The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlin...The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.展开更多
Nonlinear internal waves(NLIWs)exhibit robust dynamic submesoscale motions,connecting large-scale tides to smallscale shear instabilities in the ocean.Previous studies have mainly focused on their generation mechanism...Nonlinear internal waves(NLIWs)exhibit robust dynamic submesoscale motions,connecting large-scale tides to smallscale shear instabilities in the ocean.Previous studies have mainly focused on their generation mechanisms and evolution along their paths.Considering their global distribution resulting from the primary origin in tide-topography interaction,there is an increasing cross-disciplinary interest in understanding how these energetic and ubiquitous NLIWs contribute to sediment redistribution in the ocean.This paper presents fundamental theories on NLIWs and comprehensively reviews triggering mechanisms,different types of instability,and sediment responses by summarizing recent theoretical parameterizations,numerical simulations,laboratory experiments,and in-situ observations.We specifically focus on elucidating various types of instability along with their impact on sediment dynamic processes.Finally,we outline several unresolved issues that require further exploration for a quantitative investigation into NLIWinduced sediment transfer in the ocean.展开更多
The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonl...The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonlinearity is incorporated into the model,and the constitutive equations are derived.The physical parameters of functionally graded materials(FGMs),which exhibit continuous variation across the thickness gradient,are of particular interest.The nonlinear magneto-thermoelastic governing equations are derived in accord with Hamilton's principle.The nonlinear partial differential equations are discretized with the Galerkin method,and the analytical expression of traveling wave frequencies is derived with an approximate method.The accuracy of the proposed method is validated through the comparison with the results from the literature and numerical solutions.Finally,the visualization analyses are conducted to examine the effects of key parameters on the traveling wave frequencies.The results show that the factors including the power-law index,temperature,magnetic field intensity,and rotating speed have the coupling effects with respect to the nonlinear vibration behavior.展开更多
The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields ...The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.展开更多
Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation...Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants.Despite this,there has been a notable absence of research exploring this phenomenon.Consequently,this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials.It delves into the impact of pre-stress on higher-order material parameters,and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress.This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.展开更多
This paper studied the propagating characteristics of(2+1)-dimensional nonlinear ion acoustic waves in a multicomponent plasma with nonthermal electrons,positrons,and bipolar ions.The dispersion relations are initiall...This paper studied the propagating characteristics of(2+1)-dimensional nonlinear ion acoustic waves in a multicomponent plasma with nonthermal electrons,positrons,and bipolar ions.The dispersion relations are initially explored by using the small amplitude wave's dispersion relation.Then,the Sagdeev potential method is employed to study large amplitude ion acoustic waves.The analysis involves examining the system's phase diagram,Sagdeev potential function,and solitary wave solutions through numerical solution of an analytical process in order to investigate the propagation properties of nonlinear ion acoustic waves under various parameters.It is found that the propagation of nonlinear ion acoustic waves is subject to the influence of various physical parameters,including the ratio of number densities between the unperturbed positrons,electrons to positive ions,nonthermal parameters,the mass ratio of positive ions to negative ions,and the charge number ratio of negative ions to positive ions,the ratio of the electrons'temperature to positrons'temperature.In addition,the multicomponent plasma system has a compressive solitary waves with amplitude greater than zero or a rarefactive solitary waves with amplitude less than zero,in the meantime,compressive and rarefactive ion acoustic wave characteristics depend on the charge number ratio of negative ions to positive ions.展开更多
