The numerical simulation is based on the authors' high-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth. Corresponding finite-difference equations and general condit...The numerical simulation is based on the authors' high-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth. Corresponding finite-difference equations and general conditions for open and fixed natural boundaries with an arbitrary reflection coefficient and phase shift are also given in this paper. The systematical tests of numerical simulation show that the theoretical models, the finite-difference algorithms and the boundary conditions can give good calculation results for the wave propagating in shallow and deep water with an arbitrary slope varying from gentle to steep.展开更多
The three-dimensional spectral analysis method was applied to airglow data from September 2023 to August 2024 derivedfrom an OH airglow imager located at the Hejing station (42.79°N, 83.73°E) to study the pr...The three-dimensional spectral analysis method was applied to airglow data from September 2023 to August 2024 derivedfrom an OH airglow imager located at the Hejing station (42.79°N, 83.73°E) to study the propagation characteristics of gravity waves(GWs) over Northwest China. We found that obvious seasonal variations occur in the propagation of GWs. In spring, GWs mainlypropagate in the northeast direction. In summer and autumn, GWs mainly propagate in the north direction. However, GWs mainlypropagate in the south direction in winter. The direction of GW propagation in the zonal direction is controlled by the wind-filteringeffect, whereas the north–south meridional direction is mainly determined by the location of the wave source. We found that the averageenergy spectrum exhibits a 10%–20% higher intensity in summer and winter compared with spring and autumn. For the first time, wereport the seasonal variation characteristics of GWs over the inland areas of Northwest China, which is of great significance forunderstanding the regional distribution characteristics of GWs.展开更多
Internal solitary waves(ISWs) are a common phenomenon beneath the ocean surface and represent a significant environmental hazard that must be considered for the safe navigation of submersibles. A numerical simulation ...Internal solitary waves(ISWs) are a common phenomenon beneath the ocean surface and represent a significant environmental hazard that must be considered for the safe navigation of submersibles. A numerical simulation model for the interaction of solitary waves with submersibles at a large scale has been developed. The Miyata-ChoiCamassa(MCC) equation serves as the basis for generating ISWs. The impacts of the submergence depth, wave amplitude, and advancing velocity on the motion response and load characteristics of the submersible are examined in detail. This study elucidates the governing laws and mechanisms underlying the impact of ISWs on submersibles.The research findings indicate that shorter distances to the undisturbed surface, higher wave amplitudes, and fasteradvancing speeds result in greater effects on submersibles. For a submersible operating in the lower layer, both the alteration in density near the wave interface and the dynamic pressure induced by ISWs can reduce its lift, potentially resulting in a rapid descent. It is imperative to pay considerable attention to the impact of ISWs, as they have the potential to precipitate a loss of control of the submersible.展开更多
Internal solitary waves(ISW),characterized by large amplitude and long propagation distance,are widespread in global oceans.While remote sensing images have played an essential role in studying ISWs,they mainly exploi...Internal solitary waves(ISW),characterized by large amplitude and long propagation distance,are widespread in global oceans.While remote sensing images have played an essential role in studying ISWs,they mainly exploit two-dimensional image information.However,with the launch of the surface water ocean topography(SWOT)satellite on December 16,2022,a unique opportunity has emerged to capture wide-swath three-dimensional ISW-induced sea surface information.In this study,we examine ISWs in the Andaman Sea using data from the Ka-band Radar Interferometer(KaRIN),a crucial sensor onboard SWOT.KaRIN not only provides backscattering satellite images but also employs synthetic aperture interferometry techniques to retrieve wide-swath two-dimensional sea surface height measurements.Our observations in the Andaman Sea revealed the presence of ISWs characterized by dark-bright strips and surface elevation solitons.The surface soliton has an amplitude of 0.32 m,resulting in an estimation of ISW amplitude of approximately 60 m.In contrast to traditional two-dimensional satellite images or nadir-looking altimetry data,the SWOT mission’s capability to capture threedimensional sea surface information represents a significant advancement.This breakthrough holds substantial promise for ISW studies,particularly in the context of ISW amplitude inversion.展开更多
In addition to being driven by tidal winds,the sporadic E(Es)layers are modulated by gravity waves(GWs),although the effects are not yet comprehensively understood.In this article,we discuss the effects of mesoscale G...In addition to being driven by tidal winds,the sporadic E(Es)layers are modulated by gravity waves(GWs),although the effects are not yet comprehensively understood.In this article,we discuss the effects of mesoscale GWs on the Es layers determined by using a newly developed model,MISE-1D(one-dimensional Model of Ionospheric Sporadic E),with low numerical dissipation and high resolution.Driven by the wind fields resolved by the high-resolution version of the Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension(WACCM-X),the MISE-1D simulation revealed that GWs significantly influence the evolution of the Es layer above 100 km but have a very limited effect at lower altitudes.The effects of GWs are diverse and complex,generally including the generation of fluctuating wavelike structures on the Es layer with frequencies similar to those of the GWs.The mesoscale GWs can also cause increases in the density of Es layers,or they can disperse or diffuse the Es layers and increase their thickness.In addition,the presence of GWs is a key factor in sustaining the Es layers in some cases.展开更多
Traffic engineering such as tunnels in various altitudinal gradient zone are at risk of accidental explosion,which can damage personnel and equipment.Accurate prediction of the distribution pattern of explosive loads ...Traffic engineering such as tunnels in various altitudinal gradient zone are at risk of accidental explosion,which can damage personnel and equipment.Accurate prediction of the distribution pattern of explosive loads and shock wave propagation process in semi-enclosed structures at various altitude environment is key research focus in the fields of explosion shock and fluid dynamics.The effect of altitude on the propagation of shock waves in tunnels was investigated by conducting explosion test and numerical simulation.Based on the experimental and numerical simulation results,a prediction model for the attenuation of the peak overpressure of tunnel shock waves at different altitudes was established.The results showed that the peak overpressure decreased at the same measurement points in the tunnel entrance under the high altitude condition.In contrast,an increase in altitude accelerated the propagation speed of the shock wave in the tunnel.The average error between the peak shock wave overpressure obtained using the overpressure prediction formula and the measured test data was less than15%,the average error between the propagation velocity of shock waves predicted values and the test data is less than 10%.The method can effectively predict the overpressure attenuation of blast wave in tunnel at various altitudes.展开更多
