Water waves in coastal areas are generally non- linear, exhibiting asymmetric velocity profiles with different amplitudes of crest and trough. The behaviors of the bound- ary layer under asymmetric waves are of great ...Water waves in coastal areas are generally non- linear, exhibiting asymmetric velocity profiles with different amplitudes of crest and trough. The behaviors of the bound- ary layer under asymmetric waves are of great significance for sediment transport in natural circumstances. While pre- vious studies have mainly focused on linear or symmetric waves, asymmetric wave-induced flows remain unclear, par- ticularly in the flow regime with high Reynolds numbers. Taking cnoidal wave as a typical example of asymmetric waves, we propose to use an infinite immersed plate oscillat- ing cnoidally in its own plane in quiescent water to simulate asymmetric wave boundary layer. A large eddy simulation approach with Smagorinsky subgrid model is adopted to investigate the flow characteristics of the boundary layer. It is verified that the model well reproduces experimental and theoretical results. Then a series of numerical experiments are carried out to study the boundary layer beneath cnoidal waves from laminar to fully developed turbulent regimes at high Reynolds numbers, larger than ever studied before. Results of velocity profile, wall shear stress, friction coeffi- cient, phase lead between velocity and wall shear stress, and the boundary layer thickness are obtained. The dependencies of these boundary layer properties on the asymmetric degree and Reynolds number are discussed in detail.展开更多
The volume of fluid (VOF) method is used to set up a wave flume with an absorbing wave maker of cnoidal waves. Based on the transfer function between wave surface and paddle velocity obtained by the shallow water wave...The volume of fluid (VOF) method is used to set up a wave flume with an absorbing wave maker of cnoidal waves. Based on the transfer function between wave surface and paddle velocity obtained by the shallow water wave theory, the velocity boundary condition of an absorbing wave maker is introduced to absorb reflected waves that reach the numerical wave maker. For Hid ranging from 0.1 to 0.59 and T root g/d from 7.9 to 18.3, the parametric studies have been carried out and compared with experiments.展开更多
The(2+1)-dimensional Konopelchenko–Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the(2+1)-dimensional Konopelchenko–D...The(2+1)-dimensional Konopelchenko–Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the(2+1)-dimensional Konopelchenko–Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the(2+1)-dimensional Konopelchenko–Dubrovsky equation is solved by the consistent Riccati expansion(CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the(2+1)-dimensional Konopelchenko–Dubrovsky equation.展开更多
The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find inter...The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this peper, two equivalent very simple methods, the truncated Painleve analysis and the generalized tanh function expansion approaches, are developed to find interaction solutions between solitons and any other types of Boussinesq waves.展开更多
The evolution of an initially flat sandy bed is studied in a laboratory wave flume under enoidal waves and acoustic Doppler velocimeter （ADV） was utilized in the detailed velocity measurements at different positions...The evolution of an initially flat sandy bed is studied in a laboratory wave flume under enoidal waves and acoustic Doppler velocimeter （ADV） was utilized in the detailed velocity measurements at different positions. The ripple formation and evolution have been analyzed by CCD images and the asymmetric rippled bed is induced by the nonlinear wave flow. The flow structure and a complete process of vortex formation, evolvement and disappearance were observed on the asymmetric rippled bed under cnoidal waves. With the increasing nonlinearity of waves, which is an important factor in the sand ripple formation, the vortex intensity becomes stronger and shows different characteristics on both sides of the ripple crest. The vorticity and wave velocity reach their maximum values at different phase angles. The vortex value reaches the maximum value at a small phase angle with the increasing Ursell number. The near bed flow patterns are mainly determined by the ripple forms and the averaged longitudinal velocity over a wave period above the ripple trough and crest are positive, which indicates the possibility of significant onshore sediment transport and a corresponding ripple drift. The phase averaged vertical velocity has noticeable positive values near the bottom of the ripple crest and trough. Sediments may be lifted from the ripple surface, picked up in suspension by the local velocity, and deposited over the crest and on the lee of the ripples.展开更多
Severe water waves can induce seabed liquefaction and do harm to marine structures. Dynamic response of seabed with definite thickness induced by cnoidal water waves is investigated numerically. Biot＇s consolidation ...Severe water waves can induce seabed liquefaction and do harm to marine structures. Dynamic response of seabed with definite thickness induced by cnoidal water waves is investigated numerically. Biot＇s consolidation equations are employed to model the seabed response. Parametric studies are carried out to examine the influence of the air content in the pore water and the soil hydraulic conductivity. It is been shown that the air content and soil hydraulic conductivity can significantly affect the pore pressure in seabed. An increase of air content and/or a decrease of soil hydraulic conductivity can change the pore pressure gradient sharply.展开更多
