中层大气Rossby波与惯性重力波的非线性相互作用 （Ⅰ）相互作用方程

从包含Ｒｏｓｓｂｙ波和惯性重力波的大气运动方程组出发，采用弱非线性相互作用近似，推导出耗散大气中这两种尺度相差很大的波动之间的非线性相互作用方程．以此为基础，得到了描述窄角谱Ｒｏｓｓｂｙ波包和惯性重力波包的非线性时空演变规律的三波相互作用方程．数值分析表明，当一个Ｒｏｓｓｂｙ波包与两个惯性重力波包发生相互作用时，两个惯性重力波包之间进行快速的能量交换，同时与Ｒｏｓｓｂｙ波包之间进行缓慢的能量传输．从时间尺度上讲，惯性重力波可以看作Ｒｏｓｓｂｙ波包运动的背景噪声，因此上述非线性相互作用过程可以理解为大尺度Ｒｏｓｓｂｙ波包与背景噪声之间的能量交换过程．     

中层大气Rossby波与惯性重力波的非线性相互作用（Ⅱ）波包之间的相互激发

进一步讨论了大中尺度Ｒｏｓｓｂｙ波与惯性重力波的非线性相互作用问题．从共振相互作用曲线来看，Ｒｏｓｓｂｙ波和惯性重力波可以在相当广泛的角谱范围内发生共振非线性相互作用．在一定条件下，一个大振幅波包可以激发两个小振幅波包不稳定增长而出现参量不稳定现象，这三个波包可以是同种类型或不同类型的波包．当两个大振幅波包发生相互作用时，非线性过程会产生另一个波包并使它增长，并且增长速度大于仅有一个大振幅波包时的增长速度．大尺度Ｒｏｓｓｂｙ波包税发两个较小尺度惯性重力波的过程是一种重要的能量串级（ｃａｓｃａｄｅ）过程．     

中层大气Rossby波与惯性重力波的非线性相互作用（Ⅱ）波包之间的相互激发

进一步讨论了大中尺度Ｒｏｓｓｂｙ波与惯性重力波的非线性相互作用问题．从共振相互作用曲线来看，Ｒｏｓｓｂｙ波和惯性重力波可以在相当广泛的角谱范围内发生共振非线性相互作用．在一定条件下，一个大振幅波包可以激发两个小振幅波包不稳定增长而出现参量不稳定现象，这三个波包可以是同种类型或不同类型的波包．当两个大振幅波包发生相互作用时，非线性过程会产生另一个波包并使它增长，并且增长速度大于仅有一个大振幅波包时的增长速度．大尺度Ｒｏｓｓｂｙ波包税发两个较小尺度惯性重力波的过程是一种重要的能量串级（ｃａｓｃａｄｅ）过程．     

损耗大气中重力波的非线性相互作用理论

基于中高层大气重力波动力学是由非线性过程和损耗过程共同决定的物理思想,本文采用弱非线性相互作用近似,推导出损耗大气中重力波的非线性相互作用方程.这组方程是研究固定相位和随机相位重力波相互作用问题的出发点.通过引入平均振幅,我们得到了损耗情况下离散重力波的三波相互作用方程,该方程描述了重力波波包非线性时空演变的规律.作为该方程的一个具体应用,我们考虑了由于波-波相互作用产生的不稳定性.当一大尺度大振幅的主重力波通过大气传播时,非线性相互作用可能导致两个次级波振幅随时间指数增长.由于分子损耗和频率失配,主波的振幅必须大于一个阈值,这种指数增长才可能出现.共振条件满足时,阈值变为最小.频率失配还会导致次级波本征频率发生改变,改变的大小是频率失配值的一半.     

重力波波包在向上传播过程中的破碎

采用二维全隐欧拉（FICE）格式对具有高斯分布的重力波波包在可压大气中传播时的饱和过程进行数值模拟和分析．数值计算结果表明,波振幅首先随高度增加而增加,但当波振幅接近于线性不稳定性给出的阈值时,不再增加,重力波波包达到饱和进而破碎．破碎出现的高度（86．50km）比线性理论预言的结果（84．59km）要高一些,并且一般都在波包的下游出现．波破碎过程能使波能量在空间重新分配,并对重力波能量有明显的耗散作用．并且波破碎会使波相关能量传输方向偏离线性射线理论的射线路径．     

中层大气中重力波饱和机制的数值分析

通过对向上传播的重力波波包在中层大气中的非线性传播过程进行数值模拟,讨论中层大气中重力波的饱和机制.数值模拟结果表明,向上传播的重力波波包的扰动振幅在接近波包的本征水平相速度之前随高度单调增长,而当波振幅接近本征水平相速度时,在对流不稳定区域出现等位温面的翻转,同时波振幅的增长达到饱和（波振幅随高度不发生变化）.小尺度对流在等位温面的翻转和波饱和发生后产生,随后波包开始破碎,这些非线性过程的最终结果产生湍流.表明导致重力波饱和的关键因素是等位温面的翻转而不是诸如波破碎、湍流、波-流相互作用等其他的一些物理过程.     

