A Three-dimensional Wave Activity Flux of Inertia–Gravity Waves and Its Application to a Rainstorm Event

A three-dimensional transformed Eulerian-mean(3D TEM) equation under a non-hydrostatic and non-geostrophic assumption is deduced in this study. The vertical component of the 3D wave activity flux deduced here is the primary difference from previous studies, which is suitable to mesoscale systems. Using the 3D TEM equation, the energy propagation of the inertia–gravity waves and how the generation and dissipation of the inertia–gravity waves drive the mean flow can be examined. During the mature stage of a heavy precipitation event, the maximum of the Eliassen–Palm(EP) flux divergence is primarily concentrated at the height of 10–14 km, where the energy of the inertia–gravity waves propagates forward(eastward) and upward. Examining the contribution of each term of the 3D TEM equation shows that the EP flux divergence is the primary contributor to the mean flow tendency. The EP flux divergence decelerates the zonal wind above and below the high-level jet at the height of 10 km and 15 km, and accelerates the high-level jet at the height of 12–14 km. This structure enhances the vertical wind shear of the environment and promotes the development of the rainstorm.

Analysis of the Characteristics of Inertia-Gravity Waves during an Orographic Precipitation Event

A numerical experiment was performed using the Weather Research and Forecasting（WRF） model to analyze the generation and propagation of inertia-gravity waves during an orographic rainstorm that occurred in the Sichuan area on 17 August 2014. To examine the spatial and temporal structures of the inertia-gravity waves and identify the wave types, three wavenumber-frequency spectral analysis methods（Fourier analysis, cross-spectral analysis, and wavelet cross-spectrum analysis）were applied. During the storm, inertia-gravity waves appeared at heights of 10-14 km, with periods of 80-100 min and wavelengths of 40-50 km. These waves were generated over a mountain and propagated eastward at an average speed of 15-20 m s^（-1）. Meanwhile, comparison between the reconstructed inertia-gravity waves and accumulated precipitation showed there was a mutual promotion process between them. The Richardson number and Scorer parameter were used to demonstrate that the eastward-moving inertia-gravity waves were trapped in an effective atmospheric ducting zone with favorable reflector and critical level conditions, which were the primary causes of the long lives of the waves. Finally, numerical experiments to test the sensitivity to terrain and diabatic heating were conducted, and the results suggested a cooperative effect of terrain and diabatic heating contributed to the propagation and enhancement of the waves.

NONLINEAR INERTIA—GRAVITY INTERNAL WAVE IN STRATIFIED FLUID

Based on the fundamental equations of geophysical fluid dynamics and on the consequence of verticaldensity stratification,travelling wave coordinates are used in this work to study the geometric topologicalstructures of nonlinear permanent wave in phase plane.Rigorous mathematical mechanics demonstratethat the solution of permanent solitary wave does not exist.Hamilton functions and 'action-angle' varia-bles are used to express the travelling wave system in the simplest form and the analytic solution of the nonlinear inertia-gravity internal wave is obtained.

ON RELATION OF MESO-α INERTIA WAVE DEVELOPMENT TORAINSTORM ENHANCEMENT IN TYPHOON POLLY

Numerical simulation and diagnosis show that the amplified rainstorm from Typhoon Poily is related to the development/migration of meso-α gravity waves, inhomoseneous stratification distribution andcumulus convection latent heating feedback in the storm; such waves at a large scale are excited bylarge-scale nonlinear advection; substantially amplified ageostrophic wind perturbation resulting fromthe latent heating gives rise to intensified wave amplitude, leading to enhanced rising and thus torrentialrainfall; as the waves migrate towards reduced stability, wave energy is most likely to increase.

Generation of Vertical Fine Structure by Internal Waves in a Shear Flow

The generation of vertical fine structure by inertia-gravity internal waves in a two-dimensional stratified shear flow is investigated. In the linear approximation, the boundary value problem for the amplitude of the vertical velocity of internal waves has complex coefficients, the imaginary part of which is small. The wave frequency and the eigenfunction of the boundary problem for the internal waves are complex (and we show that a weak damping of the wave occurs). The phase shift between the fluctuations of density and vertical velocity differs from π/2;therefore, the wave-induced vertical mass flux is non-zero. It is shown that dispersion curves are cut off in the low-frequency domain due to the influence of critical layers, where the frequency of the wave with the Doppler shift is equal to the inertial one. The Stokes drift velocity is determined in the weakly nonlinear approximation, on the second order in the amplitude of the wave. The vertical component of the Stokes drift velocity is also non-zero and contributes to wave transfer. The summary wave mass flux exceeds the turbulent one and leads to irreversible deformation of the average density profile which can be interpreted like a fine structure generated by the wave. On the shelf, this deformation is more than in deep-water part of the Black Sea at the same amplitude of а wave. The vertical scale of the fine structure of Brunt-V?is?l? frequency, generated by a wave, corresponds to really observed value.

