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.     

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.     

Observations indicating parametric instabilities in internal gravity waves at thermospheric heights

Abstract

Theoretical studies predict a parametric instability of finite-amplitude internal gravity waves which hitherto has been observed only in laboratory experiments. The occurrence of this process in the atmosphere is of basic interest because finite-amplitude gravity waves, which are almost ubiquitous especially at upper atmospheric heights, would produce unstable flows even at large Richardson numbers. Maximum entropy power spectra of a strong internal gravity wave in the thermosphere, which was generated by a volcanic eruption and detected on records of the Doppler shift of high-frequency radio waves, in fact show good agreement with the spectra of synthetic Doppler records obtained from a calculated unstable gravity wave. The frequencies and wavenumbers observed in the gravity wave domain satisfy in particular the theoretically predicted resonance conditions. The observed Doppler records also show two significant lines in the acoustic domain which probably result from a nonlinear interaction with the basic gravity wave. It is suggested that acoustic double peaks, which are commonly observed in high-frequency Doppler spectra in the presence of nearby thunderstorms, represent parametric instabilities of internal gravity waves generated by penetrative cumulus convection.     

Gravity wave reflection: Case study based on rocket data

Since gravity waves significantly influence the atmosphere by transporting energy and momentum, it is important to study their wave spectrum and their energy dissipation rates. Besides that, knowledge about gravity wave sources and the propagation of the generated waves is essential. Originating in the lower atmosphere, gravity waves can move upwards; when the background wind field is equal to their phase speed a so-called critical layer is reached. Their breakdown and deposition of energy and momentum is possible. Another mechanism which can take place at critical layers is gravity wave reflection.In this paper, gravity waves which were observed by foil chaff measurements during the DYANA (DYnamics Adapted Network for the Atmosphere) campaign in 1990 in Biscarrosse (44°N, 1°W)—as reported by Wüst and Bittner [2006. Non-linear wave–wave interaction: case studies based on rocket data and first application to satellite data. Journal of Atmospheric and Solar-Terrestrial Physics 68, 959–976]—are investigated to look for gravity wave reflection processes. Following nonlinear theory, energy dissipation rates according to Weinstock [1980. Energy dissipation rates of turbulence in the stable free atmosphere. Journal of the Atmospheric Sciences 38, 880–883] are calculated from foil chaff cloud and falling sphere data and compared with the critical layer heights. Enhanced energy dissipation rates are found at those altitudes where the waves’ phase speed matches the zonal background wind speeds. Indication of gravity wave trapping is found between two altitudes of around 95 and 86 km.     

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.     

A Note on Standing Internal Inertial Gravity Waves of Finite Amplitude

The effects of finite amplitude are examined in two-dimensional, standing, internal gravity waves in a rectangular container which rotates about a vertical axis at frequency f/ 2. Expressions are given for the velocity components, density fluctuations and isopycnal displacements to second order in the wave steepness in fluids with buoyancy frequency, N , of general form, and the effect of finite amplitude on wave frequency is given in an expansion to third order. The first order solutions, and the solutions to second order in the absence of rotation, are shown to conserve energy during a wave cycle. Analytical solutions are found to second order for the first two modes in a deep fluid with N proportional to sech( az ), where z is the upward vertical coordinate and a is scaling factor. In the absence of rotation, results for the first mode in the latter stratification are found to be consistent with those for interfacial waves. An analytical solution to fourth order in a fluid with constant N is given and used to examine the effects of rotation on the development of static instability or of conditions in which shear instability may occur. As in progressive internal waves, an effect of rotation is to enhance the possibility of shear instability for waves with frequencies close to f . The analysis points to a significant difference between the dynamics of standing waves in containers of limited size and progressive internal waves in an unlimited fluid; the effect of boundaries on standing waves may inhibit the onset of instability. A possible application of the analysis is to transverse oscillations in long, narrow, steep-sided lakes such as Loch Ness, Scotland.     

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.     

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.     

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.     

