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
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
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
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
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
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
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
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
In this paper,the focused wave groups with different parameters and their actions on a vertical cylinder are experimentally studied. The harmonic wave characteristics of the focusing waves are analyzed by the addition...In this paper,the focused wave groups with different parameters and their actions on a vertical cylinder are experimentally studied. The harmonic wave characteristics of the focusing waves are analyzed by the addition and subtraction of the crest and trough focusing waves. The analyzed results show that higher order harmonics can be generated because of the interaction of component waves. Nonlinearity increases with the inputted wave amplitude and the frequency width increment. Further, the wave run-up around the vertical circular cylinder is experimentally studied. It increases with the wave steepness and the relative cylinder diameter increase. However, the variations of wave run-up around the circular cylinder are different. The researches provide a reference for further numerical studies.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
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
Ning et al. (2015) developed a 2D fully nonlinear potential model to investigate the interaction between focused waves and uniform currents. The effects of uniform current on focusing wave crest, focal time and foca...Ning et al. (2015) developed a 2D fully nonlinear potential model to investigate the interaction between focused waves and uniform currents. The effects of uniform current on focusing wave crest, focal time and focal position were given. As its extension, harmonic energy transfer for focused waves in uniform current is studied using the proposed model by Ning et al. (2015) and Fast Fourier Transformation (FFT) technique in this study. It shows that the strong opposing currents, inducing partial wave blocking and reducing the extreme wave crest, make the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide an explanation to address the shifts of focal points in consideration of the combination effects of wave nonlinearity and current.展开更多
Owing to the complexity of the physical mechanisms of rouge waves,the theoretical study of the rogue-wavestructure interaction problems still makes little progress.However,for regular-shaped structures,it is possible ...Owing to the complexity of the physical mechanisms of rouge waves,the theoretical study of the rogue-wavestructure interaction problems still makes little progress.However,for regular-shaped structures,it is possible to give a theoretical analysis,if a relatively simple model of the rogue waves is used.The wave load,induced by a focusing wave which is known as an intuitive basic model of the rouge waves,upon a semi-submerged cylinder is studied analytically.The focusing wave is approximate by the Gauss envelope wave,an ideal model which contains most features of the rogue wave.The diffraction velocity potential is derived through the separation of flow field,and the formulas of the horizontal force and bending moment are proposed.The derived formulas are simplified appropriately,and validated through comparison against numerical results.In addition,the influence of parameters,such as the focusing degree,the submerging depth and the wave focusing position,is thoroughly investigated.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
In this study, wave propagation anisotropy in a triangular lattice crystal structure and its associated waveform shaping in a crystal structure are investigated theoretically. A directional variation in wave velocity ...In this study, wave propagation anisotropy in a triangular lattice crystal structure and its associated waveform shaping in a crystal structure are investigated theoretically. A directional variation in wave velocity inside a crystal structure is shown to cause bending wave envelopes. The authors report that a triangular lattice sonic crystal possesses six numbers of a high symmetry direction, which leads to a wave convergence caused by wave velocity anisotropy inside the crystal. However, two of them are utilized mostly in wave focusing by an acoustic fiat lens. Based on wave velocity anisotropy, the pseudo ideal imaging effect obtained in the second band of the flat lens is discussed.展开更多
We demonstrate the hybrid focusing points of sonic crystals for a multi-source array applied to flat sonic crystal lenses. The contributions of different point source couples form hybrid focusing points. Ray-trace ana...We demonstrate the hybrid focusing points of sonic crystals for a multi-source array applied to flat sonic crystal lenses. The contributions of different point source couples form hybrid focusing points. Ray-trace analyses are conducted for acoustic flat lenses with multi-source configurations. The finite-difference time-domain (FDTD) simulation of flat lenses with multi-source configurations demonstrates the establishment of pure and hybrid focusing points in a pyramidal constellation. The number of focusing points in the pyramidal constellation depends on the number of point sources. We propose an acoustic device for fine-tuning the location of a far-field hybrid focusing point and discuss its benefits for acoustic energy focusing application.展开更多
Three-dimensional ( 3-D) directional wave focusing is one of the mechanisms that contribute to the generation of freak waves. To simulate and analyze this phenomenon,a 3-D wave focusing model is proposed based on the ...Three-dimensional ( 3-D) directional wave focusing is one of the mechanisms that contribute to the generation of freak waves. To simulate and analyze this phenomenon,a 3-D wave focusing model is proposed based on the enhanced high-order spectral method,which solves the fully nonlinear potential flow equations with a free surface within periodic unbounded 3-D domains. The numerical model is validated against a fifth-order Stokes solution for regular waves. Laboratory-scale freak waves are observed with wave components having equal amplitudes. Investigations of the appearance and propagation of freak-wave events in a 3-D open wavefield defined by a directional wave spectrum are then realized.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
“Green–Naghdi Theory,Part A:Green–Naghdi(GN)Equations for Shallow Water Waves”have investigated the linear dispersion relations of high-level GN equations in shallow water.In this study,the GN equations for deep w...“Green–Naghdi Theory,Part A:Green–Naghdi(GN)Equations for Shallow Water Waves”have investigated the linear dispersion relations of high-level GN equations in shallow water.In this study,the GN equations for deep water waves are investigated.In the traditional GN equations for deep water waves,the velocity distribution assumption involves only one representative wave number.Herein,a new velocity distribution shape function with multiple representative wave numbers is employed.Further,we have derived the three-dimensional GN equations and analyzed the linear dispersion relations of the GN-3 and GN-5 equations.In this study,the finite difference method is used to simulate focus waves in the time domain.Additionally,the GN-5 equations are used to validate the wave profile and horizontal velocity distribution along water depth for different focused waves.展开更多
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.
