Some Aspects of the Characteristics of Monsoon Disturbances Using a Combined Barotropic－Baroclinic Model

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维向切变流中的非线性对称不稳定

讨论了维向切变流中的非线性对称不稳定问题。中采用绝热无粘的非线性对称扰动方程组，利用多尺度摄动方法分析其不稳定波动的有限振幅特性。研究结果表明：不稳定波的有限振幅在强度上呈现出振荡趋势。无论是超临界切变情况，还是次临界切变情况，对称扰动振幅都随时间呈现出周期性的变化，振荡周期的大小不仅与基本场稳定度参数及波的特性有关，而且还与初始扰动的振幅及其增长率有关。     

分层气流条件下地形降水的二维理想数值试验

利用WRF v3.5中尺度数值模式,在条件不稳定层结下,针对分层气流(基本气流风速和大气湿浮力频率呈二层均匀分布)过山时,地形对降水的影响进行了多组二维理想数值试验,以研究不同高度、尺度山脉和不同方向基本气流对降水形态和分布的影响。模拟结果表明,地形重力波触发对流是地形降水的主要机制之一,地形波的特征(波长、振幅)和传播均受到地形和基本气流的影响,其中,强基本气流流经高而陡峭的山脉时,更容易在其背风坡捕捉到重力波,地形降水呈现多种模态,反之亦然;当改变基本气流与山脉交角时,主要通过影响地形强迫抬升速度、基流对波动稳定性发展来进一步影响地形降水的强度和分布。     

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.     

二维波状地形上的流场

在一个简化的二层模式中，求解大气波动方程，得到了二维波状起伏地形上扰动流线的分析解。研究了在上、下两层大气中，不同的温度廓线和风速廓线情况下，地形引起扰动的流场形式，同时讨论了支配扰动振幅的大气因子和地形特征。分析解的结果表明:若大气低层为深厚的不稳定层，地形引起的波动很微弱;如低层大气强稳定，上层大气弱稳定，则可能产生较强的波动;而当上层稳定度增加时，可产生非陷波，有利于高层动量下传，造成较大的地面风速。     

平均流变化对波反馈的A-B混合方程理论及应用

从两层模式的基本方程出发,推导了描述平均流对波振幅反馈的A-B混合方程,并通过适当变换把混合方程转化为洛仑兹系统,用于研究平均流对边缘波扰动振幅增长的反馈机制,以及在中性廓线附近边缘波的稳定性问题。这是对研究波流相互作用的E-P通量理论的一个重要扩充。同时,作者还指出了A-B混合方程理论在研究大气中的波流相互作用及对流方面有相当应用前景。     

平均流变化对波反馈的A-B混合方程理论

从两层模式的基本方程出发，推导了描述平均流对波振幅反馈的A－B混合方程，并通过适当变换把混合方程转化为洛仑兹系统，用于研究平均流对边缘波扰动振幅增长的反馈机制，以及在中性廓线附近边缘波的稳定性问题。这是对研究波流相互作用的E-P通量理论的一个重要扩充。同时，作者还指出了A－B混合方程理论在研究大气中的波流相互作用及对流方面有相当应用前景。     

ON THE BAROTROPIC INSTABILITY OF LARGE SCALE VORTICES*

By using the linearized barotropic vorticity equation in polar coordinates the stability of perturbations on a large scale circular basic flow is transformed into a generalized eigenvalue problem,yielding the relationship between the growth rate of the amplitude of perturbations and the azimuthal wave number. Then, numerical experiments whose integration time is 60 model hours are performed in terms of a quasi-geostrophic barotropic model in Cartesian coordinates using the perturbation stream function field of unstable mode superimposed on a strong and weak circular basic flows as the initial fields. The experimental results reveal that the amplitudes of the initial perturbations in the model atmosphere grow with time. The amplitude of the perturbations superimposedon the strong circular basic flow grows quicker and forms a spiral-band-like structure.     

Propagation and Effects of a Mesoscale Gravity Wave Over a Weakly-Stratified Nocturnal Boundary Layer During the SABLES2006 Field Campaign

During the SABLES2006 (Stable Atmospheric Boundary Layer Experiment in Spain 2006) field campaign, a gravity-wave episode was observed on the night of July 11 by the microbarometers deployed at the surface and on the 100-m tower. The high-amplitude, low-frequency periodic pressure fluctuations were very well correlated with the wind speed and direction. Data from neighbouring automatic stations showed that the gravity wave was not local, but long-lived and mesoscale. The propagation of the wave over the experimental site had significant effects on the structure of the weakly-stratified nocturnal boundary layer that developed that night: the stability increased, turbulent vertical motions were suppressed, the nocturnal low-level jet was disrupted, and periodic temperature fluctuations of amplitude up to 3–4 K were observed. In this work we analyse the different available data sources (tower data, RASS-SODAR, microbarometric, satellite imagery, automatic stations) to describe the phenomena in depth and to find a suitable explanation for the generation and propagation of the wave. The linear wave theory explains remarkably well most of the observations, and the wave parameters could be estimated by applying a wavelet-based technique to surface microbarometric measurements. We also analyse the vertical structure of the wave and find wave ducting conditions above the surface. Finally, by means of the multi-resolution flux decomposition, we analyse in detail the changes in vertical turbulent fluxes and the spectra of turbulent motions produced by the interaction between the gravity wave and the local flow.     

