Modulational Instability of Radial Oscillations of Coronal Loops

Geomagnetism and Aeronomy - The radial modes of the coronal loops are used to interpret the observed microwave and hard x-ray pulsations during flares. The properties of radial oscillations are...     

Analysis of a 12-Hour Artifact in LF Oscillations of the Magnetic Field of Sunspots According to SDO/HMI Data

The properties of the 12-h artifact in the data of the SDO/HMI instrument (Helioseismic and Magnetic Imager) caused by the nonzero radial velocity of the station relative to the Sun are investigated. The study has been carried out with respect to long-period oscillations of the magnetic field of sunspots for different station positions in the Earth’s orbit by the alternative spectral method of singular decomposition of the signal CaterPillarSSA. Features of artifact filtering, both in special positions of the station (at the points of aphelion and perihelion) and at arbitrarily selected orbital points, are considered. It is shown that the 12-h artifact mode can be completely filtered from the time series of the observed variable, not only at these two orbital points (because of the symmetry of the station’s radial velocity with respect to the zero mean here) but also at any others. It is shown that only a 12-h mode is physically justified, while the 24-h harmonic appears only as an artifact in the Fourier decomposition of the amplitude-modulated signal. It is emphasized that the values of the magnetic field measured with SDO/HMI are sensitive only to the station’s radial velocity absolute values with respect to the Sun and do not depend on its direction. It has been noted that the periods of sunspot oscillation as a whole obtained from SDO/HMI data after orbital artifact filtration fit well into the dependence diagram of the period of sunspot oscillations on the value of its magnetic field strength constructed earlier by SOHO/MDIdata.     

Nonlinear dynamics of long-wave perturbations of the Kolmogorov flow for large Reynolds numbers

The nonlinear dynamics of long-wave perturbations of the inviscid Kolmogorov flow, which models periodically varying in the horizontal direction oceanic currents, is studied. To describe this dynamics, the Galerkin method with basis functions representing the first three terms in the expansion of spatially periodic perturbations in the trigonometric series is used. The orthogonality conditions for these functions formulate a nonlinear system of partial differential equations for the expansion coefficients. Based on the asymptotic solutions of this system, a linear, quasilinear, and nonlinear stage of perturbation dynamics is identified. It is shown that the time-dependent growth of perturbations during the first two stages is succeeded by the stage of stable nonlinear oscillations. The corresponding oscillations are described by the oscillator equation containing a cubic nonlinearity, which is integrated in terms of elliptic functions. An analytical formula for the period of oscillations is obtained, which determines its dependence on the amplitude of the initial perturbation. Structural features of the field of the stream function of the perturbed flow are described, associated with the formation of closed vortex cells and meandering flow between them. As a supplement, an asymptotic analysis of nonlinear dynamics of long-wave perturbations superimposed on a damped by small viscosity Kolmogorov flow (very large, but finite Reynolds numbers) is made. It is strictly shown that all velocity components of the perturbed flow remain bounded in this case.     

Correlation between the parameters of coronal mass ejections and features of their propagation in the corona with the large-scale structure of the solar magnetic field

Correlation between the parameters of coronal mass ejections (CMEs) that are detected on the LASCO coronographs and are associated with eruptive prominences and the distances of CME axes from the coronal streamer belt has been analyzed. The deviations of CME trajectories from the radial direction have been investigated.     

Secondary planetary waves in the middle atmosphere: numerical simulation and analysis of the neutral wind data

A numerical simulation of secondary waves generated by nonlinear interaction has been used to interpret the behaviour of planetary waves observed by a meteor radar in the UK (53°27′N, 1°35′W) during the summer of 1992. A new explanation is proposed for the long-period variability of the (3,0) mode quasi-two-day wave in the mesosphere and lower-thermosphere, involving the (2,0) Rossby-gravity mode and pseudo-two-day secondary waves with the same zonal wavenumbers as those of the primary (2,0) and (3,0) modes. These pseudo-two-day secondary waves arise from the nonlinear interaction of the Rossby-gravity modes with long-period oscillations of the zonally averaged flow in the equatorial stratosphere, which can be generated by the interaction between the 10 and 16 day planetary waves. Other maxima existing in the neutral wind power spectra can be identified with various secondary waves originating from nonlinear interaction between the quasi-two-day and long-period planetary waves.     

Intensity of Pc5 geomagnetic pulsations observed on the Earth’s surface, depending on the corresponding oscillation mode (poloidal or toroidal) in the magnetosphere

Thirty-six cases of Pc5 geomagnetic pulsations on the GOES-8 geostationary satellite for 2001, which had amplitudes equal to several nanoteslas and continued for more than an hour, have been studied. Twenty-two and 14 pulsations were toroidal and poloidal, respectively. All these pulsations were compared with geomagnetic observations at the Poste-de-la-Baleine observatory (PBQ), which was located near the satellite projection. It was established that the pulsation frequencies on the ground and in the magnetosphere do not always coincide. It has been detected that poloidal oscillations have small and large amplitudes on the ground and in the magnetosphere, respectively; the situation is opposite for toroidal oscillations. The amplitude of ground-level pulsations to a larger degree depends on the azimuthal field component in the magnetosphere than on the radial component.     

