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.     

Spatiotemporal spectrum and momentum flux of the stratospheric gravity waves generated by a typhoon

The simulation results of Typhoon Matsa (2005) by using the Weather Research and Forecasting (WRF) model show that pronounced stratospheric gravity waves (GWs) are generated in the vicinity of the typhoon. Using the model output, we investigate the spatial structures and the temporal variations of the GWs through a three dimensional (3-d) spectral analysis, i.e. the spectrum with respect to two horizontal wavenumbers and frequency. We further derive the momentum flux carried by the GWs. Spectral investigation results show that the power spectral density (PSD) of the GWs exhibits a single-peaked spectrum, which consists primarily of a distinct spectrum at horizontal wavelength of ~1000km, time period of 12-18h, and vertical wavelength of 7-9km. This spectrum is different from the spectra of GWs generated by deep convections disclosed by the previous researches. Both the PSD and momentum flux spectrum are prominent in positive k h portion, which is consistent with the fact that the GWs propagate in the upstream of mean flow. Large momentum flux is found to be associated with the GWs, and the net zonal momentum flux is 0.7845×10 3 Pa at 20km height, which can account for ~26% of the momentum flux that is required in driving the QBO phenomenon.     

Simulation of the stratospheric gravity waves generated by the Typhoon Matsa in 2005

The generation of stratospheric gravity waves(GWs) due to typhoon is simulated by using a meso-scale model(WRF) with a typhoon case,the Matsa in 2005.An 8-day model run that covers the major stages of the Matsa’s development reproduces the key features of the typhoon.For example,good agreements in the typhoon’s track,the intensity,and the spiral clouds,as well as mean state of stratosphere,are seen between the simulation results and the observation.Simulation results clearly show that with typhoon propagates northwestward,pronounced stratospheric GWs are generated continuously in the vicinity of Matsa.The GWs exhibit the typical curve-like wave fronts away from the Typhoon Matsa,and propagate preferentially in the upstream of the background winds.These characteristics reflect that the stratospheric GWs are closely associated with the typhoon,and thus the GWs are referred to as Tropical Cyclone related Gravity Waves(TC-GWs).The results also show that these waves should have a rather large horizontal scale so that the outmost wave fronts can be seen at the distance of ～1000 km to the typhoon center in the horizontal plane of 20 km.This is consistent with the phenomenon of stratospheric TC-GWs with ～1000 km horizontal scale disclosed by the previous observational analysis results.     

热源激发重力波特征以及波流作用的数值模拟研究

本文在二维等温可压大气中引入了一个随时间和空间变化的热源扰动,分别以静止风和中纬1月份月平均向东的纬向风急流为背景,对不同背景下热源激发的重力波的传播详细过程及其特性进行了数值模拟研究.热源激发出来的重力波在初始阶段有很宽的频谱范围,随后由于重力波的传播效应,水平波长和垂直波长分布范围随时间都有所减小.顺风传播的重力波的小尺度和低频部分会容易被急流吸收,从而加强了对流层急流,而逆风传播的重力波更容易上传,会导致中间层区域向西的背景风增强.这体现了低层大气急流对中间层大气风场结构的影响.热源的尺度直接决定激发波的尺度;激发波的垂直尺度和时间尺度对热源的变化比其水平尺度更敏感.     

VHF radar observed characteristics of convectively generated gravity waves during wet and dry spells of Indian summer monsoon

A powerful VHF radar observed characteristics of Convectively generated Gravity Waves (CGW) excited during the wet and dry spells of Indian summer monsoon over a tropical station Gadanki (13.5°N, 79.2°E) are discussed. The characteristics of gravity waves in the lower stratosphere during these two spells are discussed in terms of their wavelet spectra along with height–time sections of vertical velocity. A total of 31 events are analyzed and in more than 50% of the events, the lower stratospheric gravity wave amplitudes were found to be relatively large in dry spell compared to that in the wet spell. The wavelet analysis of lower stratospheric vertical velocities showed a dominant periodicity of about ～20–40 min in wet spell and ～10–20 min in dry spell. The analysis also indicates that wet spell is found to be more conducive for the generation of gravity waves. However, the propagation of these waves into the stratosphere is found to be more efficient in dry spell of monsoon. The strengthening/weakening of the tropical easterly jet during wet/dry spell of monsoon is found to be the main reason for the inhibited/enhanced wave activity in the lower stratosphere during wet/dry spell. The present analysis also suggests that the static stability of the mid- and upper-troposphere during these two spells have implications in the observed frequency of the CGW. Thus, the present analyses brought out for the first time the features of CGW during two distinctive regimes of convective systems and emphasized the importance of prevailing background conditions in exciting/filtering them.     

