Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,...Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves.展开更多
To address the complex seismic response of long tunnels longitudinally crossing heterogeneous geological formations,this study proposes a three-dimensional SV-wave oblique-incidence input method that accounts for the ...To address the complex seismic response of long tunnels longitudinally crossing heterogeneous geological formations,this study proposes a three-dimensional SV-wave oblique-incidence input method that accounts for the initial disturbance of the wave field induced by geological heterogeneity.The method transforms equivalent twodimensional free-field responses into equivalent nodal forces applied at the boundaries of a 3D numerical model.A longitudinally heterogeneous“hard-soft-hard”site and tunnel system is established,in which the surrounding rock is modeled using the Mohr-Coulomb constitutive law,while the concrete lining is described by the concrete damaged plasticity model.The deformation patterns and failure mechanisms of the site-tunnel system under SV-wave excitation are systematically investigated.The results indicate that seismic damage under SV-wave loading is mainly concentrated in the soft-rock region.Failure of the soft surrounding rock induces pronounced sliding of the overlying hard rock,and the tunnel suffers severe damage due to the combined effects of soft-rock failure and strong ground shaking.Parametric analyses further show that smaller impedance ratios,larger soft-rock widths,and larger incidence angles significantly intensify the seismic response of the tunnel.The findings of this study provide valuable insights for the seismic design of tunnels crossing longitudinally heterogeneous geological formations.展开更多
Observational analysis of the Earth’s stratospheric temperature structure and its dynamical behavior is of great significance for atmospheric dynamics research.In this paper,we present stratospheric temperatures in t...Observational analysis of the Earth’s stratospheric temperature structure and its dynamical behavior is of great significance for atmospheric dynamics research.In this paper,we present stratospheric temperatures in the range of 30–50 km above the Yinchuan observation site,retrieved from diurnal continuous Rayleigh scattering signal observation data collected by a 589 nm lidar throughout a single day.We also present observational studies of atmospheric tides and gravity wave cases.The diurnal temperature background field and perturbation field were obtained from the lidar data using the linear fitting method;these results exhibit good consistency with the temperature perturbation field extracted from ERA5.An obvious quasi-monochromatic inertial gravity wave was detected by application of a two-dimensional Fourier transform to the nighttime observation data with complete height coverage,which revealed these characteristic gravity wave parameters:a vertical wavelength of 8.53 km,a period of 8.46 h,and a downward-propagating vertical phase velocity.A nonlinear least-squares harmonic fitting method was used to extract amplitudes and phases of atmospheric diurnal and semi-diurnal tides in the 30−34 km range,where the diurnal data were relatively complete.The amplitudes increased with height,ranging from 0.6 to 2.5 K(diurnal tide)and 0.3 to 1.9 K(semi-diurnal tide),respectively.The phases showed a decreasing trend with height,indicating that the vertical phase velocity of the tides propagates downward while the energy propagates upward.These results indicate that diurnal 589 nm lidar observations data can provide important reference values for understanding the temperature structure of the stratosphere and the dynamical characteristics of atmospheric gravity waves and tides.展开更多
Fragment velocity distribution is an important parameter affecting the terminal effects of warheads.The rarefaction wave,end cap,and its confinement state can significantly affect the fragmentation of the cylindrical ...Fragment velocity distribution is an important parameter affecting the terminal effects of warheads.The rarefaction wave,end cap,and its confinement state can significantly affect the fragmentation of the cylindrical charge casing.Most of the existing studies have performed experiments and simulations considering the rarefaction wave and unfixed end caps;research on fixed end caps and sufficient theoretical explanations are limited.In this work,the effects of rarefaction waves,end caps,and their fixed states,on the fragment velocity distribution,were studied via experimentation and simulation,and reasonable theoretical explanations were provided.The results show that the rarefaction wave and end caps affect the fragment velocity by changing the pressure states of the detonation products.At the initiation end,the fragment velocities of casings with unfixed initiation ends are 33.3%(300 m/s)greater than that of casings without end caps,because of the weakening of the attenuation effect of the rarefaction wave.The fragment velocities of the casings with fixed initiation ends are 8.3%(100 m/s)greater than that of casings with unfixed initiation ends.At the non-initiation end,the fragment velocities are 24.8%(297 m/s)greater than that of a casing without end caps,and the reflecting shock wave generated by the fixed non-initiation end increases the fragment velocity by 7.3%(113 m/s),compared to the theoretical velocity.This work provides a basis for the structural design and analysis of the terminal effects of warheads.展开更多
This letter introduces the novel concept of Painlevé solitons—waves arising from the interaction between Painlevé waves and solitons in integrable systems.Painlevé solitons can also be viewed as solito...This letter introduces the novel concept of Painlevé solitons—waves arising from the interaction between Painlevé waves and solitons in integrable systems.Painlevé solitons can also be viewed as solitons propagating against a Painlevé wave background,in analogy to the established notion of elliptic solitons,which refers to solitons on an elliptic wave background.By employing a novel symmetry decomposition method aided by nonlocal residual symmetries,we explicitly construct (extended) Painlevé Ⅱ solitons for the Korteweg-de Vries equation and (extended) Painlevé Ⅳ solitons for the Boussinesq equation.展开更多
Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analyt...Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analytical solution to determine the longitudinal mechanical responses of tunnels subjected to the combined effects of seismic waves and strike-slip faulting.Adopting the elastic springbeam model,the seismic waves are modelled as shear horizontal(SH)waves and the fault dislocation follows an S-shaped pattern;the superposition principle for free-fielddisplacements caused by both effects is assumed.In addition,the transmission and reflectionof seismic waves at the fault-rock geological interface and the tangential contact conditions at the tunnel-rock interface are considered.The analytical model is validated against numerical simulations,confirmingits accuracy in calculating tunnel responses.Moreover,a parametric study is conducted to evaluate the impact of key factors,including fault displacement,fault zone width,fault dip angle,earthquake frequency,rock conditions,tunnel lining stiffness,and tangential contact conditions,on tunnel responses.Compared with each effect alone,the combined effects of seismic waves and strike-slip faulting significantlychange the tunnel deformation and internal forces,leading to increased tunnel responses,especially within the fault zone and near the fault-rock interfaces.Depending on specificparameters,tunnel responses can be classifiedinto seismic-dominated,faulting-dominated,and seismic-faulting coupled responses on the basis of the relative contributions of each effect.The proposed analytical solution can be applied to quickly predict the longitudinal mechanical behaviour of tunnels under such combined effects in engineering applications.展开更多
