Accurate simulation of the evolution of freak waves by the wave phase focusing method requires accurate linear and nonlinear properties,especially in deep-water conditions.In this paper,we analyze the ability to simul...Accurate simulation of the evolution of freak waves by the wave phase focusing method requires accurate linear and nonlinear properties,especially in deep-water conditions.In this paper,we analyze the ability to simulate deep-water focused waves of a two-layer Boussinesq-type(BT)model,which has been shown to have excellent linear and nonlinear performance.To further improve the numerical accuracy and stability,the internal wavegenerated method is introduced into the two-layer Boussinesq-type model.Firstly,the sensitivity of the numerical results to the grid resolution is analyzed to verify the convergence of the model;secondly,the focused wave propagating in two opposite directions is simulated to prove the symmetry of the numerical results and the feasibility of the internal wave-generated method;thirdly,the limiting focused wave condition is simulated to compare and analyze the wave surface and the horizontal velocity of the profile at the focusing position,which is in good agreement with the measured values.Meanwhile the simulation of focused waves in very deep waters agrees well with the measured values,which further demonstrates the capability of the two-layer BT model in simulating focused waves in deep waters.展开更多
Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house C...Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional（2-D） box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile（CIP）-based Cartesian grid model, in which a more accurate VOF（Volume of Fluid） method, the THINC/SW scheme（THINC： tangent of hyperbola for interface capturing; SW： Slope Weighting）, is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.展开更多
Accurate simulation of the horizontal-two-dimension(H2D)focused wave group in deep water requires high accuracy of a numerical model.The two-layer Boussinesq-type model(Liu and Fang,2016;Liu et al.,2018)with the highe...Accurate simulation of the horizontal-two-dimension(H2D)focused wave group in deep water requires high accuracy of a numerical model.The two-layer Boussinesq-type model(Liu and Fang,2016;Liu et al.,2018)with the highest spatial derivative of 2 has high accuracy in both linear and nonlinear properties.Based on the further development of the velocity equations(Liu et al.,2023),the H2D numerical model for water waves is established with the prediction-correction-iteration model in the finite difference method,and a composite fourth-order Adams-Bashforth-Moulton scheme is used for time integration.The wave generation method proposed by Hsiao et al.(2005)is applied and calibrated in this H2D model.The numerical calculations lead to the following three main conclusions:First,compared with the analytical solution of Stokes linear waves,the calculated velocity profiles show higher accuracy by using the improved velocity formulas.Second,the simulations of the focused multidirectional wave group are carried out,and good agreements are found,demonstrating that the present H2D numerical model shows high accuracy in simulating focused multidirectional wave groups,and the effectiveness of the improved velocity formulas is also validated.Furthermore,the velocity profiles throughout the computational domain at the time of maximum wave crest are given.Finally,the FFT method is used to obtain the amplitude with different frequencies for several locations,and the changes of the wavelet energy spectrum at different locations are presented for several cases.展开更多
This paper presents a numerical study on the high-frequency wave loads and ringing response of offshore wind turbine foundations exposed to moderately steep transient water waves.Input wave groups are generated by the...This paper presents a numerical study on the high-frequency wave loads and ringing response of offshore wind turbine foundations exposed to moderately steep transient water waves.Input wave groups are generated by the technique of frequency-focusing,and the numerical simulation of focused waves is based on the NewWave model and a Fourier time-stepping procedure.The proposed model is validated by comparison with the published laboratory data.In respect of both the wave elevations and the underlying water particle kinematics,the numerical results are in excellent agreement with the experimental data.Furthermore,the local evolution of power spectra and the transfer of energy into higher frequencies can be clearly identified.Then the generalized FNV theory and Rainey’s model are applied respectively to calculate the nonlinear wave loads on a bottom-hinged vertical cylinder in focused waves.Resonant ringing response excited by the nonlinear high-frequency wave loads is found in the numerical simulation when frequency ratios(natural frequency of the structure to peak frequency of wave spectra)are equal to 3–5.Dynamic amplification factor of ringing response is also investigated for different dynamic properties(natural frequency and damping ratio)of the structure.展开更多
Rogue waves pose a significant threat to the safety of ships and offshore structures,making it crucial to understand their physical mechanisms,such as spatial-temporal focusing,which can lead to their formation.This s...Rogue waves pose a significant threat to the safety of ships and offshore structures,making it crucial to understand their physical mechanisms,such as spatial-temporal focusing,which can lead to their formation.This study investigates three-dimensional focused waves using the newly developed deep-water high-level Green-Naghdi(HLGN)model.Through numerical simulations,we evaluate the selection of the involved wave numbers within the HLGN model and present the algorithm for the three-dimensional implementation.Validation of the model is conducted through numerical reproduction of the three-dimensional focused waves considered in other’s laboratory measurements.The simulated wave profiles and velocity fields are compared with experimental data,demonstrating strong agreement.Discussion is provided about the robustness and accuracy of the HLGN model in simulating three-dimensional focused waves under deep-water conditions.展开更多
