Charney's Model—the Renowned Prototype of Baroclinic Instability—Is Barotropically Unstable As Well

The Charney model is reexamined using a new mathematical tool, the multiscale window transform(MWT), and the MWT-based localized multiscale energetics analysis developed by Liang and Robinson to deal with realistic geophysical fluid flow processes. Traditionally, though this model has been taken as a prototype of baroclinic instability, it actually undergoes a mixed one. While baroclinic instability explains the bottom-trapped feature of the perturbation, the second extreme center in the perturbation field can only be explained by a new barotropic instability when the Charney–Green number γ 1, which takes place throughout the fluid column, and is maximized at a height where its baroclinic counterpart stops functioning.The giving way of the baroclinic instability to a barotropic one at this height corresponds well to the rectification of the tilting found on the maps of perturbation velocity and pressure. Also established in this study is the relative importance of barotropic instability to baroclinic instability in terms of γ. When γ 1, barotropic instability is negligible and hence the system can be viewed as purely baroclinic; when γ 1, however, barotropic and baroclinic instabilities are of the same order;in fact, barotropic instability can be even stronger. The implication of these results has been discussed in linking them to real atmospheric processes.     

The effect of barotropic shear on baroclinic instability Part I: Normal mode problem

The effect of barotropic shear in the basic flow on baroclinic instability is investigated using a linear multilevel quasi-geostrophic β-plane channel model and a nonlinear spherical primitive equation model. Barotropic shear has a profound effect on baroclinic instability. It reduces the growth rates of normal modes by severely restricting their structure, confirming earlier results with a two-layer model. Dissipation, in the form of Ekman pumping and Newtonian cooling, does not change the main characteristics of the effect of the shear on normal mode instability.Barotropic shear in the basic state, characterized by large shear vorticity with small horizontal curvature, also effects the nonlinear development of baroclinic waves. The shear limits the energy conversion from the zonal available potential energy to eddy energy, reducing the maximum eddy kinetic energy level reached by baroclinic waves. Barotropic shear, which controls the level of eddy activity, is a major factor which should be considered when parameterizing the eddy temperature and momentum fluxes induced by baroclinic waves in a climate model.     

Baroclinic instability: Energy transfer and the role of potential vorticity conservation

Abstract

In this note some aspects of the dynamics involved in the process of baroclinic instability are discussed using simple physical arguments. In particular, the connection between the requirement for unstable perturbations to release potential energy from the mean state and the conservation of potential vorticity is examined. It is shown how the conservation of potential vorticity results in perturbation phase propagation relative to the mean flow, which is a necessity for potential energy to be released from the mean state. Eady's (1949) problem is discussed as an illustrative example.     

气候平均场上西太平洋副热带高压双脊线过程可能成因的动力诊断分析

利用NCEP-DOE再分析数据集II,诊断分析了气候平均场上6次西太平洋副热带高压双脊线过程,借助一个两层半大气模式,从动力学上初步揭示了西太平洋热带大气准10天振荡（Quasi Ten-day Oscillation,简称QTO）向西北方向传播与季风槽东伸西撤之间的相互作用过程,探讨了气候平均场上西太副高双脊线可能的形成机制。分析表明季风槽准10天东西振荡是气候平均场上西太副高双脊线形成的主要原因,而季风槽东伸西撤与QTO传播密切相关。进一步分析发现,QTO向西北方向传播,东风切变作用于斜压辐散的经向梯度,在对流中心北侧生成正扰动涡度。QTO在季风槽东侧激发的气旋性扰动涡度,诱导季风槽东伸,侵入副高,造成副高外围变形,形成双脊线。因此,形成西太副高双脊线的主要原因之一可能是西太平洋热带大气QTO。尽管季风槽东伸直接引起副高双脊线发生,但是它只不过是受QTO影响的一种表现。本文仅为诊断结果,其结果还有待于模式敏感性试验的验证。     

The effect of barotropic shear on baroclinic instability Part II: The initial value problem

