斜压大气亚临界不稳定的数值试验

利用一个由表面摩擦和辐射线弛强迫驱动的斜压准地转两层模式作数值试验，来研究斜压大气中的亚临界不稳定现象。试验结果表明，当无量纲量β≥0.25时，斜压两层大气中能够发生亚临界不稳定现象。亚临界不稳定现象的发生与初始扰动的选择有关。科氏参数的经向梯度的大小又是影响斜压稳定性强度的一个重要因素，其值越大，斜压稳定性强度越小。     

一次梅雨期苏北大暴雨的时空结构及其非线性亚临界对称不稳定

利用WRF V2.2模式对2006年6月30日00时—7月1日12时（世界时）江苏宝应地区的大暴雨过程进行数值模拟,并利用从模拟结果提取出的环境风场和中尺度扰动风场对此次大暴雨过程的时空结构,尤其是风场的垂直切变和非线性亚临界对称稳定性进行分析,结果表明：整层大气平均风垂直切变矢量转为西南偏西风后其南风分量随时间增大到最大值,对暴雨的发生有提前5-4 h的指示意义,相应时刻绝对水平螺旋度亦达到极值;暴雨发生前3 h首次出现强烈的整层垂直上升气流,预示大暴雨发生;在暴雨发生前9 h,高层200 hPa涡度、散度两波呈π/2位相差,对应强烈地转不平衡重力波,随时间向下传播,至暴雨发生前3 h下传到800 hPa;中尺度扰动风场的加强与降水的加强关系密切,在暴雨发生前3 h,出现中尺度非线性亚临界对称不稳定,激发暴雨发生,并对大暴雨的发生有重要的指示意义。     

对称不稳定的非线性问题和对称型重力惯性波的非线性周期解

本文利用密度的空间分布不均匀性引入非线性项，从准动量无辐散模式出发导出了一个自治的二阶非线性系统，应用这个系统讨论了非线性项对对称不稳定以及对称型重力惯性波非线性周期解的作用。从本系统的一次近似系统可得到类似Hoskins于1974年得到的结论，同样可导出对称不稳定的位涡判据。由于本系统是一有限次的非线性系统，故应用Poincare形式级数法可证明非线性周期解的存在性，并可求得周期解的一系列近似解。     

非线性垂直切变基流中横波型扰动的不稳定

通过数值计算扰动的波谱和谱函数,对垂直非线性切变基流中横波型扰动的不稳定作了数值研究,给出了不稳定谱函数的结构,讨论了不稳定的性质。主要结论有:在基流为非线性垂直切变时,对三支波动连续谱区互不重叠的天气尺度情况,此时出现的不稳定扰动其性质是准地转涡旋波的不稳定,即Rossby波的斜压不稳定。在中α尺度中高端,虽有涡旋波和重力惯性波连续谱区的部分重叠,但这时不稳定的性质仍是涡旋波的不稳定,即准平衡的斜压不稳定。在中α尺度低端,既有准平衡涡旋波的不稳定,又有非平衡的涡旋-重力惯性混合波的不稳定(第一类混合波不稳定)。中β尺度不稳定的性质则是非平衡的涡旋-重力惯性混合波的不稳定,包括第一类混合波不稳定和第二类混合波不稳定。上述情况与线性垂直切变基流的结论相一致,但这里因基流垂直分布较复杂,垂直方向会出现散涡比以1为界的多段交替分布。综上,对于横波型扰动,只要基流不是常数,且层结稳定,虽此时存在纯重力惯性波连续谱区,但均无纯重力惯性波的不稳定,只有涡旋-重力惯性混合波的不稳定。     

Nonlinearity and finite-time instability in a T21L3 quasigeostrophic model

In this paper, a nonlinear optimization method is used to explore the finite-time instability of the atmospheric circulation with a three-level quasigeostrophic model under the framework of the conditional nonlinear optimal perturbation (CNOP). As a natural generalization of linear singular vector (SV), CNOP is defined as an initial perturbation that makes the cost function the maximum at a prescribed forecast time under certain physical constraint conditions. Special attentions are paid to the different structures and energy evolutions of the optimal perturbations.     

