Internal gravity waves in atmospheres with realistic dissipation and temperature part I. Mathematical development and propagation of waves into the thermosphere

Abstract

In this, the first part of a three part study, we develop a model for the theoretical analysis of 3‐dimensional internal gravity waves in atmospheres with arbitrary distributions of basic temperature, molecular weight, viscosity and conductivity (both eddy and molecular), Newtonian cooling, anisotropic hydromagnetic (ion) drag, and thermal excitation. Attention is given to the physical bases for our models, and a detailed outline is given of the numerical method used to solve the resulting system of equations.

As an application of the above development, we study the ability of five particular gravity waves (chosen for their observed importance in the neighborhood of 90–100 km—four of the waves are simulated tidal modes) to propagate from 90 km into the thermosphere. We choose to define the thermosphere as that portion of the atmosphere above the turbopause (ca. 110 km). Among the most significant results to emerge are the following: (i) the effects of molecular viscosity and conductivity appear to be more significant than the effects of hydromagnetic drag, and (ii) while most waves considered are significantly attenuated somewhere between 90 Ian and the thermosphere, the main semidiurnal tidal mode is not. In fact, semidiurnal temperature oscillations of only a few degrees amplitude at 90 km can give rise to oscillations of over a hundred degrees amplitude in the exosphere.     

Alfvén wave coupling in the auroral current circuit

Auroral phenomena are controlled by the geomagnetic field.Since the terrestrial field lines connect the auroral oval to the equatorial region at large distances, the collisionless plasma in this remote space environment can act as a power supply for the high-latitude upper atmosphere where auroral emissions take place. The coupling process is intimately linked to currents which flow across the local magnetic field direction both in the equatorial part and at the atmospheric end of the auroral field lines. These two auroral key regions are connected through currents flowing along the terrestrial field lines, thereby completing the auroral current circuit. Such field-aligned currents are carried by Alfvén waves, that is, magnetohydrodynamic shear waves, which are thus a means to exchange momentum and energybetween rather remote parts of the geomagnetically controlledspace environment. Auroral dynamics is further affected by a third key region in the auroral current circuit, namely the auroral acceleration region, where parallel electric fields accelerate particle to keV energies. This review focuses on key region coupling through Alfvén waves. Continuity requirements for currents and electric fields provide a convenient means to describe the interaction of Alfvén waves with different plasma regimes. Basic coupling aspects can be demonstrated with the help of a simplified model. Inhomogeneities and nonlinear feedback can lead to resonance effects and instabilities.     

Reflection of an internal wave at an interface representing a rapid increase in viscosity

Abstract

Internal waves at high altitudes are greatly damped by the drastic increase in molecular viscosity and thermal diffusivity, resulting in important heating and other effects at those altitudes. Here we consider the case where this increase in viscosity is very rapid, idealized as an interface with inviscid flow in the lower layer and constant viscosity in the upper layer. The results show that waves are partially reflected by this interface, with a reflection coefficient that increases monotonically with an increase in the viscosity of the upper layer. This mechanism would have a significant impact on the vertical distribution of thermal energy at high altitudes.     

Body force circulations in a compressible atmosphere: Key concepts

The body force circulation problem of Eliassen is extended to spherical geometry and a quasi-compressible atmosphere using the zonally symmetric tidal theory. The concept of body force circulation is generalized to include the effects of mechanical friction and Newtonian cooling. This viewpoint is conceptually advantageous when the circulation is driven by body forces against radiative relaxation. The resulting linear theory is qualitatively useful in middle atmosphere applications, including the equatorial momentum source for which an analytic solution has not been given previously. Further generalizations of the theory are possible by including dynamical and photochemical feedback effects.     

Global Dynamics of the MLT

The transition between the middle atmosphere and the thermosphere is known as the MLT region (for mesosphere and lower thermosphere). This area has some characteristics that set it apart from other regions of the atmosphere. Most notably, it is the altitude region with the lowest overall temperature and has the unique characteristic that the temperature is much lower in summer than in winter. The summer-to-winter-temperature gradient is the result of adiabatic cooling and warming associated with a vigorous circulation driven primarily by gravity waves. Tides and planetary waves also contribute to the circulation and to the large dynamical variability in the MLT. The past decade has seen much progress in describing and understanding the dynamics of the MLT and the interactions of dynamics with chemistry and radiation. This review describes recent observations and numerical modeling as they relate to understanding the dynamical processes that control the MLT and its variability. Results from the Whole Atmosphere Community Climate Model (WACCM), which is a comprehensive high-top general circulation model with interactive chemistry, are used to illustrate the dynamical processes. Selected observations from the Sounding the Atmosphere with Broadband Emission Radiometry (SABER) instrument are shown for comparison. WACCM simulations of MLT dynamics have some differences with observations. These differences and other questions and discrepancies described in recent papers point to a number of ongoing uncertainties about the MLT dynamical system.     

