Wave interaction for a generalized higher-dimensional Boussinesq equation describing the nonlinear Rossby waves

Based on an algebraically Rossby solitary waves evolution model,namely an extended(2+1)-dimensional Boussinesq equation,we firstly introduced a special transformation and utilized the Hirota method,which enable us to obtain multi-complexiton solutions and explore the interaction among the solutions.These wave functions are then employed to infer the influence of background flow on the propagation of Rossby waves,as well as the characteristics of propagation in multi-wave running processes.Additionally,we generated stereogram drawings and projection figures to visually represent these solutions.The dynamical behavior of these solutions is thoroughly examined through analytical and graphical analyses.Furthermore,we investigated the influence of the generalized beta effect and the Coriolis parameter on the evolution of Rossby waves.

Mesoscale Barotropic Instability of Vortex Rossby Waves in Tropical Cyclones

In this study, the barotropic stability of vortex Rossby waves （VRWs） in 2D inviscid tropical cyclone （TC）-like vortices is explored in the context of rotational dynamics on an f-plane. Two necessary instable conditions are discovered： （a） there must be at least one zero point of basic vorticity gradient in the radial scope; and （b） the relative propagation velocity of perturbations must be negative to the basic vorticity gradient, which reflects the restriction relationship of instable energy. The maximum growth rate of instable waves depends on the peak radial gradient of the mean vorticity and the tangential wavenumber （WN）. The vortex-semicircle theorem is also derived to provide bounds on the growth rates and phase speeds of VRWs. The typical basic states and different WN perturbations in a tropical cyclone （TC） are obtained from a high resolution simulation. It is shown that the first necessary condition for vortex barotropic instability can be easily met at the radius of maximum vorticity （RMV）. The wave energy tends to decay （grow） inside （outside） the RMV due mainly to the negative （positive） sign of the radial gradient of the mean absolute vorticity. This finding appears to help explain the developemnt of strong vortices in the eyewall of TCs.

Rossby波传播特征及其对北极东北航道起始段海域天气的影响研究

北极东北航道起始段海域位于我国黄渤海,大风和强降水是可能威胁到该海域航运安全的主要灾害性天气类型。其中寒潮天气过程伴随的冷空气大风以及热带气旋、温带气旋等天气系统产生的大风、强降水等灾害性天气,对该海域航运安全造成很大影响。利用1991—2020年美国国家环境预报中心(National Centers for Environmental Prediction,NCEP)全球逐日再分析资料,分析了北极东北航道适航期(7—10月)Rossby波沿高空急流能量传播特征及其对北极东北航道起始段海域天气的影响,特别是对强降水的影响。结果表明:(1)沿北半球副热带地区250hPa高空西风急流轴经向风表现为纬向三波型准静止的Rossby波形态;(2)高空250hPa大气准静止Rossby波波源位于地中海地区,波动在此激发并沿急流向东传播,传播过程中波动能量耗散,但波源即地中海地区能量的不断注入,使其得以维持和加强;(3)波作用通量散度指数与北极东北航道起始段海域降水量、风速相关系数绝对值达0.5以上,其中位于我国东北部至鄂霍茨克海地区的波作用通量指数与降水量和风速相关系数的绝对值均接近0.9,属于强相关,说明Rossby波沿高空急流传播时能量汇集、加强,对北极东北航道起始段海域的降水量、风速影响较大,从而可触发强降水、大风等灾害性天气;(4)当Rossby波扰动偏强时,向下游传播能量偏强,则西风急流加强,垂直上升运动增强,导致北极东北航道起始段海域降水异常偏多。

近赤道Rossby孤立波的新模型及动力学机制研究

基于Verkley和Velde的数学模型,研究了线性基本流和非线性地形共同作用下的近赤道非线性Rossby波动力学机制,利用多重尺度和弱非线性法,得到Rossby波振幅新的非线性演化方程,进一步讨论了在给定参数条件下的热带大气和海洋的动力学机制。

Rossby波3波—4波通量异常下传与中国东部冬季寒潮的联系

利用ERA5再分析资料,对2000—2020年受Rossby波3波—4波反射影响的8个中国东部寒潮个例进行合成分析,探讨了3波—4波异常的物理过程及其在该类寒潮降温事件中的作用。结果表明,乌拉尔高压多与纬向3波—4波异常活跃有关。寒潮发生前,平流层极涡呈3波结构,中高平流层(500~600 K)极涡向亚欧大陆偏移,其北边界达到欧洲北部,在亚欧大陆的高纬度出现异常东风,有利于Rossby波作用通量的异常下传;低平流层(450 K)极涡向亚洲东部延伸。3波—4波作用通量在西欧地区异常上传,在东欧地区异常下传,在对流层顶附近形成波反射。该反射能够加强乌拉尔高压,有利于中国寒潮的发生。以200 hPa涡动热量通量在西欧和东欧上空的差异,建立区域波反射指数。该指数与中国东部3波—4波反射型寒潮降温相关性较好,在最低气温出现前一周左右,指数达到峰值,可以为中国寒潮预报预警提供参考。