斜压不稳定理论的发展历程分析

斜压不稳定理论是中高纬度地区天气尺度扰动生成和发展的机制,是继长波理论之后大气动力学上的又一重大进展,对现代天气预报具有重要的指导意义。按照斜压不稳定理论发展的时间脉络,阐述了赵九章、查尼和伊迪在斜压不稳定方面开展的研究工作,分析了3位科学家各自的研究特点及历史贡献。赵九章1946年发表在《Journal of Meteorology》上的论文,最早提出了"斜压不稳定"这一概念,给出了不稳定的临界波长,并阐述了在不稳定扰动情况下能量的转换,以及不稳定波对大气环流带来的可能影响,尽管得出的不稳定临界波长与观测差别较大,但其对波-流相互作用的讨论在当时是超前的。查尼于1947年采用滤波和尺度分析等方法,将大气扰动方程简化为一个可以求解的系统,推导出大气稳定状态的判据,建立了斜压不稳定理论,其结果与实况比较接近;并据此把准地转模式成功应用于数值天气预报实践中,促使数值天气预报获得首次成功。1949年,伊迪在查尼研究工作的基础上通过合理的简化方法,得到了更为简洁的模型。最后,通过对比他们的研究思路,重点分析了赵九章未能使得斜压不稳定理论提前一年建立的原因:由于其研究思路始终局限在大气水平运动上,忽略了斜压系统发展中散度项的贡献,因而未能抓住天气系统发生、发展的本质,致使其最终与斜压不稳定理论的成功建立失之交臂,其论文本身存在的一些亮点也因此被后人忽视。      

A further investigation of the decadal variation of ENSO characteristics with instability analysis

Based on instability theory and some former studies, the Simple Ocean Data Assimilation （SODA） data are analyzed to further study the difference between the propagation of the ENSO-related oceanic anomaly in the off-equatorial North Pacific Ocean before and after 1976. The investigation shows that after 1976 in the off-equatorial North Pacific Ocean, there is a larger area where the necessary conditions for baroclinic and/or barotropic instability are satisfied, which may help oceanic anomaly signals propagating in the form of Rossby waves to absorb energy from the mean currents so that they can grow and intensify. The baroclinic energy conversion rate in the North Pacific after 1976 is much higher than before 1976, which indicates that the baroclinic instability has intensified since 1976. Prom another perspective, the instability analysis gives an explanation of the phenomena that the ENSO-related oceanic anomaly signal in the North Pacific has intensified since 1976.     

The impact of nonlinear stability and instability on the validity of the tangent linear model

l.Intr0ducti0nTheequationsgoverningthemotionsoftheatmosphereandoceanaren0nlinear0nes.Itisdiffcultandcomplicatedtodealwiththenonlinearproblem.Sothetangentlinearmodel(TLM),whichisobtainedbylinearizingthenonlinearmodelinthevicinityofthebasicflow.iswidelyutilizedinthetheoreticalresearchandpracticalimplementationintheatmosphericandoceanicsciences.First-TLMcanbeusedtoestimatetheev0luti0nofsmallPerturbati0nsinaf0recastmodel.Second,itisadoptedinextendedKalmanfilterinthedataassimilation(Evensen,l99…     

The generalized energy equation and instability in the two-layer barotropic vortex

The linear two-layer barotropic primitive equations in cylindrical coordinates are used to derive a gen- eralized energy equation, which is subsequently applied to explain the instability of the spiral wave in the model. In the two-layer model, there are not only the generalized barotropic instability and the super high- speed instability, but also some other new instabilities, which fall into the range of the Kelvin-Helmholtz instability and the generalized baroclinic instability, when the upper and lower basic flows are different. They are perhaps the mechanisms of the generation of spiral cloud bands in tropical cyclones as well.     

中尺度对流系统演变中的非线性对流对称不稳定

应用ARPS(Advanced Regional Prediction System)模式用数值试验的方法分析了中尺度对流系统中非线性对流-对称不稳定的发展, 结果表明, 非线性对流-对称不稳定的发展过程首先是对流的发展, 为对称不稳定的发展创造了条件, 而对称不稳定发展的结果使对流组织化, 环流加强, 生命史增长, 并且对流发展与对称不稳定的释放存在一个正反馈过程, 从而给出了其中物理过程相互作用的概念模型.     

