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
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
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
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
Adhesively bonded joints are widely used in modern lightweight structures due to their high strengthto-weight ratio and design flexibility.However,the reliable non-destructive evaluation of bond integrity remains a si...Adhesively bonded joints are widely used in modern lightweight structures due to their high strengthto-weight ratio and design flexibility.However,the reliable non-destructive evaluation of bond integrity remains a significant challenge.This study presents a numerical investigation of adhesively bonded joints with different adhesive properties using ultrasonic guided waves.The main focus of the investigation is to evaluate the feasibility of using guided waves to assess bond integrity,particularly for detecting challenging weak bonds.For this purpose,a theoretical analysis of dispersion curves was conducted,revealing that the S0 Lamb wave mode is significantly sensitive to variations in adhesive properties in the 300-700 kHz frequency range.Finite element modelling was used to analyse the propagation of guided waves in two scenarios:an adhesively bonded aluminum structure and a more complex configuration-adhesively bonded lap joints.The Short-Time Fourier Transform(STFT)was used to process the obtained results and determine the group velocities of guided waves.By analysing the group velocity characteristics,their dependence on the adhesive properties was identified.In the first scenario,a clear separation of S0 modes from A0 modes was observed in the STFT analysis,with a decrease in group velocity as adhesive stiffness increased.For the more complex lap joint scenario,the separation between A0 and S0 modes was less distinct.However,the analysis of the average group velocity shows a dependence of average group velocity on adhesive properties.This is similar to the first scenario.There is a decrease in average group velocity as adhesive stiffness increases.The results obtained demonstrate that guided wavebased methods have a high potential for non-destructive evaluation of adhesively bonded structures,including the detection of weak bonds.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
Energy transfers among internal waves in the northern South China Sea are not well characterized,particularly during typhoons,owing to the lack of in situ observations.Based on high-resolution mooring data collected d...Energy transfers among internal waves in the northern South China Sea are not well characterized,particularly during typhoons,owing to the lack of in situ observations.Based on high-resolution mooring data collected during Typhoon Trami(2024),this study reveals the occurrence of robust vertical energy redistribution among diurnal internal tides(D1 ITs)and near-inertial waves(NIWs).Strikingly,the typhoon not only amplified the NIW energy but also triggered an unexpected surge in the D1 IT energy.The observed average net energy transfer rate of 1×10^(-7) W kg^(−1) from typhoon-forced NIWs to D1 ITs occurred at water depths of 120-170 m.Further bispectral analysis indicated that the energy transfer is driven by nonlinear wave—wave interaction.These results reveal the existence of a new energy transfer pathway—from atmospheric forcing to D1 ITs—and redefine the redistribution of the internal wave energy during extreme weather events.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
The Hall effect of elastic waves has attracted much attention due to its unique properties.A hexagonal lattice phononic crystal plate model is designed in this paper.By changing the spatial symmetry of the unit cell,a...The Hall effect of elastic waves has attracted much attention due to its unique properties.A hexagonal lattice phononic crystal plate model is designed in this paper.By changing the spatial symmetry of the unit cell,a band gap for the A_(0) Lamb wave is opened.The existence of the edge state of the phononic crystal plate is obtained by finite element simulation.It is found that both zigzag-type edge and bridge edge are topological edge states by analysis of the band structure of the supercell.A rectangular model with a straight channel is designed and the simulation results show that the two types of channels are topologically protected only for the A_(0) mode Lamb wave but not for the S_(0) mode.In addition,the results of numerical simulation are verified by experimental data measured by a laser vibrometer.Finally,it is found that neither upside V-shaped channels nor channels with defects will affect the stable propagation of A_(0) Lamb waves along the proposed route.This proposed model and method are helpful in broadening the means of regulating elastic waves in phononic crystal structures,and extending practical application of topological edge states in such structures.展开更多
Arc faults within the transformers can generate sudden pressure surges,constituting significant hazards that may precipitate oil tank explosions and severely compromise power system stability.Conventional power−freque...Arc faults within the transformers can generate sudden pressure surges,constituting significant hazards that may precipitate oil tank explosions and severely compromise power system stability.Conventional power−frequency arc discharge experiments encounter limitations in isolating pressure wave characteristics due to persistent gas generation and arc reignition.To circumvent these challenges,an oil-immersed impulse voltage discharge platform was conceived and engineered to investigate pressure wave propagation dynamics.A pressure numerical simulation model and theoretical model of oil−solid interface reflection and refraction were subsequently established to elucidate the pressure propagation mechanism.The experimental and simulation results show that the pressure wave generated by pulsed arc discharge in oil propagates radially in the form of spherical waves.Due to the viscous loss and wave front expansion of transformer oil,the peak pressure decays exponentially with distance,with a decay coefficientβ=1.15.When pressure waves encounter metal obstacles inside transformer oil,there are two propagation paths:direct transmission through and multiple reflections through,and a mode transformation of pressure waves occurs at the oil−solid interface,mainly propagating through obstacles in the form of transverse waves.This work quantitatively delineates the energy pressure wave coupling,propagation dynamics,and attenuation mechanisms,providing critical insights for assessing and mitigating arc fault-induced transformer explosion risks.展开更多
