The present study investigates the interaction of steep waves with semi-circular breakwater with the complex plane's Cauchy boundary integral theorem. The boundary integral method is used to transform the calculat...The present study investigates the interaction of steep waves with semi-circular breakwater with the complex plane's Cauchy boundary integral theorem. The boundary integral method is used to transform the calculation in fluid domain into its boundary alone. In the calculation the computation domain is moved with the propagation of waves. A numerical solution is obtained for incident Stokes waves passing the submerged obstacles. This method has been extended to the calculation of wave run-up on a slope for estimating wave overtopping.展开更多
Linear and nonlinear analyses of water waves in an elastic vessel are carried out to study the dramatic phenomena of Dragon Wash as well as related controllable experiments. It is proposed that the capillary edge wave...Linear and nonlinear analyses of water waves in an elastic vessel are carried out to study the dramatic phenomena of Dragon Wash as well as related controllable experiments. It is proposed that the capillary edge waves are generated by parametric resonance, which is shown to be a possible mechanism for both rectangular an circular vessels. For circular vessel, the normal geometric resonance is also operating, thus greatly. enhance the dramatic effect. The mechanism of nonlinear mode-mode interaction is proposed far the generation of axisymmetric low-frequency gravity waves by the high-frequency external excitation. A simple model system is studied numerically to demonstrate explicitly this interaction mechanism.展开更多
Recent experiments related to the Dragon Wash phenomena showed that axisymmetric capillary waves appear first from excitation, and circumferential capillary waves appear after increase of the excitation strength. Base...Recent experiments related to the Dragon Wash phenomena showed that axisymmetric capillary waves appear first from excitation, and circumferential capillary waves appear after increase of the excitation strength. Based on this new finding, a theory of parametric resonance is developed in detail to explain the on- set of the prominent circumferential capillary waves. Numerical computation is also carried out and the results agree generally with the experiments. Analysis and nu- merical computation are also presented to explain the generation of axisymmetric low-frequency gravity waves by tile high-frequency external excitation.展开更多
A computational method for steady water waves is presented on the basis of potential theory in the physical plane with spatial variables as independent quantities. The finite Fourier series are applied to approximatin...A computational method for steady water waves is presented on the basis of potential theory in the physical plane with spatial variables as independent quantities. The finite Fourier series are applied to approximating the free surface and potential function. A set of nonlinear algebraic equations for the Fourier coefficients are derived from the free surface kinetic and dynamic boundary conditions. These algebraic equations are numerically solved through Newton＇s iterative method, and the iterative stability is further improved by a relaxation technology. The integral properties of steady water waves are numerically analyzed, showing that （1） the set-up and the set-down are both non-monotonic quantities with the wave steepness, and （2） the Fourier spectrum of the free surface is broader than that of the potential function. The latter further leads us to explore a modification for the present method by approximating the free surface and potential function through different Fourier series, with the truncation of the former higher than that of the latter. Numerical tests show that this modification is effective, and can notably reduce the errors of the free surface boundary conditions.展开更多
This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flex...This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear （1961）, confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7.展开更多
Based on linear water-wave theory, this study investigated the scattering of oblique incident water waves by two unequal surface-piercing thin vertical rigid plates with stepped bottom topography. By using the matched...Based on linear water-wave theory, this study investigated the scattering of oblique incident water waves by two unequal surface-piercing thin vertical rigid plates with stepped bottom topography. By using the matched eigenfunction expansion method and a least square approach, the analytical solutions are sought for the established boundary value problem. The effects of the incidence angle, location of step, depth ratio of deep to shallow waters,and column width between two plates, on the reflection coefficients, the horizontal wave forces acting on the two plates, and the mean surface elevation between the two plates, are numerically examined under a variety of wave conditions. The results show that the existence of the stepped bottom between two plates considerably impacts the hydrodynamic performances of the present system. It is found that the effect of stepped bottom on the reflection coefficient of the present two-plate structure is evident only with waves of the low dimensionless frequency.Moreover, the influence of the step location on the hydrodynamic performance of the present two-plate structure is slight if the step is placed in between the two plates.展开更多
Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,ar...Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.展开更多
