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
The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations(NLWWEs)in oceans through the invariant subspace scheme(ISS).In this respect,the NLWWEs which describe specific...The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations(NLWWEs)in oceans through the invariant subspace scheme(ISS).In this respect,the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations(ODEs)such that the resulting systems can be efficiently handled by computer algebra systems.As an accomplishment,the performance of the well-designed ISS in extracting a group of exact solutions is formally confirmed.In the end,the stability analysis for the NLWWE is investigated through the linear stability scheme.展开更多
In this paper we study nonlinear periodic deep water waves propagating on a background shear current,which decays exponentially with depth.We extend the study of Cheng,Cang and Liao(2009) by introducing a second param...In this paper we study nonlinear periodic deep water waves propagating on a background shear current,which decays exponentially with depth.We extend the study of Cheng,Cang and Liao(2009) by introducing a second parameter which measures the depth of the shear current.A high-order convergent analytical series solution is obtained by the homotopy analysis method(HAM).A detailed analysis of the impact of the depth parameter is given.We find that increasing this parameter so that the shear current is thinner reduces the wave phase speed,smoothes the wave crest,sharpens the trough,and enlarges the maximum wave height for the case of propagating waves on an opposing current;while it produces the opposite effect on an aiding current.展开更多
In this paper, it is dealt with that the Hamiltonian formulation of nonlinear water waves in a two_fluid system,which consists of two layers of constant_density incompressible inviscid fluid with a horizontal bottom,a...In this paper, it is dealt with that the Hamiltonian formulation of nonlinear water waves in a two_fluid system,which consists of two layers of constant_density incompressible inviscid fluid with a horizontal bottom,an interface and a free surface. The velocity potentials are expanded in power series of the vertical coordinate. By taking the kinetic thickness of lower fluid_layer and the reduced kinetic thickness of upper fluid_layer as the generalized displacements, choosing the velocity potentials at the interface and free surface as the generalized momenta and using Hamilton's principle, the Hamiltonian canonical equations for the system are derived with the Legendre transformation under the shallow water assumption. Hence the results for single_layer fluid are extended to the case of stratified fluid.展开更多
Investigated in the present paper is a fifth-order nonlinear evolution(FONLE)equation,known as a nonlinear water wave(NLWW)equation,with applications in the applied sciences.More precisely,a traveling wave hypothesis ...Investigated in the present paper is a fifth-order nonlinear evolution(FONLE)equation,known as a nonlinear water wave(NLWW)equation,with applications in the applied sciences.More precisely,a traveling wave hypothesis is firstly applied that reduces the FONLE equation to a 1D domain.The Kudryashov methods(KMs)are then adopted as leading techniques to construct specific wave structures of the governing model which are classified as W-shaped and other solitons.In the end,the effect of changing the coefficients of nonlinear terms on the dynamical features of W-shaped and other solitons is investigated in detail for diverse groups of the involved parameters.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
An improved model for numerically predicting nonlinear wave forces exerted on an offshore structure is pro- posed.In a previous work[9],the authors presented a model for the same purpose with an open boundary condi- t...An improved model for numerically predicting nonlinear wave forces exerted on an offshore structure is pro- posed.In a previous work[9],the authors presented a model for the same purpose with an open boundary condi- tion imposed,where the wave celerity has been defined constant.Generally,the value of wave celerity is time-de- pendent and varying with spatial location.With the present model the wave celerity is evaluated by an upwind dif- ference scheme,which enables the method to be extended to conditions of variable finite water depth,where the value of wave celerity varies with time as the wave approaches the offshore structure.The finite difference method incorporated with the time-stepping technique in time domain developed here makes the numerical evolution effec- tive and stable.Computational examples on interactions between a surface-piercing vertical cylinder and a solitary wave or a cnoidal wave train demonstrates the validity of this program.展开更多
In this paper the KdV equation has been derived by using the Lagrangian coordinates and the head-on collision between solitary waves was studied without the assumption of irrotational motion condition. It is found tha...In this paper the KdV equation has been derived by using the Lagrangian coordinates and the head-on collision between solitary waves was studied without the assumption of irrotational motion condition. It is found that the results obtained in Lagrangian coordinates are consistent with those obtained in Euler coordinates.展开更多
