Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are use...Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV-mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.展开更多
The 'surface roller' to simulate wave energy dissipation of wave breaking is introduced into the random wave model based on approximate parabolic mild slope equation in this paper to simulate the random wave t...The 'surface roller' to simulate wave energy dissipation of wave breaking is introduced into the random wave model based on approximate parabolic mild slope equation in this paper to simulate the random wave transportation in chiding diffraction, refraction and breaking in nearshore areas. The roller breaking random wave higher-order approximate parabolic equation model has been verified by the existing experimental data for a plane slope beach and a circular shoal, and the numerical results of random wave breaking model agree with the experimental data very well, This model can be applied to calculate random wave propagation from deep to shallow water in large areas near the shore over natural topography.展开更多
The interaction of wave-particles and wave-wave in the space plasmas are essentially non-linear or non-Gaussian processes. Using the higher-order statistical analyses methods (higher-order moments and bi-tri correlati...The interaction of wave-particles and wave-wave in the space plasmas are essentially non-linear or non-Gaussian processes. Using the higher-order statistical analyses methods (higher-order moments and bi-tri correlation or bi-tri spectrum), its physical properties can be described. The question addressed in this paper is that of the usefulness of higher-order statistical analysis for identification of the wave-particles interaction in space plasmas. The signals handled are from the ARCAD-3 ISOPROBE experiment on ELF frequency range, then strong electrostatic turbulence and electron density irregularities. Second and third order statistical analyses are applied: first, on time series associated with each type of measurement, then, on the two types. All results are presented for one typical case. Correlation functions estimated over the corresponding time intervals point out the existence of a, non-linear interaction between these fluctuations and electrostatic filed.展开更多
It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squ...It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the hlgher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.展开更多
A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobiell...A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobielliptic functions in the seed solution,special types of periodic folded waves are derived.In long wave limit theseperiodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions ofthe periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are foundto be completely elastic.展开更多
We reduce the variable-coefficient higher-order nonlinear Schrodinger equation (VCHNLSE) into the constantcoefficient (CC) one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical ...We reduce the variable-coefficient higher-order nonlinear Schrodinger equation (VCHNLSE) into the constantcoefficient (CC) one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.展开更多
High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of ...High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).展开更多
In this paper, a numerical model is developed based on the High Order Spectral (HOS) method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident bou...In this paper, a numerical model is developed based on the High Order Spectral (HOS) method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.展开更多
The travelling solitary wave solutions to the higher order Korteweg-de Vries equation are obtained by using tanh-polynomial method. The method is effective and concise, which is also applied to various partial differe...The travelling solitary wave solutions to the higher order Korteweg-de Vries equation are obtained by using tanh-polynomial method. The method is effective and concise, which is also applied to various partial differential equations to obtain traveling wave solutions. The numerical simulation of the solutions is given for completeness. Numerical results show that the tanh-polynomial method works quite well.展开更多
In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some e...In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.展开更多
By using the theories on Stokes multicolored water waves and taking the two- layer ocean as a basic model of stratified ocean, the paper analyzes the problems related to the effects of the nonlinear water wave on offs...By using the theories on Stokes multicolored water waves and taking the two- layer ocean as a basic model of stratified ocean, the paper analyzes the problems related to the effects of the nonlinear water wave on offshore structures. A mathematical expression is presented to describe second order wave radiation conditions. Using integral principle, the analytical integral solutions are given to evaluate second order scattered wave loads on general vertical circular cylinders in the two-layer ocean, and the special recurrence formulas for infinite integrals over free and stratified surfaces are derived.展开更多
A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solu- tion of an ...A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solu- tion of an initial value problem, and using Laplace transformation method and Tauberian theorem, the boundary value problems of stationary solution of the first and second order diffraction potential have been de- rived in this paper. Furthermore, the explicit solution of the second order stationary diffraction potential has been obtained with the method of the double Fourier transformation. It is found that the asymptotic behaviour of the second order stationary solution at far field is dependent on two wave systems, the first is 'free wave', travelling independently of the first order wave system, the other is 'phase locked waves', which accompany the first order waves. At the same time, the radiation conditions of the second order diffraction problems are derived. We also find that one can still pursue a steady state formulation with the inclusion of Rayleigh damping. Finally, as an example, the second order wave forces upon a fixed vertical cir- cular cylinder have been calculated, and the numerical results agree well with the experimental data.展开更多