How the state of living muscles modulates the features of nonlinear elastic waves generated by external dynamic loads remains unclear because of the challenge of directly observing and modeling nonlinear elastic waves...How the state of living muscles modulates the features of nonlinear elastic waves generated by external dynamic loads remains unclear because of the challenge of directly observing and modeling nonlinear elastic waves in skeletal muscles in vivo,considering their active deformation behavior.Here,this important issue is addressed by combining experiments performed with an ultrafast ultrasound imaging system to track nonlinear shear waves(shear shock waves)in muscles in vivo and finite element analysis relying on a physically motivated constitutive model to study the effect of muscle activation level.Skeletal muscle was loaded with a deep muscle stimulator to generate shear shock waves(SSWs).The particle velocities,second and third harmonics,and group velocities of the SSWs in living muscles under both passive and active states were measured in vivo.Our experimental results reveal,for the first time,that muscle states have a pronounced effect on wave features;a low level of activation may facilitate the occurrence of both the second and third harmonics,whereas a high level of activation may inhibit the third harmonic.Finite element analysis was further carried out to quantitatively explore the effect of active muscle deformation behavior on the generation and propagation of SSWs.The simulation results at different muscle activation levels confirmed the experimental findings.The ability to reveal the effects of muscle state on the features of SSWs may be helpful in elucidating the unique dynamic deformation mechanism of living skeletal muscles,quantitatively characterizing diverse shock wave-based therapy instruments,and guiding the design of muscle-mimicking soft materials.展开更多
The characteristics of nonlinear and supernonlinear Alfvén waves propagating in a multicomponent plasma composed of a double spectral electron distribution and positive and negative ions were investigated.The Sag...The characteristics of nonlinear and supernonlinear Alfvén waves propagating in a multicomponent plasma composed of a double spectral electron distribution and positive and negative ions were investigated.The Sagdeev technique was employed,and an energy equation was derived.Our findings show that the proposed system reveals the existence of a double-layer solution,periodic,supersoliton,and superperiodic waves.The phase portrait and potential analysis related to these waves were investigated to study the main features of existing waves.It was also found that decreasing the electron temperature helps the superperiodic structure to be excited in our plasma model.Our results help interpret the nonlinear and supernonlinear features of the recorded Alfvén waves propagating in the ionosphere D-region.展开更多
The(2 + 1)-dimensional generalized fifth-order Kd V(2GKd V) equation is revisited via combined physical and mathematical methods. By using the Hirota perturbation expansion technique and via setting the nonzero backgr...The(2 + 1)-dimensional generalized fifth-order Kd V(2GKd V) equation is revisited via combined physical and mathematical methods. By using the Hirota perturbation expansion technique and via setting the nonzero background wave on the multiple soliton solution of the 2GKd V equation, breather waves are constructed, for which some transformed wave conditions are considered that yield abundant novel nonlinear waves including X/Y-Shaped(XS/YS),asymmetric M-Shaped(MS), W-Shaped(WS), Space-Curved(SC) and Oscillation M-Shaped(OMS) solitons. Furthermore, distinct nonlinear wave molecules and interactional structures involving the asymmetric MS, WS, XS/YS, SC solitons, and breathers, lumps are constructed after considering the corresponding existence conditions. The dynamical properties of the nonlinear molecular waves and interactional structures are revealed via analyzing the trajectory equations along with the change of the phase shifts.展开更多
In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite tim...This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite time to the mixed problems with respect to Neumann boundary and Dirichlet boundary for various nonlinear conditions and initial value conditions which usually meet.展开更多
Edinburgh Duck wave energy converter(ED WEC)has excellent energy extraction performance and shows a great potential to integrate with other marine structures.This paper aims to investigate its wave energy extraction p...Edinburgh Duck wave energy converter(ED WEC)has excellent energy extraction performance and shows a great potential to integrate with other marine structures.This paper aims to investigate its wave energy extraction performance as a WEC and wave attenuation performance as a protection method for shoreline or marine structures.The wave and ED WEC interactions in regular waves are modeled using the Star-CCM+software and verified by comparisons with published experimental results.The motion response,energy conversion efficiency,and transmission coefficient of the ED WEC with different attack angles,rotation center,and incident wave heights are investigated.Results indicate that the ED WEC with an attack angle of 42°and a rotation center of 0.55 m below the mean water line can achieve both good wave energy extraction and wave attenuation performances.The wave energy extraction and wave attenuation performance of the ED WEC decrease significantly with the increase of wave nonlinearity characterized by the wave steepness.This paper can guide the practical application of the ED WEC at the early stage of design.展开更多