The effect of barotropic shear on baroclinic instability has been investigated using both a linear quasi-geostrophic β-plane channel model and a multilevel primitive equation model on the sphere when a nonmodal disturbance is used as the initial perturbation condition. The analysis of the initial value problem has demonstrated the existence of a rapid transient growth phase of the most unstable mode. The inclusion of a linear barotropic shear reduces initial rapid transient growth, although at intermediate times the transient growth rates of the sheared cases can be larger than in the unsheared case owing to downgradient eddy momentum fluxes. Certain disturbances can amplify by factors of 4.5–60 times (for the L₂ norm), or 3–30 times (for the perturbation amplitude maximum), as large as disturbances based on the linear normal modes. However, linear horizontal shear always reduces the amplification factors. The mechanism is that the shear confines the disturbance meriodionally and therefore limits the energy conversion from the zonal available potential energy to eddy energy. The effect of barotropic shear on the transient growth is not changed much in the presence of either thermal damping or Ekman pumping. Nonmodal integrations of baroclinic wave lifecycles show that the energy level reached by eddies is not very sensitive to the structure of the initial disturbance if the amplitude of the initial disturbance is small. Although in some cases the eddy kinetic energy level reached by the wave integrated from nonmodal disturbance can be 25–150% larger than the normal mode integrations, barotropic shear, characterized by large shear vorticity with small horizontal curvature, always reduces the eddy kinetic energy level reached by the wave, confirming the results of normal mode studies.     

MOIST POTENTIAL VORTICITY DIAGNOSIS OF A MEIYU FRONTAL HEAVY RAIN PROCESS SIMULATION DURING SUMMER,1991

In this paper,the heavy rain process from June 30 to July 2,1991,has been simulated by MM4.and three-dimensional moist potential vorticity distribution of the simulation results has beencalculated.It is shown that moist potential vorticity is an important physical variable to reveal heavyrain structure and dynamic mechanisms.Negative moist potential vorticity corresponds to the Meiyufront-wind shear line system and the negative center corresponds to the heavy rain center.Negativemoist potential vorticity mainly attributes to the effects of meridional baroclinic term and convectiveunstable term.The former is favourable to the maintenance of zonal precipitation and the latter is themechanism of the heavy rain center propagating along the rain belt.The heavy rain is contributed bythe cooperative effects of conditional convective instability,baroclinic instability and upper air inertialinstability.     

MOIST POTENTIAL VORTICITY DIAGNOSIS OF A MEIYU FRONTAL HEAVY RAIN PROCESS SIMULATION DURING SUMMER, 1991

In this paper,the heavy rain process from June 30 to July 2,1991,has been simulated by MM4.and three-dimensional moist potential vorticity distribution of the simulation results has been calculated.It is shown that moist potential vorticity is an important physical variable to reveal heavy rain structure and dynamic mechanisms.Negative moist potential vorticity corresponds to the Meiyu front-wind shear line system and the negative center corresponds to the heavy rain center.Negative moist potential vorticity mainly attributes to the effects of meridional baroclinic term and convective unstable term.The former is favourable to the maintenance of zonal precipitation and the latter is the mechanism of the heavy rain center propagating along the rain belt.The heavy rain is contributed by the cooperative effects of conditional convective instability,baroclinic instability and upper air inertial instability.     

Finite-amplitude, neutral baroclinic eddies and mean flows in an internally heated rotating fluid: 1. Numerical simulations and quasi-geostrophic ‘free modes’