Considered under their standard form, the fifth-order KdV equations are a sort of reading table on which new prototypes of higher order solitary waves residing there, have been uncovered and revealed to broad daylight...Considered under their standard form, the fifth-order KdV equations are a sort of reading table on which new prototypes of higher order solitary waves residing there, have been uncovered and revealed to broad daylight. The mathematical tool that made it possible to explore and analyze this equation is the Bogning-Djeumen Tchaho-Kofané method extended to the new implicit Bogning' functions. The analytical form of the solutions chosen in this manuscript is particular in the sense that it contains within its bosom, a package of solitary waves made up of three solitons, especially, the bright type soliton, the hybrid soliton and the dark type soliton which we estimate capable in their interactions of generating new hybrid or multi-form solitons. Existence conditions of the obtained solitons have been determined. It emerges that, these existence conditions of the chosen ansatz could open the way to other new varieties of fifth-order KdV equations including to which it will be one of the solutions. Some of the obtained solitons are exact solutions. Intense numerical simulations highlighted numerical stability and confirmed the hybrid character of the obtained solutions. These results will help to model new nonlinear wave phenomena, in plasma media and in fluid dynamics, especially, on the shallow water surface.展开更多
Higher order Boussinesq-type equations for wave propagation over variable bathymetry were derived. The time dependent free surface boundary conditions were used to compute the change of the free surface in time domain...Higher order Boussinesq-type equations for wave propagation over variable bathymetry were derived. The time dependent free surface boundary conditions were used to compute the change of the free surface in time domain. The free surface velocities and the bottom velocities were connected by the exact solution of the Laplace equation. Taking the velocities on half relative water depth as the fundamental unknowns, terms relating to the gradient of the water depth were retained in the inverse series expansion of the exact solution, with which the problem was closed. With enhancements of the finite order Taylor expansion for the velocity field, the application range of the present model was extended to the slope bottom which is not so mild. For linear properties, some validation computations of linear shoaling and Booij' s tests were carried out. The problems of wave-current interactions were also studied numerically to test the performance of the enhanced Boussinesq equations associated with the effect of currents. All these computational results confirm perfectly to the theoretical solution as well as other numerical solutions of the full potential problem available.展开更多
The power performances of a point absorber wave energy converter(WEC)operating in a nonlinear multidirectional random sea are rigorously investigated.The absorbed power of the WEC Power-Take-Off system has been predic...The power performances of a point absorber wave energy converter(WEC)operating in a nonlinear multidirectional random sea are rigorously investigated.The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter.This is a new approach,and,as the second order random wave model can be utilized to accurately simulate the nonlinear waves in an irregular sea,avoids the inaccuracies resulting from using a first order linear wave model in the simulation process.The predicted results have been systematically analyzed and compared,and the advantages of using this new approach have been convincingly substantiated.展开更多
In this study, the coupled heave-pitch motion equations of a spar platform were established by considering 1st-order and 2nd-order random wave loads and the effects of time-varying displacement volume and transient wa...In this study, the coupled heave-pitch motion equations of a spar platform were established by considering 1st-order and 2nd-order random wave loads and the effects of time-varying displacement volume and transient wave elevation. We generated random wave loads based on frequency-domain wave load transfer functions and the Joint North Sea Wave Project(JONSWAP) wave spectrum, designed program codes to solve the motion equations, and then simulated the coupled heave-pitch motion responses of the platform in the time domain. We then calculated and compared the motion responses in different sea conditions and separately investigated the effects of 2nd-order random wave loads and transient wave elevation. The results show that the coupled heave-pitch motion responses of the platform are primarily dominated by wave height and the characteristic wave period, the latter of which has a greater impact. 2nd-order mean wave loads mainly affect the average heave value. The platform's pitch increases after the 2nd-order low frequency wave loads are taken into account. The platform's heave is underestimated if the transient wave elevation term in the motion equations is neglected.展开更多
Variational principle for non-vortex, non-linear wave theories is established in this paper. By using this variational principle and related functional minimum condition, the fifth and sixth order Stokes Vaves are giv...Variational principle for non-vortex, non-linear wave theories is established in this paper. By using this variational principle and related functional minimum condition, the fifth and sixth order Stokes Vaves are given as an example and the results are compared with those in Reference (Skjel-breia, 1961).展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No 40775069)
文摘Higher-order Korteweg-de Vries (KdV)-modified KdV (mKdV) equations with a higher-degree of nonlinear terms are derived from a simple incompressible non-hydrostatic Boussinesq equation set in atmosphere and are used to investigate gravity waves in atmosphere. By taking advantage of the auxiliary nonlinear ordinary differential equation, periodic wave and solitary wave solutions of the fifth-order KdV-mKdV models with higher-degree nonlinear terms are obtained under some constraint conditions. The analysis shows that the propagation and the periodic structures of gravity waves depend on the properties of the slope of line of constant phase and atmospheric stability. The Jacobi elliptic function wave and solitary wave solutions with slowly varying amplitude are transformed into triangular waves with the abruptly varying amplitude and breaking gravity waves under the effect of atmospheric instability.