In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed.We assume that the free surface is almost periodic in the horizontal dir...In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed.We assume that the free surface is almost periodic in the horizontal direction.Using conformal mappings,one can change the free boundary problem into a fixed boundary problem for some unknown functions with the boundary condition.By virtue of the Hilbert transform,the problem is equivalent to a quasilinear pseudodifferential equation for an almost periodic function of one variable.The bifurcation theory ensures that we can obtain an existence result.Our existence result generalizes and covers the recent result in[15].Moreover,our result implies a non-uniqueness result at the same bifurcation point.展开更多
Green-Naghdi （G-N） theory is a fully nonlinear theory for water waves. Some researchers call it a fully nonlinear Boussinesq model. Different degrees of complexity of G-N theory are distinguished by ＂levels＂ where...Green-Naghdi （G-N） theory is a fully nonlinear theory for water waves. Some researchers call it a fully nonlinear Boussinesq model. Different degrees of complexity of G-N theory are distinguished by ＂levels＂ where the higher the level, the more complicated and presumably more accurate the theory is. In the research presented here a comparison was made between two different levels of G-N theory, specifically level II and level III G-N restricted theories. A linear analytical solution for level III G-N restricted theory was given. Waves on a planar beach and shoaling waves were both simulated with these two G-N theories. It was shown for the first time that level III G-N restricted theory can also be used to predict fluid velocity in shallow water. A level III G-N restricted theory is recommended instead of a level II G-N restricted theory when simulating fullv nonlinear shallow water waves.展开更多
This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equ...This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.展开更多
The main aim of this work is to introduce the analytical approximate solutions of the water wave problem for a fluid layer of finite depth in the presence of gravity. To achieve this aim, we begun with the derivation ...The main aim of this work is to introduce the analytical approximate solutions of the water wave problem for a fluid layer of finite depth in the presence of gravity. To achieve this aim, we begun with the derivation of the Korteweg-de Vries equations for solitons by using the method of multiple scale expansion. The proposed problem describes the behavior of the system for free surface between air and water in a nonlinear approach. To solve this problem, we use the well-known analytical method, namely, variational iteration method (VIM). The proposed method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. The proposed method provides a sequence of functions which may converge to the exact solution of the proposed problem. Finally, we observe that the elevation of the water waves is in form of traveling solitary waves.展开更多
When wind appears over the free surface, water waves and turbulence are generated by an interfacial shear stress. In particular, turbulent diffusion promotes significantly mass and momentum transport beneath the inter...When wind appears over the free surface, water waves and turbulence are generated by an interfacial shear stress. In particular, turbulent diffusion promotes significantly mass and momentum transport beneath the interface between the water and air significantly in ocean and lakes, and thus it is very important for global environment problems to reveal such turbulence property and coherent structure. Simultaneous measurements of velocities and free-surface elevation allow us to conduct reasonably the phase analysis of the coherent structure in interfacial shear layer. Furthermore, multi-point measurements such as PIV are very powerful to detect the space-time structure of coherent motions. Therefore, in the present study, we developed a specially designed PIV system which can measure the velocity components and surface-elevation fluctuation simultaneously by using two sets of high-speed cameras to reveal the coherent structure in the interfacial shear layer.展开更多
In this paper, the water waves and wave-induced longshore currents in Obak6y coastal water which is located at the Mediterranean coast of Turkey were numerically studied. The numerical model is based on the parabolic ...In this paper, the water waves and wave-induced longshore currents in Obak6y coastal water which is located at the Mediterranean coast of Turkey were numerically studied. The numerical model is based on the parabolic mild-slope equation for coastal water waves and the nonlinear shallow water equation for the wave-induced currents. The wave transformation under the effects of shoaling, refraction, diffraction and breaking is considered, and the wave provides radiation stresses for driving currents in the model. The numerical results for the water wave-induced longshore currents were validated by the measured data to demonstrate the efficiency of the numerical model. Then the water waves and longshore currents induced by the waves from main directions were numerically simulated and analyzed based on the numerical results. The numerical results show that the movement of the longshore currents was different while the wave proDaRated to a coastal zone from different directions.展开更多
