the electrostatic ion acoustic resonances and their corresponding phase shifts due to the interactions among solitons and produce rogue waves in the plasma.
基金supported by the National Natural Science Foundation of China(No.11301326)。
文摘In order to construct global solutions to two-dimensional(2 D for short)Riemann problems for nonlinear hyperbolic systems of conservation laws,it is important to study various types of wave interactions.This paper deals with two types of wave interactions for a 2 D nonlinear wave system with a nonconvex equation of state:Rarefaction wave interaction and shock-rarefaction composite wave interaction.In order to construct solutions to these wave interactions,the authors consider two types of Goursat problems,including standard Goursat problem and discontinuous Goursat problem,for a 2 D selfsimilar nonlinear wave system.Global classical solutions to these Goursat problems are obtained by the method of characteristics.The solutions constructed in the paper may be used as building blocks of solutions of 2 D Riemann problems.
基金Acknowledgements The first author would like to express her sincere thanks to Prof. Xing-Biao ttu for his helpful discussion and encouragement. This work was supported by the Program of Higher-level Talents of Inner Mongolia University （2011153, 21100-5145101）, the National Natural Science Foundation of China （Grant Nos. 11561048, 11547101） and the Natural Science Foundation of Inner Mongolia Autonomous Region （2015MS0116）.
文摘A discrete three-dimensional three wave interaction equation with self-consistent sources is constructed using the source generation procedure. The algebraic structure of the resulting fully discrete system is clarified by presenting its discrete Gram-type determinant solution. It is shown that the discrete three-dimensional three wave interaction equation with self-consistent sources has a continuum limit into the three-dimensional three wave interaction equation with self-consistent sources.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51579122,51609109,and 51622902)the Natural Science Found of Jiangsu Province(Grant No.BK20160556)+1 种基金the University Natural Science Research Project of Jiangsu Province(Grant No.16kjb70003)the Key Lab Foundation for Advanced Manufacturing Technology of Jiangsu Province(Grant No.CJ1506)
文摘This paper investigates the hydrodynamic performance of a cylindrical-dual or rectangular-single pontoon floating breakwater using the numerical method and experimental study. The numerical simulation work is based on the multi-physics computational fluid dynamics(CFD) code and an innovative full-structured dynamic grid method applied to update the three-degree-of-freedom(3-DOF) rigid structure motions. As a time-marching scheme, the trapezoid analogue integral method is used to update the time integration combined with remeshing at each time step.The application of full-structured mesh elements can prevent grids distortion or deformation caused by large-scale movement and improve the stability of calculation. In movable regions, each moving zone is specified with particular motion modes(sway, heave and roll). A series of experimental studies are carried out to validate the performance of the floating body and verify the accuracy of the proposed numerical model. The results are systematically assessed in terms of wave coefficients, mooring line forces, velocity streamlines and the 3-DOF motions of the floating breakwater. When compared with the wave coefficient solutions, excellent agreements are achieved between the computed and experimental data, except in the vicinity of resonant frequency. The velocity streamlines and wave profile movement in the fluid field can also be reproduced using this numerical model.
文摘In this paper, the tropical air-sea interaction is discussed by using a simple air-sea coupled model, in which the inertia-gravity waves are filtered off and only the equatorial Rossby waves are reserved in both the atmosphere and the ocean. There exist two kinds of air-sea interaction waves in the coupled model, that is, the high-frequency fast waves and the low-frequency slow waves. The phase speed of the fast waves is westward and the frequencies are close to those of the equatorial Rossby waves in the atmosphere. The slow waves propagate westward in the part of short wavelengths and eastward in that of long wavelengths. There exist instabilities for both the westward and eastward propagating slow waves. If the fast waves are filtered off, there is little effect on the slow waves which have great influence on the long range process in the tropical air-sea coupled system. According to the tropical air-sea interaction waves we obtain here, a possible explanation to the propagating process of ENSO events is given.
基金The National Natural Science Foundation of China under contract Nos 50839001,51179025 and 50709004the Specialized Research Fund for the Doctoral Program of Higher Education of China under contract No.20070141032
文摘Wave and longshore current interaction was examined based on the numerical models.In these models,water waves in the presence of longshore currents were modeled by parabolic mild slope equation,and wave breaking induced longshore currents were modeled by shallow water equation.Water wave provided the radiation stress gradients to drive current.Wave and longshore current interactions were considered by cycling the wave and longshore current models to a steady state.The experiments for regular and irregular breaking wave induced longshore currents by Hamilton and Ebersole (2001) and Reniers and Battjes (1997) were simulated.The numerical results indicate that the present models are effective for simulating the interaction of wave and breaking wave induced longshore currents,and the numerically simulated longshore current at wave breaking point considering wave and longshore current interaction show some disagreement with those neglecting the wave-current interaction,and the breaking wave induced longshore current effect on wave transformation is not obvious.