基金This work was financially supported by the National Natural Science Foundation of China(Grant No.59839330 and No.19772031)
文摘The 'surface roller' to simulate wave energy dissipation of wave breaking is introduced into the random wave model based on approximate parabolic mild slope equation in this paper to simulate the random wave transportation in chiding diffraction, refraction and breaking in nearshore areas. The roller breaking random wave higher-order approximate parabolic equation model has been verified by the existing experimental data for a plane slope beach and a circular shoal, and the numerical results of random wave breaking model agree with the experimental data very well, This model can be applied to calculate random wave propagation from deep to shallow water in large areas near the shore over natural topography.
文摘The interaction of wave-particles and wave-wave in the space plasmas are essentially non-linear or non-Gaussian processes. Using the higher-order statistical analyses methods (higher-order moments and bi-tri correlation or bi-tri spectrum), its physical properties can be described. The question addressed in this paper is that of the usefulness of higher-order statistical analysis for identification of the wave-particles interaction in space plasmas. The signals handled are from the ARCAD-3 ISOPROBE experiment on ELF frequency range, then strong electrostatic turbulence and electron density irregularities. Second and third order statistical analyses are applied: first, on time series associated with each type of measurement, then, on the two types. All results are presented for one typical case. Correlation functions estimated over the corresponding time intervals point out the existence of a, non-linear interaction between these fluctuations and electrostatic filed.
文摘It is found that the field of the combined mode of the probe wave and the phase conjugate wave in the process of non-degenerate four-wave mixing exhibits higher-order squeezing to all even orders. The higher-order squeezed parameter and squeezed limit due to the modulation frequency are investigated. The smaller the modulation frequency is, the stronger the degree of higher-order squeezing becomes. Furthermore, the hlgher-order uncertainty relations in the process of non-degenerate four-wave mixing are presented for the first time. The product of higher-order noise moments is related to even order number N and the length L of the medium.
基金National Natural Science Foundation of China under Grant Nos 10472063 and 10772110
文摘A general solution including three arbitrary functions is obtained for the (2+1)-dimensional higher-orderBroer-Kaup equation by means of WTC truncation method.Introducing proper multiple valued functions and Jacobielliptic functions in the seed solution,special types of periodic folded waves are derived.In long wave limit theseperiodic folded wave patterns may degenerate into single localized folded solitary wave excitations.The interactions ofthe periodic folded waves and their degenerated single folded solitary waves are investigated graphically and are foundto be completely elastic.
基金Project supported by the National Natural Science Foundation of China (Grant No. 11005092)the Program for Innovative Research Team of Young Teachers of Zhejiang Agricultural and Forestry University, China (Grant No. 2009RC01)
文摘We reduce the variable-coefficient higher-order nonlinear Schrodinger equation (VCHNLSE) into the constantcoefficient (CC) one. Based on the reduction transformation and solutions of CCHNLSE, we obtain analytical soliton solutions embedded in the continuous wave background for the VCHNLSE. Then the excitation in advancement and sustainment of soliton arrays, and postponed disappearance and sustainment of the bright soliton embedded in the background are discussed in an exponential system.
