Generalized polarization relationships for acoustic gravity waves in the nonisothermal atmosphere with the wind

The nonlinear equation of the first order of the Riccati type has been obtained for the wave impedance of acoustic gravity waves in the nonisothermal atmosphere. The vertically nonuniform horizontal wind and the effect of viscosity on the horizontal components of the velocity field have been taken into account in the calculations. The boundary-value problem for the Riccati equation is defined by the boundary emission condition at high altitudes. Upon finding the wave impedance along with the generalized polarization relationship, all remaining disturbances of the atmospheric parameters related to acoustic gravity waves are found with the help of a simple integration. The results of using a developed formalism are illustrated by the numerical computation of acoustic gravity wave fields in the atmosphere with real vertical profiles of temperature and horizontal field velocity.     

利用瑞利激光雷达观测北京地区上平流层地形重力波活动

本文利用中国科学院空间科学与应用研究中心的瑞利激光雷达首次观测到了平流层地形重力波活动的现象,并结合美国国家环境预报中心(NCEP)的全球预报系统(GFS)的风场数据分析了该地形重力波的基本参数.与惯性重力波相比较,地形重力波的密度扰动没有下传的相位,在同一高度上,其扰动相位保持不变.北京空间科学与应用研究中心瑞利激光雷达自2012年开始观测实验以来,已经观测到多起地形重力波活动事件.本文以2013年11月11日的观测数据为例,研究北京上空的地形重力波活动,并结合GFS风场数据分析了北京上平流层地形重力波的波长、传播方向、传播速度等参量.通过分析得到在2013年11月11日北京上空存在一列传播方向为北偏西52.4°,水平波长为5.5km,平均垂直波长约为6.0km的地形重力波.     

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.     

Gravity wave exclusion circles in background flows modulated by the semidiurnal tide

In this short paper the exclusion circles and vertical phase locities for gravity waves launched from the ground into a time-varying wind are studied using a ray-tracing technique. It is shown that waves with initial observed phase speeds that should place them within the local temporally varying exclusion circle, are often Doppler shifted outside of the circle. This, and the finite lifetime of some critical levels, allow waves to survive the critical layer and reach higher altitudes. Also, for slower phase-speed waves, the temporally varying wind can shift the observed frequency to negative values, so that the observed phase motions will be opposite (i.e. horizontally reversed and vertically upward), even though the energy still propagates upward. This effect can also cause the phase velocity to move inside the local exclusion circle. Due to the directional filtering of wave sources by the stratospheric wind, the percentage of such reverse-propagating waves will change systematically with local time and height in our simplified but realistic model. These results are related to ground-based systems, optical and radar, which sample the wind field and gravity waves in the middle atmosphere.     

台风“梅花”诱发平流层重力波的数值模拟与AIRS观测

为了分析台风这类强对流诱发平流层重力波的过程,本文利用中尺度数值模式WRF-ARW(V3.5)和卫星高光谱红外大气探测器AIRS数据对2011年第9号强热带气旋"梅花"的重力波特征进行了分析.首先,针对模式输出的垂直速度场资料的分析表明,台风在对流层各个方向上几乎都具有诱发重力波的能量,而在平流层内则呈现出只集中于台风中心以东的半圆弧状波动,且重力波到达平流层后其影响的水平范围可达1000km.此外,平流层波动与对流层雨带在形态、位置以及尺度上均具有一定的相似性.其次,对风场的分析结果表明,不同高度上波动形态的差异主要是由于重力波垂直上传的过程中受到了平流层向西传的背景风场以及风切变的调制作用,揭示了重力波逆着背景流垂直上传的特征.随后,基于FFT波谱分析的结果表明,"梅花"诱发的平流层重力波水平波长中心值达到了1000km,周期在15~25h,垂直波长主要在8~12km.最后,利用AIRS观测资料分析了平流层30~40km高度上的大气波动,得到了与数值模拟结果相一致的半圆弧状波动.对比结果也验证了WRF对台风诱发平流层重力波的波动形态、传播方向、不同时刻扰动强度的变化以及影响范围的模拟效果.此外,也揭示了多资料的结合对比有助于更加全面地了解台风诱发平流层重力波的波动特征.     