ON THE BAROTROPIC INSTABILITY OF LARGE SCALE VORTICES

By using the linearized barotropic vorticity equation in polar coordinates the stability of pertur-bations on a large scale circular basic flow is transformed into a generalized eigenvalue problem,yielding the relationship between the growth rate of the amplitude of perturbations and the az-imuthal wave number. Then, numerical experiments whose integration time is 60 model hours areperformed in terms of a quasi-geostrophic barotropic model in Cartesian coordinates using the per-turbation stream function field of unstable mode superimposed on a strong and weak circular basicflows as the initial fields. The experimental results reveal that the amplitudes of the initial pertur-bations in the model atmosphere grow with time. The amplitude of the perturbations superimposedon the strong circular basic flow grows quicker and forms a spiral-band-like structure.     

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.     

On the three-dimensional internal waves excited in the flow of a linearly stratified Boussinesq fluid

Three-dimensional flow of a linearly stratified Boussinesq fluid is studied numerically. The flow is assumed to be confined in a rectangular channel and internal waves are excited by bottom topography. Near resonance of the first vertical internal wave mode, it was found that the reflection of the internal wave at the sidewall is ‘abnormal’ in the sense that the reflection angle is larger than the incident angle and a third wave perpendicular to the sidewall is generated. The waves become straight crested (two-dimensional) as this third wave becomes longer. The whole mechanism is similar to the ‘Mach reflection’ observed in the general stratified fluid in which the usual solitary waves are generated. In the case of the linearly stratified Boussinesq fluid, the abnormal reflection occurs even though the wave near the sidewall has a sinusoidal profile and not a sech² profile. This suggests that the abnormal reflections similar to Mach reflection always occur when the wave amplitude is large enough, irrespective of the wave profile.     

地形强迫对大气长波调整的可能影响

地形作为大气的外部强迫,其动力和热力作用对波动结构演变及极端天气出现都有不能忽视的作用。本文通过数值求解考虑地形强迫的β平面正压准地转位势涡度方程,探讨了地形强迫作用对大气长波调整的可能影响,结果表明:同非线性作用和纬向非均匀基流作用一样,无基流情形下具有纬向差异的地形分布影响了大气长波结构的演变,也能强迫出大气长波调整现象。大气长波调整依赖于地形的高度和地形分布,地形越高,长波越容易出现波数的调整;地形波数越大,即地形结构复杂,越不易出现波数变化。大气长波调整还与纬度有关,纬度越高,β越小,地形强迫作用越突出,长波调整容易出现;反之,低纬度以β效应为主的线性波动不易出现波数调整。大气长波调整对波动初始波动的振幅不敏感,但依赖于波动的初始结构。此外,有基流作用时,地形强迫还是诱发定常波的重要因素,且定常波流场结构依赖于地形高度分布,与波动初始结构无关。     

层结大气中非线性椭圆余弦波和孤立波的研究

在前文采用半地转近似和行波法来研究层结大气中的非线性波动的基础上,进一步探讨非线性方程及其级数近似方程的解的稳定性,波动解的存在条件和波动的一些特征。研究指出,在平衡点附近,将非线性方程用其级数近似方程代替是可行的、合理的。在初始拟能满足一定的条件下,椭圆余弦波和孤立波是存在的。文中还求得了椭圆余弦波解的周期、ｘ向波长和振幅以及孤立波的宽度和振幅。并指出,孤立波的宽度和振幅不但与波速有关,还与β因子和层结稳定度有关,而且在相同的某条件下,西行的混合Ｒｏｓｓｂｙ－重力孤立波比起东行的惯性重力孤立波来,宽度要小但振幅却大。     

正压大气中的代数Rossby孤立波

本文研究了基本气流具有线性弱切变的非线性Rossby波,得到了一个非线性发展方程为Kubota方程,在一定的条件下,可变为Benjamin-Ono方程,并指出当代数Rossby孤立波的振幅越大时,代数Rossby孤立波的传播速度越小,基流切变越强,代数Rossby孤立波越慢,同时我们还指出在代数Rossby孤立波的振幅满足一定的条件下,代数Rossby孤立波才随纬度的增高(β减小)而减慢。并且代数Rossby孤立波的结构与大气中的偶极子阻塞是一致的。     