A series of numerical simulations of steady wave flows in a rotating fluid annulus, subject to internal heating and various thermal boundary conditions, is examined to characterise their structures, energetics and potential vorticity transport properties. The last of these characteristics, together with more conventional scaling considerations, indicate the possibility of applying quasi-geostrophic theory to the interior flow in a formulation similar to the inviscid, adiabatic models of Kuo and White.The analytical model of White, describing finite amplitude, neutral baroclinic eddies and mean flows as illustrations of the Charney-Drazin non-acceleration theorem, is then extended to include uniform diabatic heating and the effects of different forms of lateral shear in the background mean zonal flow. Like the solutions discussed by White, those obtained in the present paper consist of steady, internal jet, mean zonal flows, and baroclinic and barotropic Rossby wave components, all having the same three-dimensional wavenumber. Provided the diabatic heating is proportional to the stratification of the background flow, measured by the square of the Brunt-Vaisälä frequency N, the potential vorticity equation remains homogeneous. All the solutions are then characterised by zero net transfer of potential vorticity despite the possibility of non-zero eddy fluxes of heat or momentum and non-trivial Lorenz energy cycles.A series of particular three-component solutions (which, like some of the solutions discussed by White, do not obey conventional lateral boundary conditions) is examined as possible theoretical analogues of the steady waves observed in the numerical simulations of the laboratory flows, and is found to agree encouragingly well in the spatial variations of their mean flows, eddy stream function (pressure) and eddy fluxes of heat and momentum. Potential vorticity fluxes in the numerical simulations are relatively small (though crucially non-zero), supporting the possible analogy with the analytical model and exposing some limitations of the latter in not accounting for weak dissipation and forcing processes present in the laboratory flows.Further implications of the results are discussed, including possible analogies between the laboratory experiments and certain features in planetary atmospheres and oceans.     

华北一次强对流暴雨的湿位涡诊断分析

应用常规地面观测资料、区域加密站降水资料、NCEP再分析资料（水平分辨率1°×1°,间隔为6 h）,对2009年6月8日发生在华北的一次强对流暴雨过程的湿位涡场进行了诊断分析。结果表明:湿位涡的分布对强对流暴雨的发生、落区有较强的指示性作用,MPV1“正负值区垂直叠加”的配置是强对流暴雨发生、发展的有利形势。暴雨出现在850 hPa上MPV、MPV1、MPV2正负值过渡带附近,是对流不稳定与斜压不稳定相结合的地区。θse的等值线接近垂直的地区有利于垂直涡度的增长,亦有利于强降水发生。     

Localized multiscale energy and vorticity analysis: I. Fundamentals

A new methodology, multiscale energy and vorticity analysis (MS-EVA), is developed to investigate the inference of fundamental processes from oceanic or atmospheric data for complex dynamics which are nonlinear, time and space intermittent, and involve multiscale interactions. Based on a localized orthogonal complementary subspace decomposition through the multiscale window transform (MWT), MS-EVA is real problem-oriented and objective in nature. The development begins with an introduction of the concepts of scale and scale window and the decomposition of variables on scale windows. We then derive the evolution equations for multiscale kinetic and available potential energies and enstrophy. The phase oscillation reflected on the horizontal maps from Galilean transformation is removed with a 2D large-scale window synthesis. The resulting energetic terms are analyzed and interpreted. These terms, after being carefully classified, provide four types of processes: transport, transfer, conversion, and dissipation/diffusion. The key to this classification is the transfer–transport separation, which is made possible by looking for a special type of transfer, the so-called perfect transfer. The intricate energy source information involved in perfect transfers is differentiated through an interaction analysis.The transfer, transport, and conversion processes form the basis of dynamical interpretation for GFD problems. They redistribute energy in the phase space, physical space, and space of energy types. These processes are all referred to in a context local in space and time, and therefore can be easily applied to real ocean problems. When the dynamics of interest is on a global or duration scale, MS-EVA is reduced to a classical Reynolds-type energetics formalism.     