To address the problem of multi-missile cooperative interception against maneuvering targets at a prespecified impact time and desired Line-of-Sight(LOS)angles in ThreeDimensional(3D)space,this paper proposes a 3D lea...To address the problem of multi-missile cooperative interception against maneuvering targets at a prespecified impact time and desired Line-of-Sight(LOS)angles in ThreeDimensional(3D)space,this paper proposes a 3D leader-following cooperative interception guidance law.First,in the LOS direction of the leader,an impact time-controlled guidance law is derived based on the fixed-time stability theory,which enables the leader to complete the interception task at a prespecified impact time.Next,in the LOS direction of the followers,by introducing a time consensus tracking error function,a fixed-time consensus tracking guidance law is investigated to guarantee the consensus tracking convergence of the time-to-go.Then,in the direction normal to the LOS,by combining the designed global integral sliding mode surface and the second-order Sliding Mode Control(SMC)theory,an innovative 3D LOS-angle-constrained interception guidance law is developed,which eliminates the reaching phase in the traditional sliding mode guidance laws and effectively saves energy consumption.Moreover,it effectively suppresses the chattering phenomenon while avoiding the singularity issue,and compensates for unknown interference caused by target maneuvering online,making it convenient for practical engineering applications.Finally,theoretical proof analysis and multiple sets of numerical simulation results verify the effectiveness,superiority,and robustness of the investigated guidance law.展开更多
The thermochemical non-equilibrium phenomena encountered by hypersonic vehicles present significant challenges in their design.To investigate the thermochemical reaction flow behind shock waves,the non-equilibrium rad...The thermochemical non-equilibrium phenomena encountered by hypersonic vehicles present significant challenges in their design.To investigate the thermochemical reaction flow behind shock waves,the non-equilibrium radiation in the visible range using a shock tube was studied.Experiments were conducted with a shock velocity of 4.7 km/s,using nitrogen at a pressure of 20 Pa.To address measurement difficulties associated with weak radiation,a special square section shock tube with a side length of 380 mm was utilized.A high-speed camera characterized the shock wave’s morphology,and a spectrograph and a monochromator captured the radiation.The spectra were analyzed,and the numerical spectra were compared with experimental results,showing a close match.Temperature changes behind the shock wave were obtained and compared with numerical predictions.The findings indicate that the vibrational temperatures are overestimated,while the vibrational relaxation time is likely underestimated,due to the oversimplified portrayals of the non-equilibrium relaxation process in the models.Additionally,both experimental and simulated time-resolved profiles of radiation intensity at specific wavelengths were analyzed.The gathered data aims to enhance computational fluid dynamics codes and radiation models,improving their predictive accuracy.展开更多
Ice-breaking methods have become increasingly significant with the ongoing development of the polar regions.Among many ice-breaking methods,ice-breaking that utilizes a moving load is unique compared with the common c...Ice-breaking methods have become increasingly significant with the ongoing development of the polar regions.Among many ice-breaking methods,ice-breaking that utilizes a moving load is unique compared with the common collision or impact methods.A moving load can generate flexural-gravity waves(FGWs),under the influence of which the ice sheet undergoes deformation and may even experience structural damage.Moving loads can be divided into above-ice loads and underwater loads.For the above-ice loads,we discuss the characteristics of the FGWs generated by a moving load acting on a complete ice sheet,an ice sheet with a crack,and an ice sheet with a lead of open water.For underwater loads,we discuss the influence on the ice-breaking characteristics of FGWs of the mode of motion,the geometrical features,and the trajectory of motion of the load.In addition to discussing the status of current research and the technical challenges of ice-breaking by moving loads,this paper also looks ahead to future research prospects and presents some preliminary ideas for consideration.展开更多
Liposarcoma is one of the most common soft tissue sarcomas,however,its occurrence rate is still rare compared to other cancers.Due to its rarity,in vitro experiments are an essential approach to elucidate liposarcoma ...Liposarcoma is one of the most common soft tissue sarcomas,however,its occurrence rate is still rare compared to other cancers.Due to its rarity,in vitro experiments are an essential approach to elucidate liposarcoma pathobiology.Conventional cell culture-based research(2D cell culture)is still playing a pivotal role,while several shortcomings have been recently under discussion.In vivo,mouse models are usually adopted for pre-clinical analyses with expectations to overcome the issues of 2D cell culture.However,they do not fully recapitulate human dedifferentiated liposarcoma(DDLPS)characteristics.Therefore,three-dimensional(3D)culture systems have been the recent research focus in the cell biology field with the expectation to overcome at the same time the disadvantages of 2D cell culture and in vivo animal models and fill in the gap between them.Given the liposarcoma rarity,we believe that 3D cell culture techniques,including 3D cell cultures/co-cultures,and Patient-Derived tumor Organoids(PDOs),represent a promising approach to facilitate liposarcoma investigation and elucidate its molecular mechanisms and effective therapy development.In this review,we first provide a general overview of 3D cell cultures compared to 2D cell cultures.We then focus on one of the recent 3D cell culture applications,Patient-Derived Organoids(PDOs),summarizing and discussing several PDO methodologies.Finally,we discuss the current and future applications of PDOs to sarcoma,particularly in the field of liposarcoma.展开更多
Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons.Previous ...Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons.Previous quantitative analyses often simplified the chorus dispersion relation by using the cold plasma assumption.However,the applicability of the cold plasma assumption is doubtful,especially during geomagnetic disturbances.We here present a systematic statistical analysis on the validity of the cold plasma dispersion relation of chorus waves based on observations from the Van Allen Probes over the period from 2012 to 2018.The statistical results show that the observed magnetic field intensities deviate substantially from those calculated from the cold plasma dispersion relation and that they become more pronounced with an increase in geomagnetic activity or a decrease in background plasma density.The region with large deviations is mainly concentrated in the nightside and expands in both the radial and azimuthal directions as the geomagnetic activity increases or the background plasma density decreases.In addition,the bounce-averaged electron scattering rates are computed by using the observed and cold plasma dispersion relation of chorus waves.Compared with usage of the cold plasma dispersion relation,usage of the observed dispersion relation considerably lowers the minimum resonant energy of electrons and lowers the scattering rates of electrons above tens of kiloelectronvolts but enhances those below.Furthermore,these differences are more pronounced with the enhancement of geomagnetic activity or the decrease in background plasma density.展开更多