In this paper, a nonlinear model is presented to describe wave transformation in shallow water with the zero- vorticity equation of wave- number vector and energy conservation equation. The nonlinear effect due to an ...In this paper, a nonlinear model is presented to describe wave transformation in shallow water with the zero- vorticity equation of wave- number vector and energy conservation equation. The nonlinear effect due to an empirical dispersion relation (by Hedges) is compared with that of Dalrymple's dispersion relation. The model is tested against the laboratory measurements for the case of a submerged elliptical shoal on a slope beach, where both refraction and diffraction are significant. The computation results, compared with those obtained through linear dispersion relation, show that the nonlinear effect of wave transformation in shallow water is important. And the empirical dispersion relation is suitable for researching the nonlinearity of wave in shallow water.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
This article describes transformation of nonlinear surface gravity waves under shallow-water conditions with the aid of the suggested semigraphical method. There are given profiles of surface gravity waves on the cres...This article describes transformation of nonlinear surface gravity waves under shallow-water conditions with the aid of the suggested semigraphical method. There are given profiles of surface gravity waves on the crests steepening stages, their leading edges steepening. There are discussed the spectral component influence on the transformation of surface wave profile.展开更多
This work considers the problems of numerical simulation of non-linear surface gravity waves transformation under shallow bay conditions. The discrete model is built from non-linear shallow-water equations. Are result...This work considers the problems of numerical simulation of non-linear surface gravity waves transformation under shallow bay conditions. The discrete model is built from non-linear shallow-water equations. Are resulted boundary and initial conditions. The method of splitting into physical processes receives system from three equations. Then we define the approximation order and investigate stability conditions of the discrete model. The sweep method was used to calculate the system of equations. This work presents surface gravity wave profiles for different propagation phases.展开更多
In this manuscript, we first perform a complete Lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained Lie symmetries....In this manuscript, we first perform a complete Lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained Lie symmetries. Moreover, with the extended <em>F</em>-expansion method, we obtain several new nonlinear wave solutions involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function and trigonometric function.展开更多
The split-step pseudo-spectral method is a useful method for solving nonlinear wave equations. However, it is not widely used because of the limitation of the periodic boundary condition. In this paper, the method is ...The split-step pseudo-spectral method is a useful method for solving nonlinear wave equations. However, it is not widely used because of the limitation of the periodic boundary condition. In this paper, the method is modified at its second step by avoiding transforming the wave height function into a frequency domain function. Thus, the periodic boundary condition is not required, and the new method is easy to implement. In order to validate its performance, the proposed method was used to solve the nonlinear parabolic mild-slope equation and the spatial modified nonlinear Schrodinger （MNLS） equation, which were used to model the wave propagation under different bathymetric conditions. Good agreement between the numerical and experimental results shows that the present method is effective and efficient in solving nonlinear wave eouations.展开更多
The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation.The third-order asymptotic solution is a periodi...The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation.The third-order asymptotic solution is a periodic bounded function of Lagrangian labels and time,which imply that the entire solution is uniformly-valid.The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form.The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian.The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.展开更多
In this paper, the(3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation for water waves is investigated. Through the Hirota method and Kadomtsev–Petviashvili hierarchy reduction, we obtain the first-o...In this paper, the(3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation for water waves is investigated. Through the Hirota method and Kadomtsev–Petviashvili hierarchy reduction, we obtain the first-order,higher-order, multiple rogue waves and lump solitons based on the solutions in terms of the Gramian. The first-order rogue waves are the line rogue waves which arise from the constant background and then disappear into the constant background again, while the first-order lump solitons propagate stably. Interactions among several first-order rogue waves which are described by the multiple rogue waves are presented. Elastic interactions of several first-order lump solitons are also presented. We find that the higher-order rogue waves and lump solitons can be treated as the superpositions of several first-order ones, while the interaction between the second-order lump solitons is inelastic.展开更多