A three-dimensional numerical model of sand wave dynamics,incorporating the interaction of currents and waves at various angles,has been developed using the Regional Ocean Modeling System(ROMS).This model accounts for...A three-dimensional numerical model of sand wave dynamics,incorporating the interaction of currents and waves at various angles,has been developed using the Regional Ocean Modeling System(ROMS).This model accounts for both bedload and suspended load sediment transport under combined waves and current conditions.The investigation examines the influence of several key parameters,including the rotation angle of sand waves relative to the main current,tidal current velocity amplitude,residual current,water depth,wave height,wave period,and wave direction,on sand wave evolution.The growth rate and migration rate of sand waves decrease as their rotation angle increases.For rotation angles smaller than 15°,sand wave evolution can be effectively simulated by a vertical 2D model with an error within 10%.The numerical results demonstrate that variations in tidal current velocity amplitude or residual current affect both vertical growth and horizontal migration of sand waves.As tidal current velocity amplitude and residual current increase,the growth rate initially rises to a maximum before decreasing.The migration rate shows a consistent increase with increasing tidal current amplitude and residual current.Under combined waves and current,both growth and migration rates decrease as water depth increases.With increasing wave height and period,the growth rate and migration rate initially rise to maximum values before declining,while showing a consistent increase with wave height and period.The change rate of sand waves reaches its maximum when wave propagation aligns parallel to tidal currents,and reaches its minimum when wave propagation is perpendicular to the currents.This phenomenon can be explained by the fluctuation of total bed shear stress relative to the angle of interaction between waves and current.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
We uncover the virtual monopoles underlying the nontrivial phases of the one-dimensional nonlinear excitations of rogue waves by extending the Dirac magnetic monopole theory to a complex plane. We find that the densit...We uncover the virtual monopoles underlying the nontrivial phases of the one-dimensional nonlinear excitations of rogue waves by extending the Dirac magnetic monopole theory to a complex plane. We find that the density zeros of the nonlinear waves on the extended complex plane constitute the virtual monopole fields with a quantized flux of elementary π. We then explain the exotic properties of rogue waves by means of a virtual monopole collision mechanism and find that the maximum amplitude amplification ratio and multiple phase steps of the high-order rogue waves are closely related to the number of their contained monopoles. These results open a new avenue for studying topological properties of nonlinear waves and provide an alternative way to understand their dynamics.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
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
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
Spin-momentum locking is widely regarded as an inherent property of evanescent waves,where the transverse spin angular momentum is intrinsically tied to the wave's polarization.This principle is well established i...Spin-momentum locking is widely regarded as an inherent property of evanescent waves,where the transverse spin angular momentum is intrinsically tied to the wave's polarization.This principle is well established in systems such as surface plasmon polaritons,surface elastic waves,and other evanescent modes.Here,we theoretically unveil an anomalous breakdown of spin-momentum locking in evanescent electromagnetic waves at a metalgyromagnetic interface.We show that the hybrid polarization of the field induces two successive reversals of transverse spin near the interface—directly violating the conventional locking between spin and momentum.As a result,identical chiral sources placed at different heights above the interface excite evanescent waves propagating in opposite directions,defying standard expectations.This discovery challenges the presumed universality of spin-momentum locking and opens new degrees of freedom for controlling wave propagation in photonic and plasmonic systems.展开更多
Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity.However,the path that the rays travel along in media with irregular interfaces is not cl...Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity.However,the path that the rays travel along in media with irregular interfaces is not clear.Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements（SEMO） that can accurately evaluate waves traveling along an irregular interface.Consequently,the head waves are separated from interface waves by a time window.Thus,their energy and arrival time changes can be analyzed independently.These analyses demonstrate that,contrary to the case for head waves propagating along a flat interface,there are two mechanisms for head waves traveling along an irregular interface：a refraction mechanism and transmission mechanism.That is,the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media.Such knowledge will be helpful in constructing a more accurate inversion method,such as head wave travel-time tomography,and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas,such as the Tibetan Plateau.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
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 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(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 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 Research Council of Lithuania(LMTLT),agreement no.S-MIP-22-5.
