一类双曲-抛物型方程的广义解

讨论了一类奇摄动双曲-抛物型方程广义初边值问题,在适当的条件下,用Galerkin方法研究了广义解的存在性、唯一性,同时得到了解的渐近估计式。     

计算凸域弦长分布函数的方法

利用广义支持函数和限弦函数讨论了弦长分布函数的计算问题,得到正三角形的弦长分布函数的显式表达式,所提供的方法具有普适性.     

冷迳流的稳定性及其解析解的分析

本文利用相法讨论了y方向无限伸延的冷迳流方程.首先发现其非线性项作用由于z方向上的补偿作用而消失,即其相空间的方程是四阶线性常微分方程.利用Hurwitz方法分析其稳定时,证明了唯有中性大气符合冷迳流的稳定性条件.其解析解的趋势表明与观测结果类似.     

降水概率预报方程的预报稳定性检验

通过将预报方程的预报稳定性检验转化为预报方程的历史拟合准确率（f_1）与试报准确率（f_2）是否有显著差异的统计检验,并将该方法用于西安市降水概率预报方程的预报稳定性检验,取得了较好的效果．     

奇异摄动系统的有限频段正实引理和界实引理

利用GKYP引理研究了奇异摄动系统的有限频段正实引理和界实引理,证明了全阶系统的有限频段正实性可以由快、慢子系统的有限频段正实性得到,同样可以证明奇异摄动系统的有限频段界实引理具有类似性质.最后作为应用,给出了一个两频域尺度模型降阶实现方案,表明了该方法的有效性.     

用解析的垂直正规模展开对大气数值模式进行垂直积分

本文提出了一个用大气自由振荡解析的垂直正规模为正交函数系构成一个完备的Hilbert空间,利用广义Fourier展开的概念,在垂直方向进行广义Fourier展开,对大气数值模式进行垂直积分.我们利用两组垂直正规模为正交函数系.第一组是等温大气的垂直正规模;第二组是多元大气的垂直正规模,并用变系数的一维平流方程进行试验积分,将积分结果与差分法、有限元法、Legendre多项式展开的结果进行比较.比较的标准是它们与解析解的均方根误差和相关系数.     

发展方程计算稳定性的比较分析

对线性与非线性发展方程的几种差分格式,以一维线性和非线性平流方程为例,对线性与非线性发展方程差分格式的计算稳定性进行了比较分析,揭示了差分格式结构和初值形式与非线性计算稳定性的关系。     

二维大气中定常广义地转流的稳定性分析

本文归纳总结了在绝热、无耗散对称二维大气中定常广义地转流稳定性分析中的扰动方程组的基本特征，并将其概括为具有这类问题共同基本特征的统一形式的扰动方程组的定解问题。在此基础上，统一地证明了：１）由统一的扰动方程组所确定的定解问题的解是存在唯一的；２）基态的性质是由Λｍｉｎ（Ｇ）的性质决定的：ａ．当Λｍｉｎ（Ｇ）＞０时，基态是稳定的；ｂ．当Λｍｉｎ（Ｇ）＜０时，基态是不稳定的。３）基态的全局稳定性质可以通过局部稳定性分析来确定；４）合理的、充分简化的局部稳定性分析结论在局部分析中是严格有效的     

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.     

The computational stability of boundary conditions in numerical integration of the vorticity equation

In forecasting large-scale flow patterns by numerical integration of the vorticity equation, errors are permitted near the boundaries of the region of integration. The magnitude of these errors depends upon the nature of the boundary conditions. Three simple types of boundary conditions are examined in this paper, and it is shown that two cases lead to computational instability while one is stable. The degree of instability is estimated in the former cases.

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Zusammenfassung Bei der Vorhersage großräumiger Strömungszustände durch numerische Integration der Vorticity-Gleichung sind an den Grenzen des Integrationsbereiches Fehler gestattet, deren Größe von der Art der Grenzbedingungen abhängig ist. In der vorliegenden Arbeit werden drei einfache Fälle von Grenzbedingungen untersucht und es wird gezeigt, daß zwei Fälle zu Instabilität führen, während der dritte stabil ist; der Instabilitätsgrad der ersteren wird abgeschätzt.