The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied w...The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied with the boundary condition u=（u）/（υ）=0 onΩ and the initial condition u（x,0）=u0（x）,ut（x,0）=u1（x,0） in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method.展开更多
Installing the Edinburgh Duck Wave Energy Converter(ED WEC)on a floating breakwater provides a potential solution to reduce costs and improve the reliability of the ED WEC.To investigate the interactions between the E...Installing the Edinburgh Duck Wave Energy Converter(ED WEC)on a floating breakwater provides a potential solution to reduce costs and improve the reliability of the ED WEC.To investigate the interactions between the ED WEC and the breakwater,a two-dimensional numerical model of a hybrid WEC-breakwater system is established based on Star-CCM+Computational Fluid Dynamics(CFD)software.The wave energy extraction performance,wave attenuation performance,and wave forces on the breakwater of the hybrid system are compared with those of the corresponding single device.The effects of the initial attack angle,the distance between the WEC and the breakwater,and the incident wave height on the pitch motion,energy conversion efficiency,transmission coefficient,and wave forces on the breakwater of the hybrid system are analyzed.The results indicate that combing the ED WEC with a breakwater can improve the energy extraction performance of the ED WEC and reduce the wave forces on the breakwater in shorter-period waves.The conversion efficiency of the hybrid system with the initial attack angle of 42°is the largest in shorter-period waves,but is reduced with the increase of initial attack angle in longer-period waves.The wave attenuation performance of the hybrid system is determined by the draft of the breakwater.The distance between the WEC and the breakwater has little effect on the hybrid system.Wave energy extraction of the ED WEC of the hybrid system decreases significantly with the increase of the incident wave height.展开更多
The South China Sea is rich in wind and wave energy resources,and the wind-wave combined power generation device is currently in the concept research and development stage.In recent years,extreme sea conditions such a...The South China Sea is rich in wind and wave energy resources,and the wind-wave combined power generation device is currently in the concept research and development stage.In recent years,extreme sea conditions such as super typhoons have frequently occurred,which poses a serious challenge to the safety of offshore floating platforms.In view of the lack of safety analysis of wind-wave combined power generation devices in extreme sea conditions at present,this paper takes the OC4-WEC combined with semi-submersible wind turbine(Semi-OC4)and the oscillating buoy wave energy converter as the research object,and establishes a mesoscale WRF-SWANFVCOM(W-S-F)real-time coupling platform based on the model coupling Toolkit(MCT)to analyze the spatial and temporal evolution of wind-wave-current in offshore wind farms during the whole process of super typhoon“Rammasun”transit.Combined with the medium/small scale nested method,the flow field characteristics of OC4-WEC platform are analyzed.The results show that the simulation accuracy of the established W-S-F platform for typhoon track is 42.51%higher than that of the single WRF model.Under the action of typhoon-wave-current,the heave motion amplitude of OC4-WEC platform is reduced by 38.1%,the surge motion amplitude is reduced by 26.7%,and the pitch motion amplitude is reduced by 23.4%.展开更多
Abstract Recently,the numerical methods for long-time dynamics of PDEs with weak nonlinearity have received more and more attention.For the nonlinear Schrödinger equation(NLS)with wave operator(NLSW)and weak nonl...Abstract Recently,the numerical methods for long-time dynamics of PDEs with weak nonlinearity have received more and more attention.For the nonlinear Schrödinger equation(NLS)with wave operator(NLSW)and weak nonlinearity controlled by a small valueε∈(0,1],an exponential wave integrator Fourier pseudo-spectral(EWIFP)discretization has been developed(Guo et al.,2021)and proved to be uniformly accurate aboutεup to the time atΟ(1/ε^(2))However,the EWIFP method is not time symmetric and can not preserve the discrete energy.As we know,the time symmetry and energy-preservation are the important structural features of the true solution and we hope that this structure can be inherited along the numerical solution.In this work,we propose a time symmetric and energy-preserving exponential wave integrator Fourier pseudo-spectral(SEPEWIFP)method for the NLSW with periodic boundary conditions.Through rigorous error analysis,we establish uniform error bounds of the numerical solution atΟ(h^(mo)+ε^(2-βτ2))up to the time atΟ(1/ε^(β))forβ∈[0,2]where h andτare the mesh size and time step,respectively,and m0 depends on the regularity conditions.The tools for error analysis mainly include cut-off technique and the standard energy method.We also extend the results on error bounds,energy-preservation and time symmetry to the oscillatory NLSW with wavelength atΟ(1/ε^(2))in time which is equivalent to the NLSW with weak nonlinearity.Numerical experiments confirm that the theoretical results in this paper are correct.Our method is novel because that to the best of our knowledge there has not been any energy-preserving exponential wave integrator method for the NLSW.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