Effect of sediment resuspension on underwater light field in shallow lakes in the middle and lower reaches of the Yangtze River: A case study in Longgan Lake and Taihu Lake

Based on three continuous in situ underwater light field measurement under different wind waves conditions in Longgan Lake, Meiliang Bay of Taihu Lake in July 2003 and littoral zone near TLLER in July 2004, respectively, the effects of sediment resuspension caused by wind waves on PAR diffuse attenuation, absorption coefficients and euphotic depths are analyzed. In Longgan Lake, PAR diffuse attenuation coefficients during small, middle and large wind waves were 1.74, 2.02 and 2.45 m-1, respectively, and the corresponding PAR spectral diffuse attenuations ranged from 0.98 to 2.97, 1.34 to 3.95 and 1.80 to 5.40 m-1, respectively. In Meiliang Bay, PAR diffuse attenuation coefficients were 2.63, 3.72, 4.37 m-1 during small, middle and large wind waves. PAR diffuse attenuation coefficients increased by 41% and 66% from small to middle, large wind waves, respectively. Absorption coefficients integrated over the range of PAR of CDOM, phytoplankton were 0.26, 0.28 m-1; 0.76, 0.49 m-1, respectively during middle and large wind waves. Absorption coefficients integrated over the range of PAR of non-algal particulate matter and total suspended particulate matter increased from 0.94 to 1.73 m-1, and from 1.70 to 2.22 m-1, respectively during middle and large wind waves. Relative contributions of absorption coefficients of non-algal particulate matter to total absorption coefficient integrated over the range of PAR were 44.14%, 65.05%, respectively, during middle and large wind waves. PAR euphotic depths decreased by 0.40, 0.19, 0.20 m from middle to large wind waves in Longganhu Lake, Meliang Bay and littoral zone near TLLER. Significant correlations were found between transparency, PAR diffuse attenuation coefficients, euphotic depths and total suspended paniculate matter, wind velocity, wave height. Most significant correlations were found between transparency, PAR diffuse attenuation coefficients, euphotic depths and inorganic suspended paniculate matter but low correlations for chlorophyll a, dissolved organic carbon. Increase of total suspended paniculate matter, especially inorganic suspended paniculate matter caused by wind waves was the dominant factor affecting underwater light field in shallow lakes in the middle and lower reaches of the Yangtze River based on observations at three stations.     

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...     

A numerical model of the zonal mean circulation of the middle atmosphere

The annual cycle of the zonally averaged circulation in the middle atmosphere (16–96 km) is simulated using a numerical model based on the primitive equations in log pressure coordinates. The circulation is driven radiatively by heating due to solar ultraviolet absorption by ozone and infrared cooling due to carbon dioxide and ozone (parameterized as a Newtonian cooling). Since eddy fluxes due to planetary waves are neglected in the model, the computed mean meridional circulation must be interpreted as thediabatic circulation, not as the total eulerian mean. Rayleigh friction with a short (2–4 day) time constant above 70 km is included to simulate the strong mechanical dissipation which is hypothesized to exist in the vicinity of the mesopause due to turbulence associated with gravity waves and tides near the mesopause.Computed mean winds and temperatures are in general agreement with observations for both equinox and solstice conditions. In particular, the strong mechanical damping specified near the mesopause makes it possible to simulate the cold summer and warm winter mesopause temperatures without generating excessive mean zonal winds. In addition, the model exhibits a strong semiannual cycle in the mean zonal wind at the equator, with both amplitude and vertical structure in agreement with the easterly phase of the observed equatorial semiannual oscillation.Contribution No. 497, Department of Atmospheric Sciences, University of Washington, Seattle.     

Rossby波的螺旋斑图

应用描写大气大尺度运动的准地转方程组，求得了大气Rossby波的三维定常流场以及相应的位温场、涡度场和散度场，其中的三维流场构成了物理空间的一个非线性自治动力系统. 研究表明，Rossby波具有     

On the dissipation of atmospheric alfvén waves in uniform and non-uniform magnetic fields