In this study, we examine the water wave radiation by arrays of truncated circular cylinders. Each cylinder can oscillate independently in any rigid oscillation mode with a prescribed amplitude, including translationa...In this study, we examine the water wave radiation by arrays of truncated circular cylinders. Each cylinder can oscillate independently in any rigid oscillation mode with a prescribed amplitude, including translational and rotational modes such as surge, sway, heave, pitch, roll, and their combinations. Based on the eigenfunction expansion and Graf＇s addition theorem for Bessel functions, we developed an analytical method that includes the effects of evanescent modes in order to analyze such arrays of cylinders. To investigate the effects of several influential factors on convergence,our objective is to dramatically reduce the number of tests required and determine the influencing relationships between truncation number and convergence behavior for different factor combinations. We use the orthogonal test method to fulfill the objective. Lastly, we present our results regarding the effects of evanescent modes on hydrodynamic coefficients.展开更多
The complete band gaps （CBGs） of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, ...The complete band gaps （CBGs） of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, containing triangular, square, hexagonal and circular cross-sectioned holes arranged into triangular lattices. Results show that the width of CBGs can be changed by adjusting the orientation of noncircular holes and the effect of hole shape on the width of the maximal CBGs is discussed.展开更多
In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or...In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or an ice-cover modelled as a thin elastic plate. For the case of free surface, the effect of surface tension may be neglected or taken into account. Here, the wave-free potentials are singular solutions of the modified Helmholtz equation, having singularity at a point in the fluid region and they satisfy the conditions at the upper surface and the bottom of water region and decay rapidly away from the point of singularity. These are useful in obtaining solutions to oblique water wave problems involving bodies with circular cross-sections such as long horizontal cylinders submerged or half-immersed in water of uniform fmite depth with a free surface or an ice-cover modelled as a floating elastic plate. Finally, the forms of the upper surface related to the wave-free potentials constructed here are depicted graphically in a number of figures to visualize the wave motion. The results for non-oblique wave-free potentials and the upper surface wave-free potentials are obtained. The wave-free potentials constructed here will be useful in the mathematical study of water wave problems involving infinitely long horizontal cylinders, either half-immersed or completely immersed in water.展开更多
Obliquely incident water wave scattering by an uneven channel-bed in the form of a small bottom undulation in a two-layer fluid is investigated within the frame work of three-dimensional linear water wave theory. The ...Obliquely incident water wave scattering by an uneven channel-bed in the form of a small bottom undulation in a two-layer fluid is investigated within the frame work of three-dimensional linear water wave theory. The upper fluid is assumed to be bounded above by a rigid lid, while the lower one is bounded below by a bottom surface having a small deformation and the channel is unbounded in the horizontal directions. Assuming irrotational motion, perturbation technique is employed to calculate the first-order corrections to the velocity potentials in the two fluids by using Fourier transform approximately, and also to calculate the reflection and transmission coefficients in terms of integrals involving the shape function representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that the reflection coefficient is an oscillatory function of the ratio of twice the component of the wave number along x-axis and the ripple wave number. When this ratio approaches one, the theory predicts a resonant interaction between the bed and interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of incident wave energy occurs if this number is large.展开更多
Based on the evolution equation for water waves, a mathematical model for wave propaga tion in large mild - slope areas is derived. The model is solved by the finite difference method with the staggered grid system. ...Based on the evolution equation for water waves, a mathematical model for wave propaga tion in large mild - slope areas is derived. The model is solved by the finite difference method with the staggered grid system. The computational results are in good agreement with experimental data and show that the model can obtain better results with relatively coarser grids. The model can be used to simulate water wave propagation in large coastal areas and can be efficiently solved without much programming effort.展开更多