The decay of gravity waves

Summary The decay of waves of small amplitude in a viscous liquid of finite depth is investigated. It is shown that the various modes may be conveniently classified and that in many limiting cases the modes of aperiodic decay are of particular importance. Detailed numerical results are given for these modes.     

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532 nm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30~60 km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.

     

Some characteristics of atmospheric gravity waves observed by radio-interferometry

Observations of atmospheric acoustic-gravity waves (AGWs) are considered through their effect on the horizontal gradient G of the slant total electron content (slant TEC), which can be directly obtained from two-dimensional radio-interferometric observations of cosmic radio-sources with the Nançay radioheligraph (2.2^°E, 47.3^°N). Azimuths of propagation can be deduced (modulo 180^°). The total database amounts to about 800 h of observations at various elevations, local time and seasons. The main results are:a) AGWs are partially directive, confirming our previous results.b) The propagation azimuths considered globally are widely scattered with a preference towards the south.c) They show a bimodal time distribution with preferential directions towards the SE during daytime and towards the SW during night-time (rather than a clockwise rotation as reported by previous authors).d) The periods are scattered but are larger during night-time than during daytime by about 60%.e) The effects observed with the solar radio-sources are significantly stronger than with other radio-sources (particularly at higher elevations), showing the role of the geometry in line of sight-integrated observations.     

On solitary waves generated by a moving pressure field

Summary The waves generated by a steadily moving two-dimensional pressure distribution are examined using non-linear shallow water theory. The applied pressure is zero ahead of the disturbance, that is in the downstream direction, and is a constantP ₀ in the upstream direction, these regions being joined smoothly by a cubic function.We consider here only the case of supercritical flow in both regions, the solution representing an asymmetric solitary wave travelling with the disturbance. The wave profiles are determined by an iterative method previously employed for non-linear waves. Wave amplitudes and profiles, and the wave drag, associated with each system are computed for various values ofP ₀/Q g h, whereh is the undisturbed depth of water ahead of the wave.The solution obtained reduces to the classical solitary wave of finite amplitude when the applied pressure is everywhere zero.

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Résumé Nous avons calculé les expressions des profils d'ondes solitaires produites par une pression, qui se propagent sur la surface d'une couche d'eau peu profonde avec une vitesseU plus grande que (g h)^1/2. La pression appliquée est nulle en avant de l'onde, elle est une constanteP ₀ en arrière, et entre ces deux régions elle est representée par une fonction cubique. Les profils sont calculés par une methode iterative déjà employée pour des ondes non-linéaires. L'amplitude, le profil et la force ont été evalués pour diverses valeurs deP ₀/Q g h, ouh est la profondeur en avant de l'onde.

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Division of Numerical and Applied Mathematics, National Physical Laboratory.     

Earlier days of gravity waves revisited

The means whereby the author came to be involved in the study of atmospheric gravity waves, and then came to involve others in that study, are outlined. In particular, events leading up to, during and following the International Symposium on Fluid Mechanics in the Ionosphere, of July 1959, are described.     

Nonlinear interactions between gravity waves and tides

In this study, we present the nonlinear interactions between gravity waves (GWs) and tides by using the 2D numerical model for the nonlinear propagation of GWs in the compressible atmosphere. During the propagation in the tidal background, GWs become instable in three regions, that is z = 75―85 km, z = 90―110 km and z = 115―130 km. The vertical wavelength firstly varies gradually from the initial 12 km to 27 km. Then the newly generated longer waves are gradually compressed. The longer and shorter waves occur in the regions where GWs propagate in the reverse and the same direction of the hori-zontal mean wind respectively. In addition, GWs can propagate above the main breaking region (90—110 km). During GWs propagation, not only the mean wind is accelerated, but also the amplitude of tide is amplified. Especially, after GWs become instable, this amplified effect to the tidal amplitude is much obvious.     

On the production of traveling ionospheric disturbances by atmospheric gravity waves

This paper deals with how atmospheric gravity waves produce the traveling ionospheric disturbances (TIDs) that are observed by ionosondes. It is shown that, rather than directly producing variations of ionospheric height, a likely mechanism involves changes in ionization density by gradients in the horizontal atmospheric gravity wave air motion. These density changes can be observed as variations of the height of an ionospheric isodensity surface (the usual way of measuring TIDs). This mechanism involving enhancement/depletion of ionospheric density requires quite moderate atmospheric gravity wave air motion speeds, and works well at almost all latitudes.     