This paper explores the phenomenon of fluid resonance occurring within a narrow gap between a vessel and a vertical wharf, taking ships berthing in front of a gravity wharf as the research background. Using the open-s...This paper explores the phenomenon of fluid resonance occurring within a narrow gap between a vessel and a vertical wharf, taking ships berthing in front of a gravity wharf as the research background. Using the open-source software Open FOAM~?, a two-dimensional viscous-flow numerical wave flume was developed to simulate the fluid resonant motions induced by transient focused wave groups with different spectral peak periods and wave amplitudes. The results indicate that for all the incident focused wave amplitudes considered, the amplitudes of the free surface elevation in the gap, horizontal wave force and moment all exhibit a bimodal variation trend with increasing spectral peak period. The peak values of the above amplitude-period curve appear near the resonant period of the first and second harmonic components of the free surface elevation. However, the variation in the vertical wave force versus the spectral peak period presents different patterns. In addition, the first-to fourth-order harmonic components in the wave surface and forces are further examined via the four-phase combination method. The results show that the first-to secondorder harmonic components play a dominant role in the overall amplitude.展开更多
Efficient elastic wave focusing is crucial in materials and physical engineering.Elastic coding metasurfaces,which are innovative planar artificial structures,show great potential for use in the field of wave focusing...Efficient elastic wave focusing is crucial in materials and physical engineering.Elastic coding metasurfaces,which are innovative planar artificial structures,show great potential for use in the field of wave focusing.However,elastic coding lenses(ECLs)still suffer from low focusing performance,thickness comparable to wavelength,and frequency sensitivity.Here,we consider both the structural and material properties of the coding unit,thus realizing further compression of the thickness of the ECL.We chose the simplest ECL,which consists of only two encoding units.The coding unit 0 is a straight structure constructed using a carbon fiber reinforced composite material,and the coding unit 1 is a zigzag structure constructed using an aluminum material,and the thickness of the ECL constructed using them is only 1/8 of the wavelength.Based on the theoretical design,the arrangement of coding units is further optimized using genetic algorithms,which significantly improves the focusing performance of the lens at different focus and frequencies.This study provides a more effective way to control vibration and noise in advanced structures.展开更多
A two-dimensional numerical wave flume is developed to study the focused waves group propagation and the consequent breaking processes. The numerical model is based on the Reynolds-Averaged Navier-Stokes （PANS） equa...A two-dimensional numerical wave flume is developed to study the focused waves group propagation and the consequent breaking processes. The numerical model is based on the Reynolds-Averaged Navier-Stokes （PANS） equations, with the standard k - c turbulence model to simulate the turbulence effects. To track the complicated and broken free-surface, the Volume Of Fluid （VOF） method is employed. The numerical model combines the ＂Partial Cell Treatment （PCT）＂ method with the ＂Locally Relative Stationary （LRS）＂ concept to treat the moving wave paddle so that various waves can be generated directly in a fixed Cartesian grid system. The theoretical results of the linear and nonlinear waves are used to validate the numerical wave flume firstly, and then a plunging breaking wave created by a focused waves group is simulated. The numerical results are compared to the experimental data and other simulation results, with very good agreements. The turbulence intensity, the flow field and the energy dissipation in the breaking processes are analyzed based on the numerical results. It is shown that the present numerical model is efficient and accurate for studying the waves group generation, the waves packet propagation, and the wave breaking processes.展开更多
A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations....A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.展开更多
The current study investigates the hydrodynamic characteristics of gap resonance within a narrow gap formed by two adjacent boxes subjected to incident focused transient wave groups.A two-dimensional(2D)numerical wave...The current study investigates the hydrodynamic characteristics of gap resonance within a narrow gap formed by two adjacent boxes subjected to incident focused transient wave groups.A two-dimensional(2D)numerical wave tank based on the OpenFOAM package is utilized for this purpose.The weather-side box is fixed while the lee-side box is allowed to heave freely under wave actions.The effects of the focused wave amplitude and spectral peak period on the wave amplification within the gap,motion of the lee-side box,and wave forces(including horizontal and vertical wave forces)acting on each box are systematically examined.For comparison,another structural layout consisting of two fixed boxes is also considered.The results reveal that the release of the heave degree of freedom(DoF)of the lee-side box results in remarkably distinct resonance features.In the heave-box system,both its fluid resonant period and the period corresponding to the maximum heave displacement of the lee-side box are significantly larger(i.e.,1.6-1.7 times)than the fluid resonant period of the fixed-box system.However,the wave amplification factor inside the gap in the heave-box system is significantly lower than that in the fixed-box one.Both the variations of the maximum horizontal and vertical wave forces with the spectral peak period and their magnitudes are also significantly different between the two structural systems.展开更多