Metasurfaces and metagratings offer new platforms for electromagnetic wave control with significant responses.However,metasurfaces based on abrupt phase change and resonant structures suffer from the drawback of high ...Metasurfaces and metagratings offer new platforms for electromagnetic wave control with significant responses.However,metasurfaces based on abrupt phase change and resonant structures suffer from the drawback of high loss and face challenges when applied in water waves.Therefore,the application of metasurfaces in water wave control is not ideal due to the limitations associated with high loss and other challenges.We have discovered that non-resonant metagratings exhibit promising effects in water wave control.Leveraging the similarity between bridges and metagratings,we have successfully developed a water wave metagrating model inspired by the ancient Luoyang Bridge in China.We conduct theoretical calculations and simulations on the metagrating and derive the equivalent anisotropic model of the metagrating.This model provides evidence that the metagrating has the capability to control water waves and achieve unidirectional surface water wave.The accuracy of our theory is strongly supported by the clear observation of the unidirectional propagation phenomenon during simulation and experiments conducted using a reduced version of the metagrating.It is the first time that the unidirectional propagation of water waves has been seen in water wave metagrating experiment.Above all,we realize the water wave metagrating experiment for the first time.By combining complex gratings with real bridges,we explore the physics embedded in the ancient building—Luoyang Bridge,which are of great significance for the water wave metagrating design and provide a new method for analyzing the effects of water waves on bridges.At the same time,this discovery also provides a new idea for ocean cargo transportation,ocean garbage cleaning,and the development and protection of ancient bridges.展开更多
文摘The present study investigates the interaction of steep waves with semi-circular breakwater with the complex plane's Cauchy boundary integral theorem. The boundary integral method is used to transform the calculation in fluid domain into its boundary alone. In the calculation the computation domain is moved with the propagation of waves. A numerical solution is obtained for incident Stokes waves passing the submerged obstacles. This method has been extended to the calculation of wave run-up on a slope for estimating wave overtopping.
文摘Linear and nonlinear analyses of water waves in an elastic vessel are carried out to study the dramatic phenomena of Dragon Wash as well as related controllable experiments. It is proposed that the capillary edge waves are generated by parametric resonance, which is shown to be a possible mechanism for both rectangular an circular vessels. For circular vessel, the normal geometric resonance is also operating, thus greatly. enhance the dramatic effect. The mechanism of nonlinear mode-mode interaction is proposed far the generation of axisymmetric low-frequency gravity waves by the high-frequency external excitation. A simple model system is studied numerically to demonstrate explicitly this interaction mechanism.
文摘Recent experiments related to the Dragon Wash phenomena showed that axisymmetric capillary waves appear first from excitation, and circumferential capillary waves appear after increase of the excitation strength. Based on this new finding, a theory of parametric resonance is developed in detail to explain the on- set of the prominent circumferential capillary waves. Numerical computation is also carried out and the results agree generally with the experiments. Analysis and nu- merical computation are also presented to explain the generation of axisymmetric low-frequency gravity waves by tile high-frequency external excitation.
基金The Jiangsu Province Natural Science Foundation for the Young Scholar under contract No.BK20130827the Fundamental Research Funds for the Central Universities of China under contract No.2010B02614+1 种基金the National Natural Science Foundation of China under contract Nos 41076008 and 51009059the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘A computational method for steady water waves is presented on the basis of potential theory in the physical plane with spatial variables as independent quantities. The finite Fourier series are applied to approximating the free surface and potential function. A set of nonlinear algebraic equations for the Fourier coefficients are derived from the free surface kinetic and dynamic boundary conditions. These algebraic equations are numerically solved through Newton＇s iterative method, and the iterative stability is further improved by a relaxation technology. The integral properties of steady water waves are numerically analyzed, showing that （1） the set-up and the set-down are both non-monotonic quantities with the wave steepness, and （2） the Fourier spectrum of the free surface is broader than that of the potential function. The latter further leads us to explore a modification for the present method by approximating the free surface and potential function through different Fourier series, with the truncation of the former higher than that of the latter. Numerical tests show that this modification is effective, and can notably reduce the errors of the free surface boundary conditions.
基金supported by the Jiangsu Province Natural Science Foundation for the Young Scholars(Grant No.BK20130827)the National Natural Science Foundation of China(Grant Nos.41076008 and 51479055)
文摘This paper presents a universal fifth-order Stokes solution for steady water waves on the basis of potential theory. It uses a global perturbation parameter, considers a depth uniform current, and thus admits the flexibilities on the definition of the perturbation parameter and on the determination of the wave celerity. The universal solution can be extended to that of Chappelear （1961）, confirming the correctness for the universal theory. Furthermore, a particular fifth-order solution is obtained where the wave steepness is used as the perturbation parameter. The applicable range of this solution in shallow depth is analyzed. Comparisons with the Fourier approximated results and with the experimental measurements show that the solution is fairly suited to waves with the Ursell number not exceeding 46.7.
