垂直切变基流中东西向地形对惯性重力波稳定性的影响

利用分层浅水波方程和小参数(WKB)方法,考虑具有垂直切变的基流和地形的作用,求得惯性重力波的局地频率方程,并根据此方程分析讨论了在多种环境条件下波动的稳定性情况。     

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。     

经向基流和地形对惯性重力波的影响

采用分层浅水波方程组和ＷＫＢ方法，分别讨论了经向基流的垂直切变和南北走向的地形对二维惯性重力波的移速，稳定性以及发展的影响。     

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。     

地形对重力惯性波发展的影响

本文研究了具有南北坡的地形对重力惯性波发展的影响。利用WKB方法，建立了含地形作用的重力惯性波能量方程。研究结果表明:在层结稳定的情况下，当扰动“上坡”（沿地形高度的升度方向传播）时，其能量将减少，即扰动将减弱；当扰动“下坡”（沿地形高度的负升度方向传播）时，其能量将增加，即扰动将发展。如层结为不稳定，情形则相反，即扰动“上坡”时将发展，“下坡”时将减弱。此外，文中对波动的稳定性问题也作了一些讨论。     

切变流中的CISK机制与惯性重力波

利用板对称，有切变的大气动力学方程组，由行波法导出非线性微分方程，通过非线性稳定性理论讨论方程的稳定性，求解了ＫＤＶ方程，并讨论了线性ＣＩＳＫ，非线性ＣＩＳＫ，惯性稳定度参数和大气风速垂切变对惯性重力孤波强度和宽度的影响，目的早通过了解影响惯性重力孤波发展的因子，更深入地理解低纬中尺度天气系统形成和发展的过程。     

地形对重力惯性波传播与发展的影响

本文用ＷＫＫＢＪ方法研究了地形对重力惯性波传播与发展的影响，得到了地形影响下重力惯性波的波作用量守恒方程。结果表明：重力惯性波能量有向地形较高的区域传播的趋势，并且波包振幅上坡时加大，下坡时减小。     

CISK 影响下的线性和非线性惯性重力波

利用板对称的大气动力学方程组,考虑线性和非线性两种CISK加热过程,由行波法和非线性常微分方程定性理论,讨论了CISK影响下的线性和非线性惯性重力波的稳定性,以及CISK对惯性重力孤波强度和宽度的影响。结果指出,线性CISK既影响孤立波的强度,又影响孤立波的宽度,而非线性CISK只影响孤立波的强度。     

THE CISK MECHANISM AND THE INERTIAL GRAVITATIONAL WAVES IN SHEAR FLOW

By using the symmetric equations of atmospheric dynamics in y-z plane with vertical and horizontal shear of wind, the nonlinear ordinary differential equation is derived with the method of travelling wave.Its stability is discussed by using the theory of nonlinear stability and the KDV equation is solved. The effects of linear CISK, nonlinear CISK, inertial stability and vertical shear of wind on the amplitude and the width of isolated inertial gravitational wave are discussed. In order to understand deeply the formation and development of meso-scale synoptic systems, such as the squall line, MCC, the cold surge of Asia high and typhoon, the factors of development of the isolated inertial gravity wave are analysed.     

纬向切变基流中的非线性Rossby波

本文在半地转近似下讨论了纬向切变基流中的非线性正压Ｒｏｓｓｂｙ波，给出了存在波解的切变基流条件。     

地形与纬向切变基流中的非线性Rossby波

在半地转近似下,用相角函数方法得到了含地形强迫作用与纬向切变基流的非线性常微分方程.利用微分方程解的几何定性理论,直接得到该方程存在有限振幅的周期波与孤立波解的存在条件.利用函数逼近法求得波解的显式解,得到了一些有意义的结果。     

基本气流的垂直切变对热带行星尺度大气波动的影响

通过一个赤道β平面上的绝热无摩擦的两层模式,讨论了线性垂直切变的纬向基本气流对热带行星尺度大气波动的影响。在长波近似下,当有纬向基本气流垂直切变时,可得到与东传Kelvin波和西传Rossby波对应的不稳定模态。对不稳定的Kelvin波模态,其相速受垂直切变的影响不大,而对不稳定的Rossby波模态,切变越大,西传速度越小。基本气流的垂直切变主要影响热带Rossby波。     

MESOSCALE NONLINEAR GRAVITATIONAL WAVES AND THEIR INTERACTION IN VERTICAL SHEAR FLOW*

Interaction equations of two nonlinear gravitational waves in baroclinic atmosphere are presented via multi-scale perturbation method,which can be classified into coupling nonlinear Schrodinger equations.In particular,the interaction course of two nonlinear gravitational waves of basic flow in vertical linear and quadratic shear is illustrated.Numerical calculation displays that wave amplitude enlarges and wave width narrows when two solitary gravitational waves meet and chase;that basic flow with single shear is more beneficial than that with quadratic shear to the interaction of two nonlinear wave packets;and that the interaction of two wave packets makes wave shape change more greatly and energy more dispersive,which contributes to the occurrence of changeable weather.Therefore,one of the probable mechanisms for the appearance of strong convection weather is the interaction between mesoscale nonlinear gravitational waves.     

THE EFFECTS OF VERTICAL VARIATION OF BASIC FLOW AND HORIZONTAL GRADIENT OF TEMPERATURE ON LINEAR AND NONLINEAR GRAVITY WAVES

By using two-dimensional dynamical equations in x-z plane with Boussinesq approximation,the effects of the second-order vertical shear of the basic flow u_zz and the horizontal gradient of temperature (M) on the gravity wave and the isolated gravity wave are discussed.The magnitudes of u_zz and M corresponding to the linear and nonlinear stabilities of the gravity waves are worked out,respectively.The results show that amplitude and width of the isolate dgravity wave are closely related to u_zz and M.It is indicated that the isolated gravity wave with a width of about 10 km can be motivated by the disturbance of sub-synoptic scale in the certain ranges of flow field shear and temperature gradient,while the motivated waves may be associated with the cold surge ahead of a cold front and the other mesoscale synoptic systems.