阻塞过程中正斜压涡度拟能相互转换机制的重要性

使用正斜压涡度拟能方程对一次乌拉尔山阻塞过程的研究表明，虽然正、斜压涡度拟能向阻塞区内的净输送、阻塞区域内正斜压涡度拟能的净生成以及β效应是阻塞环流建立、维持和崩溃的基本能源，但正斜压涡度拟能相互转换机制则是阻塞过程得以形成的根本原因。如果没有正斜压涡度拟能相互转化机制，则阻塞环流不但不能形成，反而使大气的斜压性不断增强，正压性不断减弱。     

Localized multi-scale energy and vorticity analysis: II. Finite-amplitude instability theory and validation

A novel localized finite-amplitude hydrodynamic stability analysis is established in a unified treatment for the study of real oceanic and atmospheric processes, which are in general highly nonlinear, and intermittent in space and time. We first re-state the classical definition using the multi-scale energy and vorticity analysis (MS-EVA) developed in Liang and Robinson [Liang, X.S., Robinson, A.R., 2005. Localized multiscale energy and vorticity analysis. I. Fundamentals. Dyn. Atmos. Oceans 38, 195–230], and then manipulate certain global operators to achieve the temporal and spatial localization. The key of the spatial localization is transfer-transport separation, which is made precise with the concept of perfect transfer, while relaxation of marginalization leads to the localization of time. In doing so the information of transfer lost in the averages is retrieved and an easy-to-use instability metric is obtained. The resulting metric is field-like (Eulerian), conceptually generalizing the classical formalism, a bulk notion over the whole system. In this framework, an instability has a structure, which is of particular use for open flow processes. We check the structure of baroclinic instability with the benchmark Eady model solution, and the Iceland–Faeroe Frontal (IFF) intrusion, a highly localized and nonlinear process occurring frequently in the region between Iceland and Faeroe Islands. A clear isolated baroclinic instability is identified around the intrusion, which is further found to be characterized by the transition from a spatially growing mode to a temporally growing mode. We also check the consistency of the MS-EVA dynamics with the barotropic Kuo model. An observation is that a local perturbation burst does not necessarily imply an instability: the perturbation energy could be transported from other processes occurring elsewhere. We find that our analysis yields a Kuo theorem-consistent mean–eddy interaction, which is not seen in a conventional Reynolds stress framework. Using the techniques of marginalization and localization, this work sets up an example for the generalization of certain geophysical fluid dynamics theories for more generic purposes.     

摩擦和非线性对斜压初始扰动发展的影响

通过一个二维非线性斜压Eady波模式,讨论了斜压系统中初始扰动快速发展的动力学机制.由于斜压切变气流存在,其对扰动位涡的平流作用可引起初始扰动位涡的"位涡非屏蔽"(potential vorticity unshielding),导致线性系统初始扰动的快速增长.摩擦作用主要通过耗散局地扰动位涡,改变扰动位涡异常结构,特别是水平方向的位涡异常分布,从而减弱初始扰动位涡的"位涡非屏蔽"作用,抑制系统初始扰动动能的快速增长.非线性作用可以抑制较大振幅扰动的增长,同时引起扰动位涡异常丰富的垂直结构产生,导致初始扰动位涡的"位涡非屏蔽"的减弱,从而抑制初始扰动的快速增长.不同的初始扰动结构,可以产生不同的扰动位涡异常结构,相应存在不同的"位涡非屏蔽"作用,导致初始扰动的快速增长过程不同.位涡异常水平结构为"正负正"或"负正负"分布时,有利于初始扰动的快速增长,而上下层异号的扰动位涡异常在垂直方向间隔的距离越大,越有利于初始扰动的快速发展,这些结果进一步深化了对"位涡非屏蔽"的理解.     

"1998年二度梅"暴雨与非线性亚临界对称不稳定的初步研究

对1998年7月20日00时8月1日12时这段梅雨暴雨过程进行诊断分析，并利用MM5V3中尺度模式作梅雨暴雨的数值试验，结果表明：(1)本次梅雨暴雨分为3大段过程，非线性亚临界对称不稳定可能是3段梅雨暴雨形成的重要机制；(2)扰动风场增长与降水增长关系密切，扰动风场的增长会超前于降水的增长，非线性亚临界对称不稳定的增强可能使降水增强；(3)非线性亚临界对称不稳定主要发生在高层200hPa，中层500hPa也有发生。非线性亚临界对称不稳定使线性对称稳定的大气变为不稳定。降水区和暴雨中心主要位于高层200hPa和中层500hPa扰动风场极大值南侧与低层850hPa扰动风场极大值北侧之间。(4)非线性亚临界对称不稳定扰动的P折时间和空间尺度，分别为5～8h和200～300km。