The Role of Topography and Diabatic Heating in the Formation of Dipole Blocking in the Atmosphere

In this paper, the nonlinear stationary waves forced by topography and diabatic heating are investigated. It is pointed out that (1) the nonlinear interaction of different stationary waves forced only by topography might form dipole blocking in the atmosphere, this might explain the dipole blocking appeared in the Pacific and Atlantic regions; (2) the dipole blocking could not be caused by the nonlinear interaction of the different stationary waves forced by the diabatic heating alone; (3) the nonlinear interaction of the diffferent stationary waves forced by both topography and diabatic heating could initiate dipole blocking in the atmosphere. In winter, the dipole blocking mainly occurs in the west regions of the Pacific and the Atlantic, and the heat source over the western part of the two oceans is advantageous to the formation of dipole blocking in the west of two oceans. However, in summer, the dipole blocking could be formed in the east part of the two oceans, and the heat source over the eastern     

The role of topography and diabatic heating in the formation of dipole blocking in the atmosphere

In this paper, the nonlinear stationary waves forced by topography and diabatic heating are investigated. It is pointed out that (1) the nonlinear interaction of different stationary waves forced only by topography might form dipole blocking in the atmosphere, this might explain the dipole blocking appeared in the Pacific and Atlantic regions; (2) the dipole blocking could not be caused by the nonlinear interaction of the different stationary waves forced by the diabatic heating alone; (3) the nonlinear interaction of the diffferent stationary waves forced by both topography and diabatic heating could initiate dipole blocking in the atmosphere. In winter, the dipole blocking mainly occurs in the west regions of the Pacific and the Atlantic, and the heat source over the western part of the two oceans is advantageous to the formation of dipole blocking in the west of two oceans. However, in summer, the dipole blocking could be formed in the east part of the two oceans, and the heat source over the eastern part of two continents is favourable for the formation of dipole blocking in the east regions of two oceans.     

The effect of topographic forcing on the formation and maintenance of blocking

A barotropic channel model in β-plane is used to study the effect of topographic forcing on the formation and maintenance of blocking. The approximate analytical solution of potential vorticity equation can show the main property of the whole process of blocking. It is indicated that the topographic forcing is one of the main factors caus-ing the blocking process. The results suggest that the nonlinear interaction plays a very important role in the stable “Ω” situation of blocking. The atmospheric circulation with periodic and low-frequency oscillation, perhaps, is partly caused by topographic forcing.     

The Stability and Existence Condition of Nonlinear Travelling Wave Solution in Basic Uniform Flow

Summary  Nonlinear waves in a stratified atmosphere with basic uniform flow are studied by adopting geostrophic momentum approximation (cf. Hoskins, 1975) and the method of travelling wave solution. A nonlinear equation containing a unique variable of vertical p velocity is derived from a complete system of equations considering frictionless and adiabatic fluid. The stability of the solution for the nonlinear equation is discussed then. Furthermore, the approximate cnoidal wave solution, solitary wave solution and their existence condition are obtained. Received July 8, 1998 Revised December 1, 1998     

MESOSCALE NONLINEAR GRAVITATIONAL WAVES AND THEIR INTERACTION IN VERTICAL SHEAR FLOW*

Interaction equations of two nonlinear gravitational waves in baroclinic atmosphere are presented via multi-scale perturbation method,which can be classified into coupling nonlinear Schrodinger equations.In particular,the interaction course of two nonlinear gravitational waves of basic flow in vertical linear and quadratic shear is illustrated.Numerical calculation displays that wave amplitude enlarges and wave width narrows when two solitary gravitational waves meet and chase;that basic flow with single shear is more beneficial than that with quadratic shear to the interaction of two nonlinear wave packets;and that the interaction of two wave packets makes wave shape change more greatly and energy more dispersive,which contributes to the occurrence of changeable weather.Therefore,one of the probable mechanisms for the appearance of strong convection weather is the interaction between mesoscale nonlinear gravitational waves.     

低纬大气Kelvin波和Rossby波的非线性相互作用

利用多重尺度摄动法,对低纬大气Kelvin波和Rossby波的波包演变进行了分析,得到两波的非线性相互作用方程为耦合的非线性复系数Landau方程组。数值计算表明两波相遇将使波振幅变化,波宽变窄;两波非线性相互作用可能是低纬强烈天气突然爆发的原因之一。     

垂直切变流中非线性重力波及其相互作用

利用多重尺度摄动法，推导出斜压大气中(基本风场具有垂直切变)两个非线性重力波相互作用方程，这两个方程联立组合为耦合非线性schrǒdīnger方程组。两个重力波相互作用时可激发出重力驻波。数值计算表明：两个孤立重力波相遇，相追会使波振幅增大，波宽变窄。强烈对流天气突然爆发的可能原因之一是中尺度重力波非线性相互作用的结果。     

Algebraic rossby solitary wave and blocking in the atmosphere

In this paper, the atmosphere is divided into two regions which are governed by different equations. Furthermore, multiple-scale method is used to obtain the Benjamin-Ono equation satisfied by the nonlinear Rossby wave in weak shear zonal flow. The equation has algebraic solitary wave solution, and the stationary streamfunction fields in-ithe atmosphere are calculated by using numerical method, and the results demonstrate that the stationary solution is antisymmetric dipoles with the anticyclone north of the cyclone, and the structure is similar to the equivalent modon obtained by Mcwilliams (1980). Because the modon obtained here is an algebraic solitary wave, the modon may be called “algebraic modon”, and the stationary algebraic modon is consistent with observations of blocking pattern in the atmosphere.     