基金financially supported by the National Natural Science Foundation of China(Grant No.11702244)the Project of the Cooperation of Zhoushan City and Zhejiang University(Grant No.2017C82223)+1 种基金the Open Foundation of Key Laboratory of Port,Waterway and Sedimentation Engineering of the Ministry of Transport(Grant No.Yn216006)the Fundamental Research Funds for the Central Universities(WUT:2017IVA009)
文摘Based on linear water-wave theory, this study investigated the scattering of oblique incident water waves by two unequal surface-piercing thin vertical rigid plates with stepped bottom topography. By using the matched eigenfunction expansion method and a least square approach, the analytical solutions are sought for the established boundary value problem. The effects of the incidence angle, location of step, depth ratio of deep to shallow waters,and column width between two plates, on the reflection coefficients, the horizontal wave forces acting on the two plates, and the mean surface elevation between the two plates, are numerically examined under a variety of wave conditions. The results show that the existence of the stepped bottom between two plates considerably impacts the hydrodynamic performances of the present system. It is found that the effect of stepped bottom on the reflection coefficient of the present two-plate structure is evident only with waves of the low dimensionless frequency.Moreover, the influence of the step location on the hydrodynamic performance of the present two-plate structure is slight if the step is placed in between the two plates.
基金NASI (National Academy of Sciences, India) for providing financial support
文摘Two problems of scattering of surface water waves involving a semi-infinite elastic plate and a pair of semi-infinite elastic plates,separated by a gap of finite width,floating horizontally on water of finite depth,are investigated in the present work for a two-dimensional time-harmonic case.Within the frame of linear water wave theory,the solutions of the two boundary value problems under consideration have been represented in the forms of eigenfunction expansions.Approximate values of the reflection and transmission coefficients are obtained by solving an over-determined system of linear algebraic equations in each problem.In both the problems,the method of least squares as well as the singular value decomposition have been employed and tables of numerical values of the reflection and transmission coefficients are presented for specific choices of the parameters for modelling the elastic plates.Our main aim is to check the energy balance relation in each problem which plays a very important role in the present approach of solutions of mixed boundary value problems involving Laplace equations.The main advantage of the present approach of solutions is that the results for the values of reflection and transmission coefficients obtained by using both the methods are found to satisfy the energy-balance relations associated with the respective scattering problems under consideration.The absolute values of the reflection and transmission coefficients are presented graphically against different values of the wave numbers.
基金partially the National Key R&D Program of China(2021YFA1002100)the NSFC(12171493,11701586)+2 种基金the FDCT(0091/2018/A3)the Guangdong Special Support Program(8-2015)the Key Project of NSF of Guangdong Province(2021A1515010296)。
文摘In this paper we investigate the traveling wave solution of the two dimensional Euler equations with gravity at the free surface over a flat bed.We assume that the free surface is almost periodic in the horizontal direction.Using conformal mappings,one can change the free boundary problem into a fixed boundary problem for some unknown functions with the boundary condition.By virtue of the Hilbert transform,the problem is equivalent to a quasilinear pseudodifferential equation for an almost periodic function of one variable.The bifurcation theory ensures that we can obtain an existence result.Our existence result generalizes and covers the recent result in[15].Moreover,our result implies a non-uniqueness result at the same bifurcation point.
基金Supported by the National Natural Science Foundation of China under Grant No. 50779008the 111 Project (B07019)
文摘Green-Naghdi （G-N） theory is a fully nonlinear theory for water waves. Some researchers call it a fully nonlinear Boussinesq model. Different degrees of complexity of G-N theory are distinguished by ＂levels＂ where the higher the level, the more complicated and presumably more accurate the theory is. In the research presented here a comparison was made between two different levels of G-N theory, specifically level II and level III G-N restricted theories. A linear analytical solution for level III G-N restricted theory was given. Waves on a planar beach and shoaling waves were both simulated with these two G-N theories. It was shown for the first time that level III G-N restricted theory can also be used to predict fluid velocity in shallow water. A level III G-N restricted theory is recommended instead of a level II G-N restricted theory when simulating fullv nonlinear shallow water waves.
