对称不稳定理论及其应用问题(二)非线性理论

文章对对称不稳定理论及其应用的现状进行了全面的评述。主要讨论非线性理论，这包括非线性对称不稳定的一般研究方法（能量积分法，奇异摄动法，气块质点法，分岔和突变理论，数值试验），二维定常非线性对称环流的稳定性等问题。最后讨论了线性理论和非线性理论在实际应用方面的差异。     

大气中对称运动的非线性稳定性分析

本文利用分岔和突变理论讨论了非线性对称运动的稳定性,结果表明: (1)在的情况下,非线性对称运勃方程在平衡点P(0,0)和Q((fs)/β,0)附近具有完全不同的性质。 (2)在的情况下,当时,对称运动可以产生亚临界分岔,而当时,对称运动可以产生超临界分岔。 (3)在的情况下,当条件和同时满足时,对称运动可以产生尖点(cusp)突变。     

"93.5"黑风暴的对称不稳定诊断分析

利用一次较好地模拟了“９３．５”黑风暴的ＭＭ４中尺度模式三个时次的输出资料,应用线性和非线性对称不稳定的判据对这次强沙尘暴天气过程进行诊断分析。结果表明,线性理论判据中的湿对称不稳定为这次过程的一种可能机制。非线性理论的分析结果表明,这次飑线过程不但与条件对称不稳定和尖点突变有关,且其移速较线性理论更符合实际过程。     

对称不稳定理论

本文从四个方面概述了对称不稳定理论的主要研究成果,其中包括:无粘性干大气的对称不稳定问题;粘性大气的对称不稳定问题;湿大气的对称不稳定问题;非线性对称不稳定的研究。     

线性与非线性对称不稳定的数值试验

设计了一个准二维非静力数值模式，用该模式研究了对称不稳定的发展和演变特征。线性和非线性对称不稳定的数值试验结果表明。线性和非线性对称环流的演变特征及其结构有很大差异。在基本状态是对称不稳定的情况下，线性对称不稳定在其发展过程中始终维持着向冷区倾斜的对称环流；而非线性对称不稳定在其发展初期与线性情况相同，当扰动增长到一定程度时非线性平流项的作用不可忽略，原来对称的环流则被破坏。     

广义非线性亚临界湿对称不稳定

从含摩擦耗散与凝结潜热的f平面Boussinesq近似下的非线性扰动方程组出发,得到了湿空气中的广义能量方程,推导出非线性亚临界湿对称不稳定的必要条件,并将不稳定判据与干空气情况相比较,首先解析地分析得到凝结加热反馈机制对亚临界对称不稳定的影响。其次针对中尺度大气层结不稳定和稳定的情况,分别计算出初始扰动振幅的临界值,结果表明,相对干空气而言,饱和湿空气情况下,当中尺度大气层结不稳定时,亚临界对称不稳定更容易发生,即使中尺度大气层结稳定,亚临界对称不稳定也容易发生。这一结果改进了干空气下的非线性亚临界对称不稳定理论。     

弱环境流场中台风运动的若干问题

概述弱环境流场中台风运动研究的若进展，包括对称结构理论，非线性作用强迫影响和准均匀流理论等４个方面，并初步讨论了理论结果的应用前景。     

"96.1"高原暴雪过程湿对称不稳定的数值研究

利用一次较成功的模拟了“９６．１”青藏高原东北部暴雪过程的ＭＭ４中尺度模式输出资料,根据条件对称不稳定（ＧＳＩ）的非线性理论判据对这次暴雪过程进行了诊断,结果表明,ＣＳＩ是“９６．１”暴雪发生和发展的一种动力机制。在诊断的基础上,用非线性对称不稳定和非纬向非平行期流对称不稳定模式对“９６．１”暴雪发生发展过程的动力学机制进行了数值试验,结果指出：用两种方法进行数值模拟时,都会出现对称环流,不仅ψ场     

非静力平衡大气非线性层结对称运动的稳定性和突变

在假定了环境地转风具有水平和垂直的线性切变的情况下,考虑大气层结的线性和非线性切变的作用,建立了一个非线性常微分方程组,然后构造了一个Hamilton函数,通过讨论Hamilton函数的凸凹性,得到了非线性层结对称运动的不稳定判据,同时讨论了非线性层结对称运动产生突变的条件。     

98.6连续暴雨的对称不稳定研究

通过分析98.6连续暴雨过程的扰动风场与降水强度之间的关系,以及扰动风场与非线性和线性对称不稳定之间的关系,进而研究非线性和线性对称不稳定与降水强度和位置之间的关系,认为在日常降水预报中应注意扰动风场的变化以及非线性和线性对称不稳定。     

一次华北强降雪过程的湿对称不稳定性研究

运用湿球位涡和倾斜有效位能的概念从条件性对称不稳定（ＣＳＩ）和局地对称不稳定（ＬＳＩ）这两个侧面计算了一次华北强降雪过程的湿对称不稳定的水平分布和垂直分布状况，并比较详细地讨论了湿对称不稳定对１９８６年１１月２２—２３日发生在内蒙古河套地区和林东、林西地区附近的一条狭长的强降雪带的可能作用以及湿对称不稳定与基本气流走向、风垂直切变和水汽的关系，发现：这条降雪带与雪区附近低层的湿球位涡负值区走向大体平行；在降雪带中分别位于呼和浩特、东胜地区和林东、林西地区的强降雪中心有着不同的动力学机制，前者主要为在暖区具有弱的对称不稳定的情形下锋生强迫作用所致，后者则是由明显的湿对称不稳定所致。     