We review recent advances in the finite element method (FEM) simulations of interactions between waves and structures. Our focus is on the potential theory with the fully nonlinear or second-order boundary condition. ...We review recent advances in the finite element method (FEM) simulations of interactions between waves and structures. Our focus is on the potential theory with the fully nonlinear or second-order boundary condition. The present paper has six sections. A review of previous work on interactions between waves and ocean structures is presented in Section one. Section two gives the mathematical formulation. In Section three, the finite element discretization, mesh generation and the finite element linear system solution methods are described. Section four presents numerical methods including time marching schemes, computation of velocity, remeshing and smoothing techniques and numerical radiation conditions. The application of the FEM to the wave-structure interactions are presented in Section five followed by the concluding remarks in Section six.展开更多
This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculat...This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculation. In the proposed Transformed Rayleigh method, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The proposed new method has been applied for calculating the wave height exceedance probabilities of a sea state with the surface elevation data measured at the Poseidon platform. It is demonstrated in this case that the proposed new method can offer better predictions than those by using the conventional Rayleigh wave height distribution model. The proposed new method has been further applied for calculating the total horizontal loads on a generic jacket, and its accuracy has once again been substantiated. The research findings gained from this study demonstrate that the proposed Transformed Rayleigh model can be utilized as a promising alternative to the well-established nonlinear wave height distribution models.展开更多
This paper considers the nonlinear transformation of irregular waves propagating over a mild slope （1：40）. Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this ...This paper considers the nonlinear transformation of irregular waves propagating over a mild slope （1：40）. Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this purpose. The results indicate that the wave heights obey the Rayleigh distribution at the offshore location; however, in the shoaling region, the heights of the largest waves are underestimated by the theoretical distributions. In the surf zone, the wave heights can be approximated by the composite Weibull distribution. In addition, the nonlinear phase coupling within the irregular waves is investigated by the wavelet-based bicoherence. The bicoherence spectra reflect that the number of frequency modes participating in the phase coupling increases with the decreasing water depth, as does the degree of phase coupling. After the incipient breaking, even though the degree of phase coupling decreases, a great number of higher harmonic wave modes are also involved in nonlinear interactions. Moreover, the summed bicoherence indicates that the frequency mode related to the strongest local nonlinear interactions shifts to higher harmonics with the decreasing water depth.展开更多
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The key purpose of the present research is to derive the exact solutions of nonlinear water wave equations(NLWWEs)in oceans through the invariant subspace scheme(ISS).In this respect,the NLWWEs which describe specific nonlinear waves are converted to a number of systems of ordinary differential equations(ODEs)such that the resulting systems can be efficiently handled by computer algebra systems.As an accomplishment,the performance of the well-designed ISS in extracting a group of exact solutions is formally confirmed.In the end,the stability analysis for the NLWWE is investigated through the linear stability scheme.
基金supported by the National Natural Science Foundation of China (Grant No.51002195)
文摘In this paper we study nonlinear periodic deep water waves propagating on a background shear current,which decays exponentially with depth.We extend the study of Cheng,Cang and Liao(2009) by introducing a second parameter which measures the depth of the shear current.A high-order convergent analytical series solution is obtained by the homotopy analysis method(HAM).A detailed analysis of the impact of the depth parameter is given.We find that increasing this parameter so that the shear current is thinner reduces the wave phase speed,smoothes the wave crest,sharpens the trough,and enlarges the maximum wave height for the case of propagating waves on an opposing current;while it produces the opposite effect on an aiding current.
文摘In this paper, it is dealt with that the Hamiltonian formulation of nonlinear water waves in a two_fluid system,which consists of two layers of constant_density incompressible inviscid fluid with a horizontal bottom,an interface and a free surface. The velocity potentials are expanded in power series of the vertical coordinate. By taking the kinetic thickness of lower fluid_layer and the reduced kinetic thickness of upper fluid_layer as the generalized displacements, choosing the velocity potentials at the interface and free surface as the generalized momenta and using Hamilton's principle, the Hamiltonian canonical equations for the system are derived with the Legendre transformation under the shallow water assumption. Hence the results for single_layer fluid are extended to the case of stratified fluid.