中层重力波运动学特性的VHF雷达观测

利用ＳＯＵＳＹＶＨＦ雷达１９８７年６月在挪威的观测数据，分析了一个典型的内重力波事件的运动学特征．结果表明，该重力波的等相面明显下传，垂直波长随高度的增加而增大，背景风随高度增加而减弱，可以推断波顺风传播，与内重力波色散方程的预言是一致的；利用重力波色散方程导出的重力波运动学参量量值与其他探测手段得到的结果一致．     

Solitary and cnoidal planetary waves

Abstract

A class of long planetary waves in a zonal channel analogous to the solitary and cnoidal waves of surface and internal gravity wave theory is discussed. On a mid-latitude β-plane, such waves exist as the result of divergence, non-uniform zonal velocity fields or bottom topography. In all cases studied the wave profile along the channel was found to satisfy the Korteweg-de Vries equation.     

Observations of short-period waves with an all-sky camera in the infrared airglow above Yakutsk

The parameters of internal gravity waves detected based on the variations in the hydroxyl molecule emission are statistically analyzed. The wave structures were registered with an all-sky infrared camera at Maimaga optical station (? = 63° N, λ = 129.5° E). The data obtained in the winter period of 1998–2002 are analyzed. In total, 162 waves, the majority of which propagated westward, were recorded. The wavelengths vary from 15.4 to 100 km (the average value is ～31 km); the observed horizontal phase velocities change from 19 to 166 m/s (the average value is ～60 m/s), and the estimated periods are 9–90 min (the average value is ～11 min). The statistical characteristics of the waves do not differ from those of similar waves at middle and low latitudes. The azimuthal dependence of the wave propagation direction is consistent with the theory of wave filtration by a background wind in the middle atmosphere. Probable sources of the waves are mountain ranges located at a distance of 200 km east of the observation site. Somewhat greater values of the mean wavelength and wave propagation velocities than those recorded at lower latitudes may be due to the lower loss of energy and velocity of the waves during their propagation from the source to the mesosphere, although other causes are not ruled out. Ripple-type waves have the same direction of propagation as band-type waves.     

Characteristics of disturbances in the atmosphere and oceans

The characteristics of the disturbances in the atmosphere and oceans and in other stably stratified and rotating fluids are analyzed according to their phase and group velocities. It is shown that both stable stratification and rotation augment the velocity of the sound waves, and that the internal gravity waves and inertial waves are mutually exclusive when the Brunt-Väisälä frequency is different from the Coriolis parameter. It is also shown that both the barotropic and the internal Rossby waves are well separated from the gravity waves and that they can be represented accurately by the quasi-geostrophic potential vorticity equation, even close to the equator, except for the one member withn=0 which is coupled with an eastward propagating gravity wave.     

基于OH全天空气辉成像仪观测的中国低纬地区的重力波传播统计特征

利用位于海南富克(19.5°N,109.1°E)和广西桂平(23.4°N,110.1°E)两个台站两年多的OH全天空气辉成像仪观测数据,对中国低纬地区的重力波传播统计特征进行了研究.从富克和桂平的气辉成像观测中, 分别提取了65和86个重力波事件.研究结果表明,观测水平波长,观测周期和水平相速度分别集中分布在10~35 km, 4~14 min和20~90 m·s^-1范围.重力波传播方向,在夏季表现出很强的东北方向传播.然而,在冬季主要沿东南和西南方向传播. 同时,结合流星雷达风场观测和TIMED/SABER卫星的温度数据,也发现在中层-低热层中传播的大多数重力波表现为耗散传播.且低层-中层大气中背景风场的滤波作用和多普勒频移可能对纬向方向传播的重力波产生的各向异性起到重要的调制作用.然而,经向方向传播的重力波产生的各向异性可能同时被低层大气中波源的非均匀分布以及潮汐变化所影响.     

Measurements of Reynolds stress in a wind-driven lagoonal estuary

Acoustic Doppler current profilers (ADCPs) have been used to measure Reynolds stresses in tidally dominated environments where wave action was minimal. In this paper, we examine observations from a microtidal estuary where the effects of wind stress and surface waves dominate the velocity variance. Reynolds stress measurements in this setting require a technique for addressing surface gravity wave contamination. We present here a method of reducing the effect of wave motion on Reynolds stresses by subtracting coincident observations along the axis of the ADCP beam. Linear wave theory is used to account for the attenuation of wave orbital velocities with depth. Using this method, Reynolds stress values are brought in line with those predicted by drag laws at the surface and bottom. The apparent Reynolds stress that is removed by the along-axis subtraction is shown to be largely due to the interaction of a slight tilt (1°) in the ADCP and the wave orbital velocity. During periods of stronger wind and waves, there is evidence of enhanced near-surface turbulence and momentum flux, presumably due to breaking waves. During these events, our calculated Reynolds stress magnitudes still appear reasonable, although the directions are suspect. We develop a diagnostic technique that clearly demarcates this region when it occurs. Coincident density profile measurements are used with the ADCP data to compute gradient Richardson numbers throughout the water column. Enhanced Reynolds stresses appear to correspond to Richardson numbers less than one. Responsible editor: Alejandro Souza     