The damage evolution of polycrystalline Al with helium(He)bubbles under strongly decaying shock waves is studied by molecular dynamics simulations.A new damage region is observed near the loading side of the sample,an...The damage evolution of polycrystalline Al with helium(He)bubbles under strongly decaying shock waves is studied by molecular dynamics simulations.A new damage region is observed near the loading side of the sample,and the evolution characteristics and underlying mechanisms are elucidated.The development of damage in the new damage region begins after complete unloading of the incident shock wave and is further enhanced when the tensile stress arrives later.The damage evolution is completely controlled by the expansion-merging of He bubbles,without nucleation–growth of voids.This new damage region can be divided into two sections,each of which exhibits a unique dominant mechanism.The damage in the section closer to the loading side is due to the reverse velocity gradient formed after complete unloading of the incident shock wave,depending on the rate of decrease and the amplitude of the initial peak pressure.A high initial peak pressure that can lead to melting of material near the loading side is a necessary condition for the formation of the new damage region,since a significant reverse velocity gradient can only be established if melting occurs.The dominant mechanism in the section distant from the loading side is the action of tensile stress,associated with the profile of the incident shock wave upon reaching the free surface,which determines the material phase near the free surface.Moreover,the presence of He bubbles is another critical factor for formation of the new damage region,which does not occur in pure Al samples.展开更多
We show that in Schwarzschild equivalent mediums,the massless spin particles obey the same dynamical equation,from which we obtain remarkably simple formulae for the frequencies of the quasibound states.We find that t...We show that in Schwarzschild equivalent mediums,the massless spin particles obey the same dynamical equation,from which we obtain remarkably simple formulae for the frequencies of the quasibound states.We find that the quasibound frequencies of different bosons can be identical at the same quantum number l,and the same is true of different fermions,but a quasibound frequency for bosons can never equal a quasibound frequency for fermions.These results mean that in Schwarzschild equivalent mediums with the quasibound-state boundary conditions,characteristics of electromagnetic waves are the same as those for all the massless bosonic waves,thereby allowing electromagnetic waves to simulate gravitational waves.Our predictions can be tested in future experiments,building upon the successful preparation of Schwarzschild equivalent mediums.展开更多
Laser-driven inertial confinement fusion(ICF)is an important experimental platform for high-energy-density physics research under extreme conditions.In ICF research,high-quality shock waves are key to fusion energy re...Laser-driven inertial confinement fusion(ICF)is an important experimental platform for high-energy-density physics research under extreme conditions.In ICF research,high-quality shock waves are key to fusion energy release.The velocity interferometer system for any reflector(VISAR)is the most important diagnostic technique for measuring quantities such as shock wave and particle velocities with high precision and high spatiotemporal resolution.This paper provides a detailed introduction to the various configurations of VISAR on 10 and 100 kJ-level laser facilities in China,including Line VISAR,Dual-Axis VISAR,Wide-Angle VISAR,and Compressed Ultrafast Photography-VISAR.Recent advances and applications of VISAR diagnostics at these laser facilities are presented,and the future trend of development of high-spatiotemporal-resolution velocity diagnostic technology is described.展开更多
The vibration caused by blasting excavation of rock mass frequently poses a threat to the stability of adjacent tunnels.Previous research is limited by the simplification of a rock mass as a homogeneous elastic medium...The vibration caused by blasting excavation of rock mass frequently poses a threat to the stability of adjacent tunnels.Previous research is limited by the simplification of a rock mass as a homogeneous elastic medium,without considering the wave attenuation caused by viscoelasticity and wave separation induced by rock discontinuities,as well as plane waves while neglecting geometric attenuation of near-field nonplane blast waves.This paper establishes a theoretical model of cylindrical P-wave propagation across a fault to an adjacent existing tunnel.Based on the time-domain recursive method,vibration equations and peak particle velocity on the adjacent existing tunnel wall caused by a cylindrical wave passing through a fault are derived.The rock mass and fault are assumed to satisfy Kelvin viscoelastic bodies,and contact interfaces between fault and rock mass follow a nonlinear hyperbolic deformation model in the normal direction and a linear model in the tangential direction.The results show that tunnel vibration caused by the blast cylindrical P-wave is primarily induced by transmitted P-waves.With the increase of the fault dip angle,vibration on the upper side of the adjacent existing tunnel gradually decreases,while vibration on the lower side increases.The closer the vibration to the upper and lower sides,the stronger the shear effect on the tunnel wall,and the closer the vibration to the middle,the stronger the pressure effect on the tunnel wall.Larger fault thickness and higher initial blast wave frequency result in weaker vibration of the adjacent tunnel.The deeper the burial depth,the stronger the vibration of the adjacent tunnel wall.Findings of this study provide insight into the dynamic response of rock construction and safety evaluation in engineering service.展开更多
Since Blanford(1884)first linked Himalayan snowfall to subsequent Indian summer monsoon(ISM)rainfall,the potential for long-range forecasting has been recognized.Key advances followed:discovery of the Southern Oscilla...Since Blanford(1884)first linked Himalayan snowfall to subsequent Indian summer monsoon(ISM)rainfall,the potential for long-range forecasting has been recognized.Key advances followed:discovery of the Southern Oscillation(Walker,1925;Walker and Bliss,1932);identification of the Pacific-North American pattern(Wallace and Gutzler,1981);and Bjerknes’(1969)seminal study of ENSO as a predictable climate driver.Foundational theory—including equatorial wave dynamics(Matsuno,1966;Webster,1972;Gill,1980).展开更多
