Resistive wave breaking in the Earth's outer core

The equations for an electrically conducting fluid in cylindrical coordinates are linearized assuming that the inertial terms in the momentum equation can be ignored (small Rossby number), and that the ratio of the Elsasser number and magnetic Reynolds number is one. After these assumptions, the governing equations are linearized about an ambient solution which vanishes at the the equator. Upon assuming large Elsasser and magnetic Reynolds number, the solutions to the linearized equations are approximated by wave trains having very short wave length (relative to the core radius) but which vary slowly (on a scale of the core radius). The period of the waves is much longer than a day but much shorter than the period of the slow hydromagnetic oscillations. These waves are found to be trapped in a region about the equator and away from the axis of rotation. The waves break at a latitudinal wave region boundary, in the sense that the waves become exponentially large in a boundary layer, having as an exponent some positive power of the large azimuthal wave number. This behavior is amplified as the Elsasser number becomes smaller while still remaining relatively large. Waves in more Earth-like parameter regimes are discussed briefly.     

A reduced model for nonlinear dispersive waves in a rotating environment

Abstract

The simplest model for geophysical flows is one layer of a constant density fluid with a free surface, where the fluid motions occur on a scale in which the Coriolis force is significant. In the linear shallow water limit, there are non-dispersive Kelvin waves, localized near a boundary or near the equator, and a large family of dispersive waves. We study weakly nonlinear and finite depth corrections to these waves, and derive a reduced system of equations governing the flow. For this system we find approximate solitary Kelvin waves, both for waves traveling along a boundary and along the equator. These waves induce jets perpendicular to their direction of propagation, which may have a role in mixing. We also derive an equivalent reduced system for the evolution of perturbations to a mean geostrophic flow.     

Structure of the low-latitude magnetopause: MAGION-4 observations

The aims of this paper are (1) briefly to describe the plasma devices onboard the MAGION-4 satellite, launched on 3 August 1995, of the INTER-BALL project, and (2) to discuss first observations made near the magnetopause region. During the presented boundary crossings the MAGION–4 observed quasi-periodic pulses of magnetosheath-like plasma in a region of low plasma density. This region is located just earthwards of the magnetopause and is populated by a plasma which, except for the density, has the same parameters as in the magnetosheath. Deeper in the magnetosphere, the encounter of a layer of hot electrons and high-energy ions was interpreted as low-latitude boundary layer.     

Ion Pressure in Different Regions of the Dayside Auroral Precipitation

Geomagnetism and Aeronomy - The ion pressure in the regions of ionospheric projections of the plasma mantle, polar cusp, low-latitude boundary layer, and the region of structured precipitation of...     

Travelling convection vortices in the ionosphere map to the central plasma sheet

We investigate the magnetospheric domain responsible for the generation of ionospheric travelling convection vortices (TCV) by comparing the location of the TCV to the locations of the low-altitude particle-precipitation boundaries deduced from the DMSP satellite measurements. For three very well documented TCV events we are able to identify suitable satellite passes, in the sense that for each event we can identify two to three passes occurring close to the TCV observation in both time and space. In all three cases the comparisons place the TCV centres at or equatorward of the central plasma sheet/boundary plasma sheet precipitation boundary. Thus our results indicate that the field-aligned currents related to the TCV originate in the plasma sheet rather than at the magnetopause or in the low-latitude boundary layer, as previous studies suggest.Permanent address: Polar Geophysical Institute, Apatity, Murmansk region, 184200, Russia     

Boundary layer dissipation and the nonlinear interaction of equatorial baroclinic and barotropic rossby waves

Two-layer equatorial primitive equations for the free troposphere in the presence of a thin atmospheric boundary layer and thermal dissipation are developed here. An asymptotic theory for the resonant nonlinear interaction of long equatorial baroclinic and barotropic Rossby waves is derived in the presence of such dissipation. In this model, a self-consistent asymptotic derivation establishes that boundary layer flows are generated by meridional pressure gradients in the lower troposphere and give rise to degenerate equatorial Ekman friction. That is to say, the asymptotic model has the property that the dissipation matrix has one eigenvalue which is nearly zero: therefore the dynamics rapidly dissipates flows with pressure at the base of the troposphere and creates barotropic/baroclinic spin up/spin down. The simplified asymptotic equations for the amplitudes of the dissipative equatorial barotropic and baroclinic waves are studied by linear theory and integrated numerically. The results indicate that although the dissipation slightly weakens the tropics to midlatitude connection, strong localized wave packets are nonetheless able to exchange energy between barotropic and baroclinic waves on intraseasonal timescales in the presence of baroclinic mean shear. Interesting dissipation balanced wave-mean flow states are discovered through numerical simulations. In general, the boundary layer dissipation is very efficient for flows in which the barotropic and baroclinic components are of the same sign at the base of the free troposphere whereas the boundary layer dissipation is less efficient for flows whose barotropic and baroclinic components are of opposite sign at the base of the free troposphere.     

