Self-organization of IGW structures in an inhomogeneous ionosphere: 2. Nonlinear vortex structures

The generation and further nonlinear dynamics of internal gravity wave (IGW) structures in a dissipative ionosphere in the presence of an inhomogeneous zonal wind (shear flow) have been studied. The effectiveness of the IGW amplification mechanism during the interaction with an inhomogeneous zonal wind is analyzed based on the corresponding model system of nonlinear dynamic equations constructed in (Aburjania et al., 2013). It has been indicated that IGWs effectively obtain the shear flow energy at the initial linear evolution stage and substantially (by an order of magnitude) increase their amplitude and, correspondingly, energy. The nonlinear self-localization mechanism starts operating with increasing amplitude, and the process terminates with the self-organization of nonlinear solitary strongly localized vortex structures. A new degree of system freedom and the disturbance evolution trend in a medium with a shear flow appear in such a way. Nonlinear IGW structures can be a purely monopoly vortex, a transverse vortex chain, and/or a longitudinal vortex path against the background of an inhomogeneous zonal wind, depending on the shear flow velocity profile. The accumulation of such vortices in the ionospheric medium can generate a strongly turbulent state.     

Self-organization of internal gravity wave structures in an inhomogeneous ionosphere: 1. Nonlinear model dynamic equations

A corresponding model system of nonlinear dynamic equations for the lower ionosphere has been constructed in order to study the generation and further nonlinear dynamics of internal gravity wave (IGW) structures in a dissipative ionosphere in the presence of a nonuniform zonal wind (shear flow). The criterion for the development of the IGW shear instability in the ionosphere has been obtained.     

Shear flow driven magnetized planetary wave structures in the ionosphere

The generation and further linear and nonlinear dynamics of planetary ultra-low-frequency (ULF) waves are investigated in the rotating dissipative ionosphere in the presence of inhomogeneous zonal wind (shear flow). Planetary ULF magnetized Rossby type waves appear as a result of interaction of the medium with the spatially inhomogeneous geomagnetic field. An effective linear mechanism responsible for the intensification and mutual transformation of large scale magnetized Rossby type and small scale inertial waves is found. For shear flows, the operators of the linear problem are not self-conjugate, and therefore the eigenfunctions of the problem may not be orthogonal and can hardly be studied by the canonical modal approach. Hence, it becomes necessary to use the so-called nonmodal mathematical analysis. The nonmodal analysis shows that the transformation of wave disturbances in shear flows is due to the non-orthogonality of eigenfunctions of the problem in the conditions of linear dynamics. Using numerical modeling, the peculiar features of the interaction of waves with the background flow as well as the mutual transformation of wave disturbances are illustrated in the ionosphere. It has been shown that the shear flow driven wave perturbations effectively extract an energy of the shear flow increasing the own energy and amplitude. These perturbations undergo self-organization in the form of the nonlinear solitary vortex structures due to nonlinear twisting of the perturbation’s front. Depending on the features of the velocity profiles of the shear flows the nonlinear vortex structures can be either monopole vortices or vortex streets and vortex chains.     

Amplification and energy transformation of the magnetized Rossby waves in the ionosphere with an inhomogeneous zonal wind. I. A theory

The generation and further dynamics of the planetary magnetized Rossby waves and inertial waves in a dissipative ionosphere in the presence of a smooth inhomogeneous zonal wind (shear flow) have been studied. The magnetized Rossby waves are caused by the interaction with the spatially inhomogeneous geomagnetic field and represent the ionospheric manifestations of usual tropospheric Rossby waves. The effective linear mechanism of amplification and mutual transformation of the Rossby and inertial waves has been revealed. For shear flows, the operators of linear problems are not self-adjoint, and the corresponding eigenfunctions are non-orthogonal; therefore, a canonical modal approach is of little use in studying such motions. It becomes necessary to apply the so-called nonmodal mathematical analysis, which has actively been developed for the last years. The nonmodal approach makes it possible to reveal that the transformation of wave-like disturbances in shear flows is caused by the nonorthogonality of eigenfunctions in the problem of linear dynamics. Thus, there appear a new degree of the system freedom and a new way of disturbance evolution in the medium.     

Parametrization of momentum and energy depositions from gravity waves generated by tropospheric hydrodynamic sources

The mechanism of generation of internal gravity waves (IGW) by mesoscale turbulence in the troposphere is considered. The equations that describe the generation of waves by hydrodynamic sources of momentum, heat and mass are derived. Calculations of amplitudes, wave energy fluxes, turbulent viscosities, and accelerations of the mean flow caused by IGWs generated in the troposphere are made. A comparison of different mechanisms of turbulence production in the atmosphere by IGWs shows that the nonlinear destruction of a primary IGW into a spectrum of secondary waves may provide additional dissipation of nonsatu-rated stable waves. The mean wind increases both the effectiveness of generation and dissipation of IGWs propagating in the direction of the wind. Competition of both effects may lead to the dominance of IGWs propagating upstream at long distances from tropospheric wave sources, and to the formation of eastward wave accelerations in summer and westward accelerations in winter near the mesopause.     