Most existing path planning approaches rely on discrete expansions or localized heuristics that can lead to extended re-planning,inefficient detours,and limited adaptability to complex obstacle distributions.These iss...Most existing path planning approaches rely on discrete expansions or localized heuristics that can lead to extended re-planning,inefficient detours,and limited adaptability to complex obstacle distributions.These issues are particularly pronounced when navigating cluttered or large-scale environments that demand both global coverage and smooth trajectory generation.To address these challenges,this paper proposes a Wave Water Simulator(WWS)algorithm,leveraging a physically motivated wave equation to achieve inherently smooth,globally consistent path planning.In WWS,wavefront expansions naturally identify safe corridors while seamlessly avoiding local minima,and selective corridor focusing reduces computational overhead in large or dense maps.Comprehensive simulations and real-world validations-encompassing both indoor and outdoor scenarios-demonstrate that WWS reduces path length by 2%-13%compared to conventional methods,while preserving gentle curvature and robust obstacle clearance.Furthermore,WWS requires minimal parameter tuning across diverse domains,underscoring its broad applicability to warehouse robotics,field operations,and autonomous service vehicles.These findings confirm that the proposed wave-based framework not only bridges the gap between local heuristics and global coverage but also sets a promising direction for future extensions toward dynamic obstacle scenarios and multi-agent coordination.展开更多
Biochar and biochar composites are versatile materials that can be used in many applications.In this study,biochar was prepared from sawdust and combined with the yttrium iron garnet(YIG)nanocrystal to investigate the...Biochar and biochar composites are versatile materials that can be used in many applications.In this study,biochar was prepared from sawdust and combined with the yttrium iron garnet(YIG)nanocrystal to investigate the shielding effectiveness of the composite structure.Firstly,the effect of the pyrolysis temperature on the shielding effectiveness of biochar was investigated.Secondly,biochars combined with YIG nanocrystals with different contents and shielding effectiveness of the composites were investigated.The electromagnetic effectiveness of the samples was investigated within the X band(8-12 GHz).The findings indicate that biochar demonstrates enhanced absorption properties with elevated pyrolysis temperatures.Biochars demonstrated an approximate 40 d B shielding effectiveness,while YIG exhibited approximately 7 d B,corresponding to absorption at 8 GHz.However,the combination of biochar and YIG exhibited exceptional absorption,reaching 67.12 d B at 8 GHz.展开更多
Numerical simulations and theoretical models are developed in this paper for the Detonation-Wave/Boundary-Layer Interactions(DWBLIs)under reflections.Transient flow fields demonstrate the highly non-stationarity of th...Numerical simulations and theoretical models are developed in this paper for the Detonation-Wave/Boundary-Layer Interactions(DWBLIs)under reflections.Transient flow fields demonstrate the highly non-stationarity of the DWBLIs when Mach Reflection(MR)occur,and subsequent analyses show that the subsonic region introduced by the boundary layer exacerbates the instability.Further quantitative analyses show that viscosity has little effect on propulsive performance and the separation wave can be considered as an oblique detonation wave.Influence parameters to DWBLIs such as combustion chamber height,incoming Mach number,equivalence ratio,and inlet channel length are categorized and studied.Besides simulations,theoretical analytical modeling is established for Regular Reflection(RR)and MR of DWBLIs.Multiple formulas for the separation zone length are obtained according to the mass conservation under different transformation type between inviscid and viscid reflections.Comparison with the numerical simulations verifies the validity of the model and it can be further generalized to the curved DWBLIs.The developed model makes the theoretical solution process of DWBLIs possible and provides the key foundation for further analysis and solution.展开更多
Aluminum nanoparticles,owing to their high energy density and excellent reactivity,are widely used to enhance the energy release efficiency of explosives.In this study,reactive molecular dynamics simulations were empl...Aluminum nanoparticles,owing to their high energy density and excellent reactivity,are widely used to enhance the energy release efficiency of explosives.In this study,reactive molecular dynamics simulations were employed to systematically investigate the hotspot evolution and reaction kinetics of aluminum nanoparticles under shock loading.The results show that hotspots predominantly form and evolve along the oxide layer interface,exhibiting a typical"hot shell-cold core"structure.A thicker oxide layer significantly delays the heating and reaction initiation of the aluminum core,with reversible crystal structure transformations observed inside the core.Larger particles facilitate heat accumulation and promote sustained reactions.As the oxide layer thickness increases,the reaction mechanism of aluminum nanoparticles transitions from melting-diffusion and micro-explosion oxidation to an oxidation-diffusion dominated process.A dense nitrogen-containing reaction layer forms on the surface,which suppresses the later-stage reaction.A nonlinear reaction kinetics model based on bond statistics reveals that particles with a thin oxide layer exhibit rapid reaction saturation and are insensitive to shock velocity.Particles with intermediate oxide thickness exhibit a reaction behavior that gradually slows down over time,while those with a thick oxide layer can exhibit accelerated reactions under high-velocity shocks due to enhanced diffusion.Small particles show significantly increased reaction rates at high velocities,whereas large particles tend to slow down due to the thickening of the surface reaction layer.The oxide layer thickness,particle size,and shock velocity exhibit complex competitive and synergistic effects that jointly regulate the initiation,rate,and evolution of aluminum nanoparticle reactions.展开更多
Using high-resolution observations,mesoscale simulations,and idealized experiments,this study investigates the mechanisms governing an episode of orographic convection initiation(CI)during the North China Heavy Rainfa...Using high-resolution observations,mesoscale simulations,and idealized experiments,this study investigates the mechanisms governing an episode of orographic convection initiation(CI)during the North China Heavy Rainfall Experiment.On 4 August 2024,repeated CI occurred over the eastern slopes of the Taihang Mountains in the late afternoon,subsequently enhancing an upstream downhill convective storm.Wind profiler radar data and dense automatic weather stations reveal that CI was supported by strengthening southeasterly upslope winds.These winds primarily resulted from the migration of the mountain-plain solenoid and the mountainward-propagating outflow from a convective cold pool over the plain,with sensitivity experiments showing the latter contributed roughly 22%of the wind strength.The upslope flows gradually transported unstable air from the plain to the slope,fostering CI.Mesoscale simulations further highlight the key role of orographic waves near the mountain ridge,which generated strong downslope winds.The near-surface convergence between downslope and upslope flows,combined with wave-induced divergence aloft,produced deep ascent over the slope.Removing mountain ridges weakened wave strength and reduced downslope wind speeds by~8 m s^(-1).Without orographic heating in the idealized simulation(i.e.,no mountain-plain solenoid),only strong wave descent occurred below 2km,inhibiting CI.These findings underscore the critical interplay among plain convection,orographic waves,and the mountain-plain solenoid,offering new insight into the processes controlling orographic CI in North China.展开更多
Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in ...Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in this paper.The five-point central difference method is used for spatial discretization,and the fourth-order Adams predictor-corrector scheme is employed for marching in time.The domain-decomposition method is applied for the wave-current generation and absorption.The effects of currents on the wave profile and velocity field are examined under two conditions:the same velocity of currents at the still-water level and the constant flow volume of currents.Wave profiles and velocity fields demonstrate substantial differences in three types of currents owing to the diverse vertical distribution of current velocity and vorticity.Then,loads on small-scale vertical cylinders subjected to regular waves and three types of background currents with the same flow volume are investigated.The maximum load intensity and load fluctuation amplitude in uniform,linear shear,and quadratic shear currents increase sequentially.The stretched superposition method overestimates the maximum load intensity and load fluctuation amplitude in opposing currents and underestimates these values in following currents.The stretched superposition method obtains a poor approximation for strong nonlinear waves,particularly in the case of the opposing quadratic shear current.展开更多
This study investigated the characteristics and mechanisms of summer regional persistent extreme precipitation events(RPEPEs)over South China(SC)modulated by distinct intensity regimes of 10-30-day intraseasonal oscil...This study investigated the characteristics and mechanisms of summer regional persistent extreme precipitation events(RPEPEs)over South China(SC)modulated by distinct intensity regimes of 10-30-day intraseasonal oscillation(ISO).Diagnostic analyses revealed that the spatiotemporal evolution of RPEPEs exhibits robust phase-locking with the 10-30-day intraseasonal precipitation.By classifying RPEPEs into strong-ISO(SRPEPE)and weak-ISO(WRPEPE)composites based on the amplitude of 10-30-day filtered precipitation,we demonstrate a 14.6%enhancement in peak precipitation intensity during SRPEPEs compared to WRPEPEs.These distinct precipitation regimes are governed by fundamentally different Rossby wave teleconnection patterns over Eurasia.During SRPEPEs,a robust southeastward-propagating 10-30-day Rossby wave train originating from the Barents Sea traverses midlatitude Eurasia,effectively perturbing the northwestern Pacific upper-level circulation and establishing a favorable dynamic environment over SC.In contrast,WRPEPEs are associated with weaker eastward-propagating wave trains constrained along the subtropical jet stream.The horizontal convergence of background moisture driven by 10-30-day winds significantly amplifies lower-tropospheric humidity during SRPEPEs.The thermal advection of background temperature by 10-30-day geostrophic winds enhances baroclinic instability and vertical motion,intensifying precipitation under these moisture conditions.展开更多
Residents living near drill-and-blast tunnels often experience disturbances from blasting operations.This motivates us to investigate the characteristics of airblasts and resulting noise through on-site monitoring at ...Residents living near drill-and-blast tunnels often experience disturbances from blasting operations.This motivates us to investigate the characteristics of airblasts and resulting noise through on-site monitoring at three tunnels.The research focuses on both the temporal evolution and spatial propagation of airblasts.Temporal analysis,including peak overpressure(POp),positive duration(PD),and Fourier main frequency(MF),emphasizes the relationship between airblast characteristics,blasting delays,and rock grade.It shows that airblast bandwidths are typically in the range of 3e200 Hz,with noise levels exceeding 130 dB,which is comparable to jet engines and rocket launch.Spatial propagation analysis reveals the impact of tunnel space on airblast propagation.Although POp and PD typically decrease with distance inside the tunnel,wave superposition can cause increased overpressure and prolonged durations at far-field distances(above 60 m kg^(-1/3)).Outside the tunnel,sound radiation was influenced by azimuth and was basically determined by sound power d an often-overlooked factor.To address the anisotropic propagation of airblasts,a predictive model was proposed for external noise levels,considering variables like distance,azimuth angle,initial sound power,and wave expansion.Validated by tests,this model successfully unifies data from three studies,helping to explain and predict airblast disturbances near tunnels.展开更多
This study investigates the relationship between atmospheric stratification (i.e., static stability given by N^(2)) and the vertical energy transfer of stationary planetary waves, and further illustrates the underlyin...This study investigates the relationship between atmospheric stratification (i.e., static stability given by N^(2)) and the vertical energy transfer of stationary planetary waves, and further illustrates the underlying physical mechanism. Specifically, for the simplified case of constant stratospheric N^(2), the refractive index square of planetary waves has a theoretical tendency to increase first and then decrease with an increased N^(2), whereas the group velocity weakens. Mechanistically, this behavior can be understood as an intensified suppression of vertical isentropic surface displacement caused by meridional heat transport of planetary waves under strong N^(2) conditions. Observational analysis corroborates this finding, demonstrating a reduction in the vertical-propagation velocity of waves with increased N^(2). A linear, quasi- geostrophic, mid-latitude beta-plane model with a constant background westerly wind and a prescribed N^(2) applicable to the stratosphere is used to obtain analytic solutions. In this model, the planetary waves are initiated by steady energy influx from the lower boundary. The analysis indicates that under strong N^(2) conditions, the amplitude of planetary waves can be sufficiently increased by the effective energy convergence due to the slowing vertical energy transfer, resulting in a streamfunction response in this model that contains more energy. For N^(2) with a quasi-linear vertical variation, the results bear a resemblance to the constant case, except that the wave amplitude and oscillating frequency show some vertical variations.展开更多
文摘Nonlinear Rossby waves are used to describe typical wave phenomena in large-scale atmosphere andocean.Owing to the nonlinearity of the involved problems,the weakly nonlinear method,ie the derivative ex-pansion method,was mainly used to investigate Rossby waves under the combined effects of the generalizedβ-effect and the basic flow effect.The derivative expansion method has the advantage of capturing the multi-scalecharacteristics of wave processes simultaneously.In the case where the perturbation expansion is independentof secular terms,the nonlinear equations describing the amplitude evolution of nonlinear waves were derived,such as the Korteweg-de Vries equation,the Boussinesq equation and Zakharov-Kuznetsov equation.Both quali-tative and quantitative analyses indicate that the generalizedβ-effect is the key factor inducing the evolution ofRossby solitary waves.