Statistics of gravity waves in the lower stratosphere over Beijing based on high vertical resolution radiosonde

The seasonal variation of inertia gravity-wave activity in the lower stratosphere (17―24 km) over Beijing is studied based on the high vertical resolution radionsonde observa- tions (from December 2001 to February 2003) of Beijing Observatory (116°28′E, 39°48′N). Some of the important gravity-wave parameters, such as intrinsic frequency, and propagation direction, are estimated according to the polarized relation among gravity-wave wind components and temperature. Time series of wave energy show that the largest wave amplitudes occur during the winter and the least during the summer, and the average of the KE:PE ratios is about 2.6. Zonal and meridional wind perturbations have almost the same roots of mean variances, which shows that the wave energy in the lower stratosphere is isotropic horizontally. The motion and tem- perature fields are dominated by waves with vertical wavelengths of 1.5―3 km, which occupy above 80% samples, with a mean value of about 2.3 km. The horizontal wavelengths are mainly distributed between 100―800 km, averaging 445 km. The ratio of the mean horizontal to vertical wavelength is about 200:1, which indicates that the wave propagates nearly horizontally, with a very small vertical angle. The intrinsic frequency is estimated by fitting a polarized ellipse to the wind perturbations after band-filtering waves with a wavelength of 1.5―3 km, and the results show that the intrinsic frequency is dominated by 1f―3.5f, with an averaging value of 2f, corre- sponding to an intrinsic time period of 9 hours. Wave energy is found to propagate mainly upward, and in the horizontal direction, there is clear azimuthal anisotropy, with predominate northwest propagation against the prevailing wind.

Inertia gravity wave activity in the troposphere and lower stratosphere observed by Wuhan MST radar

The troposphere and lower stratosphere(TLS) is a region with active atmospheric fluctuations. The Wuhan Mesosphere-Stratosphere-Troposphere(MST) radar is the first MST radar to have become operational in China's Mainland. It is dedicated to real-time atmospheric observations. In this paper, two case studies about inertia gravity waves(IGWs) derived from three-dimensional wind field data collected with the Wuhan MST radar are presented. The intrinsic frequencies, vertical wavelengths, horizontal wavelengths, vertical wavenumber spectra, and energy density are calculated and analyzed. In this paper, we also report on multiple waves existing in the lower stratosphere observed by the Wuhan MST radar. Lomb-Scargle spectral analysis and the hodograph method were used to derive the vertical wavenumber and propagation direction. Meanwhile, an identical IGW is observed by Wuhan MST radar both in troposphere and lower stratosphere regions. Combining the observations, the source of the latter IGW detected in the TLS would be the jet streams located in the tropopause region, which also produced wind shear above and below the tropopause.

EFFECTS OF TOPOGRAPHY ON PROPAGATION AND DEVELOPMENT OF INERTIA GRAVITY WAVE

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

高原低涡中涡旋波动特征的初步分析

将青藏高原低涡(下称高原低涡)视为受加热强迫的边界层内涡旋,分别研究了直角坐标系正压模型和柱坐标系正压模型中高原低涡所含的波动,揭示了高原低涡中各类波动的频散关系及其基本特征,对比分析了两种模型下所得结果的异同,讨论了高原低涡中的波动与流场特征的联系。本研究认为高原低涡既含有涡旋Rossby波又含有惯性重力外波,这对于加深认识高原低涡及其对高原下游广大地区天气的影响以及影响途径具有重要意义。

圆形涡旋中的惯性重力内波不稳定和对称不稳定

用Ｂｏｕｓｓｉｎｅｓｑ近似下的轴对称径向二维柱坐标系中的线性扰动方程组，讨论了圆形大气涡旋系统中扰动的惯性重力不稳定和对称不稳定。在环境为正压情形时，惯性重力内波不稳定的条件为（μｊ／Ｒ０）２Ｎ２＋ｎ２Ｆ２＜０；当环境为斜压时，具有平行型扰动特征的惯性重力波发展的条件为Ｒｉ＜１－［（３／２）＋ｍ］－２，此时表现为对称不稳定。可见，惯性重力内波不稳定和对称不稳定都可作为台风、气旋一类圆形涡旋中扰动形成和发展的机制。

涡旋流自发辐射惯性重力波的初步解析研究

平衡流(或粗略地说涡旋流)调整目前被认为是惯性重力波产生的一种新的机制并被称为自发辐射问题。基于f平面上正压模式,该文对涡旋流自发辐射惯性重力波这一问题进行了初步解析研究。首先,通过该模式讨论了慢流形和平衡流的概念并强调了平衡流的涡旋运动特征。假定Froude数F《1且Rossby数ε=O(1)(即近似为平衡流的涡旋流包括了梯度风和其他非地转成分),于是基本方程可以写为有关惯性重力波的非齐次波动方程,其非齐次项与涡旋流的非平衡性质有关,而对于严格平衡的涡旋流,非齐次项消失,故涡旋流的非平衡性实际上提供了惯性重力波的强迫源,通过找出该方程的格林函数给出了反映自发辐射的非齐次解。在远离波源的区域,该非齐次解可以展开为远场形式,包括单极、偶极和四极辐射,另一方面,在波源区域以内及其附近,解的近场形式可以看作是慢流形的近似表达式。结果表明:与涡旋流相伴随的辐合/辐散运动主要由两部分组成,即由它自发辐射出的惯性重力波以及从属于平衡流的缓慢变化的辐合/辐散运动。与Ford的匹配渐近展开方法相比较,尽管不能给出更高阶近似,但格林函数法得到的非齐次解形式,在描写自发辐射方面更具物理直观性。

