半地转近似下的混合Rossby－重力椭圆余弦波

在半地转近似［１］下，利用层结大气中的涡度方程、散度方程、连续方程和绝热方程结合行波解的方法得到了关于垂直速度的单一变量方程。这是与ＫｄＶ方程相应的非线性常微分方程，可得到椭圆余弦波或弧立波。此波动的频率有两种，表明层结大气中存在着两种性质不同的非线性波动。其一是东传的惯性重力椭圆余弦波，另一是混合Ｒｏｓｓｂｙ－重力椭圆余弦波，其性质介于Ｒｏｓｓｂｙ椭圆余弦波与西传的惯性重力椭圆余弦波之间。这两种非线性波的相速不但与波数和振幅有关，而且与β因子和静力稳定度有关，即纬度越低，则传播越慢；大气越稳定，则传播越快。     

正压大气波动的4波共振和准共振

从准地转正压涡度方程，提出新的双时间尺度，首次导得了正压大气波动的４波准共振耦合方程，即广义Ｌａｎｄａｕ方程，利用新的守恒量，求得其甚低频周期解，其周期为一年左右，这可认为是实际大气中年际振荡的一种新的物理机制。并可求出４波准共振波矢。     

平均流变化对波反馈的A-B混合方程理论

从两层模式的基本方程出发，推导了描述平均流对波振幅反馈的A－B混合方程，并通过适当变换把混合方程转化为洛仑兹系统，用于研究平均流对边缘波扰动振幅增长的反馈机制，以及在中性廓线附近边缘波的稳定性问题。这是对研究波流相互作用的E-P通量理论的一个重要扩充。同时，作者还指出了A－B混合方程理论在研究大气中的波流相互作用及对流方面有相当应用前景。     

斜压大气中尺度横波扰动的发展

为探索带状中尺度扰动发生发展的可能性及其对深厚对流云团的启动和组织作用。本文利用准动量无辐散二维模式讨论了斜压切变基流上中尺度横波扰动的发展问题。首先导出波能密度和波作用量，然后利用ＷＫＢ方法分析了波包的传播，建立波作用量方程，进而从波作用量方程出发，分别讨论了大气中各种层结下横波型扰动发展的物理背景条件。     

切变基流中惯性重力波的发展

采用分层浅水波方程、一简单的二层模式和ＷＫＢ方法，考虑基本气流的垂直切变，水平切变以及地形的影响，分析了惯性重力波的发展变化，得到有关导式波和曳式波发展的环境条件。     

垂直切变流中非线性重力波及其相互作用

利用多重尺度摄动法，推导出斜压大气中(基本风场具有垂直切变)两个非线性重力波相互作用方程，这两个方程联立组合为耦合非线性schrǒdīnger方程组。两个重力波相互作用时可激发出重力驻波。数值计算表明：两个孤立重力波相遇，相追会使波振幅增大，波宽变窄。强烈对流天气突然爆发的可能原因之一是中尺度重力波非线性相互作用的结果。     

水平切变基流中惯性重力波的发展

采用分层浅水波方程组和ＷＫＢ方法，建立了在基流的水平切变和地形的影响之下惯性重力波的能量方程，由此讨论波动的发展。主要得出：在急流的气旋性环流区，曳式波发展；在反气旋性环流区，导式波发展。在山脉的南北坡，导式波和曳式波均有发展的可能。     

副高与阻高形成的Rossby孤立波理论I:不存在临界层

针对不存在临界层情况下非均匀纬向流中的Ｒｏｓｓｂｙ孤立波，从正压、无辐散、准地转自由大气涡度方程出发，经过变量替换，用小参数展开法，得到流函数的各阶近似方程，推导出振幅函数满足的ＫｄＶ方程及修正ＫｄＶ方程（ＭＫｄＶ），并给出它们的孤立波解。对不同风速分布下伴随这些孤立波而出现的流场进行了近似计算，分别得到了副高型Ｒｏｓｓｂｙ孤立波流场、阻高型Ｒｏｓｓｂｙ孤立波流场及偶极子型流场，它们移动的规律性与实际大气的流场移动情况较一致。     

大气中的位涡守恒和Rossby波的能量、波作用与拟能守恒

推导得到普遍形式的位涡度守恒方程，其条件是外源Ｇ和摩擦Ｆ组成的矢量散度为零，放松了位涡守恒的绝热无摩擦限制，对准地转位涡方程，利用ＷＫＢ近似，得到了层结可变情况下的ＲＯｓｓｂｙ波的能量、波作用和拟能守恒的条件，对于空间缓变的基本气流，它们分别是基本气流与空间坐标无关，基本气流与ｘ无关和基本气流是空间坐标的函数。最后还给出了地形存在情况下的Ｒｏｃｓｂｙ波的能量、波作用和拟能守恒的条件。     

大气层结的非均匀性对重力内波波射线的影响

文中利用ＷＫＢ近似，讨论了非均匀层结对惯性重力内波和纯重力内波能量传播路径的影响，得到了波的能量密度，广义波作用密度，和广义拟能密度守恒的条件，导得了重力内波不稳定的必要条件，给出了在波的传播过程中控制波射线折射的方程，得到了两类不同的临界层，最后还利用四阶Ｒｕｎｇｅ－Ｋｕｔｔａ方法计算了不同层结分布下的波射线。     

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.     