强迫耗散正压大气中四波共振

本文首次研究了含Ekman摩擦和非绝热加热的四波共振动力学．使用新的双时间尺度和新的时间变换式，由四波共振的广义Landau方程，导得普遍的非线性低频周期解，Ekman摩擦使得低频周期具有滞后和突变返回两个重要特征，而非绝热加热作用与中高纬准双周振荡有关，中高纬的30－50天振荡则与自由Rossby波准共振有关．本文还研究了四波共振产生的爆发性不稳定，指出较大振幅波产生的爆发性不稳定可能是阻塞迅速形成的又一重要原因，还首次得到在正压大气中Ekman摩擦能够激发爆发性不稳定．本文结果纠正了Craik于1985年提出的在流体力学中广泛应用的两个错误论断．     

A Perspective on the Evolution of Atmospheric Blocking Theories: From Eddy-Mean flow Interaction to Nonlinear Multiscale Interaction

In this paper, we first review the research advancements in blocking dynamics and highlight the merits and drawbacks of the previous theories of atmospheric blocking. Then, the dynamical mechanisms of atmospheric blocking are presented based on a nonlinear multi-scale interaction(NMI) model. Previous studies suggested that the eddy deformation(e.g., eddy straining, wave breaking, and eddy merging) might lead to the formation and maintenance of atmospheric blocking.However, the results were specu...     

2003年淮河大水期间亚洲北部阻塞高压的形成特征

利用观测资料和NCEP再分析资料分析2003年淮河大水期间亚洲北部阻塞高压的形成维持机制, 结果表明, 2003年淮河梅汛期亚洲中高纬地区阻塞高压的异常活动中, 波流作用十分显著。6月上旬, 阻高建立前期和维持过程中, 上游地区天气尺度波动活跃, 欧洲斜压区不断有瞬变动能生成, 并在阻塞区向阻高平均流转化。从瞬变涡动的作用来看, 上游传播而来的瞬变波不断将较低纬度的低位涡空气向阻塞区输送, 有利于阻塞高压的建立维持; 平均流则使位涡呈相反形势发展, 引导阻塞高压向东频散, 削弱了扰动位涡输送的作用, 对阻高的维持起到耗散作用。阻高建立前, 瞬变涡位涡输送作用强于平均流位涡平流, 造成阻塞区位涡降低, 有利于阻高生成; 阻高维持期间, 瞬变涡位涡输送与平均流位涡平流输送量相当; 6月25～30日, 阻塞高压明显西退, 该阶段瞬变涡动明显强于平均耗散作用, 引导低位涡场向西移动。研究表明, 大气内部的波波作用对阻高的建立维持也十分重要。1波与5波在一定范围内的共同作用可能是阻高建立维持的决定因素, 而天气尺度波动扰动则对阻塞高压的建立、 维持和崩溃起到重要的作用。波波作用表明, 2003年6月份阻塞高压建立、 维持时, 尺度较长的波一般从平均动能得到扰动动能的转化, 尤其5波, 斜压能的转换不但是其能量的来源, 同时非线性作用也使得尺度更小或更长的波向其提供能量; 阻高衰退时, 5波则通过非线性作用向其他波动输送能量, 同时也存在斜压耗散, 能量逐渐失去。     

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。     

Baroclinic Instability in the Generalized Phillips’ Model Part II: Three-layer Model

The nonlinear stability of the three-layer generalized Phillips model, for which the velocity in each layer is constant and the top and bottom surfaces are either rigid or free, is studied by employing Arnol’d’s variational principle and a prior estimate method. The nonlinear stability criteria are established. For com-parison, the linear instability criteria are also obtained by using normal mode method, and the influences of the free parameter, β parameter and curvature in vertical profile of the horizontal velocity on the linear in-stability are discussed by use of the growth rate curves.The comparison between the nonlinear stability criterion and the linear one is made. It is shown that in some cases the two criteria are exactly the same in form, but in other cases, they are different. This phenom-enon, which reveals the nonlinear property of the linear instability features, is explained by the explosive resonant interaction (ERI). When there exists the ERI, i.e., the nonlinear mechanisms play a leading role in the dynamical system, the nonlinear stability criterion is different from the linear one; on the other hand, when there does not exist the ERI, the nonlinear stability criterion is the same as the linear one in form.     

