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.     

正压准地转模式中大地形作用下的低频波

利用包含大地形和常速纬向基本气流的正压准地转位涡度方程,研究了大地形对低频波激发的作用,结果表明,起作用的地形因子主要是地形的最大高度和地形坡度。地形最大高度的作用主要是使Rossby波趋向低频,而地形坡度的作用主要是对Rossby波的稳定性起决定作用,同时适当的地形坡度也可导致低频波的形成。而常速纬向基流在总体上的作用是使波动变得趋向低频,且西风基流更有利于低频（30～60天）波的形成。从纬向波数上看,纬向3波以上的波动更容易出现低频（30～60天）。     

副高与阻高形成的Rossby孤立波理论Ⅱ:存在临界层

研究了存在临界层的非均匀纬向流中的Ｒｐｓｓｂｙ孤立波。在求出振幅函数满足的ＫｄＶ方程或修正ＫｄＶ方程（ＭＫｄＶ）后，选择Ｃｈｅｂｙｓｈｅｖ多项式作为展开基函数，用假谱方法，求解本征值和本征函数。对理想风场的计算表明，在临界层存在与否两种情况下，都能得到在东西风界面处的反气旋式副高型Ｒｏｓｓｂｙ孤立波，同副高有一致的演变规律：当东风带相对强于西风时，向西移动；当西风相对强于东风时，则向东移动。在西风带，则得到阻高型Ｒｏｓｓｂｙ孤立波，与阻高也有同样的演变规律。另外，我们还用连续谱方法计算了临界层附近的连续谱及离散谱，也得到与假谱方法较一致的结论。     

赤道两层海洋模式中基本流的切变不稳定性

设计了一个热带赤道β-平面的两层海洋模式,在准长波近似下,应用最大截断模分析赤道波的基本形态,指出无论是正压模或斜压模Kelvin波、Rossby波及基本流所对应的“地形Rossby波”是最基本的波系,在基本流的一定切变条件下,它们之间可以耦合出一类不稳定波。在浅混合层近似和“快波近似”下,正压模和斜压模是可以分离的,因此可以分别分析它们的色散特征,由于它们的特征量不同,在同样波长(扰动的纬向尺度)下,扰动的增长率也不同,通过分析得出在一定参数下,斜压模扰动增长率为正压模的2倍。近似分析表明,混合层中流场的增长要快于温跃层,但温跃层的温度增长要比混合层明显。     

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 propagation 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 topographic gradient and simulated a process of persistent heavy rain that happened in May 2010 in South China. The results are shown as follows. The Tibetan Plateau’s topography is conducive to the formation of atmospheric Rossby waves. while the plateau's terrain, its friction and heating effects can all make the atmospheric Rossby waves develop into the planetary waves; The effects of plateau'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 energy dispersion, so the plateau can then affect the weather in downstream areas. Moreover, the wave group velocity increased with the degree of topographic slope.     

New approach to study the evolution of rossby wave packet

The average variational principle was employed in this paper to study the evolution of large-scale and slowly va-rying Rossby wave packet with basic flow both in barotropic and baroclinic atmospheres. The evolution of the struc-ture of Rossby wave packet with both time and space was studied. The results obtained in this paper are similar to the results of by WKBJ method. In addition, the dispersive process of the wave packet was analysed by taking Gaussian type wave packet as an initial disturbance. The valid time scale for application of wave packet theory in the atmos-phere was obtained.     

相当正压Rossby波和斜压Rossby波相互转换的分析

利用由两层准地转模式简化的低谱模式，得知相当正压结构Ｒｒｏｓｓｂｙ波为平衡态，讨论了具有相当正压结构的Ｒｏｓｓｂｙ波存在所需条件；并以定常Ｒｏｓｓｂｙ波（相当正压结构）为基态，导出反映高低层Ｒｏｓｓｂｙ波位相变化的振荡方程，指出高低层位相差的变化与垂直切交流的扰动、平均层上流函数和热成风流函数波动部分振幅扰动（Ａ’和Ｂ’）的关系，说明相当正压结构和斜医结构的Ｒｏｓｓｂｙ波是相互转换的。     