A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Enlerian-Lagrangian formulation is adopted and a higher-order boundary element metho...A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Enlerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The botmdary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.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
An experimental scheme for the generation of directional focusing waves in a wave basin is established in this paper. The effects of the directional range, frequency width and center frequency on the wave focusing are...An experimental scheme for the generation of directional focusing waves in a wave basin is established in this paper. The effects of the directional range, frequency width and center frequency on the wave focusing are studied. The distribution of maximum amplitude and the evolution of time series and spectra during wave packet propagation and the variation of water surface parameters are extensively investigated. The results reveal that the characteristics of focusing waves are significantly influenced by wave directionality and that the breaking criteria for directional waves are distinctly different from those for unidirectional waves.展开更多
Four focusing models for generation of freak waves are presented. An extreme wave focusing model is presented on the basis of the enhanced High-Order Spectral （HOS） method and the importance of the nonlinear wave-wa...Four focusing models for generation of freak waves are presented. An extreme wave focusing model is presented on the basis of the enhanced High-Order Spectral （HOS） method and the importance of the nonlinear wave-wave interaction is evaluated by comparison of the calculated results with experimental and theoretical data. Based on the modification of the Longuet-Higgins model, four wave models for generation of freak waves （a. extreme wave model ＋ random wave model; b. extreme wave model ＋ regular wave model; e. phase interval modulation wave focusing model; d. number modulation wave focusing model with the same phase） are proposed. By use of different energy distribution techniques in the four models, freak wave events are obtained with different Hmax/Hs in finite space and time.展开更多
Two-dimensional focusing waves are generated and investigated by numerical method. The numerical model is developed by introducing the wave maker boundary on the high-order spectral （HOS） method proposed by Dommermu...Two-dimensional focusing waves are generated and investigated by numerical method. The numerical model is developed by introducing the wave maker boundary on the high-order spectral （HOS） method proposed by Dommermuth and Yue in 1987 and verified by theoretical and experimental data. Some cases of focusing waves considering different parameters such as assumed focusing amplitudes, frequency bandwidth, central frequency and frequency spectrum are generated. Characteristics of the focusing wave including surface elevations, the maximum crest, shift of focusing points and frequency spectra are discussed. The results show that the focusing wave characteristics are strongly affected by focusing amplitudes, frequency bandwidth, central frequency and frequency spectrum.展开更多
Freak waves are generated based on the mechanism of wave focusing in a 2D numerical wave tank. To set up the nonlinear numerical wave tank, the Boundary Element Method is used to solve potential flow equations incorpo...Freak waves are generated based on the mechanism of wave focusing in a 2D numerical wave tank. To set up the nonlinear numerical wave tank, the Boundary Element Method is used to solve potential flow equations incorporated with fully nonlinear free surface boundary conditions. The nonlinear properties of freak waves, such as high frequency components and wave profile asymmetry, are discussed. The kinematic data, which can be useful for the evaluation of the wave forces exerted on structures to avoid underestimation of linear predictions, are obtained, and discussed, from the simulated results of freak waves.展开更多
Based on the Longuet-Higgins wave model theory, the previews studies have shown that freak waves can be generated in finite space and time successfully. However, as to generating high nonlinear freak waves, the simula...Based on the Longuet-Higgins wave model theory, the previews studies have shown that freak waves can be generated in finite space and time successfully. However, as to generating high nonlinear freak waves, the simulation results will be unrealistic. Therefore, a modified phase modulation method for simulating high nonlinear freak waves was developed. The surface elevations of some wave components at certain time and place are positive by modulating the corresponding random initial phases, then the total surface elevation at the focused point is enhanced and furthermore a freak wave event is generated. The new method can not only make the freak wave occur at certain time and place, but also make the simulated wave surface time series satisfy statistical properties of the realistic sea state and keep identical with the target wave spectrum. This numerical approach is of good precision and high efficiency by the comparisons of the simulated freak waves and the recorded freak waves.展开更多