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.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.
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supported bythe National Natural Science Foundation of China (Grant Nos.50379002 and 50921001)the New Century Excellent Talents in University (Grant No.NCET-05-0282)
文摘In this paper,the focused wave groups with different parameters and their actions on a vertical cylinder are experimentally studied. The harmonic wave characteristics of the focusing waves are analyzed by the addition and subtraction of the crest and trough focusing waves. The analyzed results show that higher order harmonics can be generated because of the interaction of component waves. Nonlinearity increases with the inputted wave amplitude and the frequency width increment. Further, the wave run-up around the vertical circular cylinder is experimentally studied. It increases with the wave steepness and the relative cylinder diameter increase. However, the variations of wave run-up around the circular cylinder are different. The researches provide a reference for further numerical studies.
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.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51679036 and 51490672)the Royal Academy of Engineering under the UK-China Industry Academia Partnership Programme(Grant No.UK-CIAPP\73)the Program for New Century Excellent Talents in University(Grant No.NCET-13-0076)
文摘Ning et al. (2015) developed a 2D fully nonlinear potential model to investigate the interaction between focused waves and uniform currents. The effects of uniform current on focusing wave crest, focal time and focal position were given. As its extension, harmonic energy transfer for focused waves in uniform current is studied using the proposed model by Ning et al. (2015) and Fast Fourier Transformation (FFT) technique in this study. It shows that the strong opposing currents, inducing partial wave blocking and reducing the extreme wave crest, make the nonlinear energy transfer non-reversible in the focusing and defocusing processes. The numerical results also provide an explanation to address the shifts of focal points in consideration of the combination effects of wave nonlinearity and current.
基金The National Natural Science Foundation of China under contract No.51609101the Natural Science Foundation of Fujian Province of China under contract Nos 2017J01701 and 2017J05085
文摘Owing to the complexity of the physical mechanisms of rouge waves,the theoretical study of the rogue-wavestructure interaction problems still makes little progress.However,for regular-shaped structures,it is possible to give a theoretical analysis,if a relatively simple model of the rogue waves is used.The wave load,induced by a focusing wave which is known as an intuitive basic model of the rouge waves,upon a semi-submerged cylinder is studied analytically.The focusing wave is approximate by the Gauss envelope wave,an ideal model which contains most features of the rogue wave.The diffraction velocity potential is derived through the separation of flow field,and the formulas of the horizontal force and bending moment are proposed.The derived formulas are simplified appropriately,and validated through comparison against numerical results.In addition,the influence of parameters,such as the focusing degree,the submerging depth and the wave focusing position,is thoroughly investigated.
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.
文摘In this study, wave propagation anisotropy in a triangular lattice crystal structure and its associated waveform shaping in a crystal structure are investigated theoretically. A directional variation in wave velocity inside a crystal structure is shown to cause bending wave envelopes. The authors report that a triangular lattice sonic crystal possesses six numbers of a high symmetry direction, which leads to a wave convergence caused by wave velocity anisotropy inside the crystal. However, two of them are utilized mostly in wave focusing by an acoustic fiat lens. Based on wave velocity anisotropy, the pseudo ideal imaging effect obtained in the second band of the flat lens is discussed.
文摘We demonstrate the hybrid focusing points of sonic crystals for a multi-source array applied to flat sonic crystal lenses. The contributions of different point source couples form hybrid focusing points. Ray-trace analyses are conducted for acoustic flat lenses with multi-source configurations. The finite-difference time-domain (FDTD) simulation of flat lenses with multi-source configurations demonstrates the establishment of pure and hybrid focusing points in a pyramidal constellation. The number of focusing points in the pyramidal constellation depends on the number of point sources. We propose an acoustic device for fine-tuning the location of a far-field hybrid focusing point and discuss its benefits for acoustic energy focusing application.
基金Sponsored by the National Natural Science Foundation of China (Grant No. 50779004)
文摘Three-dimensional ( 3-D) directional wave focusing is one of the mechanisms that contribute to the generation of freak waves. To simulate and analyze this phenomenon,a 3-D wave focusing model is proposed based on the enhanced high-order spectral method,which solves the fully nonlinear potential flow equations with a free surface within periodic unbounded 3-D domains. The numerical model is validated against a fifth-order Stokes solution for regular waves. Laboratory-scale freak waves are observed with wave components having equal amplitudes. Investigations of the appearance and propagation of freak-wave events in a 3-D open wavefield defined by a directional wave spectrum are then realized.
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.
文摘“Green–Naghdi Theory,Part A:Green–Naghdi(GN)Equations for Shallow Water Waves”have investigated the linear dispersion relations of high-level GN equations in shallow water.In this study,the GN equations for deep water waves are investigated.In the traditional GN equations for deep water waves,the velocity distribution assumption involves only one representative wave number.Herein,a new velocity distribution shape function with multiple representative wave numbers is employed.Further,we have derived the three-dimensional GN equations and analyzed the linear dispersion relations of the GN-3 and GN-5 equations.In this study,the finite difference method is used to simulate focus waves in the time domain.Additionally,the GN-5 equations are used to validate the wave profile and horizontal velocity distribution along water depth for different focused waves.