The added resistance of KVLCC2 in short and regular head waves has been studied theoretically and experimentally. Model tests are performed to determine how well the asymptotic formula （Faltinsen et al. 1980） predic...The added resistance of KVLCC2 in short and regular head waves has been studied theoretically and experimentally. Model tests are performed to determine how well the asymptotic formula （Faltinsen et al. 1980） predicts the typical level of added resistance in short waves. Because the asymptotic formula neglects the effects of ship motions, it is combined with theoretical methods to calculate the added resistance in long waves using an function to predict the added resistance in the intermediate wavelength region where both ship motions and wave reflection are important. A unique feature of this experiment is that the ship model is divided into three segments to explore the added resistance distribution with respect to hull segment. This paper discusses the sensitivity of experimental results to the quality of the incident regular head waves. Moreover, a novel procedure for analyzing added resistance is described. Finally, the experimentally determined added resistance of KVLCC2 is compared with theoretical results. It is shown that the added resistance from the combined theoretical methods agrees well with experimental results in both the intermediate and short wave regions. The use of hull segments shows that added resistance is concentrated primarily at the bow.展开更多
The Green's function is used to solve the scattering far fieldsolution of SH-wave by a mov- able rigid cylindrical interfaceinclusion in a linear elastic body. First, a suitable Green'sfunction is devel- oped,...The Green's function is used to solve the scattering far fieldsolution of SH-wave by a mov- able rigid cylindrical interfaceinclusion in a linear elastic body. First, a suitable Green'sfunction is devel- oped, which is the fundamental displacementsolution of an elastic half space with a movable rigid half-cylin-drical inclusion impacted by out-of-plane harmonic line source loadedat any point of its horizontal surface.展开更多
In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can sa...In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill’s peak on ground motion are discussed.展开更多
Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane ...Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green＇s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green＇s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.展开更多
By vertical boundary conditions, a spectral expansion of horizontal tide wave velocity is done in vertical direction in terms of a complete basis functions selected properly, hence a relation between tide levels and...By vertical boundary conditions, a spectral expansion of horizontal tide wave velocity is done in vertical direction in terms of a complete basis functions selected properly, hence a relation between tide levels and spectral components is found theoretically under condition of ignoring the horizontal friction stress and nonlinear effect. And a relation between bottom friction of tide current, which satisfies the viscous condition on sea bottom, and tide levels is determined. The relation is different from the relation of the traditional parameterizing of bottom friction. Moreover integration of the continuity equation and momentum equations is carried out in the vertical direction using zero flux condition on solid boundaries and inputting condition on open boundaries, and then a boundary value problem of elliptic form on the tide levels is constructed.展开更多
In this paper, the rogue wave solutions of the(2+1)-dimensional Myrzakulov–Lakshmanan(ML)-Ⅳ equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By usin...In this paper, the rogue wave solutions of the(2+1)-dimensional Myrzakulov–Lakshmanan(ML)-Ⅳ equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By using the Jacobian elliptic function expansion method, the Darboux transformation(DT) method and the nonlinearization of the Lax pair, two kinds of rogue wave solutions which are expressed by Jacobian elliptic functions dn and cn, are obtained.The relationship between these five kinds of potential is summarized systematically. Firstly, the periodic rogue wave solution of one potential is obtained, and then the periodic rogue wave solutions of the other four potentials are obtained directly. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.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
Flow around a ship that advances at a constant speed V in calm water of uniform finite depth D is considered within the practical,realistic and commonly-used framework of the Green-function and boundary-integral metho...Flow around a ship that advances at a constant speed V in calm water of uniform finite depth D is considered within the practical,realistic and commonly-used framework of the Green-function and boundary-integral method in conjunction with potential-flow theory.This framework entails accurate and efficient numerical evaluation of flows due to singularities(sources,dipoles)distributed over flat or curved panels of diverse geometries(quadrilaterals,triangles)that are employed to approximate the ship hull surface.This basic core element of the Green-function and boundary-integral method is considered for steady ship waves in the subcritical flow regime gD/V^(2)>1 and the supercritical flow regime gD/V^(2)<1,where g is the acceleration of gravity.The special case of deep water is also considered.An analytical representation of flows due to general distributions of singularities over hull-surface panels is given.This flow-representation adopts the Fourier-Kochin method,which prioritizes spatial integration over the panel followed by Fourier integration,in contrast to