文摘High-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth with an arbitrary sloping bottom are presented in this article. First, the formal derivations to any high order of mu(= h/lambda, depth to deep-water wave length ratio) and epsilon(= a/h, wave amplitude to depth ratio) for velocity potential, particle velocity vector, pressure and the Boussinesq-type equations for surface elevation eta and horizontal velocity vector (U) over right arrow at any given level in water are given. Then, the exact explicit expressions to the fourth order of mu are derived. Finally, the linear solutions of eta, (U) over right arrow, C (phase-celerity) and C-g (group velocity) for a constant water depth are obtained. Compared with the Airy theory, excellent results can be found even for a water depth as large as the wave legnth. The present high-order models are applicable to nonlinear regular and irregular waves in water of any varying depth (from shallow to deep) and bottom slope (from mild to steep).
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51309050 and 51221961)the National Basic Research Program of China(973 Program,Grant Nos.2013CB036101 and 2011CB013703)
文摘In this paper, a numerical model is developed based on the High Order Spectral (HOS) method with a non-periodic boundary. A wave maker boundary condition is introduced to simulate wave generation at the incident boundary in the HOS method. Based on the numerical model, the effects of wave parameters, such as the assumed focused amplitude, the central frequency, the frequency bandwidth, the wave amplitude distribution and the directional spreading on the surface elevation of the focused wave, the maximum generated wave crest, and the shifting of the focusing point, are numerically investigated. Especially, the effects of the wave directionality on the focused wave properties are emphasized. The numerical results show that the shifting of the focusing point and the maximum crest of the wave group are dependent on the amplitude of the focused wave, the central frequency, and the wave amplitude distribution type. The wave directionality has a definite effect on multidirectional focused waves. Generally, it can even out the difference between the simulated wave amplitude and the amplitude expected from theory and reduce the shifting of the focusing points, implying that the higher order interaction has an influence on wave focusing, especially for 2D wave. In 3D wave groups, a broader directional spreading weakens the higher nonlinear interactions.
文摘The travelling solitary wave solutions to the higher order Korteweg-de Vries equation are obtained by using tanh-polynomial method. The method is effective and concise, which is also applied to various partial differential equations to obtain traveling wave solutions. The numerical simulation of the solutions is given for completeness. Numerical results show that the tanh-polynomial method works quite well.
基金supported by the Research Foundation of Education Bureau of Hubei Province,China (Grant No Z200612001)the Natural Science Foundation of Yangtze University (Grant No 20061222)
文摘In this paper, the travelling wave solutions for the generalized Burgers-Huxley equation with nonlinear terms of any order are studied. By using the first integral method, which is based on the divisor theorem, some exact explicit travelling solitary wave solutions for the above equation are obtained. As a result, some minor errors and some known results in the previousl literature are clarified and improved.
基金National Natural Science Foundation of China (19802023)
文摘By using the theories on Stokes multicolored water waves and taking the two- layer ocean as a basic model of stratified ocean, the paper analyzes the problems related to the effects of the nonlinear water wave on offshore structures. A mathematical expression is presented to describe second order wave radiation conditions. Using integral principle, the analytical integral solutions are given to evaluate second order scattered wave loads on general vertical circular cylinders in the two-layer ocean, and the special recurrence formulas for infinite integrals over free and stratified surfaces are derived.
文摘A theory on the second order wave diffraction by a three dimensional body fixed in a regular sea has been developed in the present paper. By regarding the sinusoidal disturb potential as a stationary solu- tion of an initial value problem, and using Laplace transformation method and Tauberian theorem, the boundary value problems of stationary solution of the first and second order diffraction potential have been de- rived in this paper. Furthermore, the explicit solution of the second order stationary diffraction potential has been obtained with the method of the double Fourier transformation. It is found that the asymptotic behaviour of the second order stationary solution at far field is dependent on two wave systems, the first is 'free wave', travelling independently of the first order wave system, the other is 'phase locked waves', which accompany the first order waves. At the same time, the radiation conditions of the second order diffraction problems are derived. We also find that one can still pursue a steady state formulation with the inclusion of Rayleigh damping. Finally, as an example, the second order wave forces upon a fixed vertical cir- cular cylinder have been calculated, and the numerical results agree well with the experimental data.