In nonlinear physics, the modified Korteweg de-Vries （mKdV） as one of the important equation of nonfinear partial differential equations, its various solutions have been found by many methods. In this paper, the CRE...In nonlinear physics, the modified Korteweg de-Vries （mKdV） as one of the important equation of nonfinear partial differential equations, its various solutions have been found by many methods. In this paper, the CRE method is presented for constructing new exact solutions. In addition to the new solutions of the mKdV equation, the consistent Riccati expansion （CRE） method can unearth other equations.展开更多
Based on the 2nd order cnoidal wave theory, the characters of shallow water standing waves and their action on vertical walls are studied in this paper. The theoretical expressions of the wave surface elevation in fro...Based on the 2nd order cnoidal wave theory, the characters of shallow water standing waves and their action on vertical walls are studied in this paper. The theoretical expressions of the wave surface elevation in front of and the wave pressure on the vertical wall are obtained. In order to verify the theoretical results, model tests were made in the State Key Laboratory of Coastal and Offshore Engineering at DUT. For the wave surface elevation in front of the wall and the wave forces on the wall at the moment when the wave surface at the wall surface goes down to the bottom of the wave trough, the calculated results coincide quite well with the experimental results. For the wave forces on the wall at the moment when the wave surface at the wall surface goes up to the top of the wave crest, the theoretical expressions are modified by the experimental results. For the convenience of practical use, calculations are made for the wave conditions which usually occur in enginering practice by use of the investigated results obtained in this paper. Empirical formulas are fitted with these calculated results for designers to use.展开更多
Theoretical investigation of nonlinear electrostatic ion-acoustic cnoidal waves(IACWs) is presented in magnetized electron–positron–ion plasma with nonextensive electrons and Maxwellian positrons. Using reductive pe...Theoretical investigation of nonlinear electrostatic ion-acoustic cnoidal waves(IACWs) is presented in magnetized electron–positron–ion plasma with nonextensive electrons and Maxwellian positrons. Using reductive perturbation technique, Korteweg–de Vries equation is derived and its cnoidal wave solution is analyzed. For given plasma parameters, our model supports only positive potential(compressive) IACW structures. The effect of relevant plasma parameters(viz., nonextensive parameter q, positron concentration p, temperature ratio σ,obliqueness l3) on the characteristics of IACWs is discussed in detail.展开更多
In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduce...In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell-Bloch equations with solitary wave, cnoidal periodic wave, and soliton-cnoidal interactional wave solutions in an explicit form. Particularly, the soliton-cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell-Bloch equations. Finally, we present some figures to show properties of the explicit soliton-cnoidal interactional wave solutions as well as some new dynamical phenomena.展开更多
The nonlinear evolution equations have a wide range of applications,more precisely in physics,biology,chemistry and engineering fields.This domain serves as a point of interest to a large extent in the world’s mathem...The nonlinear evolution equations have a wide range of applications,more precisely in physics,biology,chemistry and engineering fields.This domain serves as a point of interest to a large extent in the world’s mathematical community.Thus,this paper purveys an analytical study of a generalized extended(2+1)-dimensional quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering.The Lie group theory of differential equations is utilized to compute an optimal system of one dimension for the Lie algebra of the model.We further reduce the equation using the subalgebras obtained.Besides,more general solutions of the underlying equation are secured for some special cases of n with the use of extended Jacobi function expansion technique.Consequently,we secure new bounded and unbounded solutions of interest for the equation in various solitonic structures including bright,dark,periodic(cnoidal and snoidal),compact-type as well as singular solitons.The applications of cnoidal and snoidal waves of the model in oceanography and ocean engineering for the first time,are outlined with suitable diagrams.This can be of interest to oceanographers and ocean engineers for future analysis.Furthermore,to visualize the dynamics of the results found,we present the graphic display of each of the solutions.Conclusively,we construct conservation laws of the understudy equation via the application of Noether’s theorem.展开更多