On the basis of the transient water wave(TWW) theory,focused wave is generated in the circulating water channel.Numerical simulation of the focused wave is carried out by solving the Reynolds averaged NavierStokes(RAN...On the basis of the transient water wave(TWW) theory,focused wave is generated in the circulating water channel.Numerical simulation of the focused wave is carried out by solving the Reynolds averaged NavierStokes(RANS) equations.The dynamic grid technique is adopted to simulate the motion of the wave maker,and the volume of fluid(VOF) method is used to capture the free surface of the wave.The simulation results are compared with the measured data,and good agreement is obtained.For quantitative estimation of the numerical simulation error and uncertainty,the uncertainty analysis method recommended by the International Towing Tank Conference(ITTC) procedure is performed for the simulation results of the surface elevations at different positions.Both grid-convergence and time-step-size convergence studies are conducted using three types of grids and time step sizes.The simulation results are all monotonously convergent in the verification procedure,and the validations of the simulated surface elevations with the positions at 3.5,4.0 and 4.5 m are all achieved by comparing with the validation uncertainty.It is found that the numerical simulation errors caused by the grid and time-step-size in the convergence studies have the same order of magnitude.In addition,the numerical errors and uncertainties for the surface elevations at different positions are compared and discussed in detail.This paper presents the first attempt to carry out the uncertainty analysis of the simulation of focused wave,and the effectiveness of the proposed verification and validation procedures in the uncertainty analysis is demonstrated.展开更多
In this paper, a numerical model for nonlinear wave propagation in currents is formulated by a set of enhanced fully nonlinear Boussinesq equations with ambient currents. This model is verified by comparison with the ...In this paper, a numerical model for nonlinear wave propagation in currents is formulated by a set of enhanced fully nonlinear Boussinesq equations with ambient currents. This model is verified by comparison with the published results. Then the influence of currents on nonlinear focusing waves is studied by use of the numerical model. It is found that the effect of currents on the surface elevations at the fecal location is negligible. Following currents can augment the maximum crest of focusing wave while decrease the focusing time, and vice versa for opposing currents. Furthermore, both opposing and following currents can shift the focal location forward relative to that in quiescent water.展开更多
A numerical wave flume with fully nonlinear free surface boundary conditions is adopted to investigate the temporal characteristics of extreme waves in the presence of wind at various speeds. Incident wave trains are ...A numerical wave flume with fully nonlinear free surface boundary conditions is adopted to investigate the temporal characteristics of extreme waves in the presence of wind at various speeds. Incident wave trains are numerically generated by a piston-type wave maker, and the wind-excited pressure is introduced into dynamic boundary conditions using a pressure distribution over steep crests, as defined by Jeffreys＇ sheltering mechanism.A boundary value problem is solved by a higher-order boundary element method（HOBEM） and a mixed Eulerian-Lagrangian time marching scheme. The proposed model is validated through comparison with published experimental data from a focused wave group. The influence of wind on extreme wave properties,including maximum extreme wave crest, focal position shift, and spectrum evolution, is also studied. To consider the effects of the wind-driven currents on a wave evolution, the simulations assume a uniform current over varying water depth. The results show that wind causes weak increases in the extreme wave crest, and makes the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide a comparison to demonstrate the shifts at focal points, considering the combined effects of the winds and the wind-driven currents.展开更多
基金The National Natural Science Foundation under contract Nos 52171247,51779022,52071057,and 51709054.
文摘Accurate simulation of the evolution of freak waves by the wave phase focusing method requires accurate linear and nonlinear properties,especially in deep-water conditions.In this paper,we analyze the ability to simulate deep-water focused waves of a two-layer Boussinesq-type(BT)model,which has been shown to have excellent linear and nonlinear performance.To further improve the numerical accuracy and stability,the internal wavegenerated method is introduced into the two-layer Boussinesq-type model.Firstly,the sensitivity of the numerical results to the grid resolution is analyzed to verify the convergence of the model;secondly,the focused wave propagating in two opposite directions is simulated to prove the symmetry of the numerical results and the feasibility of the internal wave-generated method;thirdly,the limiting focused wave condition is simulated to compare and analyze the wave surface and the horizontal velocity of the profile at the focusing position,which is in good agreement with the measured values.Meanwhile the simulation of focused waves in very deep waters agrees well with the measured values,which further demonstrates the capability of the two-layer BT model in simulating focused waves in deep waters.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51209184 and 51479175)Zhejiang Provincial Natural Science Foundation of China(Grant No.LR16E090002)the Open Foundation of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering(Grant No.2013490211)