Numerical simulation of a torrential rain event in the northeast of Huaihe Basin. Part II: Instability conditions and the mechanism of intensification and maintenance

Based on the simulation displayed in Part I of this study, the intensification and maintenance, the relationship between deep moist mesoscale convective system (DMMCS) and instability, convective vorticity vector (CVV) are analyzed in the present paper. Results show that: (1) middle-low level convective instability is the precondition of the occurrence of DMMCS. The convergence and merger enhancement of convection cells, as well as the convective instability energy transporting from the left-front of typhoon play an essential role in the re-establishment and enhancement of convective instability. (2) Baroclinic instability and conditional symmetric instability appear not only in the middle-low level, but also are distinct in the middle-upper level of DMMCS. (3) In DMMCS, there is an alternative distribution of inertial instability column and inertial stability column. In the west and south, there are negative CVV columns, which is favorable for the burst of deep moist convection. (4) The strong slantwise convection induced by inertial instability, baroclinic instability, and conditional symmetric instability enhance the upper-level southerly component. Due to the appearance of the compensated downdraft at the low level of south side of DMMCS, the low level southerly intensified, and the enhancement of upper- and low-level cores is in favor of the development of DMMCS, which will be beneficial to the reinforcement and maintenance of inertial instability, baroclinic instability, and conditional symmetric instability. It is a positive feedback process. (5) There is a downshear circulation to the east of rainfall cell. Shallow convections near this cell absorb the vapor and instability energy coming from the south. In the meanwhile, the mesoscale convergence line and meso-β-scale vortex organize and intensify convective cells. In DMMCS, there is an alternative distribution of convergence and divergence columns, and the couple between strong divergence and vorticity columns. They are both conducive to the development of DMMCS, and the instability will be intensified and maintained for its development in depth.     

影响山东的台风暴雨天气的湿位涡诊断分析

应用湿位涡理论 ,对发生在山东境内由台风和台风减弱的低压引发的两场大暴雨过程进行诊断。结果表明 :这两场暴雨都产生在θe 陡立密集区附近 ,θe 陡立密集区附近易导致湿斜压涡度发展 ;对流层中低层MPV1 <0 ,850hPa上MPV2 >0 ,综合反映了暴雨区对流不稳定和斜压不稳定的发展 ;对流层高层高值湿位涡下传 ,有利于位势不稳定能量的储存和释放 ,使降水增幅。     

高空槽对两类热带气旋变性阶段强度变化影响的数值模拟研究

选取9711号台风"Winnie"和0713号台风"Wipha"分别作为变性加强和变性减弱类台风个例进行数值模拟,而后利用模式结果对大尺度场及涡度收支场进行诊断分析。结果表明:台风"Winnie"变性过程中,其西北侧高空槽呈西北—东南走向,南亚高压强度弱,对高空槽东移阻塞作用小。变性前期阶段主要是锋面系统和斜压性起关键作用,变性完成后,"Winnie"在斜压、高层辐散及涡度平流的共同作用下再次加强。台风"Wipha"变性过程受强大的南亚高压和副高影响,其西北侧高空槽稳定少动且呈东北—西南走向,冷空气入侵不明显,斜压区面积和强度都受到了限制。另外高层辐散场和涡度平流场均未能为"Wipha"提供有利的环境使其再加强。     

On the vorticity and energy budgets of the cold vortex in Northeast China: a case study

This study examines the vorticity budgets, turbulent extended exergy and kinetic energy evolution equations to investigate the major dynamical and energy conversion processes contributing to the initiation and intensification of the cold vortex over Northeast China that occurred during June 19–22, 2009. The results show that the cyclonic vorticity was initiated in the lower troposphere due to the intense convergence of horizontal winds. The growth of cyclonic vorticity in the middle troposphere is mainly due to the vertical transportation of the vorticity, yet the increase of cyclonic vorticity in the upper troposphere primarily results from the horizontal advection of vorticity. Of special interest in this study is the evaluation of the role of thermal advections in the baroclinic development of the cold vortex. The results indicate that the rising of the air over relatively warm areas and the sinking of the air in relatively cold regions are favorable for releasing turbulent extended exergy $ \left( {e_{\text{t}} } \right) $ , which is later converted to turbulent kinetic energy $ \left( {k_{\text{t}} } \right) $ , and this process occurs during the initiation and intensification of the cold vortex. In addition, barotropic energy conversion is another important process that contributes to the growth of k _t, and it strengthens gradually after the initiation of the cold vortex. Other than frictional consumption, the flux of k _t in the vertical direction also depletes some of k _t. The fluxes of e _t, baroclinic energy conversions and diabatic generations are favorable factors for the growth of e _t, whereas it decreases with time as a result of a large amount of e _t that is released. Most of the energy conversion processes, including the baroclinic and the barotropic energy transformations and the energy conversions from e _t to k _t, as well as the fluxes of e _t, are stronger in the lower troposphere than the other areas during the formation of the cold vortex. This accounts for the initiation of the cyclonic vorticity in the lower troposphere. Finally, the fact that the turbulent extended exergy releases primarily in the middle troposphere through the vertical thermal circulation is consistent with our understanding based on the vorticity budget analyses.     