In this paper, starting with the equations describing the atmospheric motion and by arelatively simple method, we find that, nearby the mechanical equilibrium point, all thefinite amplitude nonlinear inertia waves, in...In this paper, starting with the equations describing the atmospheric motion and by arelatively simple method, we find that, nearby the mechanical equilibrium point, all thefinite amplitude nonlinear inertia waves, internal gravity waves and Rossby waves in thedispersive atmosphere satisfy the KdV (Korteweg-de Vries) equation, its solution being thecnoidal waves and solitary waves. For the finite amplitude Rossby waves, we find the newdispersive relation which is different from the Rossby formula and contains the amplitudeparameter. It is shown that the larger the amplitude and width, the faster are the wavesfor the finite amplitude inertia waves and internal gravity waves, and the slower are thewaves for the Rossby solitary waves, to which perhaps the polar vortex and the blocking orcut-off systems belong. This treatise gives the nonlinear waves a new way and inspires usto study the nonlinear adjustment process and evolution process and the turbulence structure.展开更多
The method of cnoidal wave generation in a wave flume is studied in this paper.According to the wave equa- tion in shallow water,the wave paddle motion equation for given wave parameters and water depth is derived.The...The method of cnoidal wave generation in a wave flume is studied in this paper.According to the wave equa- tion in shallow water,the wave paddle motion equation for given wave parameters and water depth is derived.The controlling signal for driving wavemaker can be converted from its solution,and high wave height shallow water waves can be generated.The experiment results show that,the parameters of the wave generated are very close to the required ones in a certain distance in front of the paddle of the wavemaker.展开更多
For the dynamics of three-dimensional electron–positron–ion plasmas,a fluid quantum hydrodynamic model is proposed by considering Landau quantization effects in dense plasma.Ion–neutral collisions in the presence o...For the dynamics of three-dimensional electron–positron–ion plasmas,a fluid quantum hydrodynamic model is proposed by considering Landau quantization effects in dense plasma.Ion–neutral collisions in the presence of the Coriolis force are also considered.The application of the reductive perturbation technique produces a wave evolution equation represented by a damped Korteweg–de Vries equation.This equation,however,is insufficient for describing waves in our system at very low dispersion coefficients.As a result,we considered the highest-order perturbation,which resulted in the damped Kawahara equation.The effects of the magnetic field,Landau quantization,the ratio of positron density to electron density,the ratio of positron density to ion density,and the direction cosine on linear dispersion laws as well as soliton and conoidal solutions of the damped Kawahara equation are explored.The understanding from this research can contribute to the broader field of astrophysics and aid in the interpretation of observational data from white dwarfs.展开更多
基金financial support to this work from the National Natural Science Foundation of China (Grants 11172307 and11232012)973 Program (2014CB046200)
文摘Water waves in coastal areas are generally non- linear, exhibiting asymmetric velocity profiles with different amplitudes of crest and trough. The behaviors of the bound- ary layer under asymmetric waves are of great significance for sediment transport in natural circumstances. While pre- vious studies have mainly focused on linear or symmetric waves, asymmetric wave-induced flows remain unclear, par- ticularly in the flow regime with high Reynolds numbers. Taking cnoidal wave as a typical example of asymmetric waves, we propose to use an infinite immersed plate oscillat- ing cnoidally in its own plane in quiescent water to simulate asymmetric wave boundary layer. A large eddy simulation approach with Smagorinsky subgrid model is adopted to investigate the flow characteristics of the boundary layer. It is verified that the model well reproduces experimental and theoretical results. Then a series of numerical experiments are carried out to study the boundary layer beneath cnoidal waves from laminar to fully developed turbulent regimes at high Reynolds numbers, larger than ever studied before. Results of velocity profile, wall shear stress, friction coeffi- cient, phase lead between velocity and wall shear stress, and the boundary layer thickness are obtained. The dependencies of these boundary layer properties on the asymmetric degree and Reynolds number are discussed in detail.
基金Trans-Century Training Program Fund for the Talent,Ministry of Education of China
文摘The volume of fluid (VOF) method is used to set up a wave flume with an absorbing wave maker of cnoidal waves. Based on the transfer function between wave surface and paddle velocity obtained by the shallow water wave theory, the velocity boundary condition of an absorbing wave maker is introduced to absorb reflected waves that reach the numerical wave maker. For Hid ranging from 0.1 to 0.59 and T root g/d from 7.9 to 18.3, the parametric studies have been carried out and compared with experiments.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11175092,11275123,11205092,and 10905038Shanghai Knowledge Service Platform for Trustworthy Internet of Things under Grant No.ZF1213+1 种基金Talent FundK.C.Wong Magna Fund in Ningbo University
文摘The(2+1)-dimensional Konopelchenko–Dubrovsky equation is an important prototypic model in nonlinear physics, which can be applied to many fields. Various nonlinear excitations of the(2+1)-dimensional Konopelchenko–Dubrovsky equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this paper, with the help of the Riccati equation, the(2+1)-dimensional Konopelchenko–Dubrovsky equation is solved by the consistent Riccati expansion(CRE). Furthermore, we obtain the soliton-cnoidal wave interaction solution of the(2+1)-dimensional Konopelchenko–Dubrovsky equation.