文摘Floating structures are commonly seen in coastal and offshore engineering. They are often subjected to extreme waves and, therefore, their nonlinear dynamic behaviors are of great concern. In this paper, an in-house CFD code is developed to investigate the accurate prediction of nonlinear dynamic behaviors of a two-dimensional（2-D） box-shaped floating structure in focused waves. Computations are performed by an enhanced Constrained Interpolation Profile（CIP）-based Cartesian grid model, in which a more accurate VOF（Volume of Fluid） method, the THINC/SW scheme（THINC： tangent of hyperbola for interface capturing; SW： Slope Weighting）, is used for interface capturing. A focusing wave theory is used for the focused wave generation. The wave component of constant steepness is chosen. Comparisons between predictions and physical measurements show good agreement including body motions and free surface profiles. Although the overall agreement is good, some discrepancies are observed for impact pressure on the superstructure due to water on deck. The effect of grid resolution on the results is checked. With a fine grid, no obvious improvement is seen in the global body motions and impact pressures due to water on deck. It is concluded that highly nonlinear phenomena, such as distorted free surface, large-amplitude body motions, and violent impact flow, have been predicted successfully.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.52171247,51779022,52071057,51709054)the National Key Research and Development Program of China(Grant No.2022YFC3106101)。
文摘Accurate simulation of the horizontal-two-dimension(H2D)focused wave group in deep water requires high accuracy of a numerical model.The two-layer Boussinesq-type model(Liu and Fang,2016;Liu et al.,2018)with the highest spatial derivative of 2 has high accuracy in both linear and nonlinear properties.Based on the further development of the velocity equations(Liu et al.,2023),the H2D numerical model for water waves is established with the prediction-correction-iteration model in the finite difference method,and a composite fourth-order Adams-Bashforth-Moulton scheme is used for time integration.The wave generation method proposed by Hsiao et al.(2005)is applied and calibrated in this H2D model.The numerical calculations lead to the following three main conclusions:First,compared with the analytical solution of Stokes linear waves,the calculated velocity profiles show higher accuracy by using the improved velocity formulas.Second,the simulations of the focused multidirectional wave group are carried out,and good agreements are found,demonstrating that the present H2D numerical model shows high accuracy in simulating focused multidirectional wave groups,and the effectiveness of the improved velocity formulas is also validated.Furthermore,the velocity profiles throughout the computational domain at the time of maximum wave crest are given.Finally,the FFT method is used to obtain the amplitude with different frequencies for several locations,and the changes of the wavelet energy spectrum at different locations are presented for several cases.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51879039 and 51490672)。
文摘This paper presents a numerical study on the high-frequency wave loads and ringing response of offshore wind turbine foundations exposed to moderately steep transient water waves.Input wave groups are generated by the technique of frequency-focusing,and the numerical simulation of focused waves is based on the NewWave model and a Fourier time-stepping procedure.The proposed model is validated by comparison with the published laboratory data.In respect of both the wave elevations and the underlying water particle kinematics,the numerical results are in excellent agreement with the experimental data.Furthermore,the local evolution of power spectra and the transfer of energy into higher frequencies can be clearly identified.Then the generalized FNV theory and Rainey’s model are applied respectively to calculate the nonlinear wave loads on a bottom-hinged vertical cylinder in focused waves.Resonant ringing response excited by the nonlinear high-frequency wave loads is found in the numerical simulation when frequency ratios(natural frequency of the structure to peak frequency of wave spectra)are equal to 3–5.Dynamic amplification factor of ringing response is also investigated for different dynamic properties(natural frequency and damping ratio)of the structure.
基金Project supported by the National Natural Science Foundation of China(Grant No.12172099).
文摘Rogue waves pose a significant threat to the safety of ships and offshore structures,making it crucial to understand their physical mechanisms,such as spatial-temporal focusing,which can lead to their formation.This study investigates three-dimensional focused waves using the newly developed deep-water high-level Green-Naghdi(HLGN)model.Through numerical simulations,we evaluate the selection of the involved wave numbers within the HLGN model and present the algorithm for the three-dimensional implementation.Validation of the model is conducted through numerical reproduction of the three-dimensional focused waves considered in other’s laboratory measurements.The simulated wave profiles and velocity fields are compared with experimental data,demonstrating strong agreement.Discussion is provided about the robustness and accuracy of the HLGN model in simulating three-dimensional focused waves under deep-water conditions.