簡单斜压大气中热成风的建立和破坏(一)

本文第一部分利用两层模式討論了热成风的适应問題.如果起始非热成风流場的热成风涡度大于溫度場的热成风涡度时,促使上升运动加强,反之,促使下沉运动加强。对于250—750毫巴之間的斜压系統,适应的特征尺度L_0,是决定流場向溫度場調整,还是溫度場向流場調整的临界水平尺度。 第二部分根据溫度場和流場的平流作用,分析了非热成风产生的机制.并由热成风适应速率和破坏速率的对比,討論了准地轉运动和非地轉运动的形成。 最后,用热成风不断破坏和建立的观点和方法,分析了长波斜压不稳定发展的过程,并进一步揭示了它的物理本貭。     

山东省春秋季暴雨天气的环流特征和形成机制初探

对山东省春秋季暴雨的气候特征和影响系统进行了分析, 制作了春秋季暴雨的平均环流形势图。分析了2003年春秋季两次大范围暴雨的环流特征和影响系统及暴雨期间大气的热力特征和水汽输送特征, 应用k-螺旋度和倾斜涡度发展理论, 分析了暴雨的形成机制。结果表明:4月暴雨均受气旋影响, 10月暴雨以冷锋影响居多。2003年4月17—18日为气旋暴雨, 10月10—12日为切变线冷锋暴雨。两次暴雨前都有低空偏南风急流向暴雨区输送水汽, 大气强烈增温增湿, 对流不稳定度增大, 湿斜压性增强。强冷锋南下触发对流不稳定能量释放, 产生暴雨。暴雨期间低层正k-螺旋度猛烈发展。暴雨前期中低层MPV1 < 0且MPV2 > 0, 冷锋影响期间MPV1 > 0且MPV2 < 0, 都有利于倾斜涡度发展, 增强了上升运动。     

CONSERVATION OF MOIST POTENTIAL VORTICITY AND DOWN-SLIDING SLANTWISE VORTICITY DEVELOPMENT*

An accurate form of the moist potential vorticity(MPV) equation was deduced from a complete set of primitive equations.It was shown that motion in a saturated atmosphere without diabatic heating and friction conserves moist potential vorticity.This property was then used to investigate the development of vertical vorticity in moist baroclinic processes.Results show that in the framework of moist isentropic coordinate,vorticity development can result from reduction of convective stability,or convergence,or latent heat release at isentropic surfaces.However,the application of the usual analysis of moist isentropic potential vorticity is limited due to the declination of moist isentropic surfaces.and a theory of development based on z-coordinate and p-coordinate was then proposed.According to this theory,whether the atmosphere is moist-symmetrically stable or unstable,on convective stable or unstable,the reduction of convective stability,the increase of the vertical shear of horizontal wind or moist baroclinity may result in the increase of vertical vorticity,so long as the moist isentropic surface is slantwise.The larger the declination of the moist isentropic surface,the more vigorous the development of vertical vorticity.In a region with a monsoon front to the north and the warm and moist air to the south,or by the north of the front,the moist isentropes are very steep.The is the region most favorable for development of vorticities and formation of torrential rain.For a case of persistent torrential rain occurring in the middle and lower reaches of the Changjiang and Huaihe Rivers in June 11-15,1991,moist potential vorticity analysis,especially the isobaric analysis of its vertical and horizontal components,i.e.MPV1 and MPV2,respectively,is effective for identifying synoptic systems not only in middle and high latitudes,but also in low latitudes and in the lower troposphere.It can serve as a powerful tool for the diagnosis and prediction of torrential rain.     