From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that ...From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions.展开更多
A total of 137 internal solitary waves （ISWs） are captured during a field experiment conducted in the deep basin west of the Luzon Strait （LS） from March to August, 2010. Mooring observations reveal that a fully d...A total of 137 internal solitary waves （ISWs） are captured during a field experiment conducted in the deep basin west of the Luzon Strait （LS） from March to August, 2010. Mooring observations reveal that a fully developed ISW owns a maximum westward velocity of more than 1.8 m/s and an amplitude of about 200 m. The ISWs in the South China Sea （SCS） are most active in July, which may be due to the strong stratification in summer. Most of the ISW episodes are detected around and after the 1st or 15th lunar day, indicating that the ISW in the SCS is triggered by astronomic tides. Half part of the observed ISWs were detected around 19：00 local time, which can be explained by the fact that type-a ISWs emerged in the evening at roughly the same time each day. The propagation direction of the ISWs and the astronomic tides in the LS show that the area south of the Batan Island is probably the main source region of the type-a ISWs, while the area south of Itbayat Island and south of the Batan Island is likely the main source region of the type-b ISWs observed at the mooring. Moreover, for the resonance of semidiurnal internal tides emitting from the double ridges in the LS, the underwater ridge south of the Itbayat Island and south of the Batan Island is believed to favor the generation of the energetic ISWs.展开更多
A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational r...A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Omega is divided into two subregions. In the near-field around a structure, Omega(2), the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-epsilon equations and numerically solved by the improved VOF method; whereas in the subregion Omega(1) (Omega(1) = Omega - Omega(2)) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.展开更多
基金financially supported by the National Key Research and Development Program of China(Grant Nos.2021YFB2600700 and 2022YFC3102302)the Central Public-Interest Scientific Institution Basal Research Fund(Grant No.Y221007)+2 种基金the National Natural Science Foundation of China(Grant No.52271274)the Key Laboratory of Ministry of Education for Coastal Disaster and Protection,Hohai University(Grant No.202205)the Key Project of NSFC-Shandong Joint Research Funding POW3C(Grant No.U1906230).
文摘The nonlinear variation of wave is commonly seen in nearshore area,and the resulting seabed response and liquefaction are of high concern to coastal engineers.In this study,an analytical formula considering the nonlinear wave skewness and asymmetry is adopted to provide wave pressure on the seabed surface.The liquefaction depth attenuation coefficient and width growth coefficient are defined to quantitatively characterize the nonlinear effect of wave on seabed liquefaction.Based on the 2D full dynamic model of wave-induced seabed response,a detailed parametric study is carried out in order to evaluate the influence of the nonlinear variation of wave loadings on seabed liquefaction.Further,new empirical prediction formulas are proposed to fast predict the maximum liquefaction under nonlinear wave.Results indicate that(1)Due to the influence of wave nonlinearity,the vertical transmission of negative pore water pressure in the seabed is hindered,and therefore,the amplitude decreases significantly.(2)In general,with the increase of wave nonlinearity,the liquefaction depth of seabed decreases gradually.Especially under asymmetric and skewed wave loading,the attenuation of maximum seabed liquefaction depth is the most significant among all the nonlinear wave conditions.However,highly skewed wave can cause the liquefaction depth of seabed greater than that under linear wave.(3)The asymmetry of wave pressure leads to the increase of liquefaction width,whereas the influence of skewedness is not significant.(4)Compared with the nonlinear waveform,seabed liquefaction is more sensitive to the variation of nonlinear degree of wave loading.
基金The Interdisciplinary Joint Research Projects of Tongji University,Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai).