一个分析大气谱模式的合理性的定性方法

利用对称运动和非对称运动的理论结果,如‘对称运动的不变性’,可以推得:如初始时刻运动是对称的,对于绝热无摩擦的谱模式,在时间积分过程中,总有 1.和反对称运动有关的谱系数等于零; 2.全球预报和半球预报在同一半球内处处相同; 3.和赤道对称的任意两个区域,其各自的运动彼此对称。 数值试验也证实了这些结果。 在有外力强迫的情形,如地形(或加热),如其分布是对称的,则在初始运动是对称的情况下,‘对称运动的不变性’仍然成立。但如果地形(或加热)分布是非对称的,则运动的对称性会减小,而变成非对称运动,并出现越赤道气流。这些也经过数值试验加以证实。 利用上述理论结果作为指导,可以用所设计的模式进行试验、分析,从而,确定模式设计是否合理,有关软件是否有误等。     

Kinetic Energy Budgets during the Rapid Intensification of Typhoon Rammasun (2014)

In this study, Typhoon Rammasun(2014) was simulated using the Weather Research and Forecasting model to examine the kinetic energy during rapid intensification(RI). Budget analyses revealed that in the inner area of the typhoon,the conversion from symmetric divergent kinetic energy associated with the collocation of strong cyclonic circulation and inward flow led to an increase in the symmetric rotational kinetic energy in the lower troposphere. The increase in the symmetric rotational kinetic e...     

RESEARCH ON MOIST SYMMETRIC INSTABILITY IN A STRONG SNOWFALL IN NORTH CHINA*

The concept of wet bulb potential vorticity and SCAPE(slantwise convective available potential energy) is used to calculate the horizontal and vertical distribution of moist symmetric instability including convective symmetric instability(CSI) and local symmetric instability(LSI) in the process of a storm snowfall in North China.The potential contribution of moist symmetric instability to a narrow storm snowfall belt occurring in the Hetao and Lindong,Linxi region of Inner Mongolia and the relationship between moist symmetric instability and direction of the basic flow,wind shear and moisture are discussed.It is found that the strong snowfall belt is almost parallel with negative value area of wet bulb potential vorticity at low levels in the vicinity of snow area.And the dynamical mechanism of the strong snowfall center in the Lindong,Linxi region is different from that in the Hetao region.The former is induced by frontogenetical forcing with weak symmetric instability in the warm section of frontal area and the latter triggered by obvious moist symmetric instability.     

RESEARCH ON MOIST SYMMETRIC INSTABILITY IN A STRONG SNOWFALL IN NORTH CHINA

The concept of wet bulb potential vorticity and SCAPE (slantwise convective available potentialenergy) is used to calculate the horizontal and vertical distribution of moist symmetric instabilityincluding convective symmetric instability (CSI) and local symmetric instability (LSI) in the processof a storm snowfall in North China.The potential contribution of moist symmetric instability to anarrow storm snowfall belt occurring in the Hetao and Lindong,Linxi region of Inner Mongolia andthe relationship between moist symmetric instability and direction of the basic flow,wind shear andmoisture are discussed.It is found that the strong snowfall belt is almost parallel with negative valuearea of wet bulb potential vorticity at low levels in the vicinity of snow area.And the dynamicalmechanism of the strong snowfall center in the Lindong,Linxi region is different from that in theHetao region.The former is induced by frontogenetical forcing with weak symmetric instability in thewarm section of frontal area and the latter triggered by obvious moist symmetric instability.     

Interaction between equatorially symmetric and asymmetric tropical eastern Pacific SSTs

The third version of the extended reconstructed sea surface temperature (SST) data spanning from 1880 to 2007 was used to investigate the interaction between equatorially symmetric and asymmetric tropical eastern Pacific SSTs. Principal component analysis and wavelet spectrum analysis showed that the asymmetric SST was dominated by an amplitude-modulated annual cycle, while the symmetric SST was a mixture of amplitude-modulated annual cycle and El Niño-Southern Oscillation (ENSO). The symmetric and asymmetric components were significantly correlated, particularly in March and October. In March, when ENSO is usually weak, the interaction between two components is mainly due to the interaction between the amplitude-modulated annual cycles of each component. On the other hand, in October, when ENSO is dominant, the interaction between amplitude-modulated asymmetric annual cycle and ENSO becomes dominant. The interaction in March is partly explained by anomalous southeasterly winds associated with the symmetric SST pattern reducing wind speed over the southeastern Pacific, causing an intensification of the asymmetric SST component. In October, the equatorial asymmetrical development of ENSO causes a significant correlation between the symmetric and asymmetric components.     

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。     

"96.1"高原暴雪过程三维条件性对称不稳定的数值研究

利用“96．1”青藏高原东北部暴雪过程的较成功的中尺度模拟的输出资料,用非纬向非平行基流中的对称不稳定模式,对“96．1”暴雪发生发展过程的动力学机制进行了三维基流中二维非线性对称不稳定数值模拟试验。结果表明,ψ场和ω场的三维配置与切变线的演变过程相当一致,说明用三维基流中二维非线性对称不稳定可能能较好地描述SI在切变线东伸南移过程中所起的作用。     

Wave-CISK与快速增长的对称不稳定

本文应用一准两维的非静力平衡数值模式研究了凝结加热反馈对线性及非线性对称不稳定的影响。数值试验结果表明:当Ri<1时，对于一定的加热廓线，Wave-CISK可以激发出快速增长的线性对称不稳定，其指数增长率比无加热时增加一倍半，并产生向暖区的移动，而加热廓线对对称不稳定的发生发展及结构都有明显的影响。具有凝结加热的非线性对称不稳定在其发展初期与线性情况相同，当扰动增长到一定强度，非线性作用增强，其不稳定增长速度就减慢，原来对称的环流结构被破坏，正环流不断减弱，负环流不断增强。