基金Supported by the National Natural Science Foundations of China under Grant No.11175092Scientific Research Fund of Zhejiang Provincial Education Department under Grant No.Y201017148K.C.Wong Magna Fund in Ningbo University
文摘The Boussinesq equation is one of important prototypic models in nonlinear physics. Various nonlinear excitations of the Boussinesq equation have been found by many methods. However, it is very difficult to find interaction solutions among different types of nonlinear excitations. In this peper, two equivalent very simple methods, the truncated Painleve analysis and the generalized tanh function expansion approaches, are developed to find interaction solutions between solitons and any other types of Boussinesq waves.
基金The study was financially supported by the National Natural Science Foundation of China under contract Nos 50479015 and 10202003also supported by Program for New Century Talents Excellent Talents in University(NCET-05-0710).
文摘The evolution of an initially flat sandy bed is studied in a laboratory wave flume under enoidal waves and acoustic Doppler velocimeter （ADV） was utilized in the detailed velocity measurements at different positions. The ripple formation and evolution have been analyzed by CCD images and the asymmetric rippled bed is induced by the nonlinear wave flow. The flow structure and a complete process of vortex formation, evolvement and disappearance were observed on the asymmetric rippled bed under cnoidal waves. With the increasing nonlinearity of waves, which is an important factor in the sand ripple formation, the vortex intensity becomes stronger and shows different characteristics on both sides of the ripple crest. The vorticity and wave velocity reach their maximum values at different phase angles. The vortex value reaches the maximum value at a small phase angle with the increasing Ursell number. The near bed flow patterns are mainly determined by the ripple forms and the averaged longitudinal velocity over a wave period above the ripple trough and crest are positive, which indicates the possibility of significant onshore sediment transport and a corresponding ripple drift. The phase averaged vertical velocity has noticeable positive values near the bottom of the ripple crest and trough. Sediments may be lifted from the ripple surface, picked up in suspension by the local velocity, and deposited over the crest and on the lee of the ripples.
基金the National Natural Science Foundation of China(No.41272317)
文摘Severe water waves can induce seabed liquefaction and do harm to marine structures. Dynamic response of seabed with definite thickness induced by cnoidal water waves is investigated numerically. Biot＇s consolidation equations are employed to model the seabed response. Parametric studies are carried out to examine the influence of the air content in the pore water and the soil hydraulic conductivity. It is been shown that the air content and soil hydraulic conductivity can significantly affect the pore pressure in seabed. An increase of air content and/or a decrease of soil hydraulic conductivity can change the pore pressure gradient sharply.
基金Supported by the National Natural Science Foundation of China under Grant No.11175092Scientific Research Fund of Zhejiang Provincial Education Department under Grant No.Y201017148K.C.Wong Magna Fund in Ningbo University
文摘In nonlinear physics, the modified Korteweg de-Vries （mKdV） as one of the important equation of nonfinear partial differential equations, its various solutions have been found by many methods. In this paper, the CRE method is presented for constructing new exact solutions. In addition to the new solutions of the mKdV equation, the consistent Riccati expansion （CRE） method can unearth other equations.
文摘Based on the 2nd order cnoidal wave theory, the characters of shallow water standing waves and their action on vertical walls are studied in this paper. The theoretical expressions of the wave surface elevation in front of and the wave pressure on the vertical wall are obtained. In order to verify the theoretical results, model tests were made in the State Key Laboratory of Coastal and Offshore Engineering at DUT. For the wave surface elevation in front of the wall and the wave forces on the wall at the moment when the wave surface at the wall surface goes down to the bottom of the wave trough, the calculated results coincide quite well with the experimental results. For the wave forces on the wall at the moment when the wave surface at the wall surface goes up to the top of the wave crest, the theoretical expressions are modified by the experimental results. For the convenience of practical use, calculations are made for the wave conditions which usually occur in enginering practice by use of the investigated results obtained in this paper. Empirical formulas are fitted with these calculated results for designers to use.
文摘Theoretical investigation of nonlinear electrostatic ion-acoustic cnoidal waves(IACWs) is presented in magnetized electron–positron–ion plasma with nonextensive electrons and Maxwellian positrons. Using reductive perturbation technique, Korteweg–de Vries equation is derived and its cnoidal wave solution is analyzed. For given plasma parameters, our model supports only positive potential(compressive) IACW structures. The effect of relevant plasma parameters(viz., nonextensive parameter q, positron concentration p, temperature ratio σ,obliqueness l3) on the characteristics of IACWs is discussed in detail.