Peculiarities of energy transport in the atmosphere by acoustic gravity waves

The dependence of energy transport by acoustic gravity waves (AGWs) on their spectral properties is studied. On the basis of the analysis of expressions for group velocities and energy fluxes of AGWs, it is shown that there exist separate frequencies and wavelengths at which the energy transport in space is most efficient. Comparison of the obtained results with the data of observations on board the Dynamic Explorer 2 satellite shows that, in the upper atmosphere of the Earth’s polar regions, AGWs with spectral parameters corresponding to the maximum of energy transport predominate.     

Elastic waves in visco-elastic half-space generated by various vehicle loads

In this paper, the response of a visco-elastic half-space subjected to moving loads with static and dynamic components is investigated. Four types of vehicle loads are considered, including the moving point load, uniformly distributed wheel load, elastically distributed wheel load, and a train load simulated as a sequence of elastically distributed wheel loads. In each case, the influence of the moving loads traveling in the subsonic, transonic and supersonic ranges on the dynamic responses of the half-space is studied. The parametric study conducted herein enables us to grasp insight into the mechanism of wave propagation for a visco-elastic half-space under moving loads.     

Turbulence-particle interactions under surface gravity waves

The dispersion and transport of single inertial particles through an oscillatory turbulent aquatic environment are examined numerically by a Lagrangian particle tracking model using a series of idealised test cases. The turbulent mixing is incorporated into the Lagrangian model by the means of a stochastic scheme in which the inhomogeneous turbulent quantities are governed by a one-dimensional k- ε turbulence closure scheme. This vertical mixing model is further modified to include the effects of surface gravity waves including Coriolis-Stokes forcing, wave breaking, and Langmuir circulations. To simplify the complex interactions between the deterministic and the stochastic phases of flow, we assume a time-invariant turbulent flow field and exclude the hydrodynamic biases due to the effects of ambient mean current. The numerical results show that the inertial particles acquire perturbed oscillations traced out as time-varying sinking/rising orbits in the vicinity of the sea surface under linear and cnoidal waves and acquire a non-looping single arc superimposed with the high-frequency fluctuations beneath the nonlinear solitary waves. Furthermore, we briefly summarise some recipes through the course of this paper on the implementation of the stochastic particle tracking models to realistically describe the drift and suspension of inertial particles throughout the water column.     

雷暴激发的环状重力波在中高层大气中的传播特征

本文使用中国科学院国家空间科学中心——子午工程朔州观测站的全天空气辉成像数据,以及FY-2气象卫星云顶亮温数据（Black Body Temperature,TBB）,气象再分析数据和地闪数据,研究了2013年8月10日（LT）发生在内蒙古地区的雷暴活动激发的中高层环状重力波（Concentric Gravity Waves,CGWs）事件.根据最小二乘法的拟合结果和色散关系理论曲线,确定了激发中高层环状重力波的强对流系统,该对流中心位于内蒙古自治区中部（108.9°E,40.47°N）,重力波激发于雷暴初期,此时TBB低于220 K的深对流面积较小,随着时间的推移,该次雷暴活动越来越强,深对流面积在23：00达到最大,在23：30-24：00 LT时闪电频数最高,达到120.7 fl/min,随后深对流逐渐消散.在中高层87 km处OH（羟基）气辉层观测到的一次CGWs事件的两组波纹,分别沿水平方向传播了149.64 km和174.25 km,相应位置处的水平波长分别为12.67 km和16.75 km,周期分别为8.56 min和10.72 min,激发时间分别为19：34 LT和19：40 LT;随着水平传播距离的增加,CGWs水平波长增大.

     

Nonlinear interaction between acoustic gravity waves

The resonant interaction between three acoustic gravity waves is considered. We improve on the results of previous authors and write the new coupling coefficients in a symmetric form. Particular attention is paid to the low-frequency limit.     

Transformation and absorption of magnetosonic waves generated by solar wind in the magnetosphere

Resonant transformation of fast magnetosonic (FMS) wave flux into Alfven and slow magnetosonic (SMS) oscillations is investigated in the one-dimensionally inhomogeneous magnetosphere. Spatial distribution of energy absorption rate of FMS oscillations penetrating into the magnetosphere from the solar wind is studied. The FMS wave energy absorption rate caused by magnetosonic resonance excitation is shown to be several orders of magnitude greater than that caused by Alfven resonance excitation at the same surface. It is connected with the spectrum of incident FMS waves. The Kolmogorov spectrum is used in numerical calculations. Magnitude of the Fourier harmonics exciting resonant Alfven oscillations is much smaller than that of the harmonics driving lower-frequency magnetosonic resonance. It is shown that resonant transformation of FMS waves into SMS oscillations can be an effective mechanism of energy transfer from the solar wind to the magnetosphere.