简单热带海气耦合模型中不同扰动形式的作用

在局地热平衡情况下,将物理量先用韦伯函数展开,然后去掉相应分量的滤波方 法,讨论了简单热带海气耦合模型中不同形式扰动的作用和贡献,结果表明,在热带海气耦合 系统中,大气准定常 Ｒｏｓｓｂｙ波和海洋 Ｒｏｓｓｂｙ波对于耦合系统贡献较大,它们决定着耦合系统 与耦合扰动的性质,而大气准定常Ｋｅｌｖｉｎ波和海洋Ｋｅｌｖｉｎ波对于耦合系统贡献相对较小．     

线性缓变下垫面和耗散共同作用的Rossby孤立波包

本文从正压流体的准地转位涡方程出发,考虑到Rossby波随时间、空间演变的多尺度特性,采用多重尺度和摄动展开的方法推导了在线性缓变下垫面和耗散共同作用下的非线性Rossby波包演变满足推广的非线性Schdinger方程,并得到单个包络的孤立波解.通过分析包络的孤立波解,指出在耗散与下垫面共同作用下,大气中会出现双曲正割形状的Rossby孤立波包.同时得到,在切变基本流存在的情况下,地形强迫和耗散对Rossby包络孤立波的传播速度、波数和频率均有影响的结论.     

正压大气模式下具有β效应与地形效应的Rossby孤立波

正压大气模式下,采用摄动方法和时空伸长变换推导了具有β效应、地形效应和耗散的mKdV-Burgers方程,得到Rossby孤立波振幅的演变满足带有β效应,地形与耗散的mKdV-Burgersm方程的结论.说明β效应、地形效应是诱导Rossby孤立波的重要因素.     

重力波包在中层大气温度波导中传播的数值模拟

给出了重力波在中层大气温度波导中的反对称形式导制传播的线性理论模型，并采用二维非线性的数值模型对重力波波包在中层大气温度波导中的传播和演变过程进行了模拟研究.模拟的结果表明，下层大气激发的重力波能量进入波导区域后被俘获形成导制传播.重力波在波导内不停地来回反射，垂直方向的自由传播受到限制，能量在波导内沿着水平方向传输，模拟得到的波参数与理论值相近.重力波包在温度波导中传播时伴随着能量泄漏，且能量泄漏的速率随时间变缓，最终总有部分能量被限制在波导区域.重力波在水平方向上传播几百公里后，依然维持着良好的波结构，同时数值模拟也给出了重力波在波导区域内能量密度的时空分布.     

The instability of internal gravity waves to localised disturbances

The instability of an internal gravity wave due to nonlinear wave-wave interaction is studied theoretically and numerically. Three different aspects of this phenomenon are examined. 1. The influence of dissipation on both the resonant and the nonresonant interactions is analysed using a normal mode expansion of the basic equations. In particular, the modifications induced in the interaction domain are calculated and as a result some modes are shown to be destabilised by dissipation. 2. The evolution of an initial unstable disturbance of finite vertical extent is described as the growth of two secondary wave packets travelling at the same group velocity. A quasi-linear correction to the basic primary wave is calculated, corresponding to a localised amplitude decrease due to the disturbance growth. 3. Numerical experiments are carried out to study the effect of a basic shear on wave instability. It appears that the growing secondary waves can have a frequency larger than that of the primary wave, provided that the shear is sufficient. The instability of waves with large amplitude and long period, such as tides or planetary waves, could therefore be invoked as a possible mechanism for the generation of gravity waves with shorter period in the middle atmosphere.     

The nonlinear effects on the characteristics of gravity wave packets: dispersion and polarization relations

By analyzing the results of the numerical simulations of nonlinear propagation of three Gaussian gravity-wave packets in isothermal atmosphere individually, the nonlinear effects on the characteristics of gravity waves are studied quantitatively. The analyses show that during the nonlinear propagation of gravity wave packets the mean flows are accelerated and the vertical wavelengths show clear reduction due to nonlinearity. On the other hand, though nonlinear effects exist, the time variations of the frequencies of gravity wave packets are close to those derived from the dispersion relation and the amplitude and phase relations of wave-associated disturbance components are consistent with the predictions of the polarization relation of gravity waves. This indicates that the dispersion and polarization relations based on the linear gravity wave theory can be applied extensively in the nonlinear region.     