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.     

High-beta plasma blobs in the morningside plasma sheet

Equator-S frequently encountered, i.e. on 30%0of the orbits between 1 March and 17 April 1998, strong variations of the magnetic field strength of typically 5–15-min duration outside about 9R_E during the late-night/early-morning hours. Very high-plasma beta values were found, varying between 1 and 10 or more. Close conjunctions between Equator-S and Geotail revealed the spatial structure of these “plasma blobs” and their lifetime. They are typically 5–10° wide in longitude and have an antisymmetric plasma or magnetic pressure distribution with respect to the equator, while being altogether low-latitude phenomena (<15°). They drift slowly sunward, exchange plasma across the equator and have a lifetime of at least 15–30 min. While their spatial structure may be due to some sort of mirror instability, little is known about the origin of the high-beta plasma. It is speculated that the morningside boundary layer somewhat further tailward may be the source of this plasma. This would be consistent with the preference of the plasma blobs to occur during quiet conditions, although they are also found during substorm periods. The relation to auroral phenomena in the morningside oval is uncertain. The energy deposition may be mostly too weak to generate a visible signature. However, patchy aurora remains a candidate for more disturbed periods.     

Nongyrotropic particle distributions in space plasmas

In nonstationary, strong inhomogeneous or open plasmas particle orbits are rather complicated. If the nonstationary time scale is smaller than the gyration period, if the inhomogeneity scale is smaller than the gyration radius, i.e. at magnetic plasma boundaries, or if the plasma has sources and sinks in phase space, then nongyrotropic distribution functions occur. The stability of such plasma configurations is studied in the framework of linear dispersion theory. In an open plasma nongyrotropy drives unstable waves parallel and perpendicular to the background magnetic field, whereas in the gyrotropic limit the plasma is stable. In nonstationary plasmas nongyrotropy drives perpendicular unstable waves only. Temporal modulation couples a seed mode with its side lobes and thus it renders unstable wave growth more difficult. As an example of an inhomogeneous plasma a magnetic halfspace is discussed. In a layer with thickness of the thermal proton gyroradius a nongyrotropic distribution is formed which may excite unstable parallel and perpendicular propagating waves.     

Generation of baroclinic topographic waves by a tropical cyclone impacting a low-latitude continental shelf

Numerical model experiments have been performed to analyze the low-latitude baroclinic continental shelf response to a tropical cyclone. The theory of coastally trapped waves suggests that, provided appropriate slope, latitude, stratification and wind stress, bottom-intensified topographic Rossby waves can be generated by the storm. Based on a scale analysis, the Nicaragua Shelf is chosen to study propagating topographic waves excited by a storm, and a model domain is configured with simplified but similar geometry. The model is forced with wind stress representative of a hurricane translating slowly over the region at 6 km h⁻¹. Scale analysis leads to the assumption that baroclinic Kelvin wave modes have minimal effect on the low-frequency wave motions along the slope, and coastal-trapped waves are restricted to topographic Rossby waves. Analysis of the simulated motions suggests that the shallow part of the continental slope is under the influence of barotropic topographic wave motions and at the deeper part of the slope baroclinic topographic Rossby waves dominate the low-frequency motions. Numerical solutions are in a good agreement with theoretical scale analysis. Characteristics of the simulated baroclinic waves are calculated based on linear theory of bottom-intensified topographic Rossby waves. Simulated waves have periods ranging from 153 to 203 h. The length scale of the waves is from 59 to 87 km. Analysis of energy fluxes for a fixed volume on the slope reveals predominantly along-isobath energy propagation in the direction of the group velocity of a topographic Rossby wave. Another model experiment forced with a faster translating hurricane demonstrates that fast moving tropical cyclones do not excite energetic baroclinic topographic Rossby waves. Instead, robust inertial oscillations are identified over the slope.     