The finite volume method was applied to numerically simulate the bottom pressure field induced by regular waves,vehicles in calm water and vehicles in regular waves.The solution of Navier-Stokes(N-S)equations in the v...The finite volume method was applied to numerically simulate the bottom pressure field induced by regular waves,vehicles in calm water and vehicles in regular waves.The solution of Navier-Stokes(N-S)equations in the vicinity of numerical wave tank's boundary was forced towards the wave theoretical solution by incorporating momentum source terms,thereby reducing adverse effects such as wave reflection.Simulations utilizing laminar flow,turbulent flow,and ideal fluid models were all found capable of effectively capturing the waveform and bottom pressure of regular waves,agreeing well with experimental data.In predicting the bottom pressure field of the submerged vehicle,turbulent simulations considering fluid viscosity and boundary layer development provided more accurate predictions for the stern region than inviscid simulations.Due to sphere's diffractive effect,the sphere's bottom pressure field in waves is not a linear superposition of the wave's and the sphere's bottom pressure field.However,a slender submerged vehicle exhibits a weaker diffractive effect on waves,thus the submerged vehicle's bottom pressure field in waves can be approximated as a linear superposition of the wave's and the submerged vehicle's bottom pressure field,which simplifies computation and analysis.展开更多
By applying the convolution-based Hilbert transform in the zonal direction on six-hourly streamfunction fields at200 h Pa, we present the climatology and trends of the local wave period, and zonal and meridional phase...By applying the convolution-based Hilbert transform in the zonal direction on six-hourly streamfunction fields at200 h Pa, we present the climatology and trends of the local wave period, and zonal and meridional phase speeds, of Rossby waves over the globe during the solstice seasons of 1979–2023. While partly similar to and inspired by Fragkoulidis and Wirth(2020), our method differs in its ability to cover both planetary-scale and synoptic-scale waves over not only the extratropics, but also the tropics and subtropics. Based on a physically reasonable global distribution of wave periods, our key new finding is a robust prolonging of wave periods over most regions of the tropics and subtropics during both solstice seasons of 1979–2023, except for the tropical Atlantic, which experiences a shortened wave period during June–July–August of 1979–2022. Both the prolonging and shortening of wave periods are mainly associated with the changes in planetary-scale waves. Regionally varying trends of the zonal phase speed(Cpx) of synoptic waves are consistent in sign with, but smaller in magnitude than, the trends of local zonal wind, confirming the conclusion of Wu and Lu(2023)on the opposite effects of zonal wind and the meridional gradient of potential vorticity on Cpx. Meanwhile, the Cpx trends of planetary-scale waves are relatively weak, and do not exhibit a robust relation with the trend of zonal wind. These new results are helpful toward better understanding the changes in atmospheric waves and extreme events under global warming.展开更多
Flume experiments play a pivotal role in studying wave propagation,with wave elements typically assumed to remain constant in the perpendicular direction.However,evident cross wave phenomena were observed within flume...Flume experiments play a pivotal role in studying wave propagation,with wave elements typically assumed to remain constant in the perpendicular direction.However,evident cross wave phenomena were observed within flumes under certain conditions.This paper presents new analytical solutions for both primary and cross waves on double shoals in a flume via linear shallow-water equations,which may be used to idealize dynamic experimental configurations of coral reefs.The primary waves on double shoals are described by the associated Legendre functions,whereas the ultimate solutions are derived by considering the incident and reflected waves in front of a bathymetry and the transmitted waves positioned behind it.The effects of the angular frequency and topographic parameters on the primary waves are subsequently analyzed.Cross waves on double shoals constitute a type of topographically trapped wave whose solutions are formulated by combining the first and second types of the associated Legendre functions.The angular frequency is not only determined by the wavenumber but also influenced by the topographic parameters.Numerical experiments are conducted to investigate the generation mechanism of cross waves.The consistency between the numerical results and analytical solutions confirms the validity of the new analytical framework of cross waves on double shoals.展开更多
In channel reservoirs,a quantitative characterization of landslide-generated impulse wave-structure interactions is essential for evaluating potential damage to infrastructure and dams.In this study,the problem of lan...In channel reservoirs,a quantitative characterization of landslide-generated impulse wave-structure interactions is essential for evaluating potential damage to infrastructure and dams.In this study,the problem of landslide-generated impulse waves that attack a vertical wall was investigated in a wave channel via a smooth particle hydrodynamics(SPH)method coupled with a Chrono model.The results indicated that the longitudinal velocity beneath the leading wave crest of an incident impulse wave deviated significantly from solitary wave theory.Moreover,the variation rate in the vertical velocity along the water column coincided with the theoretical prediction only for small wave amplitudes.Nevertheless,the maximum run-up height of an impulse wave can be accurately predicted via the solitary wave theory.Moreover,the maximum wall force during impulse wave-wall interaction was significantly larger than that during solitary wave reflection,particularly for high incident wave amplitudes.Overall,the present study demonstrated some striking differences in the interactions of landslide-generated impulse waves and solitary waves with a vertical wall.展开更多
The three-dimensional particle electrode system exhibits significant potential for application in the treatment of wastewater.Nonetheless,the advancement of effective granular electrodes characterized by elevated cata...The three-dimensional particle electrode system exhibits significant potential for application in the treatment of wastewater.Nonetheless,the advancement of effective granular electrodes characterized by elevated catalytic activity and minimal energy consumption continues to pose a significant challenge.In this research,Fluorine-doped copper-carbon(F/Cu-GAC)particle electrodes were effectively synthesized through an impregnationcalcination technique,utilizing granular activated carbon as the carrier and fluorinedoped modified copper oxides as the catalytic agents.The particle electrodes were subsequently utilized to promote the degradation of 2,4,6-trichlorophenol(2,4,6-TCP)in a threedimensional electrocatalytic reactor(3DER).The F/Cu-GAC particle electrodes were polarized under the action of electric field,which promoted the heterogeneous Fenton-like reaction in which H2O2 generated by two-electron oxygen reduction reaction(2e-ORR)of O_(2) was catalytically decomposed to·OH.The 3DER equipped with F/Cu-GAC particle electrodes showed 100%removal of 2,4,6-TCP and 79.24%removal of TOC with a specific energy consumption(EC)of approximately 0.019 kWh/g·COD after 2 h of operation.The F/Cu-GAC particle electrodes exhibited an overpotential of 0.38 V and an electrochemically active surface area(ECSA)of 715 cm^(2),as determined through linear sweep voltammetry(LSV)and cyclic voltammetry(CV)assessments.These findings suggest a high level of electrocatalytic performance.Furthermore,the catalytic mechanism of the 3DER equipped with F/Cu-GAC particle electrodes was elucidated through the application of X-ray photoelectron spectroscopy(XPS),electron spin resonance(ESR),and active species capture experiments.This investigation offers a novel approach for the effective degradation of 2,4,6-TCP.展开更多