基金Supported by the Fund of National Nature Sciences of China
文摘This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.
文摘The main aim of this work is to introduce the analytical approximate solutions of the water wave problem for a fluid layer of finite depth in the presence of gravity. To achieve this aim, we begun with the derivation of the Korteweg-de Vries equations for solitons by using the method of multiple scale expansion. The proposed problem describes the behavior of the system for free surface between air and water in a nonlinear approach. To solve this problem, we use the well-known analytical method, namely, variational iteration method (VIM). The proposed method is based on the use of Lagrange multipliers for identification of optimal value of a parameter in a functional. The proposed method provides a sequence of functions which may converge to the exact solution of the proposed problem. Finally, we observe that the elevation of the water waves is in form of traveling solitary waves.
文摘When wind appears over the free surface, water waves and turbulence are generated by an interfacial shear stress. In particular, turbulent diffusion promotes significantly mass and momentum transport beneath the interface between the water and air significantly in ocean and lakes, and thus it is very important for global environment problems to reveal such turbulence property and coherent structure. Simultaneous measurements of velocities and free-surface elevation allow us to conduct reasonably the phase analysis of the coherent structure in interfacial shear layer. Furthermore, multi-point measurements such as PIV are very powerful to detect the space-time structure of coherent motions. Therefore, in the present study, we developed a specially designed PIV system which can measure the velocity components and surface-elevation fluctuation simultaneously by using two sets of high-speed cameras to reveal the coherent structure in the interfacial shear layer.
基金The National Basic Research Program of China under contract No.2013CB430403the National Natural Science Foundation of China under contract No.51179025+1 种基金the Open Foundation of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering under contract No.2013491511the Open Foundation of State Key Laboratory of Ocean Engineering under contract No.1305
文摘In this paper, the water waves and wave-induced longshore currents in Obak6y coastal water which is located at the Mediterranean coast of Turkey were numerically studied. The numerical model is based on the parabolic mild-slope equation for coastal water waves and the nonlinear shallow water equation for the wave-induced currents. The wave transformation under the effects of shoaling, refraction, diffraction and breaking is considered, and the wave provides radiation stresses for driving currents in the model. The numerical results for the water wave-induced longshore currents were validated by the measured data to demonstrate the efficiency of the numerical model. Then the water waves and longshore currents induced by the waves from main directions were numerically simulated and analyzed based on the numerical results. The numerical results show that the movement of the longshore currents was different while the wave proDaRated to a coastal zone from different directions.
基金supported by the National Natural Science Foundation of China (Grants 11072246, 51490673)the National Basic Research Program (973 Program) of China (Grant 2014CB046801)
文摘In this study, we examine the water wave radiation by arrays of truncated circular cylinders. Each cylinder can oscillate independently in any rigid oscillation mode with a prescribed amplitude, including translational and rotational modes such as surge, sway, heave, pitch, roll, and their combinations. Based on the eigenfunction expansion and Graf＇s addition theorem for Bessel functions, we developed an analytical method that includes the effects of evanescent modes in order to analyze such arrays of cylinders. To investigate the effects of several influential factors on convergence,our objective is to dramatically reduce the number of tests required and determine the influencing relationships between truncation number and convergence behavior for different factor combinations. We use the orthogonal test method to fulfill the objective. Lastly, we present our results regarding the effects of evanescent modes on hydrodynamic coefficients.
基金supported by the National Natural Science Foundation of China (Grant No. 10674032)
文摘The complete band gaps （CBGs） of shallow water waves propagating over bottoms with periodically drilled holes are investigated numerically by the plane wave expansion method. Four different patterns are considered, containing triangular, square, hexagonal and circular cross-sectioned holes arranged into triangular lattices. Results show that the width of CBGs can be changed by adjusting the orientation of noncircular holes and the effect of hole shape on the width of the maximal CBGs is discussed.