基金financially supported by the National Natural Science Foundation of China (Grant No. 52371277)the State Key Laboratory of Hydraulic Engineering Intelligent Construction and Operation (Tianjin University)(Grant No. HESS-2323)+2 种基金the Postgraduate Research&Practice Innovation Program of Jiangsu Province (Grant No. KYCX24_4071)the Guangdong Basic and Applied Basic Research Foundation (Grant No. 2023A1515010890)the Open foundation of Key Laboratory of Port.Waterway&Sedimentation Engineering (Grant No. Yk224001-1)。
文摘This paper explores the phenomenon of fluid resonance occurring within a narrow gap between a vessel and a vertical wharf, taking ships berthing in front of a gravity wharf as the research background. Using the open-source software Open FOAM~?, a two-dimensional viscous-flow numerical wave flume was developed to simulate the fluid resonant motions induced by transient focused wave groups with different spectral peak periods and wave amplitudes. The results indicate that for all the incident focused wave amplitudes considered, the amplitudes of the free surface elevation in the gap, horizontal wave force and moment all exhibit a bimodal variation trend with increasing spectral peak period. The peak values of the above amplitude-period curve appear near the resonant period of the first and second harmonic components of the free surface elevation. However, the variation in the vertical wave force versus the spectral peak period presents different patterns. In addition, the first-to fourth-order harmonic components in the wave surface and forces are further examined via the four-phase combination method. The results show that the first-to secondorder harmonic components play a dominant role in the overall amplitude.
基金Project supported by the National Natural Science Foundation of China(Grant No.12404531)the Natural Science Foundation of the Higher Education Institutions of Jiangsu Province,China(Grant No.23KJB140011)。
文摘Efficient elastic wave focusing is crucial in materials and physical engineering.Elastic coding metasurfaces,which are innovative planar artificial structures,show great potential for use in the field of wave focusing.However,elastic coding lenses(ECLs)still suffer from low focusing performance,thickness comparable to wavelength,and frequency sensitivity.Here,we consider both the structural and material properties of the coding unit,thus realizing further compression of the thickness of the ECL.We chose the simplest ECL,which consists of only two encoding units.The coding unit 0 is a straight structure constructed using a carbon fiber reinforced composite material,and the coding unit 1 is a zigzag structure constructed using an aluminum material,and the thickness of the ECL constructed using them is only 1/8 of the wavelength.Based on the theoretical design,the arrangement of coding units is further optimized using genetic algorithms,which significantly improves the focusing performance of the lens at different focus and frequencies.This study provides a more effective way to control vibration and noise in advanced structures.
基金supported by the National Natural Science Foundation of China(Grant No.51061130547)
文摘A two-dimensional numerical wave flume is developed to study the focused waves group propagation and the consequent breaking processes. The numerical model is based on the Reynolds-Averaged Navier-Stokes （PANS） equations, with the standard k - c turbulence model to simulate the turbulence effects. To track the complicated and broken free-surface, the Volume Of Fluid （VOF） method is employed. The numerical model combines the ＂Partial Cell Treatment （PCT）＂ method with the ＂Locally Relative Stationary （LRS）＂ concept to treat the moving wave paddle so that various waves can be generated directly in a fixed Cartesian grid system. The theoretical results of the linear and nonlinear waves are used to validate the numerical wave flume firstly, and then a plunging breaking wave created by a focused waves group is simulated. The numerical results are compared to the experimental data and other simulation results, with very good agreements. The turbulence intensity, the flow field and the energy dissipation in the breaking processes are analyzed based on the numerical results. It is shown that the present numerical model is efficient and accurate for studying the waves group generation, the waves packet propagation, and the wave breaking processes.
基金Supported by the National Natural Science Foundation of China(50976072,51106099,10902070)the Leading Academic Discipline Project of Shanghai Municipal Education Commission(J50501)the Science Foundation for the Excellent Youth Scholar of Higher Education of Shanghai(slg09003)~~
文摘A numerical simulation of the toroidal shock wave focusing in a co-axial cylindrical shock tube is inves- tigated by using discontinuous Galerkin （DG） finite element method to solve the axisymmetric Euler equations. For validating the numerical method, the shock-tube problem with exact solution is computed, and the computed results agree well with the exact cases. Then, several cases with higher incident Mach numbers varying from 2.0 to 5.0 are simulated. Simulation results show that complicated flow-field structures of toroidal shock wave diffraction, reflection, and focusing in a co-axial cylindrical shock tube can be obtained at different incident Mach numbers and the numerical solutions appear steep gradients near the focusing point, which illustrates the DG method has higher accuracy and better resolution near the discontinuous point. Moreover, the focusing peak pres- sure with different grid scales is compared.