Soliton propagation for a coupled Schrödinger equation describing Rossby waves

We study a coupled Schrödinger equation which is started from the Boussinesq equation of atmospheric gravity waves by using multiscale analysis and reduced perturbation method.For the coupled Schrödinger equation,we obtain the Manakov model of all-focusing,all-defocusing and mixed types by setting parameters value and apply the Hirota bilinear approach to provide the two-soliton and three-soliton solutions.Especially,we find that the all-defocusing type Manakov model admits bright-bright soliton solutions.Furthermore,we find that the all-defocusing type Manakov model admits bright-bright-bright soliton solutions.Therefrom,we go over how the free parameters affect the Manakov model’s allfocusing type’s two-soliton and three-soliton solutions’collision locations,propagation directions,and wave amplitudes.These findings are useful for setting a simulation scene in Rossby waves research.The answers we have found are helpful for studying physical properties of the equation in Rossby waves.

Vortex Rossby Waves in Asymmetric Basic Flow of Typhoons

Wave ray theory is employed to study features of propagation pathways（rays） of vortex Rossby waves in typhoons with asymmetric basic flow, where the tangential asymmetric basic flow is constructed by superimposing the wavenumber-1 perturbation flow on the symmetric basic flow, and the radial basic flow is derived from the non-divergence equation. Results show that, in a certain distance, the influences of the asymmetry in the basic flow on group velocities and slopes of rays of vortex Rossby waves are mainly concentrated near the radius of maximum wind（RMW）, whereas it decreases outside the RMW. The distributions of radial and tangential group velocities of the vortex Rossby waves in the asymmetric basic flow are closely related to the azimuth location of the maximum speed of the asymmetric basic flow, and the importance of radial and tangential basic flow on the group velocities would change with radius. In addition, the stronger asymmetry in the basic flow always corresponds to faster outward energy propagation of vortex Rossby waves. In short, the group velocities, and thereby the wave energy propagation and vortex Rossby wave ray slope in typhoons, would be changed by the asymmetry of the basic flow.

Detection accuracy of target accelerations based on vortex electromagnetic wave in keyhole space

The influence of the longitudinal acceleration and the angular acceleration of detecting target based on vortex electromagnetic waves in keyhole space are analyzed.The spectrum spreads of different orbital angular momentum(OAM)modes in different non-line-of-sight situations are simulated.The errors of target accelerations in detection are calculated and compared based on the OAM spectra spreading by using two combinations of composite OAM modes in the keyhole space.According to the research,the effects about spectrum spreads of higher OAM modes are more obvious.The error in detection is mainly affected by OAM spectrum spreading,which can be reduced by reasonably using different combinations of OAM modes in different practical situations.The above results provide a reference idea for investigating keyhole effect when vortex electromagnetic wave is used to detect accelerations.

Dynamic and Numerical Study of Waves in the Tibetan Plateau Vortex

In terms of its dynamics, The Tibetan Plateau Vortex （TPV） is assumed to be a vortex in the botmdary layer forced by diabatic heating and friction. In order to analyze the basic characteristics of waves in the vortex, the governing equations for the vortex were established in column coordinates with the balance of gradient wind. Based on this, the type of mixed waves and their dispersion characteristics were deduced by solving the linear model. Two numerical simulations with triple-nested domains--one idealized large-eddy simulation and one of a TPV that took place on 14 August 2006---were also carried out. The aim of the simulations was to validate the mixed wave deduced from the governing equations. The high-resolution model output data were analyzed and the results showed that the tangential flow field of the TPV in the form of center heating was cyclonic and convergent in the lower levels and anticyclonic and divergent in the upper levels. The simulations also showed that the vorticity of the vortex is uneven and might have shear flow along the radial direction. The changing vorticity causes the formation and spreading of vortex Rossby （VR） waves, and divergence will cause changes to the n^otion of the excitation and evolution of inertial gravity （IG） waves. Therefore, the vortex may contain what we call mixed ：inertial gravity-vortex Rossby （IG-VR） waves. It is suggested that some strongly developed TPVs should be studied in the future, because of their effects on weather in downstream areas.