基金supported by the National Key Research and Development Program(Grant No.2024YFF0508203)the National Natural Science Foundation of China(Grant No.52378475)the Science and Technology Innovation Special Project of Xiongan New Area,National Key R&D Program(Grant No.2025XAGG0056)。
文摘To address the complex seismic response of long tunnels longitudinally crossing heterogeneous geological formations,this study proposes a three-dimensional SV-wave oblique-incidence input method that accounts for the initial disturbance of the wave field induced by geological heterogeneity.The method transforms equivalent twodimensional free-field responses into equivalent nodal forces applied at the boundaries of a 3D numerical model.A longitudinally heterogeneous“hard-soft-hard”site and tunnel system is established,in which the surrounding rock is modeled using the Mohr-Coulomb constitutive law,while the concrete lining is described by the concrete damaged plasticity model.The deformation patterns and failure mechanisms of the site-tunnel system under SV-wave excitation are systematically investigated.The results indicate that seismic damage under SV-wave loading is mainly concentrated in the soft-rock region.Failure of the soft surrounding rock induces pronounced sliding of the overlying hard rock,and the tunnel suffers severe damage due to the combined effects of soft-rock failure and strong ground shaking.Parametric analyses further show that smaller impedance ratios,larger soft-rock widths,and larger incidence angles significantly intensify the seismic response of the tunnel.The findings of this study provide valuable insights for the seismic design of tunnels crossing longitudinally heterogeneous geological formations.
基金supported by the Key Research Program of the Chinese Academy of Sciences(Grant NO.KGFZD-145-23-17)the Specialized Research Fund for State Key Laboratories.
文摘Observational analysis of the Earth’s stratospheric temperature structure and its dynamical behavior is of great significance for atmospheric dynamics research.In this paper,we present stratospheric temperatures in the range of 30–50 km above the Yinchuan observation site,retrieved from diurnal continuous Rayleigh scattering signal observation data collected by a 589 nm lidar throughout a single day.We also present observational studies of atmospheric tides and gravity wave cases.The diurnal temperature background field and perturbation field were obtained from the lidar data using the linear fitting method;these results exhibit good consistency with the temperature perturbation field extracted from ERA5.An obvious quasi-monochromatic inertial gravity wave was detected by application of a two-dimensional Fourier transform to the nighttime observation data with complete height coverage,which revealed these characteristic gravity wave parameters:a vertical wavelength of 8.53 km,a period of 8.46 h,and a downward-propagating vertical phase velocity.A nonlinear least-squares harmonic fitting method was used to extract amplitudes and phases of atmospheric diurnal and semi-diurnal tides in the 30−34 km range,where the diurnal data were relatively complete.The amplitudes increased with height,ranging from 0.6 to 2.5 K(diurnal tide)and 0.3 to 1.9 K(semi-diurnal tide),respectively.The phases showed a decreasing trend with height,indicating that the vertical phase velocity of the tides propagates downward while the energy propagates upward.These results indicate that diurnal 589 nm lidar observations data can provide important reference values for understanding the temperature structure of the stratosphere and the dynamical characteristics of atmospheric gravity waves and tides.
基金the support of the Youth Scientific Research Projects of the Basic Research Program of Shanxi Province(Grant Nos.202303021222111,202303021222113)the China Postdoctoral Science Foundation(Grant No.2025M770001).
文摘Fragment velocity distribution is an important parameter affecting the terminal effects of warheads.The rarefaction wave,end cap,and its confinement state can significantly affect the fragmentation of the cylindrical charge casing.Most of the existing studies have performed experiments and simulations considering the rarefaction wave and unfixed end caps;research on fixed end caps and sufficient theoretical explanations are limited.In this work,the effects of rarefaction waves,end caps,and their fixed states,on the fragment velocity distribution,were studied via experimentation and simulation,and reasonable theoretical explanations were provided.The results show that the rarefaction wave and end caps affect the fragment velocity by changing the pressure states of the detonation products.At the initiation end,the fragment velocities of casings with unfixed initiation ends are 33.3%(300 m/s)greater than that of casings without end caps,because of the weakening of the attenuation effect of the rarefaction wave.The fragment velocities of the casings with fixed initiation ends are 8.3%(100 m/s)greater than that of casings with unfixed initiation ends.At the non-initiation end,the fragment velocities are 24.8%(297 m/s)greater than that of a casing without end caps,and the reflecting shock wave generated by the fixed non-initiation end increases the fragment velocity by 7.3%(113 m/s),compared to the theoretical velocity.This work provides a basis for the structural design and analysis of the terminal effects of warheads.
基金supported by the National Natural Science Foundations of China (Grant Nos.12235007,12001424,12271324,and 12501333)the Natural Science Basic research program of Shaanxi Province (Grant Nos.2021JZ-21 and 2024JC-YBQN-0069)+3 种基金the China Postdoctoral Science Foundation (Grant Nos.2020M673332 and 2024M751921)the Fundamental Research Funds for the Central Universities (Grant No.GK202304028)the 2023 Shaanxi Province Postdoctoral Research Project (Grant No.2023BSHEDZZ186)Xi’an University,Xi’an Science and Technology Plan Wutongshu Technology Transfer Action Innovation Team(Grant No.25WTZD07)。
文摘This letter introduces the novel concept of Painlevé solitons—waves arising from the interaction between Painlevé waves and solitons in integrable systems.Painlevé solitons can also be viewed as solitons propagating against a Painlevé wave background,in analogy to the established notion of elliptic solitons,which refers to solitons on an elliptic wave background.By employing a novel symmetry decomposition method aided by nonlocal residual symmetries,we explicitly construct (extended) Painlevé Ⅱ solitons for the Korteweg-de Vries equation and (extended) Painlevé Ⅳ solitons for the Boussinesq equation.
基金supported by the National Natural Science Foundation of China(No.41941018)Shanghai Gaofeng Discipline Construction Funding.