基金supported by the National Natural Science Foundation of China(Grant No.51911530205)the Natural Science Foundation of Jiangsu Province(Grant No.BK20201455)+4 种基金the Guangdong Basic and Applied Basic Research Foundation(Grant No.2023A1515010890)the Key Laboratory of Port,Waterway and Sedimentation Engineering of MOT(Grant No.YK222001-2)the Open Research Fund of Key Laboratory of Water Security Guarantee in Guangdong-Hong Kong-Marco Greater Bay Area of Ministry of Water Resources(Grant No.WSGBA-KJ202309)the Qing Lan Project of Jiangsu UniversitiesThe authors also thank the Royal Society(Grant No.IEC\NSFC\181321)for providing partial support for this work。
文摘The current study investigates the hydrodynamic characteristics of gap resonance within a narrow gap formed by two adjacent boxes subjected to incident focused transient wave groups.A two-dimensional(2D)numerical wave tank based on the OpenFOAM package is utilized for this purpose.The weather-side box is fixed while the lee-side box is allowed to heave freely under wave actions.The effects of the focused wave amplitude and spectral peak period on the wave amplification within the gap,motion of the lee-side box,and wave forces(including horizontal and vertical wave forces)acting on each box are systematically examined.For comparison,another structural layout consisting of two fixed boxes is also considered.The results reveal that the release of the heave degree of freedom(DoF)of the lee-side box results in remarkably distinct resonance features.In the heave-box system,both its fluid resonant period and the period corresponding to the maximum heave displacement of the lee-side box are significantly larger(i.e.,1.6-1.7 times)than the fluid resonant period of the fixed-box system.However,the wave amplification factor inside the gap in the heave-box system is significantly lower than that in the fixed-box one.Both the variations of the maximum horizontal and vertical wave forces with the spectral peak period and their magnitudes are also significantly different between the two structural systems.
基金supported by the National Natural Science Foundation of China (Grant Nos .50709005 ,50639030 and 10772040)the National High Technology Research and Development Program of China (Grant No.2006AA09A109-3) UK EPSRC(Grant Nos . GR/T07220/01 and GR/T07220/02)
文摘A numerical model is developed to simulate fully nonlinear extreme waves in finite and infinite water-depth wave tanks. A semi-mixed Enlerian-Lagrangian formulation is adopted and a higher-order boundary element method in conjunction with an image Green function is used for the fluid domain. The botmdary values on the free surface are updated at each time step by a fourth-order Runga-Kutta time-marching scheme at each time step. Input wave characteristics are specified at the upstream boundary by an appropriate wave theory. At the downstream boundary, an artificial damping zone is used to prevent wave reflection back into the computational domain. Using the image Green function in the whole fluid domain, the integrations on the two lateral walls and bottom are excluded. The simulation results on extreme wave elevations in finite and infinite water-depths are compared with experimental results and second-order analytical solutions respectively. The wave kinematics is also discussed in the present study.
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.
基金This research was partially supported by the National Natural Science Foundation of China (Grant No. 50379002),the Korea Research Council of Public Science and Technology (Principal R&D Program) and Korea Ministry of Science and Technology (International Collaboration Research Program)
文摘An experimental scheme for the generation of directional focusing waves in a wave basin is established in this paper. The effects of the directional range, frequency width and center frequency on the wave focusing are studied. The distribution of maximum amplitude and the evolution of time series and spectra during wave packet propagation and the variation of water surface parameters are extensively investigated. The results reveal that the characteristics of focusing waves are significantly influenced by wave directionality and that the breaking criteria for directional waves are distinctly different from those for unidirectional waves.
基金supported by the National Natural Science Foundation of China (Grant No.50779004)
文摘Four focusing models for generation of freak waves are presented. An extreme wave focusing model is presented on the basis of the enhanced High-Order Spectral （HOS） method and the importance of the nonlinear wave-wave interaction is evaluated by comparison of the calculated results with experimental and theoretical data. Based on the modification of the Longuet-Higgins model, four wave models for generation of freak waves （a. extreme wave model ＋ random wave model; b. extreme wave model ＋ regular wave model; e. phase interval modulation wave focusing model; d. number modulation wave focusing model with the same phase） are proposed. By use of different energy distribution techniques in the four models, freak wave events are obtained with different Hmax/Hs in finite space and time.
基金This research was respectively supported by the National Natural Science Foundation of China(Grant No.50379002)Programfor New Century Excellent Talents in University(NCET-05-0282)the Korea ResearchCouncil of Public Science and Technology(Principal R&D Program)
文摘Two-dimensional focusing waves are generated and investigated by numerical method. The numerical model is developed by introducing the wave maker boundary on the high-order spectral （HOS） method proposed by Dommermuth and Yue in 1987 and verified by theoretical and experimental data. Some cases of focusing waves considering different parameters such as assumed focusing amplitudes, frequency bandwidth, central frequency and frequency spectrum are generated. Characteristics of the focusing wave including surface elevations, the maximum crest, shift of focusing points and frequency spectra are discussed. The results show that the focusing wave characteristics are strongly affected by focusing amplitudes, frequency bandwidth, central frequency and frequency spectrum.