Hypersonic boundary-layer receptivity to freestream entropy and vorticity waves is investigated using direct numerical simula-tions for a Mach 6 flow over a 5.08 mm nose radius cone.Two frequencies of 33 kHz and 150 k...Hypersonic boundary-layer receptivity to freestream entropy and vorticity waves is investigated using direct numerical simula-tions for a Mach 6 flow over a 5.08 mm nose radius cone.Two frequencies of 33 kHz and 150 kHz are considered to be rep-resentative of the first and second instability modes,respectively.For the first mode,wall pressure fluctuations for both entropy and vorticity wave cases exhibit a strong modulation yet without a growing trend,indicating that the first mode is not generated despite its instability predicted by linear stability theory.The potential reason for this is the absence of postshock slow acoustic waves capable of synchronizing with the first mode.By contrast,for the second mode,a typical three-stage boundary-layer response is observed,consistent with that to slow acoustic waves studied previously.Furthermore,the postshock disturbances outside the boundary layer can be decomposed into the entropy(density/temperature fluctuations)and vorticity components(ve-locity fluctuations),and the latter is shown to play a leading role in generating the second mode,even for the case with entropy waves where the density/temperature fluctuations dominate the postshock regions.展开更多
Extreme waves may considerably impact crucial coastal and marine engineering structures. The First Scientific Assessment Report on Ocean and Climate Change of China and The Fourth Assessment Report on Climate Change o...Extreme waves may considerably impact crucial coastal and marine engineering structures. The First Scientific Assessment Report on Ocean and Climate Change of China and The Fourth Assessment Report on Climate Change of China were published in 2020 and 2022, respectively.However, no concrete results on the long-term trends in wave changes in China have been obtained. In this study, long-term trends in extreme wave elements over the past 55 years were investigated using wave data from five in situ observation sites(i.e., Lao Hu Tan, Cheng Shan Tou,Ri Zhao, Nan Ji, Wei Zhou) along the coast of China. The five stations showed different trends in wave height. Results show a general downward trend in wave heights at the LHT and CST stations, reaching-0.78 and-1.44 cm/a, respectively, in summer at middle and high latitudes. NJI stations at middle-to-low latitudes are influenced by the winter monsoon and summer tropical cyclones, showing a substantial increase in extreme wave heights(0.7 cm/a in winter and 2.68 cm/a in summer). The cumulative duration of H_(1/10) ≥ 3 m at NJI and RZH has grown since 1990.展开更多
Fractures play a crucial role in various fields such as hydrocarbon exploration,groundwater resources management,and earthquake research.The determination of fracture location and the estimation of parameters such as ...Fractures play a crucial role in various fields such as hydrocarbon exploration,groundwater resources management,and earthquake research.The determination of fracture location and the estimation of parameters such as fracture length and dip angle are the focus of geophysical work.In borehole observation system,the short distance between fractures and detectors leads to weak attenuation of elastic wave energy,and high-frequency source makes it easier to identify small-scale fractures.Compared to traditional monopole logging methods,dipole logging method has advantage of exciting pure shear waves sensitive to fractures,so its application is becoming increasingly widespread.However,since the reflected shear waves and scattered shear waves of fractures correspond to different fracture properties,how to distinguish and analyze these two kinds of waves is crucial for accurately characterizing the fracture parameters.To address this issue,numerical simulation of wave responses by a single fracture near a borehole in rock formation is performed,and the generation mechanism and characteristics of shear waves scattered by fractures are investigated.It is found that when the dip angle of the fracture surpasses a critical threshold,the S-wave will propagate to both endpoints of the fracture and generate scattered S-waves,resulting in two distinct scattered wave packets on the received waveform.When the polarization direction of the acoustic source is parallel to the strike of the fracture,the scattered SH-waves always have larger amplitude than the scattered SV-waves regardless of changing the fracture dip angle.Unlike SV-waves,the SH-waves scattered by the fracture do not have any mode conversion.Additionally,propagation of S-waves to a short length fracture can induce dipole mode vibration of the fracture within a wide frequency range.The phenomena of shear waves reflected and scattered by the fracture are further illustrated and verified by two field examples,thus showing the potential of scattered waves for fracture evaluation and characterization with borehole observation system.展开更多
To propel the application of a bottom-hinged flap breakwater in real sea conditions,a two-dimensional computational fluid dynamics numerical model was conducted to investigate the pitching motion response and wave att...To propel the application of a bottom-hinged flap breakwater in real sea conditions,a two-dimensional computational fluid dynamics numerical model was conducted to investigate the pitching motion response and wave attenuation in random waves.First,the flow velocity distribution characteristic of the pitching flap at typical times was summarized.Then,the effects of random wave and flap parameters on the flap’s significant pitching angle amplitude θ_(s) and hydrodynamic coefficients were investigated.The results reveal that θ_(s) and wave reflection coefficient K_(r) values increase with increasing significant wave height Hs,random wave steepnessλs,and flap relative height.As Hs andλs increase,the wave transmission coefficient K_(t) increases while the wave dissipation coefficient K_(d) decreases.Additionally,K_(t) decreases with increasing flap relative height.With increasing equivalent damping coefficient ratio,θ_(s) and K_(t) decrease,while K_(r) and K_(d) increase.The relationships betweenλs and flap relative height on the one hand andθ_(s),K_(r),K_(t),and K_(d) in random waves on the other hand are compared to those in regular waves.Based on the equal incident wave energy and the equal incident wave energy flux,the pitching flap performs better in the wave attenuation capability under random waves than in regular waves.Finally,the dimensionless parameters with respect to random wave and flap were used to derive the K_(r) and K_(t) for-mulae,which were validated with the related data.展开更多
文摘The numerical simulation is based on the authors' high-order models with a dissipative term for nonlinear and dispersive wave in water of varying depth. Corresponding finite-difference equations and general conditions for open and fixed natural boundaries with an arbitrary reflection coefficient and phase shift are also given in this paper. The systematical tests of numerical simulation show that the theoretical models, the finite-difference algorithms and the boundary conditions can give good calculation results for the wave propagating in shallow and deep water with an arbitrary slope varying from gentle to steep.