Abstract

We deduce the dissipative Alfvén wave equation in a medium stratified in one direction, with a transverse magnetic field, in the presence of dissipation by fluid viscosity and electrical resistance; the dissipative Alfvén wave equation generalizes earlier results for homogeneous (Cowling, 1960) and inhomogeneous (Campos, 1983a) media, and corrects an error in the literature (Heyvaerts and Priest, 1983). The wave equation is solved exactly in two cases: a uniform magnetic field, and a magnetic field decreasing with height. In both cases the mean state is assumed to be isothermal, with a constant rate of ionization, so that the magnetic diffusivity is constant, but the dynamic viscosity increases with height. There are therefore two regions, a low- (high-) altitude region where electrical resistance dominates fluid viscosity (or vice versa), and an asymptotic regime relevant to the uppermost (lowermost) layers. The two regions are separated by a transition layer, across which the wave field is continuous and whose structure is expressible by hypergeometric functions, with different arguments in the low- and high-altitude regions, and over the whole altitude range. These exact solutions allow the amplitude and phase of the wave field to be plotted as a function of height for a variety of magnetoatmospheric mean states. They show that wave dissipation is more localized and intense when the magnetic field decreases with height than when it is uniform.     

电离层人工调制激发的下行ELF/VLF波辐射

通过大功率ELF/VLF调幅高频波对电离层进行加热,形成电离层虚拟天线,可以作为发射ELF/VLF波的一种有效手段.本文使用汪枫(2009)的调制加热模型,计算高频加热电离层产生的低频辐射源强度,采用全波解算法分析辐射的低频波向下传播过程中的衰减和反射问题,并采用HAARP实验参数,模拟出在海面上接收到的低频信号强度为...     

Numerical studies of non-Newtonian mantle convection

Numerical model computations have been carried out to determine how the stress-dependence of non-Newtonian viscosity affects the flow structure of thermal convection. The viscosity laws have been chosen in accordance with present knowledge of upper mantle rheology, based on the diffusion and dislocation creep laws of olivine. The results show that there are important differences between the structures of Newtonian and non-Newtonian convection. While the Newtonian models are insufficient in some respects, the non-Newtonian solutions can explain the characteristics of the real mantle flow. However, this may require a faster plastic deformation than power law dislocation creep, at least in the high-stress regions of the mantle, e.g. at the active plate margins.     

热弹性介质中波传播特征

深层-超深层油气地震勘探涉及高温介质地震波传播问题,热弹介质参数对地震波传播有重要影响.含弛豫时间修正项的Lord-Shulman双曲型耦合热弹波动方程从理论上预测了热弹性介质中存在快纵波、慢纵波(一种准静态慢纵波,简称热波)和横波的传播,两个纵波为热耗散衰减波而横波不受介质热特性的影响.本文结合平面波频散分析和格林函数法数值模拟,详细研究两个热耗散衰减波的频散和衰减特征,着重分析热导率、热膨胀系数及比热的变化对波速和衰减的影响.研究表明热导率作为主要参数决定了波速与衰减的临界变化,热膨胀系数对波速和衰减的幅度有明显影响,比热则兼顾了前两个热弹系数的影响特征.最后,利用热弹性动力学频率域的二阶格林函数进行波场快照数值模拟,展示热弹性介质中纵波、横波和热波的传播行为.     

Seismic Rheological Model and Reflection Coefficients of the Brittle–Ductile Transition

It is well established that the upper—cooler—part of the crust is brittle, while deeper zones present ductile behaviour. In some cases, this brittle–ductile transition is a single seismic reflector with an associated reflection coefficient. We first develop a stress–strain relation including the effects of crust anisotropy, seismic attenuation and ductility in which deformation takes place by shear plastic flow. Viscoelastic anisotropy is based on the eigenstrain model and the Zener and Burgers mechanical models are used to model the effects of seismic attenuation, velocity dispersion, and steady-state creep flow, respectively. The stiffness components of the brittle and ductile media depend on stress and temperature through the shear viscosity, which is obtained by the Arrhenius equation and the octahedral stress criterion. The P- and S-wave velocities decrease as depth and temperature increase due to the geothermal gradient, an effect which is more pronounced for shear waves. We then obtain the reflection and transmission coefficients of a single brittle–ductile interface and of a ductile thin layer. The PP scattering coefficient has a Brewster angle (a sign change) in both cases, and there is substantial PS conversion at intermediate angles. The PP coefficient is sensitive to the layer thickness, unlike the SS coefficient. Thick layers have a well-defined Brewster angle and show higher reflection amplitudes. Finally, we compute synthetic seismograms in a homogeneous medium as a function of temperature.     

