重力波包在中层大气温度波导中传播的数值模拟

给出了重力波在中层大气温度波导中的反对称形式导制传播的线性理论模型,并采用二维非线性的数值模型对重力波波包在中层大气温度波导中的传播和演变过程进行了模拟研究.模拟的结果表明,下层大气激发的重力波能量进入波导区域后被俘获形成导制传播.重力波在波导内不停地来回反射,垂直方向的自由传播受到限制,能量在波导内沿着水平方向传输,模拟得到的波参数与理论值相近.重力波包在温度波导中传播时伴随着能量泄漏,且能量泄漏的速率随时间变缓,最终总有部分能量被限制在波导区域.重力波在水平方向上传播几百公里后,依然维持着良好的波结构,同时数值模拟也给出了重力波在波导区域内能量密度的时空分布.     

空间尘埃等离子体中的重力波特性

建立尘埃等离子体中重力波的基本方程,推导尘埃等离子体中重力波的色散关系,分析地球极区中间层顶处尘埃等离子体层中的重力波特性,研究了重力波在电子密度垂直分层的尘埃等离子体中的反射. 结果表明尘埃等离子体改变了通常大气中的重力内波的色散关系,限制了小水平波数重力内波的传播,改变了波的能量特性,减小了重力波在不均匀大气中垂直向上传播时振幅的增长;在尘埃等离子体中传播时重力波可被电子密度垂直分层的结构反射而导致波能量的集中, 它产生的湍动所导致的空间电子密度的不均匀性分布是极区上空PMSEs的可能机制.     

Multi-scale waves in sound-proof global simulations with EULAG

EULAG is a computational model for simulating flows across a wide range of scales and physical scenarios. A standard option employs an anelastic approximation to capture nonhydrostatic effects and simultaneously filter sound waves from the solution. In this study, we examine a localized gravity wave packet generated by instabilities in Held-Suarez climates. Although still simplified versus the Earth’s atmosphere, a rich set of planetary wave instabilities and ensuing radiated gravity waves can arise. Wave packets are observed that have lifetimes ≤ 2 days, are negligibly impacted by Coriolis force, and do not show the rotational effects of differential jet advection typical of inertia-gravity waves. Linear modal analysis shows that wavelength, period, and phase speed fit the dispersion equation to within a mean difference of ∼ 4%, suggesting an excellent fit. However, the group velocities match poorly even though a propagation of uncertainty analysis indicates that they should be predicted as well as the phase velocities. Theoretical arguments suggest the discrepancy is due to nonlinearity — a strong southerly flow leads to a critical surface forming to the southwest of the wave packet that prevents the expected propagation.     

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.     

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.     

The influence of background winds and attenuation on the propagation of atmospheric gravity waves

The influence of background winds and energy attenuation on the propagation of atmospheric gravity waves is numerically analyzed. The gravity waves, both in the internal and ducted forms, are included through employing ray-tracing method and full-wave solution method. Background winds with different directions may cause ray paths of internal gravity waves to be horizontally prolonged, vertically steepened, reflected or critically coupled, all of which change the accumulation of energy attenuation along ray paths. Only the penetrating waves propagating against winds can easily reach the ionospheric height with less energy attenuation. The propagation status of gravity waves with different periods and phase speeds is classified into the cut-off region, the reflected region and the propagating region. All the three regions are influenced significantly by winds. The area of the reflected region reduces when gravity waves propagate in the same direction of winds and expands when propagating against wind. In propagating region, the horizontal attenuation distances of gravity waves increase and the arrival heights decrease when winds blow in the same direction of gravity waves, while the attenuation distances decrease and the arrival heights increase when gravity waves propagate against winds. The results for ducted gravity waves show that the influence of winds on waves of lower atmospheric modes is not noticeable for they propagate mainly under mesosphere, where the wind field is relatively weak. However, strong winds at thermospheric height lead to considerable changes of dispersion relation and attenuation distance of upper atmospheric modes. Winds against the wave propagating direction support long-distance propagation of G mode, while the attenuation distances decrease when winds blow in the same direction of the wave. The distribution of TIDs observed by HF Doppler array at Wuhan is compared with the simulation of internal gravity waves. The observation of TIDs shows agreement with our numerical calculations.     