基金supported by the National Science Foundation of China(Grant Nos.42374205 and 41974179)the Specialized Research Fund of the National Space Science Center,Chinese Academy of Sciences(Grant No.E4PD3010)supported by the Specialized Research Fund for State Key Laboratories.
文摘The three-dimensional spectral analysis method was applied to airglow data from September 2023 to August 2024 derivedfrom an OH airglow imager located at the Hejing station (42.79°N, 83.73°E) to study the propagation characteristics of gravity waves(GWs) over Northwest China. We found that obvious seasonal variations occur in the propagation of GWs. In spring, GWs mainlypropagate in the northeast direction. In summer and autumn, GWs mainly propagate in the north direction. However, GWs mainlypropagate in the south direction in winter. The direction of GW propagation in the zonal direction is controlled by the wind-filteringeffect, whereas the north–south meridional direction is mainly determined by the location of the wave source. We found that the averageenergy spectrum exhibits a 10%–20% higher intensity in summer and winter compared with spring and autumn. For the first time, wereport the seasonal variation characteristics of GWs over the inland areas of Northwest China, which is of great significance forunderstanding the regional distribution characteristics of GWs.
基金financially supported by the National Natural Science Foundation of China (Grant No. 52201380)Fundamental Research Funds for the Central Universities (Grant No. D5000230080)+2 种基金Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University (Grant Nos. CX 2024049 and CX2023006)the Chunhui Program of Ministry of Education of China (Grant No. HZKY20220538)the Practice and Innovation Funds for Graduate Students of Northwestern Polytechnical University (Grant No. PF2023057)。
文摘Internal solitary waves(ISWs) are a common phenomenon beneath the ocean surface and represent a significant environmental hazard that must be considered for the safe navigation of submersibles. A numerical simulation model for the interaction of solitary waves with submersibles at a large scale has been developed. The Miyata-ChoiCamassa(MCC) equation serves as the basis for generating ISWs. The impacts of the submergence depth, wave amplitude, and advancing velocity on the motion response and load characteristics of the submersible are examined in detail. This study elucidates the governing laws and mechanisms underlying the impact of ISWs on submersibles.The research findings indicate that shorter distances to the undisturbed surface, higher wave amplitudes, and fasteradvancing speeds result in greater effects on submersibles. For a submersible operating in the lower layer, both the alteration in density near the wave interface and the dynamic pressure induced by ISWs can reduce its lift, potentially resulting in a rapid descent. It is imperative to pay considerable attention to the impact of ISWs, as they have the potential to precipitate a loss of control of the submersible.
基金Supported by the National Key Research and Development Program of China(No.2022YFE0204600)the National Natural Science Foundation for Young Scientists of China(No.41906157)。
文摘Internal solitary waves(ISW),characterized by large amplitude and long propagation distance,are widespread in global oceans.While remote sensing images have played an essential role in studying ISWs,they mainly exploit two-dimensional image information.However,with the launch of the surface water ocean topography(SWOT)satellite on December 16,2022,a unique opportunity has emerged to capture wide-swath three-dimensional ISW-induced sea surface information.In this study,we examine ISWs in the Andaman Sea using data from the Ka-band Radar Interferometer(KaRIN),a crucial sensor onboard SWOT.KaRIN not only provides backscattering satellite images but also employs synthetic aperture interferometry techniques to retrieve wide-swath two-dimensional sea surface height measurements.Our observations in the Andaman Sea revealed the presence of ISWs characterized by dark-bright strips and surface elevation solitons.The surface soliton has an amplitude of 0.32 m,resulting in an estimation of ISW amplitude of approximately 60 m.In contrast to traditional two-dimensional satellite images or nadir-looking altimetry data,the SWOT mission’s capability to capture threedimensional sea surface information represents a significant advancement.This breakthrough holds substantial promise for ISW studies,particularly in the context of ISW amplitude inversion.
基金supported by the Project of Stable Support for Youth Teams in Basic Research Field,Chinese Academy of Sciences(CASGrant No.YSBR-018)+2 种基金the B-type Strategic Priority Program of CAS(Grant No.XDB41000000)the National Natural Science Foundation of China(Grant No.42204165)the National Key Research and Development Program(Grant No.2022YFF0504400).
文摘In addition to being driven by tidal winds,the sporadic E(Es)layers are modulated by gravity waves(GWs),although the effects are not yet comprehensively understood.In this article,we discuss the effects of mesoscale GWs on the Es layers determined by using a newly developed model,MISE-1D(one-dimensional Model of Ionospheric Sporadic E),with low numerical dissipation and high resolution.Driven by the wind fields resolved by the high-resolution version of the Whole Atmosphere Community Climate Model with thermosphere and ionosphere extension(WACCM-X),the MISE-1D simulation revealed that GWs significantly influence the evolution of the Es layer above 100 km but have a very limited effect at lower altitudes.The effects of GWs are diverse and complex,generally including the generation of fluctuating wavelike structures on the Es layer with frequencies similar to those of the GWs.The mesoscale GWs can also cause increases in the density of Es layers,or they can disperse or diffuse the Es layers and increase their thickness.In addition,the presence of GWs is a key factor in sustaining the Es layers in some cases.
基金financially supported by National Natural Science Foundation of China(Grant Nos.52378401,52278504)the Fundamental Research Funds for the Central Universities(Grant No.30922010918)。
文摘Traffic engineering such as tunnels in various altitudinal gradient zone are at risk of accidental explosion,which can damage personnel and equipment.Accurate prediction of the distribution pattern of explosive loads and shock wave propagation process in semi-enclosed structures at various altitude environment is key research focus in the fields of explosion shock and fluid dynamics.The effect of altitude on the propagation of shock waves in tunnels was investigated by conducting explosion test and numerical simulation.Based on the experimental and numerical simulation results,a prediction model for the attenuation of the peak overpressure of tunnel shock waves at different altitudes was established.The results showed that the peak overpressure decreased at the same measurement points in the tunnel entrance under the high altitude condition.In contrast,an increase in altitude accelerated the propagation speed of the shock wave in the tunnel.The average error between the peak shock wave overpressure obtained using the overpressure prediction formula and the measured test data was less than15%,the average error between the propagation velocity of shock waves predicted values and the test data is less than 10%.The method can effectively predict the overpressure attenuation of blast wave in tunnel at various altitudes.