Oscillatory Rossby Solitary Waves in the Atmosphere

The linear Rossby wave frequency expression is expanded at higher accuracy based on the scale difference char?acteristics of atmospheric long waves in the and directions. That the nature of the waves represented by the expan?sion is identical to that of the original ones is demonstrated both in phase velocity and wave energy dispersion speed , followed by the derivation of the nonlinear expression describing atmospheric long wave behaviors with the associated approximate analytic solution obtained. Then, for the first time atmospheric’ oscillatory Rossby solitary wave’ with its dispersion relation is obtained by numerical calculation with the aid of physical parameters of the real atmosphere. The solitary wave is found to be very close to such longwave systems as blocking highs and cut-off de?pressions in the actual atmosphere.     

均匀基流中非线性行波解的稳定性及其存在条件

本文利用地转动量近似＾「１」并结合行波解的方法,研究了均匀基本气流中的层结大气非线性波动,首先由绝热无磨擦的闭合方程组导得关于垂直Ｐ速度的单一变量的非线性方程,然后讨论了非线性方程解的稳定性,并求得近似的非线性方程的椭圆余弦波和孤立波解及其存在条件。     

波与波的相互作用对阻塞高压的形成、维持和衰退的影响

采用波数域的动能方程和定常波与瞬变波的波数域动能方程计算了阻塞高压形成、维持和衰退阶段的波与波相互作用项和波与平均运动相互作用项。计算结果表明波与波的非线性相互作用项在阻塞高压形成阶段是促使阻塞高压形成的能源,在维持阶段,是维持其稳定的能源,在衰退阶段又是促使其崩溃的能汇。波与平均运动的相互作用项在衰退阶段也起着促使阻塞高压崩溃的重要作用。定常波与瞬变波的非线性相互作用起着在具体时段使阻塞高压形成、维持和衰退的重要作用。     

Nonlinear resonance interactions and index cycles in the atmosphere

A barotropic spectral model is used to study the planetary-scale motions of an atmosphere whose wave ensemble modes are externally driven. Pertubations are induced by a barotropic analogue of thermal driving and by Ekman friction, bottom topography, and the vanished internal dissipation. The use of complete spectral expansions without truncation leads to that the nonlinear coupling equations between the low-index mode and the high-index mode are obtained by means of the random phase approximation and the projec-tion operator techniques. The nonlinear coupling equations are entirely equivalent to the Volterra systems in ecology.In the phase-plane, the orbits of the nonlinear coupling equations are the family of closed curves, indicat-ing a bound, and periodic motion. The qualitative behaviors of low-index and high-index modes as functions of time picture the motion of atmospheric flows, with exchanges of energy between the low-index mode and the high-index mode by nonlinear resonance interaction. It is suggested that the phenomenon of blocking be exponentially grown of the low-index mode, the atmospheric motion then evolved to the high-index mode due to relaxation process. The results therefore lead to a plausible hypothesis concerning index cycles in the atmosphere discussed by Lorenz’s early works.     

一类非线性海气耦合波的研究

建立了一类非线性海气耦合波的模式,并用该模式作了解析研究,讨论了该类海气耦合波的存在条件,发现当海气耦合较强时分别存在以海洋为主导方面及以大气为主导方面的两支海气耦合波,而耦合较弱时则仅有前者存在。还求得了该模式中该类海气耦合波的椭圆余弦波解及孤立波解,并对以海洋为主导的海气耦合波的性质作了讨论,认为海气相互作用耦合也是产生大气季节内振荡的机制之一。     

Interaction between Planetary-Scale Diffluent Flow and Synoptic-Scale Waves During the Life Cycle of Blocking

In this paper, a new transient forced quasi-resonant triad interaction theory in a beta channel is proposed to investigate the interaction between planetary-scale diffluent flow composed of zonal wavenumbers 1--3 and synoptic-scale waves produced continuously by a synoptic-scale vorticity source fixed upstream of an incipient blocking region during the life cycle of blocking. It is shown that the superposition of initial three Rossby waves for zonal wavenumbers 1 (monopole), 2 (dipole), and 3 (monopole), which permit triad quasi-resonance, can represent an incipient blocking event. The synoptic-scale eddies may act to amplify the incipient blocking and to excite a blocking circulation with a strong meander, whose flow pattern depends on the initial amplitudes of the planetary waves and both the intensity and location of preexisting synoptic-scale waves. The onset (decay) of the planetary-scale split-flow blocking is mainly represented by a strong increase (decrease) in the amplitude of the zonal wavenumber 2 component, having a dipole meridional structure related to the preexisting synoptic-scale eddies. The typical persistence time of the model blocking was of about 20 days, consistent with observations of blocking patterns. In our model, isolated asymmetric dipole blocking is formed by synoptic-scale waves. The instantaneous fields of total streamfunctions exhibit a remarkable resemblance to the synoptic maps observed during the life cycle of blocking. During the onset stage, the synoptic-scale waves are enhanced and split into two branches around the blocking region due to the feedback of the amplified blocking, in agreement with the observed changes of synoptic-scale waves in real blocking events. In addition, a diagnostic case study of blocking is presented to confirm the forced quasi-resonant triad interaction theory proposed here.