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Résumé Lors de la prévision à grande échelle des états de la circulation atmosphérique, au moyen d'intégration numérique de l'équation de la vorticity, des erreurs sont permises aux limites de la région d'intégration; la grandeur de ces erreurs dépend de la nature des conditions de ces limites. L'auteur examine ici trois types simples de conditions des limites; dans deux cas elles conduisent à une instabilité, tandis que le troisième est stable. Pour finir, il estime le degré d'instabilité des deux premiers cas.

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With 5 Figures.

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The work reported here was developed during a visit by the author to the meteorology group at the Institute for Advanced Study, Princeton, New Jersey.     

Applications of conditional nonlinear optimal perturbation to the study of the stability and sensitivity of the Jovian atmosphere

A two-layer quasi-geostrophic model is used to study the stability and sensitivity of motions on smallscale vortices in Jupiter’s atmosphere. Conditional nonlinear optimal perturbations (CNOPs) and linear singular vectors (LSVs) are both obtained numerically and compared in this paper. The results show that CNOPs can capture the nonlinear characteristics of motions in small-scale vortices in Jupiter’s atmosphere and show great difference from LSVs under the condition that the initial constraint condition is large or the optimization time is not very short or both. Besides, in some basic states, local CNOPs are found. The pattern of LSV is more similar to local CNOP than global CNOP in some cases. The elementary application of the method of CNOP to the Jovian atmosphere helps us to explore the stability of variousscale motions of Jupiter’s atmosphere and to compare the stability of motions in Jupiter’s atmosphere and Earth’s atmosphere further.     

强迫耗散非线性发展方程显式差分格式的计算稳定性

基于计算准稳定的概念来分析强迫耗散非线性方程显式差分格式的计算稳定性，给出强迫耗散非线性大气方程组显示差分格式计算准稳定的判据，为设计强迫耗散非线性大气方程组计算稳定的显式差分格式提供了新的思路和理论依据。     

华东区域夏季行星边界层大气稳定度的气候特征及其与气溶胶的联系

利用1979-2008年夏季（6—8月）逐日NCEP／NACR再分析资料、MODIS卫星的气溶胶资料等,研究了华东区域夏季行星边界层大气稳定度的气候特征与年际变化,分析了大气稳定度和相应的加热场与气溶胶光学厚度（aerosol optical depth,AOD）的联系。结果表明：华东区域夏季行星边界层大气稳定度在空间上分布不均匀,时间上具有明显的年际变化。边界层中的非绝热加热率、大气稳定度及气溶胶光学厚度三者之间可能存在密切联系。利用经验正交函数分析了华东区域总体理查森数Rib的距平场,得到了边界层稳定度分布的3个主要模态,这3个模态所代表的边界层大气稳定度异常与夏季风环流异常密切相关,特别是P-J型遥相关波列和西太平洋副热带高压在中国东部大气边界层稳定度变化中可能起着非常重要的作用。     

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 Impacts of Initial Perturbations on the Computational Stability of Nonlinear Evolution Equations

The impacts of initial perturbations on the computational stability of nonlinear evolution equations for non-conservative difference schemes and non-periodic boundary conditions are studied through theoretical analysis and numerical experiments for the case of onedimensional equations.The sensitivity of the difference scheme to initial values is further analyzed.The results show that the computational stability primarily depends on the form of the initial values if the difference scheme and boundary conditions are determined.Thus,the computational stability is sensitive to the initial perturbations.     

The Boussinesq-BO equation for algebraic gravity solitary waves in baroclinic atmosphere and the research of squall lines formation mechanism

The gravity solitary waves are a kind of waves which are caused by the disturbance of static equilibrium. The nonlinearity concentration of the gravity solitary waves makes the energy assemble together and forms disastrous weather phenomena, such as squall lines. By the calculation condition and theoretical method limit, previous studies tried hard to reduce the variable numbers and discussed the gravity solitary waves in barotropic atmosphere, but the baroclinic problem of atmosphere is inevitable topic. In this paper, from the basic kinetic equations in baroclinic non-static equilibrium atmosphere, by using multi-scale analysis and perturbation method, a new model is derived to describe the algebraic gravity solitary waves, we call it Boussinesq-BO equation. Comparing with the former models, the Boussinesq-BO model can describe the propagation process of waves in two directions and is more suitable for the real atmosphere condition. With the help of the trial function method, an exact solution of Boussinesq-BO equation is obtained and the fission property of algebraic gravity solitary waves is discussed. Finally, we can find that the fission of algebraic gravity solitary waves is also a possible formation mechanism of squall lines.