200百帕急流区大尺度重力惯性波与暴雨

本文发现在200百帕高空急流区存在着强烈的非地转现象,它可激发出大尺度的稳定的重力惯性波,并向周围传播。在高空急流右后方波能量最易发展加强。重力惯性波的形成、维持和移动也决定了暴雨的形成、维持和移动。

层结流体中的非线性惯性重力内波

根据地球流体力学基本方程组，在密度垂直层结的情况下，引进行波坐标，研究非线性定形波在相平面上的几何拓扑结构。严格论证了不存在定形孤立波，并通过Hamilton函数及其角作用变换把行波系统化成最简形式，由此而得到非线性惯性重力内波的解析解。

赤道中、东太平洋表层流速20d振荡特征分析

通过对1985年1月1日—1986年12月31日沿赤道5个锚定浮标站表层流速资料的分析,发现在140°W与108°W之间表层流速v存在一周期约为20d的显著振荡。该振荡是由波长约2000km、以1.15-1.23m／s的波速向西传播的波动引起的。该波动被推断为第二斜压模态混合Rossby惯性重力波。带通滤波和低通滤波结果表明,以110°W测站为例,20d振荡流速构方根为21.8cm／s（纬向）和22.1cm／s（经向）;单一流速振幅的特征值为30-50cm／s,最大振幅可达70cm／s;u季节变化的均方根小于17cm／s,v无明显季节变化。年平均流速通常小于5cm／s。以上各统计量表明,20d周期波动引起的v振荡在赤道东太平洋表层流速变化中非常显著。

地形对重力惯性波传播与发展的影响

本文用WKBJ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。

低纬与中纬重力惯性波在非均匀场中发展和传播的比较分析

本文用WKBJ方法得到了低纬重力惯性波的方程组,讨论了它的发展和传播,并与中纬的重力惯性波作了比较,给出了低纬与中纬环境场对各自的重力惯性波影响的差异。

200hPa层结的纬向非均匀性与暴雨

通过一次暴雨过程分析发现200hPa高空急流附近纬向层结的非均匀性对高层重力惯性波的发展有较大贡献。当重力惯性波沿层结稳定度减小方向传播时,有利于暴雨的发展。

论热带纬圈半地转运动的建立

文中在赤道β平面上 ,在滤掉低频 Rossby波的情况下 ,研究了纬圈半地转运动的建立。指出 ,只有当运动的纬圈尺度很大时 ,非地转风分量才能随着重力惯性波的频散而消失 ,从而建立起纬圈半地转平衡。应用位势涡度不变式 ,给出了纬圈半地转适应后物理场的解。同时指出 ,Kelvin波 (对赤道对称情况 )和混合波的 Rossby波波段 (对赤道反对称情况 )将不参与适应运动 ,它们属于发展运动中的角色。

对流和加热对重力惯性波的激发

用线性模型讨论了对流和加热对重力惯性波的激发，分别讨论了初始垂直速度扰动和初始位温扰动及大气内部加热在静态层结大气中激发的重力惯性波，及重力惯性波过程引起的大气温压场的变化。得到的结果可以帮助理解中小尺度系统的发生发展、对流过程与环境大气的相互作用。

混合Rossby惯性重力波致Lagrange余流

基于在一个连续层化条件下热带海洋波动的弱非线性动力学系统中建立的最低阶 Ｌａｇｒａｎｇｅ余流动力学模型及由此导出的赤道波致Ｌａｇｒａｎｇｅ余流的一般解，导出了混合Ｒｏｓｓｂｙ 惯性重力波第一斜压模态导致的最低阶Ｌａｇｒａｎｇｅ余流的表达式。从中发现，该波可产生纬 向、经向和铅垂方向的Ｌａｇｒａｎｇｅ余流，其中水平分量与赤道中、东太平洋表层流速的年平均值 （约５ｃｍ／ｓ）同量级；纬向和铅垂向余流关于赤道正对称，经向余流关于赤道反对称，在赤道上 为零，因而不会造成跨赤道的质量净输运；余流量值不但与零阶波的振幅平方成正比，与零阶 波的频率也有关系５有振幅变化的混合波所导致的Ｌａｇｒａｎｇ ｅ余流的经向结构与无振幅变化波 致余流不同。定性分析了该波致余流对赤道中、东太平洋环流与ＳＳＴ的影响，初步揭示该余流 的年际变化有利于赤道中、东太平洋 Ｅ１ Ｎｉｎｏ事件的发展。