文摘To address the problem of multi-missile cooperative interception against maneuvering targets at a prespecified impact time and desired Line-of-Sight(LOS)angles in ThreeDimensional(3D)space,this paper proposes a 3D leader-following cooperative interception guidance law.First,in the LOS direction of the leader,an impact time-controlled guidance law is derived based on the fixed-time stability theory,which enables the leader to complete the interception task at a prespecified impact time.Next,in the LOS direction of the followers,by introducing a time consensus tracking error function,a fixed-time consensus tracking guidance law is investigated to guarantee the consensus tracking convergence of the time-to-go.Then,in the direction normal to the LOS,by combining the designed global integral sliding mode surface and the second-order Sliding Mode Control(SMC)theory,an innovative 3D LOS-angle-constrained interception guidance law is developed,which eliminates the reaching phase in the traditional sliding mode guidance laws and effectively saves energy consumption.Moreover,it effectively suppresses the chattering phenomenon while avoiding the singularity issue,and compensates for unknown interference caused by target maneuvering online,making it convenient for practical engineering applications.Finally,theoretical proof analysis and multiple sets of numerical simulation results verify the effectiveness,superiority,and robustness of the investigated guidance law.
基金supported by the Key-Area Research and Development Program of Guangdong Province(Grant No.2021B0909060004)the National Natural Science Foundation of China(Grant Nos.12072355 and 92271117)the Strategic Priority Research Program of the Chinese Academy of Sciences(Grant No.XDB0620202).
文摘The thermochemical non-equilibrium phenomena encountered by hypersonic vehicles present significant challenges in their design.To investigate the thermochemical reaction flow behind shock waves,the non-equilibrium radiation in the visible range using a shock tube was studied.Experiments were conducted with a shock velocity of 4.7 km/s,using nitrogen at a pressure of 20 Pa.To address measurement difficulties associated with weak radiation,a special square section shock tube with a side length of 380 mm was utilized.A high-speed camera characterized the shock wave’s morphology,and a spectrograph and a monochromator captured the radiation.The spectra were analyzed,and the numerical spectra were compared with experimental results,showing a close match.Temperature changes behind the shock wave were obtained and compared with numerical predictions.The findings indicate that the vibrational temperatures are overestimated,while the vibrational relaxation time is likely underestimated,due to the oversimplified portrayals of the non-equilibrium relaxation process in the models.Additionally,both experimental and simulated time-resolved profiles of radiation intensity at specific wavelengths were analyzed.The gathered data aims to enhance computational fluid dynamics codes and radiation models,improving their predictive accuracy.
基金Supported by the National Natural Science Foundation of China(Nos.52192693,52192690,52371270,U20A20327)the National Key Research and Development Program of China(Nos.2021YFC2803400).
文摘Ice-breaking methods have become increasingly significant with the ongoing development of the polar regions.Among many ice-breaking methods,ice-breaking that utilizes a moving load is unique compared with the common collision or impact methods.A moving load can generate flexural-gravity waves(FGWs),under the influence of which the ice sheet undergoes deformation and may even experience structural damage.Moving loads can be divided into above-ice loads and underwater loads.For the above-ice loads,we discuss the characteristics of the FGWs generated by a moving load acting on a complete ice sheet,an ice sheet with a crack,and an ice sheet with a lead of open water.For underwater loads,we discuss the influence on the ice-breaking characteristics of FGWs of the mode of motion,the geometrical features,and the trajectory of motion of the load.In addition to discussing the status of current research and the technical challenges of ice-breaking by moving loads,this paper also looks ahead to future research prospects and presents some preliminary ideas for consideration.
文摘Liposarcoma is one of the most common soft tissue sarcomas,however,its occurrence rate is still rare compared to other cancers.Due to its rarity,in vitro experiments are an essential approach to elucidate liposarcoma pathobiology.Conventional cell culture-based research(2D cell culture)is still playing a pivotal role,while several shortcomings have been recently under discussion.In vivo,mouse models are usually adopted for pre-clinical analyses with expectations to overcome the issues of 2D cell culture.However,they do not fully recapitulate human dedifferentiated liposarcoma(DDLPS)characteristics.Therefore,three-dimensional(3D)culture systems have been the recent research focus in the cell biology field with the expectation to overcome at the same time the disadvantages of 2D cell culture and in vivo animal models and fill in the gap between them.Given the liposarcoma rarity,we believe that 3D cell culture techniques,including 3D cell cultures/co-cultures,and Patient-Derived tumor Organoids(PDOs),represent a promising approach to facilitate liposarcoma investigation and elucidate its molecular mechanisms and effective therapy development.In this review,we first provide a general overview of 3D cell cultures compared to 2D cell cultures.We then focus on one of the recent 3D cell culture applications,Patient-Derived Organoids(PDOs),summarizing and discussing several PDO methodologies.Finally,we discuss the current and future applications of PDOs to sarcoma,particularly in the field of liposarcoma.
基金supported by the National Natural Science Foundation of China (NSFC) through Grant Number 42074193
文摘Theoretical analysis has demonstrated that the dispersion relation of chorus waves plays an essential role in the resonant interaction and energy transformation between the waves and magnetospheric electrons.Previous quantitative analyses often simplified the chorus dispersion relation by using the cold plasma assumption.However,the applicability of the cold plasma assumption is doubtful,especially during geomagnetic disturbances.We here present a systematic statistical analysis on the validity of the cold plasma dispersion relation of chorus waves based on observations from the Van Allen Probes over the period from 2012 to 2018.The statistical results show that the observed magnetic field intensities deviate substantially from those calculated from the cold plasma dispersion relation and that they become more pronounced with an increase in geomagnetic activity or a decrease in background plasma density.The region with large deviations is mainly concentrated in the nightside and expands in both the radial and azimuthal directions as the geomagnetic activity increases or the background plasma density decreases.In addition,the bounce-averaged electron scattering rates are computed by using the observed and cold plasma dispersion relation of chorus waves.Compared with usage of the cold plasma dispersion relation,usage of the observed dispersion relation considerably lowers the minimum resonant energy of electrons and lowers the scattering rates of electrons above tens of kiloelectronvolts but enhances those below.Furthermore,these differences are more pronounced with the enhancement of geomagnetic activity or the decrease in background plasma density.