Alfven波在低纬电离层中的传播研究

Alfven波在低纬地区电离层的传播有其特殊性,一方面,低纬地区同样存在Alfven速度梯度的巨大变化,导致电离层Alfven谐振器(Ionospheric Alfven resonator, IAR)的形成;另一方面,由于在低纬地区磁倾角很小,所以剪切Alfven波在传播的过程中纬度方向跨度很大,不同纬度电离层参数将共同对其产生影响;并且,由于电离层水平分层,故磁力线与电离层不正交.本文选取双流体力学模型,在忽略场向电场的条件下,利用非正交坐标系,结合IRI07模型与MSISE00模型模拟低纬地区Alfven波的传播,得到其反射及耦合特性.结果表明,低纬地区同样存在电离层Alfven谐振现象,由耦合产生的压缩模有向磁赤道方向传播的趋势,夜间电离层状态相对于白天更适合IAR的形成,谐振频率沿磁力线L值增大单调递增.     

Anisotropy in the Earth's crust and uppermost mantle in southeastern Europe obtained from Rayleigh and Love surface waves

Digital seismograms from 25 earthquakes located in the southeastern part of Europe, recorded by three-component very broadband seismometers at the stations Vitosha (Bulgaria) and Muntele Rosu (Romania), were processed to obtain the dispersion properties of Rayleigh and Love surface waves. Rayleigh and Love group-velocity dispersion curves were obtained by frequency–time analysis (FTAN). The path-averaged shear-wave velocity models were computed from the obtained dispersion curves. The inversion of the dispersion curves was performed using an approach based on the Backus–Gilbert inversion method. Finally, 70 path-averaged velocity models (35 R-models computed from Rayleigh dispersion curves and 35 L-models computed from Love dispersion curves) were obtained for southeastern Europe. For most of the paths, the comparison between each pair of models (R-model and L-models for the same path) shows that for almost all layers the shear-wave velocities in the L-models are higher than in the R-models. The upper sedimentary layers are the only exception. The analysis of both models shows that the depth of the Moho boundary in the L-models is shallower than its depth in the R-models. The existence of an anisotropic layer associated with the Moho boundary at depths of 30–45 km may explain this phenomenon. The anisotropy coefficient was calculated as the relative velocity difference between both R- and L-models at the same depths. The value of this coefficient varies between 0% and 20%. Generally, the anisotropy of the medium caused by the polarization anisotropy is up to 10–12%, so the maximum observed discrepancies between both types of models are also due to the lateral heterogeneity of the shear-wave velocity structure of the crust and the upper mantle in the region.     

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.     

Hydromagnetic waves in a thin rotating spherical shell

We consider an electrically conducting fluid confined to a thin rotating spherical shell in which the Elsasser and magnetic Reynolds numbers are assumed to be large while the Rossby number is assumed to vanish in an appropriate limit. This may be taken as a simple model for a possible stable layer at the top of the Earth's outer core. It may also be a model for the thin shells which are thought to be a source of the magnetic fields of some planets such as Mercury or Uranus. Linear hydromagnetic waves are studied using a multiple scale asymptotic scheme in which boundary layers and the associated boundary conditions determine the structure of the waves. These waves are assumed to be of the form of an asymptotic series expanded about an ambient magnetic field which vanishes on the equatorial plane and velocity and pressure fields which do not. They take the form of short wave, slowly varying wave trains. The results are compared to the author's previous work on such waves in cylindrical geometry in which the boundary conditions play no role. The approximation obtained is significantly different from that obtained in the previous work in that an essential singularity appears at the equator and nonequatorial wave regions appear.     

Two-dimensional scattering of in-plane body waves due to a discontinuity in bedrock

The direct boundary integral equation technique is used to study in-plane surface amplification of in-plane seismic body waves for the case of an inhomogeneity in a bedrock half-space. In the studied soil configuration, a soil layer rests on a rock half-space which includes a rock inclusion. The rock inclusion considered is a semi-infinite horizontal rock layer in which its upper boundary borders the soil layer. Materials in the soil–rock configuration are considered viscoelastic except for the section of the rock half-space below the level of the rock inclusion which is considered elastic. A parametric study is performed to determine controlling factors for surface displacement due to in-plane body waves. The study investigates varying the stiffness and the thickness of the rock inclusion for a range of frequencies and wave incidence angles. Anti-plane waves for this type of soil-rock configuration have been addressed in a previous article by Heymsfield (Earthquake Engng. Struct. Dyn. 28 : 841–855 (1999)). Copyright © 1999 John Wiley & Sons, Ltd.     