文摘Adhesively bonded joints are widely used in modern lightweight structures due to their high strengthto-weight ratio and design flexibility.However,the reliable non-destructive evaluation of bond integrity remains a significant challenge.This study presents a numerical investigation of adhesively bonded joints with different adhesive properties using ultrasonic guided waves.The main focus of the investigation is to evaluate the feasibility of using guided waves to assess bond integrity,particularly for detecting challenging weak bonds.For this purpose,a theoretical analysis of dispersion curves was conducted,revealing that the S0 Lamb wave mode is significantly sensitive to variations in adhesive properties in the 300-700 kHz frequency range.Finite element modelling was used to analyse the propagation of guided waves in two scenarios:an adhesively bonded aluminum structure and a more complex configuration-adhesively bonded lap joints.The Short-Time Fourier Transform(STFT)was used to process the obtained results and determine the group velocities of guided waves.By analysing the group velocity characteristics,their dependence on the adhesive properties was identified.In the first scenario,a clear separation of S0 modes from A0 modes was observed in the STFT analysis,with a decrease in group velocity as adhesive stiffness increased.For the more complex lap joint scenario,the separation between A0 and S0 modes was less distinct.However,the analysis of the average group velocity shows a dependence of average group velocity on adhesive properties.This is similar to the first scenario.There is a decrease in average group velocity as adhesive stiffness increases.The results obtained demonstrate that guided wavebased methods have a high potential for non-destructive evaluation of adhesively bonded structures,including the detection of weak bonds.
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.
基金supported by the National Key R&D Plan Program of China [Grant number 2021YFC3101500]the National Natural Science Foundation of China [Grant number 42305014,42506024]。
文摘Energy transfers among internal waves in the northern South China Sea are not well characterized,particularly during typhoons,owing to the lack of in situ observations.Based on high-resolution mooring data collected during Typhoon Trami(2024),this study reveals the occurrence of robust vertical energy redistribution among diurnal internal tides(D1 ITs)and near-inertial waves(NIWs).Strikingly,the typhoon not only amplified the NIW energy but also triggered an unexpected surge in the D1 IT energy.The observed average net energy transfer rate of 1×10^(-7) W kg^(−1) from typhoon-forced NIWs to D1 ITs occurred at water depths of 120-170 m.Further bispectral analysis indicated that the energy transfer is driven by nonlinear wave—wave interaction.These results reveal the existence of a new energy transfer pathway—from atmospheric forcing to D1 ITs—and redefine the redistribution of the internal wave energy during extreme weather events.
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.
文摘The Hall effect of elastic waves has attracted much attention due to its unique properties.A hexagonal lattice phononic crystal plate model is designed in this paper.By changing the spatial symmetry of the unit cell,a band gap for the A_(0) Lamb wave is opened.The existence of the edge state of the phononic crystal plate is obtained by finite element simulation.It is found that both zigzag-type edge and bridge edge are topological edge states by analysis of the band structure of the supercell.A rectangular model with a straight channel is designed and the simulation results show that the two types of channels are topologically protected only for the A_(0) mode Lamb wave but not for the S_(0) mode.In addition,the results of numerical simulation are verified by experimental data measured by a laser vibrometer.Finally,it is found that neither upside V-shaped channels nor channels with defects will affect the stable propagation of A_(0) Lamb waves along the proposed route.This proposed model and method are helpful in broadening the means of regulating elastic waves in phononic crystal structures,and extending practical application of topological edge states in such structures.
基金funded by the Science and Technology Program of State Grid Corporation of China(5500-202356358A-2-1-ZX).
文摘Arc faults within the transformers can generate sudden pressure surges,constituting significant hazards that may precipitate oil tank explosions and severely compromise power system stability.Conventional power−frequency arc discharge experiments encounter limitations in isolating pressure wave characteristics due to persistent gas generation and arc reignition.To circumvent these challenges,an oil-immersed impulse voltage discharge platform was conceived and engineered to investigate pressure wave propagation dynamics.A pressure numerical simulation model and theoretical model of oil−solid interface reflection and refraction were subsequently established to elucidate the pressure propagation mechanism.The experimental and simulation results show that the pressure wave generated by pulsed arc discharge in oil propagates radially in the form of spherical waves.Due to the viscous loss and wave front expansion of transformer oil,the peak pressure decays exponentially with distance,with a decay coefficientβ=1.15.When pressure waves encounter metal obstacles inside transformer oil,there are two propagation paths:direct transmission through and multiple reflections through,and a mode transformation of pressure waves occurs at the oil−solid interface,mainly propagating through obstacles in the form of transverse waves.This work quantitatively delineates the energy pressure wave coupling,propagation dynamics,and attenuation mechanisms,providing critical insights for assessing and mitigating arc fault-induced transformer explosion risks.