Propagation of shear waves in viscoelastic medium at irregular boundaries

The aim of the paper is to study the shear wave propagation in a viscoelastic layer over a semi-infinite viscoelastic half space due to irregularity in the viscoelastic layer. It is of great interest to study the propaga-tion of shear waves in the assumed medium having a non planar boundary due to its similarity to most of the real situations. The perturbation method is applied to find the displacement field. The effect of complex wave number on dissipation factor is analysed. Finally, as an application, the result obtained has been used to get the reflected field in viscoelastic layer when the shear wave is incident on an irregular boundary in the shape of parabolic irregularity as well as triangular notch. It is observed that the amplitude of this reflected wave decreases with increasing length of the notch, and increases with increasing depth of the irregularity.     

A theory of enhanced saturation of the gravity wave spectrum due to increases in atmospheric stability

In this paper we consider a vertical wavenumber spectrum of vertically propagating gravity waves impinging on a rapid increase in atmospheric stability. If the high-wavenumber range is saturated below the increase, as is usually observed, then the compression of vertical scales as the waves enter a region of higher stability results in that range becoming supersaturated, that is, the spectral amplitude becomes larger than the saturation limit. The supersaturated wave energy must then dissipate in a vertical distance of the order of a wavelength, resulting in an enhanced turbulent energy dissipation rate. If the wave spectrum is azimuthally anisotropic, the dissipation also results in an enhanced vertical divergence of the vertical flux of horizontal momentum and enhanced wave drag in the same region. Estimates of the enhanced dissipation rates and radar reflectivities appear to be consistent with the enhancements observed near the high-latitude summer mesopause. Estimates of the enhanced mean flow acceleration appear to be consistent with the wave drag that is needed near the tropopause and the high-latitude summer mesopause in large-scale models of the atmosphere. Thus, this process may play a significant role in determining the global effects of gravity waves on the large-scale circulation.     

大气重力波产生大尺度赤道扩展F的理论

本文提出了大气重力波触发Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性并导致大尺度赤道扩展Ｆ的理论．重力波作为外部扰动派触发等离子体扰动，这种扰动在Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性的作用下继续增长，经过４００ｓ扰动幅度就能增长到５０％，经过７００ｓ后幅度趋近１００％，即为完全的等离子体泡．由于Ｅ区的影响，赤道扩展Ｆ主要出现于晚上．本文的理论阐明了重力波与Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性相互作用的性质，揭示了大尺度赤道扩展Ｆ的产生机制．     

Acoustic gravity wave growth and damping in convecting plasma

The propagation of acoustic gravity waves through steadily convecting plasma in the thermosphere has been analysed theoretically. The growth and damping rates of internal gravity waves due to the feedback effects of wave-modulated Joule heating and Laplace forcing have been calculated. It is found that large convection flow velocities lead to the growth of large-scale internal gravity waves, whilst small- and medium-scale waves are heavily damped, under similar conditions. It has also been shown that wave growth is favoured for waves travelling against the plasma flow direction. The effects of critical coupling when wave phase speeds match the plasma flow speed have also been investigated. The results of these calculations are discussed in the context of the atmospheric energy budget and thermosphere-ionosphere coupling.     

A note on specific variability of long surface gravity waves and drag coefficient in coastal upwelling zone

In this paper we solve analytically wave kinematic equations and the wave energy transport equation, for basic long surface gravity wave in the coastal upwelling zone. UsingGent andTaylor's (1978) parameterization of drag coefficient (which includes interaction between long surface waves and the air flow) we find variability of this coefficient due to wave amplification and refraction caused by specific surface water current in the region. The drag coefficient grows towards the shore. The growth is faster for stronger current. When the angle between waves and the current is less than 90° the growth is mainly connected with the waves steepness, but when the angle is larger, it is caused by relative growth of the wave phase velocity.     

