The instability of internal gravity waves to localised disturbances

The instability of an internal gravity wave due to nonlinear wave-wave interaction is studied theoretically and numerically. Three different aspects of this phenomenon are examined. 1. The influence of dissipation on both the resonant and the nonresonant interactions is analysed using a normal mode expansion of the basic equations. In particular, the modifications induced in the interaction domain are calculated and as a result some modes are shown to be destabilised by dissipation. 2. The evolution of an initial unstable disturbance of finite vertical extent is described as the growth of two secondary wave packets travelling at the same group velocity. A quasi-linear correction to the basic primary wave is calculated, corresponding to a localised amplitude decrease due to the disturbance growth. 3. Numerical experiments are carried out to study the effect of a basic shear on wave instability. It appears that the growing secondary waves can have a frequency larger than that of the primary wave, provided that the shear is sufficient. The instability of waves with large amplitude and long period, such as tides or planetary waves, could therefore be invoked as a possible mechanism for the generation of gravity waves with shorter period in the middle atmosphere.     

On the gravity wave-driven instability of E layer at mid-latitude

The plasma instability process during internal gravity wave propagation through the ionospheric E region is considered. The growth rate of the instability has been found and it has been shown that it depends on perturbation wavelength, gravity wave parameters and direction of propagation. The conditions for the instability are favorable when the vorticity of the associated neutral motion becomes antiparallel to the geomagnetic field. In the proposed instability mechanism plasma irregularities could seed the large-scale sporadic E layer structuring because they are generated in situ as a part of the same neutral wind structure that serves to initiate the formation of the layer.     

Physics and chemistry of the mesopause region

This paper is based on a tutorial presentation given at the 2001 CEDAR (Coupling Energetics and Dynamics of Atmospheric Regions) workshop. It gives an overview of chemical and physical processes important in the mesopause region. Topics covered include composition, photochemistry, dynamics and transport, and energy budget. Special emphasis is placed on the role of variations in composition in linking the physical and chemical processes. Examples from numerical models and observations are given to illustrate the points. Two specific cases where composition plays a role are described. The first illustrates that hemispheric differences in CO₂ due to transport by the mean circulation enhance the mesopause temperature extremes near solstices. The second shows how transport of chemical species by gravity waves can alter the heating structure in such a way as to destabilize the gravity wave.     

Generation of internal gravity vortices in the high-latitude ionosphere

It is shown that ionosphere heating by DC electric field leads to instability of acoustic-gravity waves and to the formation of solitary internal gravity vortex structures. These dipole type vortices with characteristic transverse size of the order of several kilometers are propagated in the lower ionosphere with subsonic velocity. The threshold values of the electric field needed to suppress the wave damping caused by the interaction of induced current with the geomagnetic field and to provide the vortex generation are found. The considered physical mechanism is applicable to the generation of internal gravity vortices and related ionospheric disturbances when the ionosphere is influenced by the electric field of seismic origin exceeding the threshold value.     

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.     

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.     

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.     

Cause of winter gravity wave spectrum saturation

Gravity waves play a significant role in establishing the large-scale circulation and structure of the middle atmosphere. Through gravity wave saturation proc-esses, such motions are believed to cause turbulence, resulting in divergence of momentum flux and the diffusion of heat and constituents in the meso-sphere[1,2]. The mechanisms that contribute signifi-cantly to the gravity wave saturation are thought to be the dynamical and convective instabilities[3]. However, it is difficult to distin…     

The loss of photochemical heating caused by gravity waves in the mesopause region

The influence of gravity waves on photochemical heating in the mesopause region is studied in this paper. The results indicate that gravity waves can cause a loss of photochemical heating in the region of the mesopause. The influences of the variation of background temperature and of atomic oxygen density on the loss of photochemical heating induced by gravity waves are discussed. The results indicate that, as background temperature decreases, or as the background atomic oxygen density increases, the gravity wave induced loss of photochemical heating increases and the ratio between it and the background photochemical heating rate also increases.     