文摘Strong seismic excitation and fault dislocation are likely to occur simultaneously in high-intensity seismic zones,causing severe damage to tunnels crossing active fault zones.This paper aims to develop a novel analytical solution to determine the longitudinal mechanical responses of tunnels subjected to the combined effects of seismic waves and strike-slip faulting.Adopting the elastic springbeam model,the seismic waves are modelled as shear horizontal(SH)waves and the fault dislocation follows an S-shaped pattern;the superposition principle for free-fielddisplacements caused by both effects is assumed.In addition,the transmission and reflectionof seismic waves at the fault-rock geological interface and the tangential contact conditions at the tunnel-rock interface are considered.The analytical model is validated against numerical simulations,confirmingits accuracy in calculating tunnel responses.Moreover,a parametric study is conducted to evaluate the impact of key factors,including fault displacement,fault zone width,fault dip angle,earthquake frequency,rock conditions,tunnel lining stiffness,and tangential contact conditions,on tunnel responses.Compared with each effect alone,the combined effects of seismic waves and strike-slip faulting significantlychange the tunnel deformation and internal forces,leading to increased tunnel responses,especially within the fault zone and near the fault-rock interfaces.Depending on specificparameters,tunnel responses can be classifiedinto seismic-dominated,faulting-dominated,and seismic-faulting coupled responses on the basis of the relative contributions of each effect.The proposed analytical solution can be applied to quickly predict the longitudinal mechanical behaviour of tunnels under such combined effects in engineering applications.
基金supported by the National Natural Science Foundation of China(Grant No.12172063).
文摘The damage evolution of polycrystalline Al with helium(He)bubbles under strongly decaying shock waves is studied by molecular dynamics simulations.A new damage region is observed near the loading side of the sample,and the evolution characteristics and underlying mechanisms are elucidated.The development of damage in the new damage region begins after complete unloading of the incident shock wave and is further enhanced when the tensile stress arrives later.The damage evolution is completely controlled by the expansion-merging of He bubbles,without nucleation–growth of voids.This new damage region can be divided into two sections,each of which exhibits a unique dominant mechanism.The damage in the section closer to the loading side is due to the reverse velocity gradient formed after complete unloading of the incident shock wave,depending on the rate of decrease and the amplitude of the initial peak pressure.A high initial peak pressure that can lead to melting of material near the loading side is a necessary condition for the formation of the new damage region,since a significant reverse velocity gradient can only be established if melting occurs.The dominant mechanism in the section distant from the loading side is the action of tensile stress,associated with the profile of the incident shock wave upon reaching the free surface,which determines the material phase near the free surface.Moreover,the presence of He bubbles is another critical factor for formation of the new damage region,which does not occur in pure Al samples.
基金supported by the National Natural Science Foundation of China under Grant No.12175198。
文摘We show that in Schwarzschild equivalent mediums,the massless spin particles obey the same dynamical equation,from which we obtain remarkably simple formulae for the frequencies of the quasibound states.We find that the quasibound frequencies of different bosons can be identical at the same quantum number l,and the same is true of different fermions,but a quasibound frequency for bosons can never equal a quasibound frequency for fermions.These results mean that in Schwarzschild equivalent mediums with the quasibound-state boundary conditions,characteristics of electromagnetic waves are the same as those for all the massless bosonic waves,thereby allowing electromagnetic waves to simulate gravitational waves.Our predictions can be tested in future experiments,building upon the successful preparation of Schwarzschild equivalent mediums.
基金supported by the National Key Laboratory of Plasma Physics,Laser Fusion Research Center,China Academy of Engineering Physics under the National Natural Science Foundation of China(Grant Nos.12127810 and 12475242).
文摘Laser-driven inertial confinement fusion(ICF)is an important experimental platform for high-energy-density physics research under extreme conditions.In ICF research,high-quality shock waves are key to fusion energy release.The velocity interferometer system for any reflector(VISAR)is the most important diagnostic technique for measuring quantities such as shock wave and particle velocities with high precision and high spatiotemporal resolution.This paper provides a detailed introduction to the various configurations of VISAR on 10 and 100 kJ-level laser facilities in China,including Line VISAR,Dual-Axis VISAR,Wide-Angle VISAR,and Compressed Ultrafast Photography-VISAR.Recent advances and applications of VISAR diagnostics at these laser facilities are presented,and the future trend of development of high-spatiotemporal-resolution velocity diagnostic technology is described.
基金Natural Science Basic Research Program of Shaanxi Province,Grant/Award Number:2023-YBGY-085National Natural Science Foundation of China,Grant/Award Numbers:41902277,42172302Fundamental Research Funds for the Central Universities,Grant/Award Number:CHD.300102282201。
文摘The vibration caused by blasting excavation of rock mass frequently poses a threat to the stability of adjacent tunnels.Previous research is limited by the simplification of a rock mass as a homogeneous elastic medium,without considering the wave attenuation caused by viscoelasticity and wave separation induced by rock discontinuities,as well as plane waves while neglecting geometric attenuation of near-field nonplane blast waves.This paper establishes a theoretical model of cylindrical P-wave propagation across a fault to an adjacent existing tunnel.Based on the time-domain recursive method,vibration equations and peak particle velocity on the adjacent existing tunnel wall caused by a cylindrical wave passing through a fault are derived.The rock mass and fault are assumed to satisfy Kelvin viscoelastic bodies,and contact interfaces between fault and rock mass follow a nonlinear hyperbolic deformation model in the normal direction and a linear model in the tangential direction.The results show that tunnel vibration caused by the blast cylindrical P-wave is primarily induced by transmitted P-waves.With the increase of the fault dip angle,vibration on the upper side of the adjacent existing tunnel gradually decreases,while vibration on the lower side increases.The closer the vibration to the upper and lower sides,the stronger the shear effect on the tunnel wall,and the closer the vibration to the middle,the stronger the pressure effect on the tunnel wall.Larger fault thickness and higher initial blast wave frequency result in weaker vibration of the adjacent tunnel.The deeper the burial depth,the stronger the vibration of the adjacent tunnel wall.Findings of this study provide insight into the dynamic response of rock construction and safety evaluation in engineering service.
文摘Since Blanford(1884)first linked Himalayan snowfall to subsequent Indian summer monsoon(ISM)rainfall,the potential for long-range forecasting has been recognized.Key advances followed:discovery of the Southern Oscillation(Walker,1925;Walker and Bliss,1932);identification of the Pacific-North American pattern(Wallace and Gutzler,1981);and Bjerknes’(1969)seminal study of ENSO as a predictable climate driver.Foundational theory—including equatorial wave dynamics(Matsuno,1966;Webster,1972;Gill,1980).