文摘In this paper, a method to construct oblique wave-free potentials in the linearised theory of water waves for water with uniform finite depth is presented in a systematic manner. The water has either a free surface or an ice-cover modelled as a thin elastic plate. For the case of free surface, the effect of surface tension may be neglected or taken into account. Here, the wave-free potentials are singular solutions of the modified Helmholtz equation, having singularity at a point in the fluid region and they satisfy the conditions at the upper surface and the bottom of water region and decay rapidly away from the point of singularity. These are useful in obtaining solutions to oblique water wave problems involving bodies with circular cross-sections such as long horizontal cylinders submerged or half-immersed in water of uniform fmite depth with a free surface or an ice-cover modelled as a floating elastic plate. Finally, the forms of the upper surface related to the wave-free potentials constructed here are depicted graphically in a number of figures to visualize the wave motion. The results for non-oblique wave-free potentials and the upper surface wave-free potentials are obtained. The wave-free potentials constructed here will be useful in the mathematical study of water wave problems involving infinitely long horizontal cylinders, either half-immersed or completely immersed in water.
基金partially supported by a research grant from Department of Science and Technology(DST),India(No.SB/FTP/MS-003/2013)
文摘Obliquely incident water wave scattering by an uneven channel-bed in the form of a small bottom undulation in a two-layer fluid is investigated within the frame work of three-dimensional linear water wave theory. The upper fluid is assumed to be bounded above by a rigid lid, while the lower one is bounded below by a bottom surface having a small deformation and the channel is unbounded in the horizontal directions. Assuming irrotational motion, perturbation technique is employed to calculate the first-order corrections to the velocity potentials in the two fluids by using Fourier transform approximately, and also to calculate the reflection and transmission coefficients in terms of integrals involving the shape function representing the bottom deformation. Consideration of a patch of sinusoidal ripples shows that the reflection coefficient is an oscillatory function of the ratio of twice the component of the wave number along x-axis and the ripple wave number. When this ratio approaches one, the theory predicts a resonant interaction between the bed and interface, and the reflection coefficient becomes a multiple of the number of ripples. High reflection of incident wave energy occurs if this number is large.
基金National Natural Science Foundation of China under contract No.59839330by ChinaPostdoctoral Science Foundation.
文摘Based on the evolution equation for water waves, a mathematical model for wave propaga tion in large mild - slope areas is derived. The model is solved by the finite difference method with the staggered grid system. The computational results are in good agreement with experimental data and show that the model can obtain better results with relatively coarser grids. The model can be used to simulate water wave propagation in large coastal areas and can be efficiently solved without much programming effort.
基金Shenzhen Science and Technology Program(Grant No.JCYJ20230807091300001)the National Natural Science Foundation of China(Grant Nos.12374410 and 92050102)+1 种基金the National Key Research and Development Program of China(Grant Nos.2023YFA1407100 and 2020YFA0710100)the Fundamental Research Funds for the Central Universities(Grant No.20720220033).
文摘Metasurfaces and metagratings offer new platforms for electromagnetic wave control with significant responses.However,metasurfaces based on abrupt phase change and resonant structures suffer from the drawback of high loss and face challenges when applied in water waves.Therefore,the application of metasurfaces in water wave control is not ideal due to the limitations associated with high loss and other challenges.We have discovered that non-resonant metagratings exhibit promising effects in water wave control.Leveraging the similarity between bridges and metagratings,we have successfully developed a water wave metagrating model inspired by the ancient Luoyang Bridge in China.We conduct theoretical calculations and simulations on the metagrating and derive the equivalent anisotropic model of the metagrating.This model provides evidence that the metagrating has the capability to control water waves and achieve unidirectional surface water wave.The accuracy of our theory is strongly supported by the clear observation of the unidirectional propagation phenomenon during simulation and experiments conducted using a reduced version of the metagrating.It is the first time that the unidirectional propagation of water waves has been seen in water wave metagrating experiment.Above all,we realize the water wave metagrating experiment for the first time.By combining complex gratings with real bridges,we explore the physics embedded in the ancient building—Luoyang Bridge,which are of great significance for the water wave metagrating design and provide a new method for analyzing the effects of water waves on bridges.At the same time,this discovery also provides a new idea for ocean cargo transportation,ocean garbage cleaning,and the development and protection of ancient bridges.