文摘Considered under their standard form, the fifth-order KdV equations are a sort of reading table on which new prototypes of higher order solitary waves residing there, have been uncovered and revealed to broad daylight. The mathematical tool that made it possible to explore and analyze this equation is the Bogning-Djeumen Tchaho-Kofané method extended to the new implicit Bogning' functions. The analytical form of the solutions chosen in this manuscript is particular in the sense that it contains within its bosom, a package of solitary waves made up of three solitons, especially, the bright type soliton, the hybrid soliton and the dark type soliton which we estimate capable in their interactions of generating new hybrid or multi-form solitons. Existence conditions of the obtained solitons have been determined. It emerges that, these existence conditions of the chosen ansatz could open the way to other new varieties of fifth-order KdV equations including to which it will be one of the solutions. Some of the obtained solitons are exact solutions. Intense numerical simulations highlighted numerical stability and confirmed the hybrid character of the obtained solutions. These results will help to model new nonlinear wave phenomena, in plasma media and in fluid dynamics, especially, on the shallow water surface.
基金Project supported by the National Natural Science Foundation of China (No. 10172058)the Special Fund for PhD Program of Education Ministry of China (No.2000024817)
文摘Higher order Boussinesq-type equations for wave propagation over variable bathymetry were derived. The time dependent free surface boundary conditions were used to compute the change of the free surface in time domain. The free surface velocities and the bottom velocities were connected by the exact solution of the Laplace equation. Taking the velocities on half relative water depth as the fundamental unknowns, terms relating to the gradient of the water depth were retained in the inverse series expansion of the exact solution, with which the problem was closed. With enhancements of the finite order Taylor expansion for the velocity field, the application range of the present model was extended to the slope bottom which is not so mild. For linear properties, some validation computations of linear shoaling and Booij' s tests were carried out. The problems of wave-current interactions were also studied numerically to test the performance of the enhanced Boussinesq equations associated with the effect of currents. All these computational results confirm perfectly to the theoretical solution as well as other numerical solutions of the full potential problem available.
基金The National Natural Science Foundation of China under contract No.51979165。
文摘The power performances of a point absorber wave energy converter(WEC)operating in a nonlinear multidirectional random sea are rigorously investigated.The absorbed power of the WEC Power-Take-Off system has been predicted by incorporating a second order random wave model into a nonlinear dynamic filter.This is a new approach,and,as the second order random wave model can be utilized to accurately simulate the nonlinear waves in an irregular sea,avoids the inaccuracies resulting from using a first order linear wave model in the simulation process.The predicted results have been systematically analyzed and compared,and the advantages of using this new approach have been convincingly substantiated.
基金Foundation item: Supported by the National Natural Science Foundation of China under Grant No. 51279130 and No. 51239008
文摘In this study, the coupled heave-pitch motion equations of a spar platform were established by considering 1st-order and 2nd-order random wave loads and the effects of time-varying displacement volume and transient wave elevation. We generated random wave loads based on frequency-domain wave load transfer functions and the Joint North Sea Wave Project(JONSWAP) wave spectrum, designed program codes to solve the motion equations, and then simulated the coupled heave-pitch motion responses of the platform in the time domain. We then calculated and compared the motion responses in different sea conditions and separately investigated the effects of 2nd-order random wave loads and transient wave elevation. The results show that the coupled heave-pitch motion responses of the platform are primarily dominated by wave height and the characteristic wave period, the latter of which has a greater impact. 2nd-order mean wave loads mainly affect the average heave value. The platform's pitch increases after the 2nd-order low frequency wave loads are taken into account. The platform's heave is underestimated if the transient wave elevation term in the motion equations is neglected.
文摘Variational principle for non-vortex, non-linear wave theories is established in this paper. By using this variational principle and related functional minimum condition, the fifth and sixth order Stokes Vaves are given as an example and the results are compared with those in Reference (Skjel-breia, 1961).