Determination of the dispersion of low frequency waves downstream of a quasiperpendicular collisionless shock

A method of wave mode determination, which was announced in Balikhin and Gedalin, is applied to AMPTE UKS and AMPTE IRM magnetic field measurements downstream of supercritical quasiperpendicular shock. The method is based on the fact that the relation between phase difference of the waves measured by two satellites, Doppler shift equation, the direction of the wave propagation are enough to obtain the dispersion equation of the observed waves. It is shown that the low frequency turbulence mainly consists of waves observed below 1 Hz with a linear dependence between the absolute value of wave vector |k| and the plasma frame wave frequency. The phase velocity of these waves is close to the phase velocity of intermediate waves V_int = V_acos().     

Rossby wave patterns in zonal and meridional winds

The propagation properties of Rossby waves in zonal and meridional winds are analyzed using the local dispersion relation in its wave number form, the geometry of which plays a crucial role in illuminating radiation patterns and ray trajectories. In the presence of a wind/current, the classical Rossby wave number curve, an offset circle, is distorted by the Doppler shift in frequency and a new branch, consisting of a blocking line with an eastward facing indentation, arises from waves convected with or against the flow. The radiation patterns generated by a time harmonic compact source in the laboratory frame are calculated using the method of stationary phase and are illustrated through a series of figures given by the reciprocal polars to the various types of wave number curves. We believe these results are new. Some of these wave patterns are reminiscent of a “reversed” ship wave pattern in which cusps (caustics) arise from the points of inflection of the wave number curves; whilst others bear a resemblance to the parabolic like curves characteristic of the capillary wave pattern formed around an obstacle in a stream. The Rossby stationary wave in a westerly is similar to the gravity wave pattern in a wind, whereas its counterpart in a meridional wind exhibits caustics, again arising from points of inflection in the wavenumber curve.     

On the wave field generated by a variable wind

Abstract

By using an empirical expression relating the rate of increase in wave energy to the local wind speed, an equation for the phase speed at the peak of the wave spectrum is derived. The solution of the equation is determined for some simple wind fields. In particular, the wave field caused by a localised storm moving steadily over an unbounded ocean is considered. It is also shown that only a small fraction of the momentum transferred from the wind into the water propagates away from a local storm area in the form of wave momentum.     

2-D Frequency-domain Waveform Inversion of Coupled Acoustic-Elastic Media with an Irregular Interface

In order to correctly interpret marine exploration data, which contain many elastic signals such as S waves, surface waves and converted waves, we have developed both a frequency-domain modeling algorithm for acoustic-elastic coupled media with an irregular interface, and the corresponding waveform inversion algorithm. By applying the continuity condition between acoustic (fluid) and elastic (solid) media, wave propagation can be properly simulated throughout the coupled domain. The arbitrary interface is represented by tessellating square and triangular finite elements. Although the resulting complex impedance matrix generated by finite element methods for the acoustic-elastic coupled wave equation is asymmetric, we can exploit the usual back-propagation algorithm used in the frequency domain through modern sparse matrix technology. By running numerical experiments on a synthetic model, we demonstrate that our inversion algorithm can successfully recover P- and S-wave velocity and density models from marine exploration data (pressure data only).     