文摘Investigated in the present paper is a fifth-order nonlinear evolution(FONLE)equation,known as a nonlinear water wave(NLWW)equation,with applications in the applied sciences.More precisely,a traveling wave hypothesis is firstly applied that reduces the FONLE equation to a 1D domain.The Kudryashov methods(KMs)are then adopted as leading techniques to construct specific wave structures of the governing model which are classified as W-shaped and other solitons.In the end,the effect of changing the coefficients of nonlinear terms on the dynamical features of W-shaped and other solitons is investigated in detail for diverse groups of the involved parameters.
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China National Sicence Foundation with Grant No.91870003
文摘An improved model for numerically predicting nonlinear wave forces exerted on an offshore structure is pro- posed.In a previous work[9],the authors presented a model for the same purpose with an open boundary condi- tion imposed,where the wave celerity has been defined constant.Generally,the value of wave celerity is time-de- pendent and varying with spatial location.With the present model the wave celerity is evaluated by an upwind dif- ference scheme,which enables the method to be extended to conditions of variable finite water depth,where the value of wave celerity varies with time as the wave approaches the offshore structure.The finite difference method incorporated with the time-stepping technique in time domain developed here makes the numerical evolution effec- tive and stable.Computational examples on interactions between a surface-piercing vertical cylinder and a solitary wave or a cnoidal wave train demonstrates the validity of this program.
文摘In this paper the KdV equation has been derived by using the Lagrangian coordinates and the head-on collision between solitary waves was studied without the assumption of irrotational motion condition. It is found that the results obtained in Lagrangian coordinates are consistent with those obtained in Euler coordinates.
文摘In this paper, a nonlinear model is presented to describe wave transformation in shallow water with the zero- vorticity equation of wave- number vector and energy conservation equation. The nonlinear effect due to an empirical dispersion relation (by Hedges) is compared with that of Dalrymple's dispersion relation. The model is tested against the laboratory measurements for the case of a submerged elliptical shoal on a slope beach, where both refraction and diffraction are significant. The computation results, compared with those obtained through linear dispersion relation, show that the nonlinear effect of wave transformation in shallow water is important. And the empirical dispersion relation is suitable for researching the nonlinearity of wave in shallow water.
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This article describes transformation of nonlinear surface gravity waves under shallow-water conditions with the aid of the suggested semigraphical method. There are given profiles of surface gravity waves on the crests steepening stages, their leading edges steepening. There are discussed the spectral component influence on the transformation of surface wave profile.
文摘This work considers the problems of numerical simulation of non-linear surface gravity waves transformation under shallow bay conditions. The discrete model is built from non-linear shallow-water equations. Are resulted boundary and initial conditions. The method of splitting into physical processes receives system from three equations. Then we define the approximation order and investigate stability conditions of the discrete model. The sweep method was used to calculate the system of equations. This work presents surface gravity wave profiles for different propagation phases.
文摘In this manuscript, we first perform a complete Lie symmetry classification for a higher-dimensional shallow water wave equation and then construct the corresponding reduced equations with the obtained Lie symmetries. Moreover, with the extended <em>F</em>-expansion method, we obtain several new nonlinear wave solutions involving differentiable arbitrary functions, expressed by Jacobi elliptic function, Weierstrass elliptic function, hyperbolic function and trigonometric function.
基金supported by the Central Public-Interest Scientific Institution Basal Research Fund of China(Grant No.TKS100108)
文摘The split-step pseudo-spectral method is a useful method for solving nonlinear wave equations. However, it is not widely used because of the limitation of the periodic boundary condition. In this paper, the method is modified at its second step by avoiding transforming the wave height function into a frequency domain function. Thus, the periodic boundary condition is not required, and the new method is easy to implement. In order to validate its performance, the proposed method was used to solve the nonlinear parabolic mild-slope equation and the spatial modified nonlinear Schrodinger （MNLS） equation, which were used to model the wave propagation under different bathymetric conditions. Good agreement between the numerical and experimental results shows that the present method is effective and efficient in solving nonlinear wave eouations.