北极地区低平流层惯性重力波的观测研究

南极地区重力波活动有大量报道,相对而言,北极地区重力波的研究还很少.本文利用极区Ny-Alesund站点（78.9°N,11.9°E）无线电探空仪从2012年4月1日到2017年3月31日共5年的观测数据,统计分析了北极地区低平流层惯性重力波的特征.观测显示,月平均纬向风在20 km以下盛行东向风,再随着高度增加,逐渐呈现出半年振荡现象.对流层顶高度在5~13 km范围内变化,其月平均高度显示出年循环,最高出现在夏季,约为10 km,最低出现在冬季,约为8.5 km.对流层和低平流层月平均温度都显示出明显的年周期变化,这与中低纬度观测结果有所不同.结合Lomb-Scargle谱分析和矢端曲线方法,估算了准单色惯性重力波参数.个例研究表明,低平流层惯性重力波呈现出远离源区的自由传播性质.统计结果显示,惯性重力波的水平和垂直波长分别集中在50~450 km和1~4 km范围内,本征频率集中在1~2.5倍惯性频率间,这些值都比中低纬度观测值稍小.垂直方向本征相速度主要集中在-0.3~0 m·s^-1,而纬向和经向本征相速度集中在-40~40 m·s^-1之间.在5年的观测中,大约91.5%的惯性重力波向上传播.在冬季和早春,由于极地平流层极涡活动,激发出向下传播的惯性重力波,因此,向下传播的比例上升到相应月份的20%左右.由于低层大气盛行的东向风的滤波效应,低平流层大部分惯性重力波向西传播.波能量呈现出明显的年周期变化,最大值在冬季、最小值在夏季,与北半球中低纬度观测结果一致,表明北半球重力波活动普遍冬季强、夏季弱.     

Amplification and energy transformation of the magnetized Rossby waves in the ionosphere with an inhomogeneous zonal wind. II. Analysis of numerical solution

The specific features of the amplification and mutual transformation of wave modes in a linear regime have been revealed based on an analysis of the numerical solution to the set of equations describing the interaction of the magnetized Rossby wave and the inertial wave with the spatially inhomogeneous zonal wind (shear flow) in the ionospheric D, E, and F regions. It has been established that the presence of the geomagnetic field and Hall and Pedersen currents in the ionosphere improves the interaction and energy exchange between the waves and shear flow.     

Linear mechanism of generation and intencification of internal gravity waves in the ionosphere at their interaction with a nonuniform zonal wind: 1. Model of the medium and initial dynamic equations

The specific features of the generation and intensification of internal gravity wave structures in different atmospheric-ionospheric regions, caused by zonal local nonuniform winds (shear flows), are studied. The model of the medium has been explained and an initial closed system of equations has been obtained in order to study the linear and nonlinear dynamics of internal gravity waves (IGWs) when they interact with the geomagnetic field in a dissipative ionosphere (for the D, E, and F regions).     

Climatological monthly characteristics of middle atmosphere gravity waves (10 min-10 h) during 1979–1993 at Saskatoon

Saskatoon (52° N, 107°W) medium frequency (MF) radar data from 1979 to 1993 have been analyzed to investigate the climatology of irregular wind components in the height region 60–100 km. This component is usually treated in terms of internal gravity waves (IGW). Three different band-pass filters have been used to separate the intensities of IGWs having periods 0.2-2.5; 1.5-6 and 2–10 h, respectively. Height, seasonal and inter-annual variations of IGW intensities, anisotropy and predominant directions of propagation are investigated. Mean over 14 years’ seasonal variation of the intensity of long-period IGWs shows a dominant annual component with winter maximum and summer minimum. Seasonal variations of the intensity of short-period waves have a strong semi-annual component as well, which forms a secondary maximum in summer. Predominant azimuths of long-period IGWs are generally zonal, though they vary with season. For short-period IGWs, the predominant azimuth is closer to the meridional direction. Anisotropy of IGW intensity is larger in summer, winter and at lower altitudes. The IGW intensity shows apparent correlation with both solar and geomagnetic activity. In most cases, this correlation appears to be negative. The variations versus solar activity is larger for longer-period IGW. Possible reasons and consequences of the observed climatological variations of IGW intensity are discussed.     

Modeling the Effect of Mesospheric Internal Gravity Waves in the Thermosphere and Ionosphere During the 2009 Sudden Stratospheric Warming

The results of numerical experiments on the modeling of thermospheric and ionospheric disturbances under conditions of sudden stratospheric warming are presented to study the possible mechanisms of such disturbances. Local disturbances caused by a planetary wave with zonal wave number s = 1 and internal gravity waves (IGWs) propagating from the disturbed region in the stratosphere are taken into account as sources of disturbances. It is shown that the inclusion of an additional source of thermospheric disturbances caused by mesospheric variations of atmospheric parameters with IGW periods over the region of sudden stratospheric warming leads to significant changes in the parameters of the thermosphere and ionosphere, including a change in the global structure of the distributions of the gas components of the thermosphere and a shift in maximum concentrations of atomic oxygen to low latitudes of the Southern Hemisphere; there is an increase in the mean values, the diurnal and semidiurnal variations of the ion concentration in the F region of the ionosphere. These features of changes in the parameters of the thermosphere and ionosphere occurred with insignificant disturbances of tidal variations in the thermosphere.     