The specific features of geophysical fields in the fault zones

Instrumental measurements of geophysical fields in several regions of the Earth’s crust with a complex structure and tectonics are analyzed. The observed geophysical fields include the electric field in the boundary layer of the atmosphere and in the subsurface crust, the ground magnetic field, and the fields formed by microseismic vibrations and natural radon emanation. It is shown that the fault zones are characterized by noticeably higher (compared to the middle segments of crustal blocks) variations in the geophysical fields, a stronger response to the faint external impacts in the form of lunisolar tides, and baric variations in the atmosphere, as well as by higher intensity relaxation processes. Energy transformations between the geophysical fields of different origins are observed predominantly in the fault regions.     

Effects of petrophysical parameters on attenuation and dispersion of seismic waves in the simplified poroelastic theory: Comparison between the Biot's theory and viscosity‐extended theory

The simplified macro‐equations of porous elastic media are presented based on Hickey's theory upon ignoring effects of thermomechanical coupling and fluctuations of porosity and density induced by passing waves. The macro‐equations with definite physical parameters predict two types of compressional waves (P wave) and two types of shear waves (S wave). The first types of P and S waves, similar to the fast P wave and S wave in Biot's theory, propagate with fast velocity and have relatively weak dispersion and attenuation, while the second types of waves behave as diffusive modes due to their distinct dispersion and strong attenuation. The second S wave resulting from the bulk and shear viscous loss within pore fluid is slower than the second P wave but with strong attenuation at lower frequencies. Based on the simplified porous elastic equations, the effects of petrophysical parameters (permeability, porosity, coupling density and fluid viscosity) on the velocity dispersion and attenuation of P and S waves are studied in brine‐saturated sandstone compared with the results of Biot's theory. The results show that the dispersion and attenuation of P waves in simplified theory are stronger than those of Biot's theory and appear at slightly lower frequencies because of the existence of bulk and shear viscous loss within pore fluid. The properties of the first S wave are almost consistent with the S wave in Biot's theory, while the second S wave not included in Biot's theory even dies off around its source due to its extremely strong attenuation. The permeability and porosity have an obvious impact on the velocity dispersion and attenuation of both P and S waves. Higher permeabilities make the peaks of attenuation shift towards lower frequencies. Higher porosities correspond to higher dispersion and attenuation. Moreover, the inertial coupling between fluid and solid induces weak velocity dispersion and attenuation of both P and S waves at higher frequencies, whereas the fluid viscosity dominates the dispersion and attenuation in a macroscopic porous medium. Besides, the heavy oil sand is used to investigate the influence of high viscous fluid on the dispersion and attenuation of both P and S waves. The dispersion and attenuation in heavy oil sand are stronger than those in brine‐saturated sandstone due to the considerable shear viscosity of heavy oil. Seismic properties are strongly influenced by the fluid viscosity; thus, viscosity should be included in fluid properties to explain solid–fluid combination behaviour properly.     

Effect of sediment resuspension on underwater light field in shallow lakes in the middle and lower reaches of the Yangtze River: A case study in Longgan Lake and Taihu Lake

Based on three continuous in situ underwater light field measurement under different wind waves conditions in Longgan Lake, Meiliang Bay of Taihu Lake in July 2003 and littoral zone near TLLER in July 2004, respectively, the effects of sediment resuspension caused by wind waves on PAR diffuse attenuation, absorption coefficients and euphotic depths are analyzed. In Longgan Lake, PAR diffuse attenuation coefficients during small, middle and large wind waves were 1.74, 2.02 and 2.45 m^?1, respectively, and the corresponding PAR spectral diffuse attenuations ranged from 0.98 to 2.97, 1.34 to 3.95 and 1.80 to 5.40 m^?1, respectively. In Meiliang Bay, PAR diffuse attenuation coefficients were 2.63, 3.72, 4.37 m^?1 during small, middle and large wind waves. PAR diffuse attenuation coefficients increased by 41% and 66% from small to middle, large wind waves, respectively. Absorption coefficients integrated over the range of PAR of CDOM, phytoplankton were 0.26, 0.28 m^?1; 0.76, 0.49 m^?1, respectively during middle and large wind waves. Absorption coefficients integrated over the range of PAR of non-algal particulate matter and total suspended particulate matter increased from 0.94 to 1.73 m^?1, and from 1.70 to 2.22 m^?1, respectively during middle and large wind waves. Relative contributions of absorption coefficients of non-algal particulate matter to total absorption coefficient integrated over the range of PAR were 44.14%, 65.05%, respectively, during middle and large wind waves. PAR euphotic depths decreased by 0.40, 0.19, 0.20 m from middle to large wind waves in Longganhu Lake, Meliang Bay and littoral zone near TLLER. Significant correlations were found between transparency, PAR diffuse attenuation coefficients, euphotic depths and total suspended particulate matter, wind velocity, wave height. Most significant correlations were found between transparency, PAR diffuse attenuation coefficients, euphotic depths and inorganic suspended particulate matter but low correlations for chlorophyll a, dissolved organic carbon. Increase of total suspended particulate matter, especially inorganic suspended particulate matter caused by wind waves was the dominant factor affecting underwater light field in shallow lakes in the middle and lower reaches of the Yangtze River based on observations at three stations.     