Nonlinear waves in barotropic model

In this paper, from the system of equation describing a barotropic atmosphere using the method of Taylor expansion for the nonlinear terms, the periodic solutions of the nonlinear inertio-surface gravity waves and Rossby waves have been obtained.The finite-amplitude nonlinear inertio-surface gravity waves and Rossby waves with horizontal divergence satisfy all the KdV equation. The solutions are all the cnoidal function, i, e, the cnoidal waves which in-clude the linear waves and form the solitary waves under certain conditions. For the finite-amplitude Rossby waves with horizontal divergence, we find the new dispersive relation including both the wave number and the amplitude parameter. In case of small amplitude it is reduced to the Yeh formula. It is shown that the larger the amplitude and width, the faster the finite-amplitude inertio-surface gravity waves and the slower the finite-amplitude Rossby waves with horizontal divergence propagate. The blocking or cut-off system in which the amplitude and width are large may be considered as Rossby solitary waves.     

A numerical method for solving the evolution equation of solitary Rossby waves on a weak shear

In this paper an evolution equation in integral-differential form for finite amplitude Rossby waves on a weak shear is presented and an efficient method for its numerical solution is set up. It is shown that a propa-gation of solitary wave is possible whenever a proper weak shear in basic flows acts with the nonlinear effects and dispersion of the media, both in the atmosphere and in the ocean. To test the numerical method for solving the evolution equation, a series of experiments are carried out. The results indicate that the solitary solutions do exist and interact with each other in quite a succinct, manner. Therefore the method is successful and efficient for solving initial value problems of the above equation. The time decoupling problem arising in the numerical scheme and the related filtering technique are discussed. A variety of interesting phenomena such as the interaction of solitary Rossby waves, damping, dispersion and the development of nonlinear wave train are numerically studied.     

弱耗散作用下非线性Rossby波的调制不稳定

本文使用WKB方法对弱耗散作用下基本气流具有弱切变的行星大气中非线性Rossby波进行了研究,得到了弱耗散的非线性Rossby波振幅所满足的复系数非线性Schrdinger方程,并分别就无耗散和弱耗散的Rossby波的边带稳定性问题进行了讨论,得到了一些新结果.     

切变基本纬向流中赤道Rossby包络孤立波

利用多重尺度摄动法，从描写赤道Rossby波的正压大气位涡度方程中推导出在切变基本纬向流中非线性赤道Rossby波包演变所满足的非线性Schrodinger方程，并得到其单个包络孤立子波解，分析基本流切变对非线性赤道Rossby波动的影响。     

EFFECTS OF TOPOGRAPHY ON PROPAGATION AND DEVELOPMENT OF INERTIA GRAVITY WAVE

Effects of topography on the propagation and development of inertia gravity waves areinvestigated by means of WKBJ method.The equation of wave action conservation is obtained.It isfound that the inertia gravity wave tends to propagate to the higher elevation area,meanwhile theamplitudes of the waves increase.While the inertia gravity waves propagate to a lower elevation area,their amplitudes decrease.     

The solitary waves of the barotropic quasi-geostrophic model with the large-scale orography

Starting from a modified barotropic quasi-geostrophic model equation, considering the actual situation of the large-orography of the Tibetan Plateau, neglecting its slope in x direction, and using the reductive perturbation method, then the solitary waves are obtained. The results show that the orography is essential factor exciting solitary Rossby waves in a flow without shear.     

含大地形的准地转正压模式的孤立波解

该文由修正过的含大地形的准地转正压模式方程出发,考虑青藏高原大地形的实际情况,忽略其东西向地形坡度,再利用约化摄动方法,求其孤立波解,并得到结论:当基本气流无切变时,地形是产生Rossby孤立波的必要因子。     

Why do 2-day waves propagate westward?

In observations, the 2-day waves, identified as the convectively coupled equatorial inertio-gravity (IG) waves, only propagate westward. To understand this feature, a simple theoretical model is presented for the convectively coupled equatorial waves (CCEWs). Under the assumption that the convective heating is proportional to the vertical velocity on the first baroclinic mode, the nonlinear governing equation for the meridional velocity of the CCEWs can be derived. The optimal method is used to obtain the dispersion relation from this nonlinear equation, and the results show that the deep convection can slow down the IG waves by decreasing the mean state static stability, but the key leading to the westward propagation of the IG waves is the full meridional variation of the sea surface temperature (SST). The warm SST trapped near the equator excites long westward propagating IG waves, whereas the warm SST trapped near the ITCZ centered at 10° N excites short westward propagating IG waves. This theoretical model provides a simple tool to study the CCEWs in understanding the tropical circulation.     

层结大气中非线性椭圆余弦波和孤立波的研究

在前文采用半地转近似和行波法来研究层结大气中的非线性波动的基础上,进一步探讨非线性方程及其级数近似方程的解的稳定性,波动解的存在条件和波动的一些特征。研究指出,在平衡点附近,将非线性方程用其级数近似方程代替是可行的、合理的。在初始拟能满足一定的条件下,椭圆余弦波和孤立波是存在的。文中还求得了椭圆余弦波解的周期、ｘ向波长和振幅以及孤立波的宽度和振幅。并指出,孤立波的宽度和振幅不但与波速有关,还与β因子和层结稳定度有关,而且在相同的某条件下,西行的混合Ｒｏｓｓｂｙ－重力孤立波比起东行的惯性重力孤立波来,宽度要小但振幅却大。