利用激光雷达测量重力波三维结构

激光雷达观测得到的密度、温度等数据被广泛应用于大气重力波研究.瑞利激光雷达可以获取激光路径上的大气密度、温度数据.对于大气中的三维波动而言,单条路径上的观测参量能提取得到的波动信息有限.本文首先以单色重力波为例,分析了利用激光雷达直接观测三维波动结构的可行性.激光雷达垂直观测即可得到重力波的垂直波长,当激光雷达以一定的天顶角斜向测量时,所得到的波长包含了重力波的垂直波长以及水平波长信息.因此,利用激光雷达同时以三个方向(垂直、向南(天顶角30°)以及向西(天顶角30°))测量,可以提取得到重力波的垂直波长和水平波长.本文利用中国科学院国家空间科学中心研制的车载532nm瑞利激光雷达的经向系统和纬向系统同时以不同的指向角观测大气重力波,对利用激光雷达获取三维波动结构的方法进行了分析研究.本文给出了北京地区激光雷达观测重力波的诸多案例,分析了30~60km高度范围内北京地区大气重力波的垂直及水平波长信息.并以2017年11月7日观测的准单色重力波为例,结合再分析资料的风场数据,分析了该重力波的水平波长,垂直波长及传播方向等信息.     

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.     

基于重力异常反演的三维地震波速度结构分析方法研究

利用重力异常反演测试三维地震波速度结构,存在解不唯一、可靠性不高的问题。将面波反演充分融合到重力异常反演方程中,降低传统反演方法的非唯一性,并提升可靠性。以川滇地区为例,采用融合后的重力异常反演方法分析三维地震波速度结构。通过速度和密度的关系转换,得到对应的重力异常数据。由于面波频射数据主要对地震波横波速度敏感,因此将重力异常数据和初始横波速度相连,依据地震波速度和岩石密度之间的关系,获取重力异常反演方程,用于分析速度结构。选取21.6°~34.2°N、97.1°~105.9°E范围内的川滇地区活动块体作为实验数据,经过实验分析发现：使用该方法迭代反演川滇地区地壳上地幔顶部横波速度,重力异常数据和面波频射数据的残差值分别是6.24 mGal和0.027 km/s,实际拟合效果较好;分析该地区不同深度切面横波速度发现,在24 km深度处,上地壳中含有相对低速层,在44 km深度处,中下地壳中存在低速层;且该方法分析川滇地区三维地震波速度结构解的分辨率较高。     

秦岭-大别及邻区背景噪声的瑞利波层析成像

秦岭—大别造山带西起青藏高原东北缘,东至郯庐断裂带,是华北板块和扬子板块之间的碰撞造山带.本文收集陕、豫、皖、赣、湘、鄂、渝等区域地震台网的160个宽频带地震台站连续两年地震背景噪声数据,用双台站互相关算法获得瑞利面波经验格林函数,提取相速度频散曲线,并根据面波层析成像反演得到秦岭—大别及邻区周期8~35 s范围内相速度分布图像.结果显示,大别地块在14 s相速度分布图中呈现低速异常,与8 s相速度分布图中的高速异常形成鲜明对比,反映大别HP/UHP(high pressure/ultrahigh pressure metamorphic rocks,高压/超高压变质岩)的影响仅存在于上地壳.25 s相速度图中,大致以太行一武陵重力梯度带为界,东部以高速异常为主,西部以低速异常为主,反映了地壳东薄西厚的结构特征.14~35 s相速度分布图显示郯庐断裂带南段东西两侧的显著差异,佐证了郯庐断裂带发生大规模左行平移运动时,其南段可能切入壳幔边界.同时,郯庐断裂带南段可能存在一个热物质上涌的通道,熔融的热物质通过该通道上升,混入大别地区的中下地壳,造成了红安一大别造山带的差异隆升.南秦岭与四川盆地东北部表现为低速异常,是否与青藏高原物质东流或者南秦岭的拆沉有关,还有待于进一步深入研究.     

Angle-domain imaging of relative impedance perturbation

Impedance is a physical parameter that plays an important role in seismic data processing and interpretation. A relative impedance perturbation (the ratio of the impedance perturbation and the impedance for the background models) imaging method in depth domain based on the reflection wave equation is proposed. Under the small perturbation assumption, primary wave and high-frequency approximation condition, a linear propagation equation of the primary reflection waves based on the relative impedance perturbation was first derived. On this basis, we further derived the imaging formula of the relative impedance perturbation using a linear inversion theory. Then, the source–receiver bidirectional illumination compensation was used to improve the image quality of the subsurface structures. The image result obtained by this method can be used to estimate the relative impedance perturbation. In the angle domain, the extracted near-angle-domain image gather with amplitude compensation can estimate the relative impedance perturbation, and the far-angle image gather provides the estimation of the relative velocity perturbation (the ratio of the velocity perturbation and the background velocity). Finally, several numerical tests demonstrate the effectiveness of the method.