文摘Freak waves are generated based on the mechanism of wave focusing in a 2D numerical wave tank. To set up the nonlinear numerical wave tank, the Boundary Element Method is used to solve potential flow equations incorporated with fully nonlinear free surface boundary conditions. The nonlinear properties of freak waves, such as high frequency components and wave profile asymmetry, are discussed. The kinematic data, which can be useful for the evaluation of the wave forces exerted on structures to avoid underestimation of linear predictions, are obtained, and discussed, from the simulated results of freak waves.
基金The Key Technology Program,the Ministry of Education of China under contract No.104061
文摘Based on the Longuet-Higgins wave model theory, the previews studies have shown that freak waves can be generated in finite space and time successfully. However, as to generating high nonlinear freak waves, the simulation results will be unrealistic. Therefore, a modified phase modulation method for simulating high nonlinear freak waves was developed. The surface elevations of some wave components at certain time and place are positive by modulating the corresponding random initial phases, then the total surface elevation at the focused point is enhanced and furthermore a freak wave event is generated. The new method can not only make the freak wave occur at certain time and place, but also make the simulated wave surface time series satisfy statistical properties of the realistic sea state and keep identical with the target wave spectrum. This numerical approach is of good precision and high efficiency by the comparisons of the simulated freak waves and the recorded freak waves.
基金the National Natural Science Foundation of China(No.51379124)the Knowledge-Based Ship-Design Hyper-Integrated Platform(KSHIP) 2nd Term(No.GKZY010004)
文摘On the basis of the transient water wave(TWW) theory,focused wave is generated in the circulating water channel.Numerical simulation of the focused wave is carried out by solving the Reynolds averaged NavierStokes(RANS) equations.The dynamic grid technique is adopted to simulate the motion of the wave maker,and the volume of fluid(VOF) method is used to capture the free surface of the wave.The simulation results are compared with the measured data,and good agreement is obtained.For quantitative estimation of the numerical simulation error and uncertainty,the uncertainty analysis method recommended by the International Towing Tank Conference(ITTC) procedure is performed for the simulation results of the surface elevations at different positions.Both grid-convergence and time-step-size convergence studies are conducted using three types of grids and time step sizes.The simulation results are all monotonously convergent in the verification procedure,and the validations of the simulated surface elevations with the positions at 3.5,4.0 and 4.5 m are all achieved by comparing with the validation uncertainty.It is found that the numerical simulation errors caused by the grid and time-step-size in the convergence studies have the same order of magnitude.In addition,the numerical errors and uncertainties for the surface elevations at different positions are compared and discussed in detail.This paper presents the first attempt to carry out the uncertainty analysis of the simulation of focused wave,and the effectiveness of the proposed verification and validation procedures in the uncertainty analysis is demonstrated.
基金supported by the National Natural Science Foundation of China(Grant Nos.50679010 and 50921001)the Program for New Century Excellent Talents in Universities of China(Grant No.NCET-05-0282)
文摘In this paper, a numerical model for nonlinear wave propagation in currents is formulated by a set of enhanced fully nonlinear Boussinesq equations with ambient currents. This model is verified by comparison with the published results. Then the influence of currents on nonlinear focusing waves is studied by use of the numerical model. It is found that the effect of currents on the surface elevations at the fecal location is negligible. Following currents can augment the maximum crest of focusing wave while decrease the focusing time, and vice versa for opposing currents. Furthermore, both opposing and following currents can shift the focal location forward relative to that in quiescent water.
基金The National Natural Science Foundation of China under contract Nos 51679036,51490672 and 51709038the Fundamental Research Funds for the Central Universities under contract Nos DUT17GJ202 and DUT16RC(3)113the Open Foundation of State Key Laboratory of Hydrology-Water Resources and Hydraulic Engineering under contract No.2016490111
文摘A numerical wave flume with fully nonlinear free surface boundary conditions is adopted to investigate the temporal characteristics of extreme waves in the presence of wind at various speeds. Incident wave trains are numerically generated by a piston-type wave maker, and the wind-excited pressure is introduced into dynamic boundary conditions using a pressure distribution over steep crests, as defined by Jeffreys＇ sheltering mechanism.A boundary value problem is solved by a higher-order boundary element method（HOBEM） and a mixed Eulerian-Lagrangian time marching scheme. The proposed model is validated through comparison with published experimental data from a focused wave group. The influence of wind on extreme wave properties,including maximum extreme wave crest, focal position shift, and spectrum evolution, is also studied. To consider the effects of the wind-driven currents on a wave evolution, the simulations assume a uniform current over varying water depth. The results show that wind causes weak increases in the extreme wave crest, and makes the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide a comparison to demonstrate the shifts at focal points, considering the combined effects of the winds and the wind-driven currents.