基金National Science Council in Taiwan 97-2221-E-230-023
文摘The particle trajectory on a weakly nonlinear progressive surface wave obliquely interacting with a uniform current is studied by using an Euler-Lagrange transformation.The third-order asymptotic solution is a periodic bounded function of Lagrangian labels and time,which imply that the entire solution is uniformly-valid.The explicit parametric solution highlights the trajectory of a water particle and mass transport associated with a particle displacement can now be obtained directly in Lagrangian form.The angular frequency and Lagrangian mean level of the particle motion in Lagrangian form differ from those of the Eulerian.The variations in the water particle orbits resulting from the oblique interaction with a steady uniform current of different magnitudes are also investigated.
基金Supported by the National Natural Science Foundation of China under Grant Nos.11772017,11272023,and 11471050by the Open Fund of State Key Laboratory of Information Photonics and Optical Communications(Beijing University of Posts and Telecommunications),China(IPOC:2017ZZ05)by the Fundamental Research Funds for the Central Universities of China under Grant No.2011BUPTYB02
文摘In this paper, the(3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation for water waves is investigated. Through the Hirota method and Kadomtsev–Petviashvili hierarchy reduction, we obtain the first-order,higher-order, multiple rogue waves and lump solitons based on the solutions in terms of the Gramian. The first-order rogue waves are the line rogue waves which arise from the constant background and then disappear into the constant background again, while the first-order lump solitons propagate stably. Interactions among several first-order rogue waves which are described by the multiple rogue waves are presented. Elastic interactions of several first-order lump solitons are also presented. We find that the higher-order rogue waves and lump solitons can be treated as the superpositions of several first-order ones, while the interaction between the second-order lump solitons is inelastic.
文摘We review recent advances in the finite element method (FEM) simulations of interactions between waves and structures. Our focus is on the potential theory with the fully nonlinear or second-order boundary condition. The present paper has six sections. A review of previous work on interactions between waves and ocean structures is presented in Section one. Section two gives the mathematical formulation. In Section three, the finite element discretization, mesh generation and the finite element linear system solution methods are described. Section four presents numerical methods including time marching schemes, computation of velocity, remeshing and smoothing techniques and numerical radiation conditions. The application of the FEM to the wave-structure interactions are presented in Section five followed by the concluding remarks in Section six.
基金financially supported by the Chinese State Key Laboratory of Ocean Engineering,Shanghai Jiao Tong University(Grant No.GKZD010038)
文摘This paper concerns the calculation of wave height exceedance probabilities for nonlinear irregular waves in transitional water depths, and a Transformed Rayleigh method is first proposed for carrying out the calculation. In the proposed Transformed Rayleigh method, the transformation model is chosen to be a monotonic exponential function, calibrated such that the first three moments of the transformed model match the moments of the true process. The proposed new method has been applied for calculating the wave height exceedance probabilities of a sea state with the surface elevation data measured at the Poseidon platform. It is demonstrated in this case that the proposed new method can offer better predictions than those by using the conventional Rayleigh wave height distribution model. The proposed new method has been further applied for calculating the total horizontal loads on a generic jacket, and its accuracy has once again been substantiated. The research findings gained from this study demonstrate that the proposed Transformed Rayleigh model can be utilized as a promising alternative to the well-established nonlinear wave height distribution models.
基金financially supported by the National Nature Science Foundation of China(Grant Nos.51109032 and 11172058)A Foundation for the Author of National Excellent Doctoral Dissertation of PR China(FANEDD,Grant No.201347)
文摘This paper considers the nonlinear transformation of irregular waves propagating over a mild slope （1：40）. Two cases of irregular waves, which are mechanically generated based on JONSWAP spectra, are used for this purpose. The results indicate that the wave heights obey the Rayleigh distribution at the offshore location; however, in the shoaling region, the heights of the largest waves are underestimated by the theoretical distributions. In the surf zone, the wave heights can be approximated by the composite Weibull distribution. In addition, the nonlinear phase coupling within the irregular waves is investigated by the wavelet-based bicoherence. The bicoherence spectra reflect that the number of frequency modes participating in the phase coupling increases with the decreasing water depth, as does the degree of phase coupling. After the incipient breaking, even though the degree of phase coupling decreases, a great number of higher harmonic wave modes are also involved in nonlinear interactions. Moreover, the summed bicoherence indicates that the frequency mode related to the strongest local nonlinear interactions shifts to higher harmonics with the decreasing water depth.