文摘The finite volume method was applied to numerically simulate the bottom pressure field induced by regular waves,vehicles in calm water and vehicles in regular waves.The solution of Navier-Stokes(N-S)equations in the vicinity of numerical wave tank's boundary was forced towards the wave theoretical solution by incorporating momentum source terms,thereby reducing adverse effects such as wave reflection.Simulations utilizing laminar flow,turbulent flow,and ideal fluid models were all found capable of effectively capturing the waveform and bottom pressure of regular waves,agreeing well with experimental data.In predicting the bottom pressure field of the submerged vehicle,turbulent simulations considering fluid viscosity and boundary layer development provided more accurate predictions for the stern region than inviscid simulations.Due to sphere's diffractive effect,the sphere's bottom pressure field in waves is not a linear superposition of the wave's and the sphere's bottom pressure field.However,a slender submerged vehicle exhibits a weaker diffractive effect on waves,thus the submerged vehicle's bottom pressure field in waves can be approximated as a linear superposition of the wave's and the submerged vehicle's bottom pressure field,which simplifies computation and analysis.
基金the support from the National Natural Science Foundation of China (Grant No. 42175070)supported by the National Natural Science Foundation of China (Grant No. 42288101)supported by the National Key Scientific and Technological Infrastructure project “Earth System Numerical Simulation Facility” (Earth Lab)。
文摘By applying the convolution-based Hilbert transform in the zonal direction on six-hourly streamfunction fields at200 h Pa, we present the climatology and trends of the local wave period, and zonal and meridional phase speeds, of Rossby waves over the globe during the solstice seasons of 1979–2023. While partly similar to and inspired by Fragkoulidis and Wirth(2020), our method differs in its ability to cover both planetary-scale and synoptic-scale waves over not only the extratropics, but also the tropics and subtropics. Based on a physically reasonable global distribution of wave periods, our key new finding is a robust prolonging of wave periods over most regions of the tropics and subtropics during both solstice seasons of 1979–2023, except for the tropical Atlantic, which experiences a shortened wave period during June–July–August of 1979–2022. Both the prolonging and shortening of wave periods are mainly associated with the changes in planetary-scale waves. Regionally varying trends of the zonal phase speed(Cpx) of synoptic waves are consistent in sign with, but smaller in magnitude than, the trends of local zonal wind, confirming the conclusion of Wu and Lu(2023)on the opposite effects of zonal wind and the meridional gradient of potential vorticity on Cpx. Meanwhile, the Cpx trends of planetary-scale waves are relatively weak, and do not exhibit a robust relation with the trend of zonal wind. These new results are helpful toward better understanding the changes in atmospheric waves and extreme events under global warming.
基金financially supported by the National Natural Science Foundation of China (Grant No. 52071128)the Natural Science Foundation of Jiangsu Basic Research Program (Grant No. BK20220082)
文摘Flume experiments play a pivotal role in studying wave propagation,with wave elements typically assumed to remain constant in the perpendicular direction.However,evident cross wave phenomena were observed within flumes under certain conditions.This paper presents new analytical solutions for both primary and cross waves on double shoals in a flume via linear shallow-water equations,which may be used to idealize dynamic experimental configurations of coral reefs.The primary waves on double shoals are described by the associated Legendre functions,whereas the ultimate solutions are derived by considering the incident and reflected waves in front of a bathymetry and the transmitted waves positioned behind it.The effects of the angular frequency and topographic parameters on the primary waves are subsequently analyzed.Cross waves on double shoals constitute a type of topographically trapped wave whose solutions are formulated by combining the first and second types of the associated Legendre functions.The angular frequency is not only determined by the wavenumber but also influenced by the topographic parameters.Numerical experiments are conducted to investigate the generation mechanism of cross waves.The consistency between the numerical results and analytical solutions confirms the validity of the new analytical framework of cross waves on double shoals.
基金financially supported by the Natural Science Foundation of Chongqing,China(Grant No.cstc2020jcyj-bshX0043)POWERCHINA Science and Technology Project(Grant No.DJ-ZDXM-2022-28)Yunnan Fundamental Research Projects(Grant No.202401CF070042).
文摘In channel reservoirs,a quantitative characterization of landslide-generated impulse wave-structure interactions is essential for evaluating potential damage to infrastructure and dams.In this study,the problem of landslide-generated impulse waves that attack a vertical wall was investigated in a wave channel via a smooth particle hydrodynamics(SPH)method coupled with a Chrono model.The results indicated that the longitudinal velocity beneath the leading wave crest of an incident impulse wave deviated significantly from solitary wave theory.Moreover,the variation rate in the vertical velocity along the water column coincided with the theoretical prediction only for small wave amplitudes.Nevertheless,the maximum run-up height of an impulse wave can be accurately predicted via the solitary wave theory.Moreover,the maximum wall force during impulse wave-wall interaction was significantly larger than that during solitary wave reflection,particularly for high incident wave amplitudes.Overall,the present study demonstrated some striking differences in the interactions of landslide-generated impulse waves and solitary waves with a vertical wall.
基金supported by Guangxi Science and Technology Major Program(No.AA23073008)Hubei Key Laboratory of Water System Science for Sponge City Construction(Wuhan University)(No.2023–05)Nanning Innovation and Entrepreneur Leading Talent Project(No.2021001).