文摘Nonlinear internal waves(NLIWs)exhibit robust dynamic submesoscale motions,connecting large-scale tides to smallscale shear instabilities in the ocean.Previous studies have mainly focused on their generation mechanisms and evolution along their paths.Considering their global distribution resulting from the primary origin in tide-topography interaction,there is an increasing cross-disciplinary interest in understanding how these energetic and ubiquitous NLIWs contribute to sediment redistribution in the ocean.This paper presents fundamental theories on NLIWs and comprehensively reviews triggering mechanisms,different types of instability,and sediment responses by summarizing recent theoretical parameterizations,numerical simulations,laboratory experiments,and in-situ observations.We specifically focus on elucidating various types of instability along with their impact on sediment dynamic processes.Finally,we outline several unresolved issues that require further exploration for a quantitative investigation into NLIWinduced sediment transfer in the ocean.
基金supported by the National Natural Science Foundation of China(No.12172321)。
文摘The nonlinear traveling wave vibration of rotating ferromagnetic functionally graded(FG)cylindrical shells under multi-physics fields is investigated.Grounded in the Kirchhoff-Love thin shell theory,the geometric nonlinearity is incorporated into the model,and the constitutive equations are derived.The physical parameters of functionally graded materials(FGMs),which exhibit continuous variation across the thickness gradient,are of particular interest.The nonlinear magneto-thermoelastic governing equations are derived in accord with Hamilton's principle.The nonlinear partial differential equations are discretized with the Galerkin method,and the analytical expression of traveling wave frequencies is derived with an approximate method.The accuracy of the proposed method is validated through the comparison with the results from the literature and numerical solutions.Finally,the visualization analyses are conducted to examine the effects of key parameters on the traveling wave frequencies.The results show that the factors including the power-law index,temperature,magnetic field intensity,and rotating speed have the coupling effects with respect to the nonlinear vibration behavior.
基金financially supported by the National Key R&D Program of China(No.2022YFC3104205)the National Natural Science Foundation of China(No.42377457).
文摘The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.
基金supported by the National Natural Science Foundation of China(No.12134002)。
文摘Acoustic nonlinearity holds potential as a method for assessing material stress.Analogous to the acoustoelastic effect,where the velocity of elastic waves is influenced by third-order elastic constants,the propagation of nonlinear acoustic waves in pre-stressed materials would be influenced by higher-order elastic constants.Despite this,there has been a notable absence of research exploring this phenomenon.Consequently,this paper aims to establish a theoretical framework for governing the propagation of nonlinear acoustic waves in pre-stressed materials.It delves into the impact of pre-stress on higher-order material parameters,and specifically examines the propagation of one-dimensional acoustic waves within the contexts of the uniaxial stress and the biaxial stress.This paper establishes a theoretical foundation for exploring the application of nonlinear ultrasonic techniques to measure pre-stress in materials.
文摘This paper studied the propagating characteristics of(2+1)-dimensional nonlinear ion acoustic waves in a multicomponent plasma with nonthermal electrons,positrons,and bipolar ions.The dispersion relations are initially explored by using the small amplitude wave's dispersion relation.Then,the Sagdeev potential method is employed to study large amplitude ion acoustic waves.The analysis involves examining the system's phase diagram,Sagdeev potential function,and solitary wave solutions through numerical solution of an analytical process in order to investigate the propagation properties of nonlinear ion acoustic waves under various parameters.It is found that the propagation of nonlinear ion acoustic waves is subject to the influence of various physical parameters,including the ratio of number densities between the unperturbed positrons,electrons to positive ions,nonthermal parameters,the mass ratio of positive ions to negative ions,and the charge number ratio of negative ions to positive ions,the ratio of the electrons'temperature to positrons'temperature.In addition,the multicomponent plasma system has a compressive solitary waves with amplitude greater than zero or a rarefactive solitary waves with amplitude less than zero,in the meantime,compressive and rarefactive ion acoustic wave characteristics depend on the charge number ratio of negative ions to positive ions.