重力波在中层大气温度波导中的传播模式研究

本文给出了重力波在中层大气温度波导中的导制传播模型,并在此模型的基础上详细讨论了重力波部分导制传播下的对称模式与非对称模式,导出了不同模式下相应的特征函数和色散方程,进一步用离散的方法对两类色散方程进行了求解;同时还利用二维全隐欧拉格式（FICE）对重力波在温度波导中的传播进行了模拟,模拟的结果也成功地展现了对称与非对称两种传播模式.研究表明,下边界的扰动能量在向上传播进入波导区域后被俘获,形成导制传播.不同周期的初始扰动,在波导内均会形成对称与非对称形式两种模式的导制传播,由于两者的行进速度不一致,最终会引起两种不同模式的分离.数值模拟中重力波的水平行进速度与线性模型预测值非常接近.波导中不同模式下重力波的水平波长与初始扰动的水平波长非常一致,然而波导区域内重力波的频率与初始扰动的频率无关,频率不同的初始扰动会激发出相同频率的重力波对称与非对称导制传播模式.这表明在确定的温度波导中,水平波数才是决定重力波传播特性的决定因素.进一步的分析显示,初始扰动的水平波数-频率分布越接近完全导制传播的色散关系时,温度波导中更易于生成以该种模式部分导制传播的重力波.     

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.     

Atmospheric gravity wave excitation through sum nonresonant interaction

Applying a fully nonlinear numerical scheme, sum nonresonant interaction of gravity waves is studied. The process of new wave excitation clearly exhibits that sum nonresonant interaction not only can happen in the atmosphere, but also has a considerable energy exchange magnitude, which is comparable to that of resonant interaction. The interacting waves have almost steady wavelengths and obey the dispersion relation of gravity waves, which differs from the results in the weak interaction theory. Despite the lack of the resonant condition restriction, nonresonant interactions depend on the detuning degrees of interactions.     

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1000 km.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1000 km,周期在15~25 h,垂直波长主要在8~12 km.最后,利用AIRS观测资料分析了平流层30~40 km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.     

基于人工电离层扰动对地-电离层波导传播的VLF波的影响

基于低电离层加热理论和甚低频电波在地-电离层波导中传播理论,建立低电离层扰动对甚低频电波传播影响的分析模型,并利用实验数据验证了该模型的正确性.据此模型,研究了加热功率、加热波极化以及背景参数所导致的低电离层扰动对不同频率甚低频电波传播的影响.结果表明,低电离层扰动越强,则通过该区域内甚低频波幅度和相位的相对变化越强,通过研究地-电离层波导甚低频信号通过人工扰动区域后幅度和相位的变化,可望用于诊断人工电离层扰动强度.     

TTI介质弹性波近似解耦波动方程

借助Christoffel方程可求解出各向异性介质弹性波精确频散关系.利用近似方法进行处理,再通过傅里叶逆变换将频率波数域算子变换为时空域算子,可导出解耦的qP波或qS波波动方程.本文在TTI介质弹性波精确频散关系的基础上,利用近似配方法推导了qP波和qSV波近似频散关系,通过傅里叶逆变换推导了TTI介质qP波和qSV波解耦的波动方程.为了验证近似频散关系的有效性,利用两组模型参数对其进行数值计算,分析了相对误差在不同传播方向上的分布.随后使用有限差分方法分别对均匀、层状及复杂TTI介质弹性波近似解耦波动方程进行数值模拟,结果显示qP波和qSV波完全解耦,并且在各向异性参数η < 0以及介质对称轴倾角变化较大的情况下,纯qP波和纯qSV波近似波动方程依然可以保持稳定.

     

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.     

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.     