文摘Most existing path planning approaches rely on discrete expansions or localized heuristics that can lead to extended re-planning,inefficient detours,and limited adaptability to complex obstacle distributions.These issues are particularly pronounced when navigating cluttered or large-scale environments that demand both global coverage and smooth trajectory generation.To address these challenges,this paper proposes a Wave Water Simulator(WWS)algorithm,leveraging a physically motivated wave equation to achieve inherently smooth,globally consistent path planning.In WWS,wavefront expansions naturally identify safe corridors while seamlessly avoiding local minima,and selective corridor focusing reduces computational overhead in large or dense maps.Comprehensive simulations and real-world validations-encompassing both indoor and outdoor scenarios-demonstrate that WWS reduces path length by 2%-13%compared to conventional methods,while preserving gentle curvature and robust obstacle clearance.Furthermore,WWS requires minimal parameter tuning across diverse domains,underscoring its broad applicability to warehouse robotics,field operations,and autonomous service vehicles.These findings confirm that the proposed wave-based framework not only bridges the gap between local heuristics and global coverage but also sets a promising direction for future extensions toward dynamic obstacle scenarios and multi-agent coordination.
基金support provided by the Center for Fabrication and Application of Electronic Materials at Dokuz Eylül University,Türkiye。
文摘Biochar and biochar composites are versatile materials that can be used in many applications.In this study,biochar was prepared from sawdust and combined with the yttrium iron garnet(YIG)nanocrystal to investigate the shielding effectiveness of the composite structure.Firstly,the effect of the pyrolysis temperature on the shielding effectiveness of biochar was investigated.Secondly,biochars combined with YIG nanocrystals with different contents and shielding effectiveness of the composites were investigated.The electromagnetic effectiveness of the samples was investigated within the X band(8-12 GHz).The findings indicate that biochar demonstrates enhanced absorption properties with elevated pyrolysis temperatures.Biochars demonstrated an approximate 40 d B shielding effectiveness,while YIG exhibited approximately 7 d B,corresponding to absorption at 8 GHz.However,the combination of biochar and YIG exhibited exceptional absorption,reaching 67.12 d B at 8 GHz.
基金support of the National Natural Science Foundation of China(Nos.U20A2069,U21B6003,12302389 and 12472337)the Advanced Aero-Power Innovation Workstation,China(No.HKCX2024-01-017)。
文摘Numerical simulations and theoretical models are developed in this paper for the Detonation-Wave/Boundary-Layer Interactions(DWBLIs)under reflections.Transient flow fields demonstrate the highly non-stationarity of the DWBLIs when Mach Reflection(MR)occur,and subsequent analyses show that the subsonic region introduced by the boundary layer exacerbates the instability.Further quantitative analyses show that viscosity has little effect on propulsive performance and the separation wave can be considered as an oblique detonation wave.Influence parameters to DWBLIs such as combustion chamber height,incoming Mach number,equivalence ratio,and inlet channel length are categorized and studied.Besides simulations,theoretical analytical modeling is established for Regular Reflection(RR)and MR of DWBLIs.Multiple formulas for the separation zone length are obtained according to the mass conservation under different transformation type between inviscid and viscid reflections.Comparison with the numerical simulations verifies the validity of the model and it can be further generalized to the curved DWBLIs.The developed model makes the theoretical solution process of DWBLIs possible and provides the key foundation for further analysis and solution.
基金supported by the State Key Program of National Natural Science Foundation of China(No.12272051)the BIT Research and Innovation Promoting Project(No.2023YCXY17).
文摘Aluminum nanoparticles,owing to their high energy density and excellent reactivity,are widely used to enhance the energy release efficiency of explosives.In this study,reactive molecular dynamics simulations were employed to systematically investigate the hotspot evolution and reaction kinetics of aluminum nanoparticles under shock loading.The results show that hotspots predominantly form and evolve along the oxide layer interface,exhibiting a typical"hot shell-cold core"structure.A thicker oxide layer significantly delays the heating and reaction initiation of the aluminum core,with reversible crystal structure transformations observed inside the core.Larger particles facilitate heat accumulation and promote sustained reactions.As the oxide layer thickness increases,the reaction mechanism of aluminum nanoparticles transitions from melting-diffusion and micro-explosion oxidation to an oxidation-diffusion dominated process.A dense nitrogen-containing reaction layer forms on the surface,which suppresses the later-stage reaction.A nonlinear reaction kinetics model based on bond statistics reveals that particles with a thin oxide layer exhibit rapid reaction saturation and are insensitive to shock velocity.Particles with intermediate oxide thickness exhibit a reaction behavior that gradually slows down over time,while those with a thick oxide layer can exhibit accelerated reactions under high-velocity shocks due to enhanced diffusion.Small particles show significantly increased reaction rates at high velocities,whereas large particles tend to slow down due to the thickening of the surface reaction layer.The oxide layer thickness,particle size,and shock velocity exhibit complex competitive and synergistic effects that jointly regulate the initiation,rate,and evolution of aluminum nanoparticle reactions.
基金supported by the National Key Research and Development Program of China(Grant No.2024YFC3013003)the National Natural Science Foundation of China(Grant Nos.424B2033 and 42475002)+3 种基金projects supported by the Southern Marine Science and Engineering Guangdong Laboratory(Zhuhai)(Grant Nos.SML2024SP035,SML2024SP012,311024001)the Guangdong Project of Basic and Applied Basic Research(Grant Nos.2024A1515510005 and2025A1515011974)the Key Innovation Team of the China Meteorological Administration(Grant No.CMA2023ZD08)the State Key Laboratory of Severe Weather Meteorological Science and Technology(Grant No.2025QZA10)。
文摘Using high-resolution observations,mesoscale simulations,and idealized experiments,this study investigates the mechanisms governing an episode of orographic convection initiation(CI)during the North China Heavy Rainfall Experiment.On 4 August 2024,repeated CI occurred over the eastern slopes of the Taihang Mountains in the late afternoon,subsequently enhancing an upstream downhill convective storm.Wind profiler radar data and dense automatic weather stations reveal that CI was supported by strengthening southeasterly upslope winds.These winds primarily resulted from the migration of the mountain-plain solenoid and the mountainward-propagating outflow from a convective cold pool over the plain,with sensitivity experiments showing the latter contributed roughly 22%of the wind strength.The upslope flows gradually transported unstable air from the plain to the slope,fostering CI.Mesoscale simulations further highlight the key role of orographic waves near the mountain ridge,which generated strong downslope winds.The near-surface convergence between downslope and upslope flows,combined with wave-induced divergence aloft,produced deep ascent over the slope.Removing mountain ridges weakened wave strength and reduced downslope wind speeds by~8 m s^(-1).Without orographic heating in the idealized simulation(i.e.,no mountain-plain solenoid),only strong wave descent occurred below 2km,inhibiting CI.These findings underscore the critical interplay among plain convection,orographic waves,and the mountain-plain solenoid,offering new insight into the processes controlling orographic CI in North China.