耗散大气中水平不均匀风场对内重力波传播的影响

采用包括耗散的射线跟踪方法，计算了在水平不均匀风场作用下，不同尺度重力波从对流层直至220km观测高度的传播，结果表明，垂直于重力波传播方向的风以及风剪切能够引起波射线的折射，从而导致重力波明显偏离初始传播方向.在强顺风场作用下，由于风场引起的捕获，大量重力波不能传播到观测高度.由于风场引起的多普勒频移，小周期的重力波在弱顺风条件下能够传播到观测高度.由于反射作用，强逆风场不支持周期低于约18min的较高频重力波的传播.而在弱逆风作用下，大部分中尺度范围重力波都能够传播到观测高度.本文统计了武汉电离层观象台的TID观测数据随热层风场的分布，统计结果与模拟结果符合较好.     

阿尔芬波动特征对卫星磁力仪零位标定的影响

磁通门磁力仪的零位偏移量在卫星轨道上会因诸多因素而发生改变.为此,基于剪切阿尔芬波动不改变总磁场强度这一特征的Davis-Smith方法被提出用于计算磁力仪的零位补偿.实际上,行星际空间中没有纯粹的阿尔芬波动.本文采用数值模拟分析了存在小的压缩波动情况下,阿尔芬波动的幅度、周期和相位以及数据窗口时间长度等对Davis-Smith方法计算零位补偿的影响.我们发现,只有当阿尔芬波动的周期与压缩波动周期相同时,阿尔芬波动的性质会对零位补偿的计算产生不可忽视的误差.阿尔芬波动的幅度越大,零位补偿的误差越小.磁场各分量零位补偿的误差大小还会受到阿尔芬波动初始相位的影响.此外,数据窗口时间长度越长,则零位补偿误差趋于减小至真实值.     

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.     

Mesospheric bore formation from large-scale gravity wave perturbations observed by collocated all-sky OH imager and sodium lidar

On 9 October 2007, long-horizontal-wavelength gravity waves were observed for the first time to steepen and form mesospheric bores at the altitude of ～87 km, by an all-sky OH imager located at Fort Collins (41°N, 105°W), Colorado. The collocated sodium lidar simultaneously observed the presence of a temperature inversion layer as the ducting region. One mesospheric bore uniquely later evolved into a large-amplitude soliton-like perturbation. When the gravity wave and the associated soliton-like perturbation passed through the lidar beams, the lidar detected strong vertical disturbance at 90 km, indicating convective instability. A large cold front system recorded several hours before in the troposphere was aligned to phase fronts of these large gravity waves. For all of the 7 mesospheric bores observed over a 5 year period, we found a similar alignment with a cold front 1000–1500 km away as the likely source of these large-scale gravity waves.     

大功率高频电波加热电离层中参量衰减不稳定性研究(1):数值模拟

参量衰减不稳定性(Parametric Decay Instability,PDI)在大功率高频(High frequency,HF)电波与电离层等离子体相互作用的过程中扮演着十分重要的角色,本文采用广义Zakharov方法对常规的等离子体流体力学方程组进行相应处理后,并在近似实际的电离层背景和电波传播模型下,构建了高频电波加热电离层激发PDI的数值计算模型.模拟结果发现:在毫秒量级的时间尺度上,大功率高频电波在寻常波(Ordinary wave,O波)反射点高度附近激发出了朗缪尔波(Langmuir wave)和离子声波(Ion-Acoustic wave)两种等离子体静电波模,模拟中产生的朗缪尔波和离子声波相应波数为5~11rad·m~(-1),结果与利用色散关系求出的理论值4~7 rad·m~(-1)近似一致,密度扰动幅值从10~6m~(-3)量级指数级增长到了10~(10)m~(-3)量级,直至能显著影响与"低频"密度背景相关的等离子体频率后,出现了等离子体"空穴"结构以及朗缪尔波被"俘获"现象,在扰动空间内的小尺度静电场幅值最高能达到100 V·m~(-1)量级,最终造成一种强烈的局地化"空穴"湍流现象.本文的研究有助于深入理解PDI的物理机制,对研究大功率高频电波与电离层等离子体之间复杂的非线性相互作用也有着非常重要的意义.