重力波非共振激发的数值研究

应用二阶算子分裂格式，采用全非线性模式，对可压大气中重力波波包非共振激发进行数值模拟和分析.研究表明：两个向上传播的重力波波包，通过非共振相互作用，也能激发出一个向下传播的重力波波包.生成波的能量几乎正比于主波的能量，也随次波的能量增大而增大.能量传递方向主要表现为从高频的主波向次波和生成波转移，这与共振相互作用不完全相同.非共振作用的特征时间由主次波的初始位置和波长频率决定，与主次波的初始振幅无关.生成波的波矢量并不严格满足弱非线性相互作用理论预言的波矢量匹配条件，而且生成波的波长和频率在传播的过程中会随时间发生变化，这表明了弱非线性相互作用理论的局限性.     

对流层上传重力波的非线性演化

利用二维全隐欧拉格式对重力波在可压、非等温大气中的非线性传播过程进行了数值模拟和分析.分析结果表明，从对流层顶激发的重力波能稳定地经平流层传到中层顶，从而将能量和动量从一个区域带到另一个区域；在向上传播过程中，重力波经历了发展、位温翻转、对流直至最终破碎的演变；重力波的破碎是对流和小尺度波动的重要的源，对流不稳定和翻转是非线性现象的一个基本特征.计算还显示，扰动源的大小直接影响着重力波的非线性传播过程，当扰动源足够小时，重力波能稳定传播，而大振幅扰动可以加速重力波的破碎.     

Planetary waves in coupling the lower and upper atmosphere

The purpose of the paper is to answer the question if planetary waves (PW) are capable of propagating into the thermosphere. First the simplest vertical structure equation of the classic tidal theory accounting for a realistic vertical temperature profile is considered. Analysis and simulation show that the well-known normal atmospheric modes (NM), which are trapped in the lower and middle atmosphere, exhibit a wave-like vertical structure with a large vertical wavelength in the thermosphere. Moreover, the reflection of these modes from the vertical temperature gradient in the lower thermosphere causes appearance of the wave-energy upward flux in the middle atmosphere, and in a linearized formulation this flux is constant above the source region. To investigate a possibility of the NM forcing by stratospheric vacillations and to consider the propagation of different PW up to the heights of the upper thermosphere, a set of runs with a mechanistic Middle and Upper Atmosphere Model has been performed. The results of the simulation show that quasi-stationary and longer-period PW are not able to penetrate into the thermosphere. The shorter-period NM and ultra-fast Kelvin wave propagate up to the heights of the lower thermosphere. However, above about 150 km they are strongly suppressed by dissipative processes. The role of the secondary waves (nonmigrating tides) arising from nonlinear interaction between the primary migrating tides and quasi-stationary PW is discussed. We conclude that PW are not capable of propagating directly up to the heights of the ionospheric F2 region. It is suggested that other physical processes (for instance, the electrostatic field perturbations) have to be taken into account to explain the observed PW-like structures in ionospheric parameters.     

Simultaneous observations of planetary waves from 30 to 220km

Planetary wave activity at quasi 16-, 10- and 5-day periods has been compared at various altitudes through the middle and upper atmosphere over Halley (76°S, 27°W), Antarctica, during the austral winters of 1997–1999. Observational data from the mesosphere, E-region ionosphere and F-region ionosphere have been combined with stratospheric data from the ECMWF assimilative operational analysis. Fourier and wavelet techniques have shown that the relationship between planetary wave activity at different altitudes is complex and during the winter eastward wind regime does not conform to a simple combination of vertical planetary wave propagation and critical filtering. Strong planetary wave activity in the stratosphere can coincide with a complete lack of wave activity at higher altitudes; conversely, there are also times when planetary wave activity in the mesosphere, E-region or F-region has no apparent link to activity in the stratosphere. The latitudinal activity pattern of stratospheric data tentatively suggests that when the stratospheric signatures are intense over a wide range of latitudes, propagation of planetary waves into the mesosphere is less likely than when the stratospheric activity is more latitudinally restricted. It is possible that, on at least one occasion, 16-day planetary wave activity in the mesosphere may have been ducted to high latitudes from the lower latitude stratosphere. The most consistent feature is that planetary wave activity in the mesosphere is almost always anti-correlated to planetary wave activity in the E-region even though the two are in close physical proximity. The oscillatory critical filtering of vertical gravity wave propagation by planetary waves and the re-generation of the planetary wave component at higher altitudes through subsequent critical filtering or breaking of the gravity waves may provide an explanation for some of these characteristics. Alternatively the nonlinear interaction between planetary waves and tides, indicated in the E-region data, may play a role.