Ionospheric and thermospheric couplings: vertical,latitudinal and longitudinal

The ionosphere, embedded in and tightly coupled to the thermosphere, is strongly influenced by couplings to other geophysical regions. For example, above it, both the magnetosphere and plasmasphere greatly affect the ionosphere by the precipitation of soft and energetic particles, by heat conduction, and by fluxes of thermal particles. Below, the middle atmosphere affects it with upwardly propagating waves (gravity waves, tides, and planetary waves). All the while, polar and auroral regions greatly affect the mid-latitudes by the equatorward penetration of electric fields and winds, and by the equatorward propagation of waves (traveling ionospheric disturbances or TIDs).Exploring these couplings effectively furthers our understanding of at least the dominant processes and interactions that play such an important role in determining the character of this part of the Earths environment. Significant progress during the Solar-Terrestrial Energy Program (STEP) has demanded that the observational, analytical, and theoretical thrusts of the international scientific community be global in all senses. Observationally, this has led to coordinated measurements from many regions, from the poles to the equator, and from ground- and space-based instruments. It has also led to many different instruments, including new ones, measuring an extensive variety of (related) geophysical parameters. Depending on the instrument, measurements have been made continuously or at appropriate intervals to sample different geomagnetic conditions, and diurnal, seasonal, inter-annual, and solar-cycle variations. Extensive analyses have been carried out on these observations. New empirical models have been developed and old ones improved. Theoretical work has led to new and improved first-principles models that are being used to test our understanding of the observations. Our intent is to review this progress and suggest some future directions. Our approach is to illustrate the broad front of progress with representative examples, rather than to do an exhaustive review. We apologize from the start, to those whose good work we have not noted, in order to allow a broad balanced overview of areas advanced.     

Onset of an energy cascade and nonperiodic behaviour in the nonlinear propagation of MHD waves in the solar atmosphere

Abstract

We study the nonlinear stability of MHD waves propagating in a two-dimensional, compressible, highly magnetized, viscous plasma. These waves are driven by a weak, shear body force which could be imposed by large scale internal fluctuations present in the solar atmosphere.

The effects of anisotropic viscosity (leading to a cubic damping) and of the nonlinear coupling of the Alfven and the magnetoacoustic waves are analysed using Galerkin and multiple-scale analysis: the MHD equations are reduced to a set of nonlinear ordinary differential equations which is then suitably truncated to give a model dynamical system, representing the interaction of two complex Galerkin modes.

For propagation oblique to the background magnetic field, analytical integration shows that the low-wavenumber mode is physically unstable. For propagation parallel to the background magnetic field the high-wavenumber wave can undergo saddlenode bifurcations, in way that is similar to the van der Pol oscillator; these bifurcations lead to the appearance of a hysteresis cycle.

A numerical integration of the dynamical system shows that a sequence of Hopf bifurcations takes place as the Reynolds number is increased, up to the onset of nonperiodic behaviour. It also shows that energy can be transferred from the low- wavenumber to the high-wavenumber mode.     

华北盆地滑脱构造的地震学证据

在华北盆地中西部的临城一巨鹿深地震反射剖面上，ＣＤＰ叠加剖面在双程走时２．５-４．５ｓ部分显示出一系列连续性好、能量强的低角度反射事件，在剖面上显示的延伸距离达４０ｋｍ．这些反射事件解释为滑脱断层，它自西向东倾角变缓，发育在深度为ｓｋｉｎ（剖面西端）至１０ｋｍ（东端）的结晶基岩中．在剖面的浅部显示出两个相似的单边断陷盆地，其主断裂以铲形归并到这一滑脱构造．上盘在伸展过程中向东滑移，拉张和重力滑动作用可能是形成这些断裂的主要原因．剖面东部的中下地壳内众多的反射事件具有叠层状的特征，并遭受强烈的变形，可能表示地幔物质上涌侵入至地壳内．岩浆侵入在地壳上部形成附加的伸展应力场，同时使下地壳增热，粘度下降，某些矿物发生脱水作用，脱出的水上移并储存于中地壳内．伸展应力场及热和水的作用促进滑脱构造的形成．邢台地震的震源深度分布表明，这一地区脆韧过渡带的深度为１０-２５ｋｍ，滑脱面为过渡带的上界面．