Study on the Dynamic Process of the Onset of South China Sea Summer Monsoon

By using the NCEP/NCAR reanalysis data from 1958 to 1997, we first looked into the atmospheric flow conditions in the one month immediately prior to the onset of the South China Sea summer monsoon （SCSSM） each year. A monthly-averaged zonal basic flow of 40-yr composite was then calculated. The stability of Rossby wave in the basic flow was studied based on the spherical barotropic vorticity equation. Furthermore, the spectral function expansion method was adopted to define and compute the evolvement of a developing wave packet. The results indicate that there exists barotropic instability of spherical Rossby wave in the climatically-averaged flow field before the SCSSM onset. The instability is triggered by the westerly jet stream in the Southern Hemisphere, and the strongest instable perturbation lies to the south of the westerly jet stream. The peak of the developing spherical Rossby wave packet propagates from mid and high latitudes to low latitudes, though not crossing the equator, spurring the cumulus convection in the tropical zones. The eruption of the cumulus convection and its spread to monsoon regions help to speed up the adjustment of the general circulation and the SCSSM onset. It is concluded that elements that contribute to the SCSSM onset are on global scale, albeit the onset itself looks like a local phenomenon.     

大地形与正压Rossby孤立波

文中讨论了地形对正压Rossby孤立波的影响,指出,当基本气流没有切变时,地形是产生Rossby孤立波的重要因子;不同高度的地形,其作用有很大的不同;计算得到了两类不同的孤立波流型。     

Possible impact of equatorially trapped waves on the tropical cyclone drift

The effect of equatorially trapped waves on the movement of tropical cyclones (TC) is studied numerically based on a two-dimensional barotropic model in a beta-plane approximation. According to recent studies, equatorially trapped waves contribute to the genesis of TCs. It is thus natural to assume that these waves affect also the movement of the TC. The effect of three types of equatorially trapped waves, namely Kelvin, Rossby, and n = 0 eastward inertio-Gravity (EIG) waves, on the TC trajectory is investigated with a focus on the sensitivity on some key physical parameters such as the wavenumber and wavespeed. Using a simple barotropic model forced by a prescribed baroclinic flow, the barotropic response to equatorially trapped waves is simulated for a period of 50 days, under various wave parameter configurations. This response is then used as a background flow where TC’s can evolve and propagate. TC-like flows are injected into this wavefield background at arbitrary times during the simulation, and the TC trajectories are tracked and recorded for 48h after the injection time. The resulting TC trajectory patterns with respect to the injection times and wave parameters appear to be stochastic and the mean paths and the associated standard deviations are calculated and reported here. The statistics are different for different wave types. Kelvin waves make shorter length of TC trajectories and small divergence of direction. On the contrary, Rossby waves cause rather dramatic changes in the TC path and yield longer trajectories. Meanwhile, TCs in EIG waves maintain fairly the same direction and typically have longer trajectories though less dramatic. A robustness test using a random forcing instead has also been conducted.

     

On the direction of Rossby wave breaking in blocking

The direction of Rossby wave breaking at the onset of large-scale atmospheric blocking events is shown to relate closely to its position relative to the location of the climatological storm tracks. Using ERA-Interim reanalysis data from October 1989 to March 2009 and a dynamically-based blocking index, Rossby wave breaking is shown to occur preferentially cyclonically to the north, and anticyclonically to the south of the average storm tracks location. Therefore the results support existing theory on the relation between Rossby wave breaking direction and barotropic shear of the background wind. The further away from the storm tracks the breaking occurs, the stronger this preference in breaking direction. Regional differences can also be explained. For the European region on average 70?% of the detected blocking took place after anticyclonic Rossby wave breaking event that occurred on average 6° south of the climatological storm tracks position. Over Western Pacific wave breaking prior to blocking occurs predominantly cyclonically and on average 6° north of the storm tracks. Differences in blocking duration and intensity are found to be within estimated error margins at most longitudes, except for the Atlantic-Europe sector where the blocking events following anticyclonic blocking are also the strongest.     