Rayleigh modes in anisotropic,heterogeneous poroelastic layers

The generalized Rayleigh type surface waves are studied in a multilayered medium consisting of anisotropic poroelastic solid layered stack beneath a fluid layer and overlying a heterogeneous elastic solid half-space. The heterogeneity, considered, is of vertical type. The interface between solid layer and half-space is treated as an imperfect interface and suitable boundary conditions are applied thereat. The technique of transfer matrix is used to obtain the dispersion equation in compact and convenient form. Numerical results are obtained for particular models. The effects of anisotropy and heterogeneity on the surface waves speed are discussed.     

Magnetic Rossby waves in a stably stratified layer near the surface of the Earth's outer core

Abstract

The stratification profile of the Earth's magnetofluid outer core is unknown, but there have been suggestions that its upper part may be stably stratified. Braginsky (1984) suggested that the magnetic analog of Rossby (planetary) waves in this stable layer (the ‘H’ layer) may be responsible for a portion of the short-period secular variation. In this study, we adopt a thin shell model to examine the dynamics of the H layer. The stable stratification justifies the thin-layer approximations, which greatly simplify the analysis. The governing equations are then the Laplace's tidal equations modified by the Lorentz force terms, and the magnetic induction equation. We linearize the Lorentz force in the Laplace's tidal equations and the advection term in the magnetic induction equation, assuming a zeroth order dipole field as representative of the magnetic field near the insulating core-mantle boundary. An analytical β-plane solution shows that a magnetic field can release the equatorial trapping that non-magnetic Rossby waves exhibit. A numerical solution to the full spherical equations confirms that a sufficiently strong magnetic field can break the equatorial waveguide. Both solutions are highly dissipative, which is a consequence of our necessary neglect of the induction term in comparison with the advection and diffusion terms in the magnetic induction equation in the thin-layer limit. However, were one to relax the thin-layer approximations and allow a radial dependence of the solutions, one would find magnetic Rossby waves less damped (through the inclusion of the induction term). For the magnetic field strength appropriate for the H layer, the real parts of the eigenfrequencies do not change appreciably from their non-magnetic values. We estimate a phase velocity of the lowest modes that is rather rapid compared with the core fluid speed typically presumed from the secular variation.     

ELF plasma waves in hot and cold plasma fluxes observed by Prognoz-8 in the magnetospheric tail

We present Prognoz-8 observations of low-frequency plasma waves (2-105 Hz) associated with plasma fluxes near the outer boundary of the plasma sheet. These plasma fluxes were different from the regular plasma sheet boundary layer and consisted of tailward flowing warm proton and cold oxygen beams accompanied by rather cold electrons (T _e less than 100 eV). Observed plasma characteristics were used in the numerical solution of the dispersion relation for the ion-beam acoustic instability. Detailed analysis shows that this instability can be a source of observed emissions at frequencies up to 25 Hz.     

Transmission and reflection of Rayleigh waves at a thin low velocity vertical layer: A laboratory and theoretical study

A three-dimensional ultrasonic modelling was used to study the Rayleigh waves reflected from a thin low velocity vertical layer and those transmitted through the same zone. The reflection and transmission coefficients of the Rayleigh waves have been calculated by an approximate method based on the Green function technique. Nonrigid contact boundary conditions were used for the low velocity layer modelling. A rather good correspondence between the theoretical and experimental absolute values of the reflection and the transmission coefficients was obtained. Some discrepancies between experimental and theoretical results, in particular with regard to phase shifts, may be explained by a certain inadequacy of the theoretical model to the low velocity layer investigated by the ultrasonic modelling.     

低纬磁层边界区的可压缩性Kelvin-Helmholtz不稳定波

本文用“三层模式”探讨了低纬磁层边界区的可压缩Kelvin-Helmholtz不稳定波的特性。低纬边界层的存在降低了不稳定的阈值,几乎整个低纬边界区都是不稳定的。从内边界向磁层传输的能流和动量流都比双层模式增大,扰动磁场是椭圆偏振的。还讨论了低纬边界区该不稳定性的动力学效应及其与P_c4-5脉动的联系。