大气重力波触发的Rayleigh－Taylor不稳定性的时空演变

对大气重力波触发的赤道电离层Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性的时空演变进行了数值模拟．结果表明，重力波能在Ｆ区底部触发Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性，这种等离子体不稳定扰动穿过Ｆ峰，到达Ｆ区顶部，形成等离子体泡结构．等离子体泡出现向西倾斜和分岔等特征．当夜Ｆ区较高时，产生等离子体泡的时间仅１９００ｓ．数值模拟结果证实了重力波触发．Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性的理论，解释了大量电离层观测现象．     

大气重力波触发的Rayleigh－Taylor不稳定性的时空演变

对大气重力波触发的赤道电离层Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性的时空演变进行了数值模拟．结果表明,重力波能在Ｆ区底部触发Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性,这种等离子体不稳定扰动穿过Ｆ峰,到达Ｆ区顶部,形成等离子体泡结构．等离子体泡出现向西倾斜和分岔等特征．当夜Ｆ区较高时,产生等离子体泡的时间仅１９００ｓ．数值模拟结果证实了重力波触发．Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性的理论,解释了大量电离层观测现象．     

大气重力波触发的Rayleigh－Taylor不稳定性的时空演变

对大气重力波触发的赤道电离层Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性的时空演变进行了数值模拟．结果表明，重力波能在Ｆ区底部触发Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性，这种等离子体不稳定扰动穿过Ｆ峰，到达Ｆ区顶部，形成等离子体泡结构．等离子体泡出现向西倾斜和分岔等特征．当夜Ｆ区较高时，产生等离子体泡的时间仅１９００ｓ．数值模拟结果证实了重力波触发．Ｒａｙｌｅｉｇｈ－Ｔａｙｌｏｒ不稳定性的理论，解释了大量电离层观测现象．     

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．     

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．     

Comparison of different turbulence models in predicting cohesive fluid mud gravity current propagation

A numerical study of propagation of cohesive fluid mud gravity currents in the form of lock-exchange was done using the OpenFOAM open source toolbox. An Eulerian approach solution for three separate phases was developed by incorporating a rheological model to predict the front position of cohesive fluid mud gravity currents. The model also simulates features in the complete movement phases including slumping, self-similar, and viscous in which the dynamics of propagation are affected by the balance of viscous and buoyancy forces, and the inertia force is negligible. The influence of using different turbulence models containing sub-grid scale (SGS), modified SGS, detached eddy simulation (DES), delayed-detached eddy simulation (DDES), Launder-R eece-Rodi (LRR), and k-ɛ models on the accuracy of simulation results was evaluated by comparing with available experimental data. The results show that the selection of the proper turbulence model is one of the most important issues for this type of the numerical modeling. The more efficient turbulence model was suggested and tabulated for each stage of propagation and different selected concentrations of 1,045, 1,140, and 1,214 g/L. Although different turbulence models (except k-ɛ) lead to front propagation dynamic simulation results that are in good agreement with the experimental measurements in the early stage of propagation for low concentrations, only DES, SGS, and modified SGS are able to capture the Kelvin-Helmholtz instability vortex shapes at the dense fluid interface, which is the main characteristic of the gravity current through the slumping phase. The calculated accuracies of SGS and modified SGS in predicting gravity current propagation for the both self-similar and viscous phases also are slightly better than DES, DDES, and LRR model results. The results of this study confirmed the performance and efficiency of the modified SGS model in which the interaction coefficients between phases are calibrated for the numerical modeling of fluid mud gravity current propagation.     

人工边界高频振荡失稳机理的一点注记

进一步完善了人工边界高频振荡失稳机理的解释. 解析证明了对于一维波动模型的离散模型, 当人工波速大于1.5倍的离散空间步距与时间步距的比值时, 则在某一高频段内, 其稳态波动解在人工边界上反射系数的模大于1的命题. 在此基础上对失稳的高频段作了进一步的讨论, 揭示了高频振荡失稳发生于对波动数值模拟无意义的高频段.      