the conventional method in which the Green function(defined via a Fourier integration)is initially evaluated and subsequently integrated over the panel.The mathematical and numerical complexities associated with the numerical evaluation and subsequent panel integration of the Green function for steady ship waves in finite water depth are then circumvented in the Fourier-Kochin method.A major advantage of this method is that panel integration merely amounts to integration of an exponential-trigonometric function,a straightforward task that can be accurately and efficiently performed.The analytical flow-representation proposed in the study offers a smooth decomposition of free-surface effects into waves,defined by a regular single Fourier integral,and a non-oscillatory local flow,characterized by a double Fourier integral featuring a smooth integrand that primarily dominates within a compact region near the origin of the Fourier plane.Illustrative numerical 展开更多
There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral doma...There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green's function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green's function. The numerical results demonstrated the accuracy and efficiency of the proposed method.展开更多
Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investi...Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.展开更多
基金part of the research project SeaPro, which is sponsored by Rolls-Royce Marine and the Research Council of Norway
文摘The added resistance of KVLCC2 in short and regular head waves has been studied theoretically and experimentally. Model tests are performed to determine how well the asymptotic formula （Faltinsen et al. 1980） predicts the typical level of added resistance in short waves. Because the asymptotic formula neglects the effects of ship motions, it is combined with theoretical methods to calculate the added resistance in long waves using an function to predict the added resistance in the intermediate wavelength region where both ship motions and wave reflection are important. A unique feature of this experiment is that the ship model is divided into three segments to explore the added resistance distribution with respect to hull segment. This paper discusses the sensitivity of experimental results to the quality of the incident regular head waves. Moreover, a novel procedure for analyzing added resistance is described. Finally, the experimentally determined added resistance of KVLCC2 is compared with theoretical results. It is shown that the added resistance from the combined theoretical methods agrees well with experimental results in both the intermediate and short wave regions. The use of hull segments shows that added resistance is concentrated primarily at the bow.
文摘The Green's function is used to solve the scattering far fieldsolution of SH-wave by a mov- able rigid cylindrical interfaceinclusion in a linear elastic body. First, a suitable Green'sfunction is devel- oped, which is the fundamental displacementsolution of an elastic half space with a movable rigid half-cylin-drical inclusion impacted by out-of-plane harmonic line source loadedat any point of its horizontal surface.
文摘In this paper, antiplane response of an isosceles triangular hill to incident SH waves is studied based on the method of complex function and by using moving coordinate system. The standing wave function, which can satisfy the governing equation and boundary condition, is provided. Furthermore, numerical examples are presented; the influences of wave number and angle of the incident waves and the angle of the hill’s peak on ground motion are discussed.
基金National Natural Science Foundation of China under Grant Nos.51578373 and 51578372
文摘Abstract： The scattering of plane SH-waves by topographic features in a layered transversely isotropic （TI） half-space is investigated by using an indirect boundary element method （IBEM）. Firstly, the anti-plane dynamic stiffness matrix of the layered TI half-space is established and the free fields are solved by using the direct stiffness method. Then, Green＇s functions are derived for uniformly distributed loads acting on an inclined line in a layered TI half-space and the scattered fields are constructed with the deduced Green＇s functions. Finally, the free fields are added to the scattered ones to obtain the global dynamic responses. The method is verified by comparing results with the published isotropic ones. Both the steady-state and transient dynamic responses are evaluated and discussed. Numerical results in the frequency domain show that surface motions for the TI media can be significantly different from those for the isotropic case, which are strongly dependent on the anisotropy property, incident angle and incident frequency. Results in the time domain show that the material anisotropy has important effects on the maximum duration and maximum amplitudes of the time histories.
文摘By vertical boundary conditions, a spectral expansion of horizontal tide wave velocity is done in vertical direction in terms of a complete basis functions selected properly, hence a relation between tide levels and spectral components is found theoretically under condition of ignoring the horizontal friction stress and nonlinear effect. And a relation between bottom friction of tide current, which satisfies the viscous condition on sea bottom, and tide levels is determined. The relation is different from the relation of the traditional parameterizing of bottom friction. Moreover integration of the continuity equation and momentum equations is carried out in the vertical direction using zero flux condition on solid boundaries and inputting condition on open boundaries, and then a boundary value problem of elliptic form on the tide levels is constructed.