基金the National Natural Science Foundation of China(Grant Nos.52371289 and 51979192).
文摘A three-dimensional numerical model of sand wave dynamics,incorporating the interaction of currents and waves at various angles,has been developed using the Regional Ocean Modeling System(ROMS).This model accounts for both bedload and suspended load sediment transport under combined waves and current conditions.The investigation examines the influence of several key parameters,including the rotation angle of sand waves relative to the main current,tidal current velocity amplitude,residual current,water depth,wave height,wave period,and wave direction,on sand wave evolution.The growth rate and migration rate of sand waves decrease as their rotation angle increases.For rotation angles smaller than 15°,sand wave evolution can be effectively simulated by a vertical 2D model with an error within 10%.The numerical results demonstrate that variations in tidal current velocity amplitude or residual current affect both vertical growth and horizontal migration of sand waves.As tidal current velocity amplitude and residual current increase,the growth rate initially rises to a maximum before decreasing.The migration rate shows a consistent increase with increasing tidal current amplitude and residual current.Under combined waves and current,both growth and migration rates decrease as water depth increases.With increasing wave height and period,the growth rate and migration rate initially rise to maximum values before declining,while showing a consistent increase with wave height and period.The change rate of sand waves reaches its maximum when wave propagation aligns parallel to tidal currents,and reaches its minimum when wave propagation is perpendicular to the currents.This phenomenon can be explained by the fluctuation of total bed shear stress relative to the angle of interaction between waves and current.
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supported by the National Natural Science Foundation of China (Grant Nos.12375005,12022513,and12235007)the National Safety Academic Fund(Grant No.U2330401)。
文摘We uncover the virtual monopoles underlying the nontrivial phases of the one-dimensional nonlinear excitations of rogue waves by extending the Dirac magnetic monopole theory to a complex plane. We find that the density zeros of the nonlinear waves on the extended complex plane constitute the virtual monopole fields with a quantized flux of elementary π. We then explain the exotic properties of rogue waves by means of a virtual monopole collision mechanism and find that the maximum amplitude amplification ratio and multiple phase steps of the high-order rogue waves are closely related to the number of their contained monopoles. These results open a new avenue for studying topological properties of nonlinear waves and provide an alternative way to understand their dynamics.
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 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.
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supported by the National Natural Science Foundation of China(Grant Nos.12434016 and 12474380)Science and Technology Project of Guangdong Province(Grant No.2020B0101-90001)+1 种基金the National Key Research and Development Program of China(Grant No.2023YFA1406900)the Natural Science Foundation of Guangdong Province(Grant No.2025A1515010714)。
文摘Spin-momentum locking is widely regarded as an inherent property of evanescent waves,where the transverse spin angular momentum is intrinsically tied to the wave's polarization.This principle is well established in systems such as surface plasmon polaritons,surface elastic waves,and other evanescent modes.Here,we theoretically unveil an anomalous breakdown of spin-momentum locking in evanescent electromagnetic waves at a metalgyromagnetic interface.We show that the hybrid polarization of the field induces two successive reversals of transverse spin near the interface—directly violating the conventional locking between spin and momentum.As a result,identical chiral sources placed at different heights above the interface excite evanescent waves propagating in opposite directions,defying standard expectations.This discovery challenges the presumed universality of spin-momentum locking and opens new degrees of freedom for controlling wave propagation in photonic and plasmonic systems.
基金supported by the National Natural Science Foundation of China (Grant Nos.40874027,90715020,and 90915012)the Institute of Geophysics of the China Earthquake Administration (Grant No.DQJB07B06)Special Public Welfare Industry (Grant Nos.20070804 and 200808008)
文摘Head waves are usually considered to be the refracted waves propagating along flat interfaces with an underlying higher velocity.However,the path that the rays travel along in media with irregular interfaces is not clear.Here we study the problem by simulation using a new approach of the spectral-element method with some overlapped elements（SEMO） that can accurately evaluate waves traveling along an irregular interface.Consequently,the head waves are separated from interface waves by a time window.Thus,their energy and arrival time changes can be analyzed independently.These analyses demonstrate that,contrary to the case for head waves propagating along a flat interface,there are two mechanisms for head waves traveling along an irregular interface：a refraction mechanism and transmission mechanism.That is,the head waves may be refracted waves propagating along the interface or transmitted waves induced by the waves propagating in the higher-velocity media.Such knowledge will be helpful in constructing a more accurate inversion method,such as head wave travel-time tomography,and in obtaining a more accurate model of subsurface structure which is very important for understanding the formation mechanism of some special areas,such as the Tibetan Plateau.
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.