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 Mainland China. 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.     

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．     

Analytical Solution of Direct and Inverse Problems in the Internal Gravity Waves Studies by the Doppler Frequency Shift Method

An analytical solution of direct and inverse problems arising in the study of the internal gravity waves (IGWs) dynamic via recording of the Doppler frequency shift, is presented. The direct problem is to determine the response of the Doppler shift to IGWs in the region of the radio wave reflection point; the inverse problem is the determination of IGW parameters from data on the Doppler frequency shift. Solutions were obtained in an approximation of the isothermal ionosphere for the heights of the F-region. They are presented in a form convenient for their practical use and can have a wide range of applications, including the detection of soliton-like wave structures in the F-region of the ionosphere.     

Seasonal variation of space–time parameters of internal gravity waves at Kharkiv (49°30′N, 36°51′E)

Internal gravity waves (IGWs) over Kharkiv (49°30′N, 36°51′E) have been studied by using an automatic goniometer of a meteor radar (AG MR), with its antenna directed to the East. The AG MR carries out Doppler measurements of the radial drift velocity and the position of the reflecting area of meteor trails. In order to obtain information about IGW parameters, an algorithm was used that processes the AG MR wind data by dividing the measured volume into several sub-volumes, and by carrying out wavelet analysis of wind variations in these areas. Results of 1 year (1987) of AG MR data show a good qualitative correspondence with literature results. There is an increase of IGW activity during the change of the zonal background wind in spring and autumn. It was found that the mean IGW horizontal phase velocity and predominating horizontal propagation direction change with season. However, the mean period (1.5 h), the dominant amplitude (30 m/s) and the vertical phase velocity do not strongly vary in the course of the year. The mean vertical and horizontal wavelengths were found to be 40 and 250 km, respectively.     

On the instability of internal gravity waves propagating at small but finite angles to the vertical

The question of the instability of internal gravity waves (IGWs) propagating at small angles to the vertical is re-visited. The case of an IGW of finite-amplitude propagating at a very small but finite angle to the vertical is considered. This angle serves as a small parameter in the problem, and the instability of such an IGW is investigated by using the Fourier method and the Sivashinsky integral relations. The analysis undertaken confirms the existence of short-wave instability for small IGW amplitudes and for an arbitrarily small value of their propagation angle to the vertical. For small viscosity and thermal conductivity of the fluid medium, the growth rate of the most unstable mode is proportional to the square of the amplitude of the IGW. The results obtained may be of interest for interpreting the results of observations and confirming the existence of turbulence in the middle atmosphere.     

Gravity wave intensity and momentum fluxes in the mesosphere over Shigaraki, Japan (35°N, 136°E) during 1986–1997

Averaged seasonal variations of wind perturbation intensities and vertical flux of horizontal momentum produced by internal gravity waves (IGWs) with periods 0.2/1 h and 1/6 h are studied at the altitudes 65/80 km using the MU radar measurement data from the middle and upper atmosphere during 1986/1997 at Shigaraki, Japan (35°N, 136°E). IGW intensity has maxima in winter and summer, winter values having substantial interannual variations. Mean wave momentum flux is directed to the west in winter and to the east in summer, opposite to the mean wind in the middle atmosphere. Major IGW momentum fluxes come to the mesosphere over Shigaraki from the Pacific direction in winter and continental Asia in summer.     

一次冰雹过程的惯性重力波观测及数值模拟

使用高灵敏度的电容式微压波传感器对1998年4月11日16时发生在贵州省普定县的一次降冰雹过程的重力波进行观测,利用WRF（Weather Research and Forecast）中尺度模式对这一过程进行数值模拟,使用Morlet小波方法对模拟结果进行分析,得出这一过程中惯性重力波的分布和变化规律,并分析急流、地形及切变线对惯性重力波的影响.观测发现：在降冰雹前,每隔1~4小时出现一次短周期重力波阵性增强的现象.数值模拟结果显示：在低空降冰雹前几个小时有强的短周期重力波出现,其中周期较长的出现早、存在时间长,周期较短的出现晚、存在时间短;强的低空急流和风速垂直切变触发对流或湍流的发生和加强,对流或湍流又激发了80~200 min的短周期重力波;短周期重力波更容易向垂直方向传播,而长周期重力波倾向于水平方向传播.长周期重力波在降冰雹后周期有明显变短现象,随高度越加明显.由地形形成的重力波在最高山峰上空振幅最大.     

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．