Modified KdV equation for solitary Rossby waves with β effect in barotropic fluids

This paper uses the weakly nonlinear method and perturbation method to deal with the quasi-geostrophic vorticity equation,and the modified Korteweg-de Vries（mKdV） equations describing the evolution of the amplitude of solitary Rossby waves as the change of Rossby parameter β（у） with latitude у is obtained.

Long baroclinic Rossby waves with periods of about 500 d near 20°N in the northwest Pacific Ocean

On the basis of maps of sea level anomalies data set from October 1992 to January 2004, pronounced low frequency variations with periods of about 500 d are detected in the area near 20°N from 160°W to 130°E. A linear two-layer model is employed to explain the mechanism. It is found that the first-mode long baroclinic Rossby waves at 20°N in the northwest Pacific propagate westward in the form of free waves at a speed of about 10.3 cm/s. This confirms that the observed low frequency variabilities appear as baroclinic Rossby waves. It further shows that these low frequency variabilities around 20°N in the northwest Pacific can potentially be predicted with a lead up to 900 d.

The Role of Stationary and Transient Planetary Waves in the Maintenance of Stratospheric Polar Vortex Regimes in Northern Hemisphere Winter

Using 1958-2002 NCEPNCAR reanalysis data, we investigate stationary and transient planetary wave propagation and its role in wave-mean flow interaction which influences the state of the polar vortex （PV） in the stratosphere in Northern Hemisphere （NH） winter. This is done by analyzing the Eliassen-Palm （E-P） flux and its divergence. We find that the stationary and transient waves propagate upward and equatorward in NH winter, with stronger upward propagation of stationary waves from the troposphere to the stratosphere, and stronger equatorward propagation of transient waves from mid-latitudes to the subtropics in the troposphere. Stationary waves exhibit more upward propagation in the polar stratosphere during the weak polar vortex regime （WVR） than during the strong polar vortex regime （SVR）. On the other hand, transient waves have more upward propagation during SVR than during WVR in the subpolar stratosphere, with a domain of low frequency waves. With different paths of upward propagation, both stationary and transient waves contribute to the maintenance of the observed stratospheric PV regimes in NH winter.

Flow Separation and Vortex Dynamics in Waves Propagating over A Submerged Quartercircular Breakwater

The interactions of cnoidal waves with a submerged quartercircular breakwater are investigated by a ReynoldsAveraged Navier–Stokes(RANS) flow solver with a Volume of Fluid(VOF) surface capturing scheme(RANSVOF) model. The vertical variation of the instantaneous velocity indicates that flow separation occurs at the boundary layer near the breakwater. The temporal evolution of the velocity and vorticity fields demonstrates vortex generation and shedding around the submerged quartercircular breakwater due to the flow separation. An empirical relationship between the vortex intensity and a few hydrodynamic parameters is proposed based on parametric analysis. In addition, the instantaneous and time-averaged vorticity fields reveal a pair of vortices of opposite signs at the breakwater which are expected to have significant effect on sediment entrainment, suspension, and transportation,therefore, scour on the leeside of the breakwater.

Variations in Wave Energy and Amplitudes along the Energy Dispersion Paths of Nonstationary Barotropic Rossby Waves

The variations in the wave energy and the amplitude along the energy dispersion paths of the barotropic Rossby waves in zonally symmetric basic flow are studied by solving the wave energy equation,which expresses that the wave energy variability is determined by the divergence of the group velocity and the energy budget from the basic flow.The results suggest that both the wave energy and the amplitude of a leading wave increase significantly in the propagating region that is located south of the jet axis and enclosed by a southern critical line and a northern turning latitude.The leading wave gains the barotropic energy from the basic flow by eddy activities.The amplitude continuously climbs up a peak at the turning latitude due to increasing wave energy and enlarging horizontal scale(shrinking total wavenumber).Both the wave energy and the amplitude eventually decrease when the trailing wave continuously approaches southward to the critical line.The trailing wave decays and its energy is continuously absorbed by the basic flow.Furthermore,both the wave energy and the amplitude oscillate with a limited range in the propagating region that is located near the jet axis and enclosed by two turning latitudes.Both the leading and trailing waves neither develop nor decay significantly.The jet works as a waveguide to allow the waves to propagate a long distance.

A new model for algebraic Rossby solitary waves in rotation fluid and its solution

A generalized Boussinesq equation that includes the dissipation effect is derived to describe a kind of algebraic Rossby solitary waves in a rotating fluid by employing perturbation expansions and stretching transformations of time and space.Using this equation, the conservation laws of algebraic Rossby solitary waves are discussed. It is found that the mass, the momentum, the energy, and the velocity of center of gravity of the algebraic solitary waves are conserved in the propagation process. Finally, the analytical solution of the equation is generated. Based on the analytical solution, the properties of the algebraic solitary waves and the dissipation effect are discussed. The results point out that, similar to classic solitary waves,the dissipation can cause the amplitude and the speed of solitary waves to decrease; however, unlike classic solitary waves,the algebraic solitary waves can split during propagation and the decrease of the detuning parameter can accelerate the occurrence of the solitary waves fission phenomenon.