基金supported by the National Students Training Program for Innovation(Grant No.202210007029)。
文摘How the state of living muscles modulates the features of nonlinear elastic waves generated by external dynamic loads remains unclear because of the challenge of directly observing and modeling nonlinear elastic waves in skeletal muscles in vivo,considering their active deformation behavior.Here,this important issue is addressed by combining experiments performed with an ultrafast ultrasound imaging system to track nonlinear shear waves(shear shock waves)in muscles in vivo and finite element analysis relying on a physically motivated constitutive model to study the effect of muscle activation level.Skeletal muscle was loaded with a deep muscle stimulator to generate shear shock waves(SSWs).The particle velocities,second and third harmonics,and group velocities of the SSWs in living muscles under both passive and active states were measured in vivo.Our experimental results reveal,for the first time,that muscle states have a pronounced effect on wave features;a low level of activation may facilitate the occurrence of both the second and third harmonics,whereas a high level of activation may inhibit the third harmonic.Finite element analysis was further carried out to quantitatively explore the effect of active muscle deformation behavior on the generation and propagation of SSWs.The simulation results at different muscle activation levels confirmed the experimental findings.The ability to reveal the effects of muscle state on the features of SSWs may be helpful in elucidating the unique dynamic deformation mechanism of living skeletal muscles,quantitatively characterizing diverse shock wave-based therapy instruments,and guiding the design of muscle-mimicking soft materials.
文摘The characteristics of nonlinear and supernonlinear Alfvén waves propagating in a multicomponent plasma composed of a double spectral electron distribution and positive and negative ions were investigated.The Sagdeev technique was employed,and an energy equation was derived.Our findings show that the proposed system reveals the existence of a double-layer solution,periodic,supersoliton,and superperiodic waves.The phase portrait and potential analysis related to these waves were investigated to study the main features of existing waves.It was also found that decreasing the electron temperature helps the superperiodic structure to be excited in our plasma model.Our results help interpret the nonlinear and supernonlinear features of the recorded Alfvén waves propagating in the ionosphere D-region.
基金provided by the National Natural Science Foundation of China (Grant No. 12271324)the Natural Science Basic Research Program of Shaanxi Province (Grant No. 2024JC-YBQN-0069)+2 种基金the China Postdoctoral Science Foundation (Grant No. 2024M751921)the 2023 Shaanxi Province Postdoctoral Research Project (Grant No.2023BSHEDZZ186)the Fundamental Research Funds for the Central Universities (Grant No. 1301032598)。
文摘The(2 + 1)-dimensional generalized fifth-order Kd V(2GKd V) equation is revisited via combined physical and mathematical methods. By using the Hirota perturbation expansion technique and via setting the nonzero background wave on the multiple soliton solution of the 2GKd V equation, breather waves are constructed, for which some transformed wave conditions are considered that yield abundant novel nonlinear waves including X/Y-Shaped(XS/YS),asymmetric M-Shaped(MS), W-Shaped(WS), Space-Curved(SC) and Oscillation M-Shaped(OMS) solitons. Furthermore, distinct nonlinear wave molecules and interactional structures involving the asymmetric MS, WS, XS/YS, SC solitons, and breathers, lumps are constructed after considering the corresponding existence conditions. The dynamical properties of the nonlinear molecular waves and interactional structures are revealed via analyzing the trajectory equations along with the change of the phase shifts.
文摘In this paper the decay of global solutions to some nonlinear dissipative wave equations are discussed, which based on the method of prior estimate technique and a differenece inequality.
文摘This paper deals with the initial-boundary value mixed problems for nonlinear wave equations. By introducing the 'blowing-up facts K(u,u_i)', We may discuss the blowing up behaviours of solutions in finite time to the mixed problems with respect to Neumann boundary and Dirichlet boundary for various nonlinear conditions and initial value conditions which usually meet.
基金financially supported by the National Natural Science Foundation of China(Grant No.52071096)the Student Research and Innovation Fund of the Fundamental Research Funds for the Central Universities(Grant No.3072020GIP0105).
文摘Edinburgh Duck wave energy converter(ED WEC)has excellent energy extraction performance and shows a great potential to integrate with other marine structures.This paper aims to investigate its wave energy extraction performance as a WEC and wave attenuation performance as a protection method for shoreline or marine structures.The wave and ED WEC interactions in regular waves are modeled using the Star-CCM+software and verified by comparisons with published experimental results.The motion response,energy conversion efficiency,and transmission coefficient of the ED WEC with different attack angles,rotation center,and incident wave heights are investigated.Results indicate that the ED WEC with an attack angle of 42°and a rotation center of 0.55 m below the mean water line can achieve both good wave energy extraction and wave attenuation performances.The wave energy extraction and wave attenuation performance of the ED WEC decrease significantly with the increase of wave nonlinearity characterized by the wave steepness.This paper can guide the practical application of the ED WEC at the early stage of design.