Characteristics of annulus baroclinic flow structure during amplitude vacillation

An investigation is made of the mechanics of amplitude vacillation in a numerically simulated rotating annulus flow system. Amplitude vacillation is characterized by a periodic change of vertical wave structure in concert with growth and decay of wave amplitude and phase speed. The temperature wave amplitude profile for the dominant component consists of three local maxima: (1) lower boundary layer, (2) upper half layer and (3) lower half layer. The lower layer waves lead the time-dependent structural variation during vacillation. Two types of amplitude vacillation found in the experimental measurements (Buzyna et al., 1989: J. Atmos. Sci. 46, 2716–2729) can be distinguished in the temperature wave by whether the lower layer waves split from and travel behind the upper layer waves by one wave period in each cycle of vacillation. Linear eigenvalue analyses with respect to the instantaneous axisymmetric state at various points in time are performed to elucidate the simple interaction between the dominant wave and the zonal mean state. During the vacillation cycle, the zonal mean state is modified by the wave, which causes a change in growth rate and vertical structure of the linearly most unstable eigenmode. This, in turn, forces the actual changes of the nonlinear solutions.     

纬向气流对地形Rossby波的影响

本文在半地转近似下,采用相平面方法讨论了纬向基本气流对线性和非线性地形Rossby波的稳定性及解的性质的影响。结果指出:线性和非线性稳定性判据形式一样,纬向气流及其切变对稳定性有明显影响;在非线性近似下,可形成孤立波槽和孤立波脊。     

Multiple Equilibria in a Land–Atmosphere Coupled System

Many low-order modeling studies indicate that there may be multiple equilibria in the atmosphere induced by thermal and topographic forcings. However, most work uses uncoupled atmospheric model and just focuses on the multiple equilibria with distinct wave amplitude, i.e., the high- and low-index equilibria. Here, a low-order coupled land–atmosphere model is used to study the multiple equilibria with both distinct wave phase and wave amplitude. The model combines a two-layer quasi-geostrophic channel model and an energy balance model. Highly truncated spectral expansions are used and the results show that there may be two stable equilibria with distinct wave phase relative to the topography: one (the other) has a lower layer streamfunction that is nearly in (out of) phase with the topography, i.e., the lower layer ridges (troughs) are over the mountains, called ridge-type (trough-type) equilibria. The wave phase of equilibrium state depends on the direction of lower layer zonal wind and horizontal scale of the topography. The multiple wave phase equilibria associated with ridge- and trough-types originate from the orographic instability of the Hadley circulation, which is a pitch-fork bifurcation. Compared with the uncoupled model, the land–atmosphere coupled system produces more stable atmospheric flow and more ridge-type equilibrium states, particularly, these effects are primarily attributed to the longwave radiation fluxes. The upper layer streamfunctions of both ridge- and trough-type equilibria are also characterized by either a high- or low-index flow pattern. However, the multiple wave phase equilibria associated with ridge- and trough-types are more prominent than multiple wave amplitude equilibria associated with high- and low-index types in this study.     

Formulation of a Semi-Geostrophic Model of Frontal Interaction with Isolated Orography

Summary  A semi-geostrophic model of frontal passage over topography was developed to examine the effects of the interaction of a well developed front with an isolated mountain, and the subsequent orographically induced flow evolution. The analytic representation of the primary wave and its frontal structure gives us the ability to control the environmental and geometrical constraints and perform an exploration of parameter space. A number of problems appearing because of this approach are discussed. The results shown relate the characteristics of the orographic perturbation to varying amplitude of the primary wave and varying frontal intensity, but suggest that the representation of flow blocking by the mountain,which this model lacks, is crucial for the representation of frontal intensification in the lee of orography. Received March 2, 1999/Revised May 7, 1999     

THE CISK MECHANISM AND THE INERTIAL GRAVITATIONAL WAVES IN SHEAR FLOW

By using the symmetric equations of atmospheric dynamics in y-z plane with vertical and horizontal shear of wind, the nonlinear ordinary differential equation is derived with the method of travelling wave.Its stability is discussed by using the theory of nonlinear stability and the KDV equation is solved. The effects of linear CISK, nonlinear CISK, inertial stability and vertical shear of wind on the amplitude and the width of isolated inertial gravitational wave are discussed. In order to understand deeply the formation and development of meso-scale synoptic systems, such as the squall line, MCC, the cold surge of Asia high and typhoon, the factors of development of the isolated inertial gravity wave are analysed.