中层耗散大气中Rossby波包的非线性相互作用理论

采用弱非线性近似得出中层耗散大气连续谱Ｒｏｓｓｂｙ波包的非线性时空演化方程，讨论了Ｒｏｓｓｂｙ波包的三波相互作用问题．数值计算表明，耗散和非线性的共同效应决定了Ｒｏｓｓｂｙ波包的演变．当一个Ｒｏｓｓｂｙ波包通过大气传播时，它的振幅若超过某个阈值，空间尺度分别比它大和比它小的两个次级Ｒｏｓｓｂｙ波包的振幅会随时间增长．特别当这两个次级波包同时随时空变化时，仅当主波的振幅超过一个更大的阈值，且其群速度介于两次级波包的群速度之间时，两次级波包的振幅才会随时空同时增长，即出现绝对不稳定现象，耗散和３个波包的频率失配都会增大不稳定的阈值．     

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．     

On the influence of the horizontal component of the earth's rotation on long period waves

Abstract

A general linearized wave equation for a stratified rotating fluid is derived and applied to obtain a dispersion relation for waves of short latitudinal extent in a thin shell of fluid. Long period wave solutions in three ocean models are compared: (1) for a stratified ocean with both components of the rotation vector; (2) for a stratified ocean without the horizontal component of rotation, and finally, (3) for a homogeneous ocean without horizontal rotation. The inclusion of the horizontal component of the Earth's rotation is found to have no noticeable effect on the dispersion relation of long period waves; its only influence is the introduction of a vertical phase shift in the motions. The origin of this phase shift is found in the tendency of the motions to satisfy the Taylor-Proudman theorem. The phase shift is of possible oceanographic relevance only for bottom-trapped buoyancy waves in a relatively weak stratification. The differences between the three ocean models are also discussed with the help of graphs of the numerically integrated dispersion relations. The relative influences of shell thinness and stratification in inhibiting the influence of the horizontal component of the earth's rotation are also briefly discussed.     

基于分数阶时间导数的黏弹性衰减VTI介质中平面波传播

目前在地震勘探频带范围内通常假设品质因子Q与频率无关,且呈衰减各向同性.事实上,相比较速度各向异性,介质的衰减各向异性同样不可忽视.本文将衰减各向异性和速度各向异性二者与常Q模型相结合,建立了黏弹性衰减VTI介质模型,并基于分数阶时间导数理论,给出了对应的本构关系和波动方程.利用均匀平面波分析和Poynting定理,推导出准压缩波qP、准剪切波qSV和纯剪切波SH的复速度、相速度、能量速度以及品质因子的解析表达式.对模型的正确性进行了数值验证,并分析了qP,qSV和SH波在介质中的传播特性.数值试验结果表明：本模型能够实现理想的恒定Q行为,表现了品质因子和速度的各向异性特征,显示出黏弹性增强将导致能量速度和相速度的频散曲线变化剧烈;速度和衰减各向异性参数与传播角度之间的耦合效应对qP,qSV和SH波的速度和能量影响明显;qP,qSV和SH波的频散曲线和波前面随着衰减各向异性强度的改变发生显著变化,其中耦合在一起的qP和qSV波变化趋势相同,而SH波与它们呈现相反的变化规律.本研究为从常Q模型角度分析地震波在衰减各向异性黏弹性介质中的传播特征奠定了理论基础.

     

Magnetoelastic shear wave propagation in pre-stressed anisotropic media under gravity

The present study investigates the propagation of shear wave (horizontally polarized) in two initially stressed heterogeneous anisotropic (magnetoelastic transversely isotropic) layers in the crust overlying a transversely isotropic gravitating semi-infinite medium. Heterogeneities in both the anisotropic layers are caused due to exponential variation (case-I) and linear variation (case-II) in the elastic constants with respect to the space variable pointing positively downwards. The dispersion relations have been established in closed form using Whittaker’s asymptotic expansion and were found to be in the well-agreement to the classical Love wave equations. The substantial effects of magnetoelastic coupling parameters, heterogeneity parameters, horizontal compressive initial stresses, Biot’s gravity parameter, and wave number on the phase velocity of shear waves have been computed and depicted by means of a graph. As a special case, dispersion equations have been deduced when the two layers and half-space are isotropic and homogeneous. The comparative study for both cases of heterogeneity of the layers has been performed and also depicted by means of graphical illustrations.