A NUMERICAL EXPERIMENT OF DYNAMIC EFFECT OF QINGHAI-XIZANG PLATEAU ON SUMMER ATMOSPHERIC LOW FREQUENCY VARIATION

In this paper a numerical experiment is presented of the plateau's dynamic effect in terms of a two-layer spectralmodel, and the focus is put on the large-scale orography-excited ALFV with the summer flow pattern as background.together with its propagation and distribution of some features. The main results are as follows: (1) With the summerflow pattern as background the Plateau can excite ALFV, which is characterized by strong regionality. (2) ALFV of thiskind has a baroclinic (equivalent barotropic) structure on the south (north) side of the topography. (3) Its propagation ismarked by dispersion of quasi-stationary Rossby waves over a spherical surface.     

Stationary Rossby wave propagation in a shear flow along a reflective boundary

Summary This study investigates the impact of lateral boundary conditions on the propagation and dispersion of locally excited Rossby waves in a zonally periodic, barotropic, quasigeostrophic channel model on the β-plane. We use basic flows with either a linear meridional shear or a jet-like profile. On the southern boundary of the channel we impose either a rigid wall or a radiation condition, whereas the northern sidewall is permeable for Rossby waves. We compare the numerical solutions found for a reflecting southern boundary in a weakly dissipative flow to the solutions obtained from a WKB-analysis for the corresponding unforced nondissipative situation. Furthermore, we compare the generalized Eliassen-Palm flux vectors to the ray paths of Rossby wave packets, obtained from WKB ray tracing. In particular, we focus our investigation on the two-dimensional structure of trapped modal waves and wavetrains in a simple linear numerical model. Summarizing our results, we find that along the reflective wall, trapped modal wave structures as well as reflected wavetrains occur with characteristics (e.g., wavenumbers, turning latitudes) similar to the ones computed using asymptotic methods. In a linear sheared flow wave packets are trapped for all zonal wave numbers in contrast to a jet-like mean flow which has a selective effect on the waves; i.e., a turning latitudes phenomenon between the coast and the flow maximum occurs for short waves, while long waves can propagate freely across the zonal mean flow. This comes out clearly when studying the stream lines of the Eliassen-Palm flux vectors of the numerical model simulations. Furthermore, due to the reflected wave activity, the dispersion of Rossby waves is influenced by the southern boundary condition not only in the vicinity of the border but also in regions away from the boundary. These results appear to be important on the one hand for the existence of trapped Rossby waves in large-scale oceanic shear flows along a zonally oriented coast. And, on the other hand for large-scale boundary waves in conceptional atmospheric channel models which can lead to unwanted resonance effects. Received July 18, 2000/Revised June 9, 2001     

大气中的包络Rossby孤立波——纬度效应的作用

本文进一步对旋转正压大气中的包络Rossby孤立波进行了研究，结果发现当Rossby波的波数m（m为纬向波数）满足1≤m≤2时，旋转正压大气中才存在包络Rossby孤立波，并且只有m＝2的包络Rossby孤立波才具有阻塞高压的结构。我们还对这种m＝２的包络Rossby孤立波随纬度变化的持续性进行了计算，得到了许多结果。     

A Quantitative Method of Detecting Transient Rossby Wave Phase Speed: No Evidence of Slowing Down with Global Warming

Based on the Complex Empirical Orthogonal Functions(CEOFs) of bandpass-filtered daily streamfunction fields, a quantitative method of detecting transient(synoptic) Rossby wave phase speed(RWPhS) is presented. The transient RWPhS can be objectively calculated by the distance between a high(or low) center in the real part of a CEOF mode and its counterpart in the imaginary part of the same CEOF mode divided by the time span between two adjacent peaks(or bottoms) of two principal component curves f...     