基金Project supported by the Global Change Research Program of China(Grant No.2015CB953904)the National Natural Science Foundation of China(Grant Nos.11675054 and 11435005)+3 种基金the Outstanding Doctoral Dissertation Cultivation Plan of Action(Grant No.YB2016039)Shanghai Collaborative Innovation Center of Trustworthy Software for Internet of Things(Grant No.ZF1213)the UTRGV President Endowed Professorship(Grant No.450000123)the UTRGV College of Science Seed Grant(Grant No.240000013)for partial support
文摘In this paper, we study soliton-cnoidal wave solutions for the reduced Maxwell-Bloch equations. The truncated Painlev6 analysis is utilized to generate a consistent Riccati expansion, which leads to solving the reduced Maxwell-Bloch equations with solitary wave, cnoidal periodic wave, and soliton-cnoidal interactional wave solutions in an explicit form. Particularly, the soliton-cnoidal interactional wave solution is obtained for the first time for the reduced Maxwell-Bloch equations. Finally, we present some figures to show properties of the explicit soliton-cnoidal interactional wave solutions as well as some new dynamical phenomena.
文摘The nonlinear evolution equations have a wide range of applications,more precisely in physics,biology,chemistry and engineering fields.This domain serves as a point of interest to a large extent in the world’s mathematical community.Thus,this paper purveys an analytical study of a generalized extended(2+1)-dimensional quantum Zakharov-Kuznetsov equation with power-law nonlinearity in oceanography and ocean engineering.The Lie group theory of differential equations is utilized to compute an optimal system of one dimension for the Lie algebra of the model.We further reduce the equation using the subalgebras obtained.Besides,more general solutions of the underlying equation are secured for some special cases of n with the use of extended Jacobi function expansion technique.Consequently,we secure new bounded and unbounded solutions of interest for the equation in various solitonic structures including bright,dark,periodic(cnoidal and snoidal),compact-type as well as singular solitons.The applications of cnoidal and snoidal waves of the model in oceanography and ocean engineering for the first time,are outlined with suitable diagrams.This can be of interest to oceanographers and ocean engineers for future analysis.Furthermore,to visualize the dynamics of the results found,we present the graphic display of each of the solutions.Conclusively,we construct conservation laws of the understudy equation via the application of Noether’s theorem.
文摘In this paper, starting with the equations describing the atmospheric motion and by arelatively simple method, we find that, nearby the mechanical equilibrium point, all thefinite amplitude nonlinear inertia waves, internal gravity waves and Rossby waves in thedispersive atmosphere satisfy the KdV (Korteweg-de Vries) equation, its solution being thecnoidal waves and solitary waves. For the finite amplitude Rossby waves, we find the newdispersive relation which is different from the Rossby formula and contains the amplitudeparameter. It is shown that the larger the amplitude and width, the faster are the wavesfor the finite amplitude inertia waves and internal gravity waves, and the slower are thewaves for the Rossby solitary waves, to which perhaps the polar vortex and the blocking orcut-off systems belong. This treatise gives the nonlinear waves a new way and inspires usto study the nonlinear adjustment process and evolution process and the turbulence structure.
文摘The method of cnoidal wave generation in a wave flume is studied in this paper.According to the wave equa- tion in shallow water,the wave paddle motion equation for given wave parameters and water depth is derived.The controlling signal for driving wavemaker can be converted from its solution,and high wave height shallow water waves can be generated.The experiment results show that,the parameters of the wave generated are very close to the required ones in a certain distance in front of the paddle of the wavemaker.
文摘For the dynamics of three-dimensional electron–positron–ion plasmas,a fluid quantum hydrodynamic model is proposed by considering Landau quantization effects in dense plasma.Ion–neutral collisions in the presence of the Coriolis force are also considered.The application of the reductive perturbation technique produces a wave evolution equation represented by a damped Korteweg–de Vries equation.This equation,however,is insufficient for describing waves in our system at very low dispersion coefficients.As a result,we considered the highest-order perturbation,which resulted in the damped Kawahara equation.The effects of the magnetic field,Landau quantization,the ratio of positron density to electron density,the ratio of positron density to ion density,and the direction cosine on linear dispersion laws as well as soliton and conoidal solutions of the damped Kawahara equation are explored.The understanding from this research can contribute to the broader field of astrophysics and aid in the interpretation of observational data from white dwarfs.