文摘The existence and the nonexistence,the uniqueness and the energy decay estimate of solution for the fourth-order nonlinear wave equation utt＋αΔ2 u-bΔut-βΔu＋ut｜ut｜^r＋g（u）=0 in Ω×（0,∞） are studied with the boundary condition u=（u）/（υ）=0 onΩ and the initial condition u（x,0）=u0（x）,ut（x,0）=u1（x,0） in bounded domain ΩR^n ,n≥1.The energy decay rate of the global solution is estimated by the multiplier method.The blow-up result of the solution in finite time is established by the ideal of a potential well theory,and the existence of the solution is gotten by the Galekin approximation method.
基金financially supported by the National Natural Science Foundation of China (Grant No. 52071096)the Student Research and Innovation Fund of the Fundamental Research Funds for the Central Universities (Grant No. 3072020GIP0105)。
文摘Installing the Edinburgh Duck Wave Energy Converter(ED WEC)on a floating breakwater provides a potential solution to reduce costs and improve the reliability of the ED WEC.To investigate the interactions between the ED WEC and the breakwater,a two-dimensional numerical model of a hybrid WEC-breakwater system is established based on Star-CCM+Computational Fluid Dynamics(CFD)software.The wave energy extraction performance,wave attenuation performance,and wave forces on the breakwater of the hybrid system are compared with those of the corresponding single device.The effects of the initial attack angle,the distance between the WEC and the breakwater,and the incident wave height on the pitch motion,energy conversion efficiency,transmission coefficient,and wave forces on the breakwater of the hybrid system are analyzed.The results indicate that combing the ED WEC with a breakwater can improve the energy extraction performance of the ED WEC and reduce the wave forces on the breakwater in shorter-period waves.The conversion efficiency of the hybrid system with the initial attack angle of 42°is the largest in shorter-period waves,but is reduced with the increase of initial attack angle in longer-period waves.The wave attenuation performance of the hybrid system is determined by the draft of the breakwater.The distance between the WEC and the breakwater has little effect on the hybrid system.Wave energy extraction of the ED WEC of the hybrid system decreases significantly with the increase of the incident wave height.
基金jointly funded by the National Key Research and Development Projects(No.2017YFE0132000)the National Natural Science Foundation of China(Nos.5211101879,52078251,52108456)the Natural Science Foundation of Jiangsu Province(Nos.BK20211518,BK20210309)
文摘The South China Sea is rich in wind and wave energy resources,and the wind-wave combined power generation device is currently in the concept research and development stage.In recent years,extreme sea conditions such as super typhoons have frequently occurred,which poses a serious challenge to the safety of offshore floating platforms.In view of the lack of safety analysis of wind-wave combined power generation devices in extreme sea conditions at present,this paper takes the OC4-WEC combined with semi-submersible wind turbine(Semi-OC4)and the oscillating buoy wave energy converter as the research object,and establishes a mesoscale WRF-SWANFVCOM(W-S-F)real-time coupling platform based on the model coupling Toolkit(MCT)to analyze the spatial and temporal evolution of wind-wave-current in offshore wind farms during the whole process of super typhoon“Rammasun”transit.Combined with the medium/small scale nested method,the flow field characteristics of OC4-WEC platform are analyzed.The results show that the simulation accuracy of the established W-S-F platform for typhoon track is 42.51%higher than that of the single WRF model.Under the action of typhoon-wave-current,the heave motion amplitude of OC4-WEC platform is reduced by 38.1%,the surge motion amplitude is reduced by 26.7%,and the pitch motion amplitude is reduced by 23.4%.
基金supported in part by the Natural Science Foundation of Hebei Province(Grant No.A2021205036).