基金supported by the National Natural Science Foundation of China (Grant No. 12 361 052)the Natural Science Foundation of Inner Mongolia Autonomous Region, China (Grant Nos. 2020LH01010, 2022ZD05)+2 种基金the Program for Innovative Research Team in Universities of Inner Mongolia Autonomous Region (Grant No. NMGIRT2414)the Fundamental Research Funds for the Inner Mongolia Normal University, China (Grant No. 2022JBTD007)the Key Laboratory of Infinite-dimensional Hamiltonian System and Its Algorithm Application (Inner Mongolia Normal University), and the Ministry of Education (Grant Nos. 2023KFZR01, 2023KFZR02)
文摘In this paper, the rogue wave solutions of the(2+1)-dimensional Myrzakulov–Lakshmanan(ML)-Ⅳ equation, which is described by five component nonlinear evolution equations, are studied on a periodic background. By using the Jacobian elliptic function expansion method, the Darboux transformation(DT) method and the nonlinearization of the Lax pair, two kinds of rogue wave solutions which are expressed by Jacobian elliptic functions dn and cn, are obtained.The relationship between these five kinds of potential is summarized systematically. Firstly, the periodic rogue wave solution of one potential is obtained, and then the periodic rogue wave solutions of the other four potentials are obtained directly. The solutions we find present the dynamic phenomena of higher-order nonlinear wave equations.
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.
基金supported by the China Postdoctoral Science Foundation(Grant No.2021M692044).
文摘Flow around a ship that advances at a constant speed V in calm water of uniform finite depth D is considered within the practical,realistic and commonly-used framework of the Green-function and boundary-integral method in conjunction with potential-flow theory.This framework entails accurate and efficient numerical evaluation of flows due to singularities(sources,dipoles)distributed over flat or curved panels of diverse geometries(quadrilaterals,triangles)that are employed to approximate the ship hull surface.This basic core element of the Green-function and boundary-integral method is considered for steady ship waves in the subcritical flow regime gD/V^(2)>1 and the supercritical flow regime gD/V^(2)<1,where g is the acceleration of gravity.The special case of deep water is also considered.An analytical representation of flows due to general distributions of singularities over hull-surface panels is given.This flow-representation adopts the Fourier-Kochin method,which prioritizes spatial integration over the panel followed by Fourier integration,in contrast to the conventional method in which the Green function(defined via a Fourier integration)is initially evaluated and subsequently integrated over the panel.The mathematical and numerical complexities associated with the numerical evaluation and subsequent panel integration of the Green function for steady ship waves in finite water depth are then circumvented in the Fourier-Kochin method.A major advantage of this method is that panel integration merely amounts to integration of an exponential-trigonometric function,a straightforward task that can be accurately and efficiently performed.The analytical flow-representation proposed in the study offers a smooth decomposition of free-surface effects into waves,defined by a regular single Fourier integral,and a non-oscillatory local flow,characterized by a double Fourier integral featuring a smooth integrand that primarily dominates within a compact region near the origin of the Fourier plane.Illustrative numerical
文摘There exist the complicated waveguide modes as well as the surface waves in the electromagnetic field induced by a horizontal electric dipole in layered lossless dielectrics between two ground planes. In spectral domain, all these modes can be characterized by the rational parts with the real poles of the vector and scalar potentials. The accurate extraction of these modes plays an important role in the evaluation of the Green's function in spatial domain. In this paper, a new algorithm based on rational approximation is presented, which can accurately extract all the real poles and the residues of each pole simultaneously. Thus, we can get all the surface wave modes and waveguide modes, which is of great help to the calculation of the spatial domain Green's function. The numerical results demonstrated the accuracy and efficiency of the proposed method.
文摘Scattering of surface waves by the edge of a small undulation on a porous bed in an ocean of finite depth, where the free surface has an ice-cover being modelled as an elastic plate of very small thickness, is investigated within the framework of linearized water wave theory. The effect of surface tension at the surface below the ice-cover is neglected. There exists only one wave number propagating at just below the ice-cover. A perturbation analysis is employed to solve the boundary value problem governed by Laplace＇s equation by a method based on Green＇s integral theorem with the introduction of appropriate Green＇s function and thereby evaluating the reflection and transmission coefficients approximately up to first order. A patch of sinusoidal ripples is considered as an example and the related coefficients are determined.