Large Scale Perturbations in Extratropical Atmosphere-Part Ⅰ: On Rossby Waves

This study reexamines the propagation mechanism and geostrophic property of the classical two-dimensional Rossby waves in a non-divergent barotropic atmosphere. It will be found that propagation of large scale atmospheric waves depends crucially on horizontal divergence. A small Rossby number in Rossby waves is not sufficient for the waves to have a small ageostrophic component, because the two-dimensional classical Rossby waves do not manifest the geostrophic balance as good as observed in the atmosphere.

Rossby waves with linear topography in barotropic fluids

Rossby waves are the most important waves in the atmosphere and ocean,and are parts of a large-scale system in fluid.The theory and observation show that,they satisfy quasi-geostrophic and quasi-static equilibrium approximations.In this paper,solitary Rossby waves induced by linear topography in barotropic fluids with a shear flow are studied.In order to simplify the problem,the topography is taken as a linear function of latitude variable y,then employing a weakly nonlinear method and a perturbation method,a KdV(Korteweg-de Vries) equation describing evolution of the amplitude of solitary Rossby waves induced by linear topography is derived.The results show that the variation of linear topography can induce the solitary Rossby waves in barotropic fluids with a shear flow,and extend the classical geophysical theory of fluid dynamics.

mKdV Equation for Solitary Rossby Waves with Linear Topography Effect in Barotropic Fluids

The modify Korteweg-de Vries(mKdV) equations,governing the evolution of the amplitude of solitary Rossby waves,are derived from quasi-geostrophic vorticity equation by using the perturbation method.The result manifests that the linear topography effect with the change of latitude can induce solitary Rossby wave.

THE EFFECTS OF THE PLATEAU'S TOPOGRAPHIC GRADIENT ON ROSSBY WAVES AND ITS NUMERICAL SIMULATION

By using barotropic model equations, this article analyzed the characteristics of Rossby waves, the propaga- tion features of wave energy and the influence of dynamic and thermal effects of the Tibetan Plateau on Rossby waves, and the focus is on discussing the plateau＇s topographic gradient effects on atmospheric Rossby waves. Then based on the WRF3.2 and the NCEP/NCAR FNL reanalysis data, we devised comparative tests of changing the plateau＇s topo- graphic gradient and simulated a process of persistent heavy rain that happened in May 2010 in South China. The re- sults are shown as follows. The Tibetan Platean＇s topography is conducive to the formation of atmospheric Rossby waves, while the platean＇s terrain, its friction and heating effects can all make the atmospheric Rossby waves develop into the planetary waves; The effects of platean＇s north and south slopes on the Rossby wave＇ phase velocity is opposite, and when the slope reached a certain value can the quasi-steady normal fluctuations be generated; Simultaneously, due to the plateau＇s topographic gradient, descending motion appears at the west side of the plateau while ascending motion appears at the east side, and the vertical movement increased with the amplification of topographic gradients. The plateau＇s topographic gradient also obviously amplified the precipitation in South China, and the rainfall area increased with the amplification of topographic gradients and gradually moved from south to north and from west to east, which is conducive to the occurrence and development of convective activities in the downstream areas of the Tibetan Plateau; Moreover, for the plateau＇s dynamic and thermal effects, the Rossby wave＇ propagation shows upstream effects of ener- gy dispersion, so the plateau can then affect the weather in downstream areas. Moreover, the wave group velocity in- creased with the degree of topographic slope.

Equatorward shift of annual Rossby waves in the Equatorial Pacific Ocean

Annual Rossby wave is a key component of the ENSO phenomenon in the equatorial Pacific Ocean. Due to the paucity and seasonal bias in historical hydrographic data,previous studies on equatorial Rossby waves only gave qualitative description. The accumulation of Argo measurements in recent years has greatly alleviated the data problem. In this study,seasonal variation of the equatorial Pacific Ocean is examined with annual harmonic analysis of Argo gridded data. Results show that strong seasonal signal is present in the western equatorial Pacific and explains more than 50% of the thermal variance below 500 m. Lag-correlation tracing further shows that this sub-thermocline seasonal signal originates from the eastern equatorial Pacific via downward and southwestward propagation of annual Rossby waves. Possible mechanisms for the equatorward shift of Rossby wave path are also discussed.