广义Sawyer－Eliassen方程解的存在性

本文讨论了广义Ｓａｗｙｅｒ－Ｅｌｉａｓｓｅｎ方程组的解的存在性问题。     

台风中的不稳定螺旋惯性重力波

本文提出了台风基本场可以形成内、外两种不同机制的螺旋波发展的不稳定区域,它们的位置分别相应于内、外螺旋雨带。文中分析了台风平均场在内不稳定区附近的非均匀空间变化,对一类特征波造成的反射,得到了相应的“量子化条件”,由此推出螺旋波特征频率及增长率的公式。文中还分析了优势增长特征波的增长率、波长、螺旋臂数、偏振运动及热力结构等动力学特征,得到与观测相近的结果。     

一类含有约束的变分问题中权重因子的最优选取

研究了一类含有线性对流约束的变分问题中权重因子的最优选取。在变分问题中,泛函权重因子选取的适当与否将影响数值计算的结果。针对目前权重因子选取的相对随意性,在对观测场和理想场合理假设的条件下,分别讨论了带有弱约束和强约束的变分问题,通过求解相应的Euler方程,运用矩阵理论和偏微分方程的差分方法,得到了在分析场与理想场之间方差最小意义下的客观权重因子。推证结果表明,若将带约束的变分问题的Euler方程离散成差分形式,且满足根据实际问题提出的合理假设以及差分方程稳定性条件,那么目标泛函中的权重因子在分析场与理想场的最小方差意义下存在最优选取。它们在理论上更客观可信,可以实现权重因子与数值模式、观测资料的整体协调以及各因子之间的相互协调。     

层结大气中的内惯性重力孤立波与颮线形成的非线性过程

本文从层结旋转大气三维非静力平衡方程出发,导出了平行基本气流中的有限振幅扰动波的KdV方程。对于层结为常数和矩形截面中无切变的基本气流的简单情况,进行了求解孤波解的一些基本性质,合理地解释了低空急流左侧形成飑线和雷雨群列队的现象。同时也说明了低空急流上与之相伴随的超地转脉动特征。在层结和平行气流为空间函数的一般情况下,对于孤波解波幅与斜压-惯性-层结联合稳定度之间关系的定性分析表明,在稳定度下降的地方会有更强的垂直环流在孤波中发展,并有类似暴雨的爆发性特点。     

UNSTABLE SPIRAL INERTIAL-GRAVITY WAVES IN TYPHOONS

It is proposed in this paper that there are two cireular regions of a typhoon where unstable spiral waves can occur. Furthermore, the instability mechanism is different in each region. The locations of these regions coincide with the inner and outer spiral rain bands respectively. Analysis indicates that in the inner unstable region, some eigenwaves are reflected by the strong nonuniformity of the typhoon's basic flow and a"quantum condition" is established correspondingly, which gives the eigenfrequency and growth rate. The estimated growth rate, spiral arm number, wave length, polarization and thermal structure for the proferentially growing eigenwaves are comparable with the observations of inner spiral Cb cloud bands.     

Optimal selection for the weighted coefficients of the constrained variational problems

The aim is to put forward the optimal selecting of weights in variational problemin which the linear advection equation is used as constraint. The selection of the functionalweight coefficients ( FWC) is one of the key problems for the relevant research. It wasarbitrary and subjective to some extent presently. To overcome this difficulty, thereasonable assumptions were given for the observation field and analyzed field, variationalproblems with " weak constraints" and " strong constraints" were considered separately. Bysolving Euler' s equation with the matrix theory and the finite difference method of partialdifferential equation, the objective weight coefficients were obtained in the minimumvariance of the difference between the analyzed field and ideal field. Deduction results showthat theoretically the optimal selection indeed exists in the weighting factors of the costfunction in the means of the minimal variance between the analysis and ideal field in terms ofthe matrix theory and partial differen     

An existence theorem of generalized Sawyer-Eliassen equation

ＡＮＥＸＩＳＴＥＮＣＥＴＨＥＯＲＥＭＯＦＧＥＮＥＲＡＬＩＺＥＤＳＡＷＹＥＲ－ＥＬＩＡＳＳＥＮＥＱＵＡＴＩＯＮＹｕＱｉｎｇ－ｙｕ（余庆余）（ＬａｎｚｈｏｕＵｎｉｖｅｒｓｉｔｙ,Ｌａｎｚｈｏｕ）ＸｕＱｉｎ（许秦）（ＣＩＭＭＳＩｎｓｔｉｔｕｔｅＵ．Ｓ．Ａ）...     

广义Sawyer-Eliassen方程解的存在性

本文讨论了广义Sawyer-Eliassen方程组的解的存在性问题。     

SOLITARY INTERNAL GRAVITY INERTIAL WAVE IN A STRATIFIED ATMOSPHERE AND NONLINEAR PROCESSES FOR THE FORMATION OF SQUALL LINES

In this paper the KdV equation is derived from the three dimensional primitive equations for a class of finite amplitude waves in a stratified basic flow. The solitary wave solution is given for a simple case where a constant and uniformly stratified basic flow is confined in a region bounded by solid walls with rectangular cross section. The properties of the solitary wave solution can give a possible explanation for the preferential occurrence of a squall line or storm cell train at the left side of a low level jet and the concurrent fluctuation in the low level jet. For more general cases, i. e. sheared basic flow and nonuniform stratification, the qualitative response of the wave amplitude to the symmetric baroclinic stability of the basic flow is analysed. The results indicate that the vertical circulation in a solitary wave will possibly be dramatically intensified in a local area where the stability is weak or negative.