1215号“布拉万”台风暴雨及降水非对称性分布的成因分析

利用中尺度非静力模式WRF对2012年第15号台风“布拉万”在中国东北地区造成的暴雨过程进行了数值模拟,结合观测资料对模拟结果进行了验证,利用模式输出的高分辨率资料,对“布拉万”台风造成的强降水及其非对称性分布的成因进行了诊断分析。结果表明,模式很好地再现了台风登陆过程中的路径、强度变化和降水分布,受中纬度西风槽带来的干冷空气影响,“布拉万”台风登陆后的降水和环流结构具有明显的不对称性,降水主要集中在台风中心西北侧的能量锋区附近。水汽散度通量和水汽螺旋度能够较好地描述强降水过程的发生、发展及其非对称性分布的时空特征,在强降水区,水汽散度通量表现为正值强信号,而水汽螺旋度表现为负值强信号,在非降水区和弱降水区,两者均表现为弱信号。等熵位涡分析显示,对流不稳定只是此次台风暴雨前期和初始阶段的不稳定条件,而湿位涡(MPV)的湿斜压项(MPV₂)则是暴雨增强和出现非对称性分布的主要机制。在暴雨形成过程中,由于冷空气侵入造成了在台风环流西北侧湿等熵面的陡立倾斜和水平风垂直切变的增强,导致了气旋性涡度的显著增强,气旋性涡度增强造成的强烈上升运动将降水区东南侧输送过来的暖湿空气向上输送,从而导致了暴雨的发生,这其中条件性对称不稳定是降水得以加强的一种重要不稳定机制。     

Influence of bottom topography roughness on the jet and inertial recirculation of a mid-latitude gyre

Several numerical experiments are conducted to examine the influence of mesoscale, bottom topography roughness on the inertial circulation of a wind-driven, mid-latitude ocean gyre. The ocean model is based on the quasi-geostrophic formulation, and is eddy-resolving as it features high vertical and horizontal resolutions (six layers and a 10 km grid). An antisymmetrical double-gyre wind stress curl forces the baroclinic modes and generates a strong surface jet. In the case of a flat bottom, inertia and inverse energy cascade force the barotropic mode, and the resulting circulation features strong, barotropic, inertial gyres. The sea-floor roughness inhibits the inertial circulation in the deep layers; the barotropic component of the flow is then forced by eddy-topography interactions, and its energy concentrates at the scales of the topography. As a result, the baroclinicity of the flow is intesified: the barotropic mode is reduced with regard to the baroclinic modes, and the bottom flow (constrained by the mesoscale sea-floor roughness) is decoupled from the surface flow (forced by the gyre-scale wind). Rectified, mesoscale bottom circulation induces an interfacial form stress at the thermocline, which enhances horizontal shear instability and opposes the eastward penetration of the jet. The mean jet is consequently shortened, but the instantaneous jet remains very turbulent, with meanders of large meridional extent. The sea-floor roughness modifies the energy pathways, and the eddies have an even more important role in the establishment of the mean circulation: below the thermocline, rectification processes are dominant, and eddies transfer energy toward permanent mesoscale circulations strongly correlated with topography, whereas above the thermocline mean flow and eddy generation are influenced by the mean bottom circulation through interfacial stress. The topography modifies the vorticity of the barotropic and highest baroclinic modes. Vorticity accumulates at the small topographic scales, and the vorticity content of the highest modes, which is very weak in the flat-bottom case, increases significantly. Few changes occur in surface-intensified modes. In the deep layers of the model, the inverse correlation between relative vorticity and topography at small scales ensures the homogenization of the potential vorticity, which mainly retains the largest scales of the bottom flow and the scale of β.