两层正压准平衡海洋模型的中纬度自由涡旋波动解

建立了具有瑞利摩擦且仅考虑大洋西海岸或同时考虑大洋东、西海岸的两层正压准平衡海洋模型,并做了解析求解,用以研究中纬度的自由涡旋波。得到的主要结论有:模型中该波动的解为波包。在仅考虑大洋西海岸时该波包的载频频率是连续谱;而同时考虑大洋东、西海岸时其为离散谱;且均有载频频率越高(周期越短)水平尺度越大的特点,对过分低频的波动,则会使准平衡的假定不再适用。模型中该波动波包载频的周期约在26天至24年。因考虑了摩擦,该波包的振幅随时间呈指数衰减,但摩擦系数的大小仅影响其衰减程度而不改变其空间结构,最终该波包振幅趋于0,故该两层正压海洋模型的解就趋于大气风场的强迫特解。模型中该波包的载频都是西传的;频率较高则西传较快,波包的特性和变形都很明显;频率低,则西传慢,其波形接近平面简谐波。在该两层正压模型中,该波动上层流场与正压模型中的流动类似,而下层海洋流动则其流速与上层海洋相同,而流向相反。该模型中该波动的性质是准平衡(准无辐散)的涡旋波,当摩擦不太大且其水平尺度在10km以上时,其性质则为准地转的Rossby波。     

简单的热带海气耦合波——Rossby波的相互作用

在本文中分析了当大气和海洋中未经耦合前的自由波均为Rossby模时,经相互作用后所激发出的耦合波的物理性质。结果表明,由于大气和海洋的背景状态不同,可以激发出两类不稳定耦合Rossby波。一类波要求大气的背景场是斜压的,而海洋的混合层较深,即热容量较大。这是一类弱相互作用的不稳定波。另一类要求大气的背景场趋于正压性,而海洋的混合层较浅,即热容量较小。这是一类强相互作用的不稳定波。色散关系的计算表明,这两类不稳定波产生的物理机制也不相同。文中对解不同截断模的本征值问题提出了几种数学方法,同时还进一步提出了一种使大气和海洋自由Rossby模的色散关系不受歪曲的处理方法。     

旋转正压大气中的Rossby波射线

本文将缓变介质中波动的传播理论应用于Rossby波。在基流和不同走向地形假设下，计算了Rossby波射线路径及沿射线波数的变化。结果表明大尺度地形对Rossby波射线有显著影响。     

Stable and unstable Rossby waves in the North Pacific current as inferred from the mean stratification

We have determined free Rossby waves in the North Pacific Current by numerical methods. We have found only two stable solutions — the barotropic and first-order baroclinic Rossby shear modes. The influence of the current on the dispersion features of these waves is small for the barotropic shear mode, but is significant for the baroclinic shear mode. An explicit comparison of the dispersion relations for the baroclinic wave in case of vanishing and non-vanishing current is given. We have found at most one unstable solution per wave number. The unstable wave with largest growth rate has an e-folding time of 1.1 year. We have calculated vertical profiles of the stream function and the temperature for the various shear modes at various wave numbers. The temperature shear modes have been calculated for later usage in a Rossby wave model to be fitted to observed temperature data from the North Pacific Current area.     

Variations in Amplitudes and Wave Energy along the Energy Dispersion Paths for Rossby Waves in the Quasigeostrophic Barotropic Model

Variations in wave energy and amplitude for Rossby waves are investigated by solving the wave energy equation for the quasigeostrophic barotropic potential vorticity model.The results suggest that compared with rays in the nondivergent barotropic model,rays in the divergent model can have enhanced meridional and zonal propagation,accompanied by a more dramatic variability in both wave energy and amplitude,which is caused by introducing the divergence effect of the free surface in the quasigeostrophic model.For rays propagating in a region enclosed by a turning latitude and a critical latitude,the wave energy approaches the maximum value inside the region,while the amplitude approaches the maximum at the turning latitude.Waves can develop when both the wave energy and amplitude increase.For rays propagating in a region enclosed by two turning latitudes,the wave energy approaches the minimum value at one turning latitude and the maximum value at the other latitude,while the total wavenumber approaches the maximum value inside the region.The resulting amplitude increases if the total wavenumber decreases or the wave energy increases more significantly and decreases if the total wavenumber increases or the wave energy decreases more significantly.The matched roles of the energy from the basic flow and the divergence of the group velocity contribute to the slightly oscillating wave energy,which causes a slightly oscillating amplitude as well as the slightly oscillating total wavenumber.