文摘The three-dimensional particle electrode system exhibits significant potential for application in the treatment of wastewater.Nonetheless,the advancement of effective granular electrodes characterized by elevated catalytic activity and minimal energy consumption continues to pose a significant challenge.In this research,Fluorine-doped copper-carbon(F/Cu-GAC)particle electrodes were effectively synthesized through an impregnationcalcination technique,utilizing granular activated carbon as the carrier and fluorinedoped modified copper oxides as the catalytic agents.The particle electrodes were subsequently utilized to promote the degradation of 2,4,6-trichlorophenol(2,4,6-TCP)in a threedimensional electrocatalytic reactor(3DER).The F/Cu-GAC particle electrodes were polarized under the action of electric field,which promoted the heterogeneous Fenton-like reaction in which H2O2 generated by two-electron oxygen reduction reaction(2e-ORR)of O_(2) was catalytically decomposed to·OH.The 3DER equipped with F/Cu-GAC particle electrodes showed 100%removal of 2,4,6-TCP and 79.24%removal of TOC with a specific energy consumption(EC)of approximately 0.019 kWh/g·COD after 2 h of operation.The F/Cu-GAC particle electrodes exhibited an overpotential of 0.38 V and an electrochemically active surface area(ECSA)of 715 cm^(2),as determined through linear sweep voltammetry(LSV)and cyclic voltammetry(CV)assessments.These findings suggest a high level of electrocatalytic performance.Furthermore,the catalytic mechanism of the 3DER equipped with F/Cu-GAC particle electrodes was elucidated through the application of X-ray photoelectron spectroscopy(XPS),electron spin resonance(ESR),and active species capture experiments.This investigation offers a novel approach for the effective degradation of 2,4,6-TCP.
基金supported by the National Natural Science Foundation of China(GrantNo.12072231).
文摘Hypersonic boundary-layer receptivity to freestream entropy and vorticity waves is investigated using direct numerical simula-tions for a Mach 6 flow over a 5.08 mm nose radius cone.Two frequencies of 33 kHz and 150 kHz are considered to be rep-resentative of the first and second instability modes,respectively.For the first mode,wall pressure fluctuations for both entropy and vorticity wave cases exhibit a strong modulation yet without a growing trend,indicating that the first mode is not generated despite its instability predicted by linear stability theory.The potential reason for this is the absence of postshock slow acoustic waves capable of synchronizing with the first mode.By contrast,for the second mode,a typical three-stage boundary-layer response is observed,consistent with that to slow acoustic waves studied previously.Furthermore,the postshock disturbances outside the boundary layer can be decomposed into the entropy(density/temperature fluctuations)and vorticity components(ve-locity fluctuations),and the latter is shown to play a leading role in generating the second mode,even for the case with entropy waves where the density/temperature fluctuations dominate the postshock regions.
基金Supported by the National Natural Science Foundation of China (No. 52271271)National Key Research and Development Program of China (No. 2022YFE0104500)Major Science and Technology Projects of the Ministry of Water Resources (No. SKS-2022025)。
文摘Extreme waves may considerably impact crucial coastal and marine engineering structures. The First Scientific Assessment Report on Ocean and Climate Change of China and The Fourth Assessment Report on Climate Change of China were published in 2020 and 2022, respectively.However, no concrete results on the long-term trends in wave changes in China have been obtained. In this study, long-term trends in extreme wave elements over the past 55 years were investigated using wave data from five in situ observation sites(i.e., Lao Hu Tan, Cheng Shan Tou,Ri Zhao, Nan Ji, Wei Zhou) along the coast of China. The five stations showed different trends in wave height. Results show a general downward trend in wave heights at the LHT and CST stations, reaching-0.78 and-1.44 cm/a, respectively, in summer at middle and high latitudes. NJI stations at middle-to-low latitudes are influenced by the winter monsoon and summer tropical cyclones, showing a substantial increase in extreme wave heights(0.7 cm/a in winter and 2.68 cm/a in summer). The cumulative duration of H_(1/10) ≥ 3 m at NJI and RZH has grown since 1990.
基金supported by Scientific Research and Technology Development Project of CNPC(2024ZG38,2024ZG42)the CNPC Innovation Fund(2022DQ02-0307).
文摘Fractures play a crucial role in various fields such as hydrocarbon exploration,groundwater resources management,and earthquake research.The determination of fracture location and the estimation of parameters such as fracture length and dip angle are the focus of geophysical work.In borehole observation system,the short distance between fractures and detectors leads to weak attenuation of elastic wave energy,and high-frequency source makes it easier to identify small-scale fractures.Compared to traditional monopole logging methods,dipole logging method has advantage of exciting pure shear waves sensitive to fractures,so its application is becoming increasingly widespread.However,since the reflected shear waves and scattered shear waves of fractures correspond to different fracture properties,how to distinguish and analyze these two kinds of waves is crucial for accurately characterizing the fracture parameters.To address this issue,numerical simulation of wave responses by a single fracture near a borehole in rock formation is performed,and the generation mechanism and characteristics of shear waves scattered by fractures are investigated.It is found that when the dip angle of the fracture surpasses a critical threshold,the S-wave will propagate to both endpoints of the fracture and generate scattered S-waves,resulting in two distinct scattered wave packets on the received waveform.When the polarization direction of the acoustic source is parallel to the strike of the fracture,the scattered SH-waves always have larger amplitude than the scattered SV-waves regardless of changing the fracture dip angle.Unlike SV-waves,the SH-waves scattered by the fracture do not have any mode conversion.Additionally,propagation of S-waves to a short length fracture can induce dipole mode vibration of the fracture within a wide frequency range.The phenomena of shear waves reflected and scattered by the fracture are further illustrated and verified by two field examples,thus showing the potential of scattered waves for fracture evaluation and characterization with borehole observation system.
基金supported by the National Natural Science Foundation of China(Nos.52271295,52088102).
文摘To propel the application of a bottom-hinged flap breakwater in real sea conditions,a two-dimensional computational fluid dynamics numerical model was conducted to investigate the pitching motion response and wave attenuation in random waves.First,the flow velocity distribution characteristic of the pitching flap at typical times was summarized.Then,the effects of random wave and flap parameters on the flap’s significant pitching angle amplitude θ_(s) and hydrodynamic coefficients were investigated.The results reveal that θ_(s) and wave reflection coefficient K_(r) values increase with increasing significant wave height Hs,random wave steepnessλs,and flap relative height.As Hs andλs increase,the wave transmission coefficient K_(t) increases while the wave dissipation coefficient K_(d) decreases.Additionally,K_(t) decreases with increasing flap relative height.With increasing equivalent damping coefficient ratio,θ_(s) and K_(t) decrease,while K_(r) and K_(d) increase.The relationships betweenλs and flap relative height on the one hand andθ_(s),K_(r),K_(t),and K_(d) in random waves on the other hand are compared to those in regular waves.Based on the equal incident wave energy and the equal incident wave energy flux,the pitching flap performs better in the wave attenuation capability under random waves than in regular waves.Finally,the dimensionless parameters with respect to random wave and flap were used to derive the K_(r) and K_(t) for-mulae,which were validated with the related data.