基金Supported by the Development and Application Project of Ship CAE Software.
文摘Studies of wave-current interactions are vital for the safe design of structures.Regular waves in the presence of uniform,linear shear,and quadratic shear currents are explored by the High-Level Green-Naghdi model in this paper.The five-point central difference method is used for spatial discretization,and the fourth-order Adams predictor-corrector scheme is employed for marching in time.The domain-decomposition method is applied for the wave-current generation and absorption.The effects of currents on the wave profile and velocity field are examined under two conditions:the same velocity of currents at the still-water level and the constant flow volume of currents.Wave profiles and velocity fields demonstrate substantial differences in three types of currents owing to the diverse vertical distribution of current velocity and vorticity.Then,loads on small-scale vertical cylinders subjected to regular waves and three types of background currents with the same flow volume are investigated.The maximum load intensity and load fluctuation amplitude in uniform,linear shear,and quadratic shear currents increase sequentially.The stretched superposition method overestimates the maximum load intensity and load fluctuation amplitude in opposing currents and underestimates these values in following currents.The stretched superposition method obtains a poor approximation for strong nonlinear waves,particularly in the case of the opposing quadratic shear current.
基金sponsored by the National Natural Science Foundation of China (grant 42575038)the National Key Research and Development Program of China (grant2022YFF0801702)the National Natural Science Foundation of China (grant 42206257 and 42205163)
文摘This study investigated the characteristics and mechanisms of summer regional persistent extreme precipitation events(RPEPEs)over South China(SC)modulated by distinct intensity regimes of 10-30-day intraseasonal oscillation(ISO).Diagnostic analyses revealed that the spatiotemporal evolution of RPEPEs exhibits robust phase-locking with the 10-30-day intraseasonal precipitation.By classifying RPEPEs into strong-ISO(SRPEPE)and weak-ISO(WRPEPE)composites based on the amplitude of 10-30-day filtered precipitation,we demonstrate a 14.6%enhancement in peak precipitation intensity during SRPEPEs compared to WRPEPEs.These distinct precipitation regimes are governed by fundamentally different Rossby wave teleconnection patterns over Eurasia.During SRPEPEs,a robust southeastward-propagating 10-30-day Rossby wave train originating from the Barents Sea traverses midlatitude Eurasia,effectively perturbing the northwestern Pacific upper-level circulation and establishing a favorable dynamic environment over SC.In contrast,WRPEPEs are associated with weaker eastward-propagating wave trains constrained along the subtropical jet stream.The horizontal convergence of background moisture driven by 10-30-day winds significantly amplifies lower-tropospheric humidity during SRPEPEs.The thermal advection of background temperature by 10-30-day geostrophic winds enhances baroclinic instability and vertical motion,intensifying precipitation under these moisture conditions.
基金supported by the Shenzhen Stability Support Plan(Grant No.20231122095154003)National Natural Science Foundation of China(Grant Nos.51978671 and 52422807).
文摘Residents living near drill-and-blast tunnels often experience disturbances from blasting operations.This motivates us to investigate the characteristics of airblasts and resulting noise through on-site monitoring at three tunnels.The research focuses on both the temporal evolution and spatial propagation of airblasts.Temporal analysis,including peak overpressure(POp),positive duration(PD),and Fourier main frequency(MF),emphasizes the relationship between airblast characteristics,blasting delays,and rock grade.It shows that airblast bandwidths are typically in the range of 3e200 Hz,with noise levels exceeding 130 dB,which is comparable to jet engines and rocket launch.Spatial propagation analysis reveals the impact of tunnel space on airblast propagation.Although POp and PD typically decrease with distance inside the tunnel,wave superposition can cause increased overpressure and prolonged durations at far-field distances(above 60 m kg^(-1/3)).Outside the tunnel,sound radiation was influenced by azimuth and was basically determined by sound power d an often-overlooked factor.To address the anisotropic propagation of airblasts,a predictive model was proposed for external noise levels,considering variables like distance,azimuth angle,initial sound power,and wave expansion.Validated by tests,this model successfully unifies data from three studies,helping to explain and predict airblast disturbances near tunnels.
基金supported by the National Natural Science Foundation of China(Grant No.42261134532,42405059,and U2342212)。
文摘This study investigates the relationship between atmospheric stratification (i.e., static stability given by N^(2)) and the vertical energy transfer of stationary planetary waves, and further illustrates the underlying physical mechanism. Specifically, for the simplified case of constant stratospheric N^(2), the refractive index square of planetary waves has a theoretical tendency to increase first and then decrease with an increased N^(2), whereas the group velocity weakens. Mechanistically, this behavior can be understood as an intensified suppression of vertical isentropic surface displacement caused by meridional heat transport of planetary waves under strong N^(2) conditions. Observational analysis corroborates this finding, demonstrating a reduction in the vertical-propagation velocity of waves with increased N^(2). A linear, quasi- geostrophic, mid-latitude beta-plane model with a constant background westerly wind and a prescribed N^(2) applicable to the stratosphere is used to obtain analytic solutions. In this model, the planetary waves are initiated by steady energy influx from the lower boundary. The analysis indicates that under strong N^(2) conditions, the amplitude of planetary waves can be sufficiently increased by the effective energy convergence due to the slowing vertical energy transfer, resulting in a streamfunction response in this model that contains more energy. For N^(2) with a quasi-linear vertical variation, the results bear a resemblance to the constant case, except that the wave amplitude and oscillating frequency show some vertical variations.