文摘Abstract Recently,the numerical methods for long-time dynamics of PDEs with weak nonlinearity have received more and more attention.For the nonlinear Schrödinger equation(NLS)with wave operator(NLSW)and weak nonlinearity controlled by a small valueε∈(0,1],an exponential wave integrator Fourier pseudo-spectral(EWIFP)discretization has been developed(Guo et al.,2021)and proved to be uniformly accurate aboutεup to the time atΟ(1/ε^(2))However,the EWIFP method is not time symmetric and can not preserve the discrete energy.As we know,the time symmetry and energy-preservation are the important structural features of the true solution and we hope that this structure can be inherited along the numerical solution.In this work,we propose a time symmetric and energy-preserving exponential wave integrator Fourier pseudo-spectral(SEPEWIFP)method for the NLSW with periodic boundary conditions.Through rigorous error analysis,we establish uniform error bounds of the numerical solution atΟ(h^(mo)+ε^(2-βτ2))up to the time atΟ(1/ε^(β))forβ∈[0,2]where h andτare the mesh size and time step,respectively,and m0 depends on the regularity conditions.The tools for error analysis mainly include cut-off technique and the standard energy method.We also extend the results on error bounds,energy-preservation and time symmetry to the oscillatory NLSW with wavelength atΟ(1/ε^(2))in time which is equivalent to the NLSW with weak nonlinearity.Numerical experiments confirm that the theoretical results in this paper are correct.Our method is novel because that to the best of our knowledge there has not been any energy-preserving exponential wave integrator method for the NLSW.
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).
文摘From the nonlinear sine-Gordon equation, new transformations are obtained in this paper, which are applied to propose a new approach to construct exact periodic solutions to nonlinear wave equations. It is shown that more new periodic solutions can be obtained by this new approach, and more shock wave solutions or solitary wave solutions can be got under their limit conditions.
基金The Program for New Century Excellent Talents in Universities of China under contract No.NCET-10-0764the National High Tech-nology Research and Development(863)Program of China under contract No.2013AA09A502the National Natural Science Foundation of China under contract Nos 41176010,91028008,40890153,41176008 and 40776005
文摘A total of 137 internal solitary waves （ISWs） are captured during a field experiment conducted in the deep basin west of the Luzon Strait （LS） from March to August, 2010. Mooring observations reveal that a fully developed ISW owns a maximum westward velocity of more than 1.8 m/s and an amplitude of about 200 m. The ISWs in the South China Sea （SCS） are most active in July, which may be due to the strong stratification in summer. Most of the ISW episodes are detected around and after the 1st or 15th lunar day, indicating that the ISW in the SCS is triggered by astronomic tides. Half part of the observed ISWs were detected around 19：00 local time, which can be explained by the fact that type-a ISWs emerged in the evening at roughly the same time each day. The propagation direction of the ISWs and the astronomic tides in the LS show that the area south of the Batan Island is probably the main source region of the type-a ISWs, while the area south of Itbayat Island and south of the Batan Island is likely the main source region of the type-b ISWs observed at the mooring. Moreover, for the resonance of semidiurnal internal tides emitting from the double ridges in the LS, the underwater ridge south of the Itbayat Island and south of the Batan Island is believed to favor the generation of the energetic ISWs.
基金Trans-Century Training program Fund for the Talent,Ministry of Education of China
文摘A composite model, which is the combination of Boussinesq equations and Volume of Fluid (VOF) method, has been developed for 2-D time-domain computations of nonlinear waves in a large region. The whole computational region Omega is divided into two subregions. In the near-field around a structure, Omega(2), the flow is governed by 2-D Reynolds Averaged Navier-Stokes equations with a turbulence closure model of k-epsilon equations and numerically solved by the improved VOF method; whereas in the subregion Omega(1) (Omega(1) = Omega - Omega(2)) the flow is governed by one-D Boussinesq equations and numerically solved with the predictor-corrector algorithm. The velocity and the wave surface elevation are matched on the common boundary of the two subregions. Numerical tests have been conducted for the case of wave propagation and interaction with a wave barrier. It is shown that the composite model can help perform efficient computation of nonlinear waves in a large region with the complicated flow fields near structures taken into account.