On the application of a proposed global system for measuring meteor winds

Summary This paper discusses the need for a global network of meteor wind stations for determining the general circulation of the upper mesosphere and lower thermosphere. Continuous observations of horizontal motions from such a network would permit resolution of planetary scale eddy winds, tides, and gravity waves, and hypotheses that such motions propagate vertically from the lower atmosphere or are generated in situ by solar activity could be examined critically with observational data. The observed mean winds from the lower stratosphere to the meteor wind level are summarized to support the hypothesis that a standing wave pattern in the winds extends into the lower thermosphere. Data on tidal meridional momentum transports from meteor wind stations suggest that tides in the lower thermosphere are important for the maintenance of mean winds. Some of the geomagnetic and photochemical processes in the lower thermosphere that could be investigated with meteor wind data are briefly reviewed.This paper is adapted from our presentation at the 1966 Fall URSI meeting at Palo Alto, California     

透射边界高频失稳机理及稳定实现——P-SV波动

波动数值模拟的稳定性是获得可靠结果的前提.透射边界是一类具有高阶、高效等特点的人工边界,其引发的高频失稳是由内域格式和透射边界的不当耦合所致.本文针对P-SV波动有限元模拟中透射边界引发的失稳问题,基于GKS定理的群速度解释,通过对有限元和透射边界的频散分析揭示了数值失稳机理为透射边界和相邻内域格式支持了群速度指向内域的高频P波或SV波,波动能量将从边界进入内域引发数值失稳.同时,对比连续模型频散指出引发失稳的谐波是由有限元离散引入.本文采用修改的数值积分方法调整有限元刚度,以消除有限元中引发边界失稳的高频波动成分,从而稳定实现透射边界.理论分析和数值实验均表明本文稳定措施的有效性.

     

A numerical study of island wake generated by an elliptical tidal flow

An idealized numerical study of the influence of a tidal flow around an island has been undertaken with ROMS. The study focusses on coastal island wakes which are mainly controlled by elliptical tidal current flows on shallow shelves. This model is typical of some isolated continental shelf islands. The model is forced by a semi-diurnal barotropic inertia gravity wave imposed on the four open boundaries of a rectangular domain and its propagation results in an elliptical tidal flow within the domain in which the circular island lies. The influence of the surrounding island bathymetry and of the ellipse shape has been studied both in two and three dimensions. In the island vicinity, the residual circulation patterns over a tidal period show alongshore flow divergence along the major axis and convergence along the minor axis. A thin tidal ellipse (i.e. with a large ratio between major and minor axes) leads to strong eddy activity periods in the lee of the island during the flood and ebb phases, with eddy dissipation phases in between. By contrast, an almost round ellipse (axis ratio nearly 1) leads to vorticity filaments which continuously progress around the island without eddy shedding. The presence of a topographic slope in the vicinity of the island strengthens the eddy activity. This study suggests that the tidal current rotation favors the development of the eddy rotating in the same direction and weakens the development of the second eddy. In three dimensions with a surrounding bathymetry, an intense upwelling occurs in a large area in the lee of the island and the vertical velocities are stronger with thinner ellipses. With a flat bottom the vertical motions are almost fully generated by convergence and divergence of the secondary flow. With a varying bottom topography, the vertical motions come from a combination of this mechanism with convergence and divergence of the depth averaged flow.     

The impact of freshwater discharges on the ocean circulation in the Skagerrak/northern North Sea area. Part II: energy analysis

We perform eddy-permitting to eddy-resolving simulations of the Skagerrak/northern North Sea with a terrain-following numerical ocean model. We demonstrate that realistic representations of freshwater input are not required when the focus is on modelling mesoscale structures such as meanders and eddies. To arrive at this conclusion, we analyze the results using a recently developed energy diagnostic scheme to study the sensitivity to realistic representations of the lateral freshwater flux provided to the area from the Baltic Sea and by the major rivers. The scheme is suitable for analysis of growth of instabilities, and it has four basic instability processes prominent. We recognize both horizontal and vertical shear instabilities. There are two processes where average potential energy is converted to eddy kinetic energy, and they are related to the mean gradient in surface elevation and the mean lateral density gradient, respectively. The latter process is known as frontal instability. We demonstrate that the change in the eddy kinetic energy field is small, despite the large variations in the hydrographic properties from experiment to experiment. Moreover, generation of eddy activity appears at the same locations and with approximately the same strength regardless of actual representations of freshwater input. Furthermore, we find that vertical shear instability dominates the energy conversion processes in the Norwegian Coastal Current. Finally, we find that the areas off the northwest coast of Denmark recognized with enhanced eddy kinetic energy level is not caused by instability processes but eddy–eddy interaction rooted in variations in the sea level.