Alfvèn波与慢激波的相互作用

本文分析了斜入射波矢与背景磁场和激波法线共面时,一维小幅度Alfvèn波干扰下,慢激波的稳定性问题;论证了Alfvèn波在慢激波上的射线反射和折射规律;并就日冕慢激波情形进行了具体的数值计算。结果表明,除非上游法向流速接近上游法向Alfvèn波波速,在上述斜入射的Alfvèn波干扰下,慢激波总是稳定的。日冕慢激波是这种稳定性的一个例子;日冕慢激波的存在,能使起源于日冕向行星际空间传播（不管它起源于日冕慢激波之内或外）的Alfvèn波的法向能流密度增大。     

A nonlinear displacement of Pc5 latitudinal profiles

A pronounced difference exists between the theory, which definitely indicates that magnetospheric oscillations are anharmonic, and the experimental study of geomagnetic pulsations. The experimental study of the nonlinearity of the Pc5 pulsation amplitude latitudinal profile (the range of periods is 150–600 s) is considered. The Pc5 registrations at the IMAGE meridional chain of station were used to search for nonlinear distortions of the profile. Using a specific event, it has been indicated that the Pc5 amplitude peak shifts northward along the meridian with decreasing oscillation amplitude. The coefficient of nonlinear distortions in the latitudinal profile has been determined based on the measurements. The main conclusion consists in that a delicate problem of geomagnetic pulsation anharmonicity can be entirely studied experimentally.     

On some properties in the emergence and evolution of the oscillations of the Earth after earthquakes

The records from wideband seismic stations are analyzed for studying the oscillations of the Earth that emerged after the earthquakes in Sumatra on December 26, 2004 (M = 9.2), Chile on February 27, 2010 (M = 8.8), and after the Tohoku megaearthquake on March 11, 2011 (M = 9.0). Attention is focused on the band with a period of 20.46 min, which includes the free radial mode ₀S₀. It is established that the emergence of oscillations in the frequency interval corresponding to the free oscillations of the Earth is delayed by a lag, which increases with increasing period. Pulsations of the 20.46-min band, which appear in the interval from 5 to 7 days after the earthquake and have a period of 127–129 min, are revealed. The patterns of the amplitude attenuation of the 20.46-min band are different at stations located in zones with different tectonic activity. These features manifest themselves in the search through different stations and through different earthquakes.     

高能离子束流引起低频电磁波动的特性

理论和数值模拟研究了日冕区高速低密离子束流与等离子体相互作用产生的低频电磁波动特征. 结果表明,在线性阶段,系统波动主要表现为短波长的非共振模的激发;在非线性阶段,长波模占优,短波长波逐渐衰减,此时系统波动表现为具有Alfvén波动特征,波的能谱为双幂律谱. 这些结果可用来解释太阳风中的Alfvén湍动现象.     

Perturbation of the magnetic field in the Earth’s magnetosphere due to plateau creation in the radial distribution of plasma pressure

The nonlinear perturbation of a dipole field by a system of transverse currents, which arises due to the radial pressure distribution when the pressure is almost independent of the radial distance, is analyzed. This distribution of pressure was observed in the experiment. The radial dependences of the magnetic field depression, transverse current density, and volumes of magnetic flux tubes have been obtained at different values of the plasma parameter via nonlinear simulation. It is shown that a dependence of the volume of magnetic flux tube on the radial distance can change and a region of the negative gradient of volume can appear at some plasma-parameter values.     

日冕绿区与地磁扰动間的某些問題

一、引言地磁場扰动的原因,至今仍是地球物理学者与天体物理学者所共同关切的問題.有許多理由說明太阳是使地磁产生扰动的主要根源.一般說来,在任何时期內,太阳活动愈強,地磁活动也愈強.然而,即使是在太阳活动最弱的年份,地磁場也可能产生不小的扰动.既然在太阳活动低年,作为太阳活动标誌的黑子数很少,那么,使地磁产生扰动的根源又是什么呢?对于这个問題,20多年以前提出了所謂M区来做答案.     

Oscillations of galactic cosmic rays and solar indices before the arrival of relativistic solar protons

Using modern wavelet analysis techniques, we have made an attempt to search for oscillations of intensity of galactic cosmic rays (GCR), sunspot numbers (SS) and magnitudes of coronal index (CI) implying that the time evolution of those oscillations may serve as a precursor of Ground Level Enhancements (GLEs) of solar cosmic rays (SCR). From total number of 70 GLEs registered in 1942–2006, the four large events — 23 February 1956, 14 July 2000, 28 October 2003, and 20 January 2005 — have been chosen for our study. By the results of our analysis, it was shown that a frequency of oscillations of GCR decreases as time approaches to the event day. We have also studied a behaviour of common periodicities of GCR and SCR within the time interval of individual GLE. The oscillations of GLE occurrence rate (OR) at different stages of the solar activity (SA) cycle is of special interest. We have found some common periodicities of SS and CI in the range of short (2.8, 5.2, 27 and 60 days), medium (0.3, 0.5, 0.7, 1.3, 1.8 and 3.2 years) and long (4.6 and 11.0 years) periods. Short and medium periodicities, in general, are rather concentrated around the maxima of solar cycles and display the complex phase relations. When comparing these results with the behaviour of OR oscillations we found that the period of 11 years is dominating (controlling); it is continuous over the entire time interval of 1942–2006, and during all this time it displays high synchronization and clear linear ratios between the phases of oscillations of η, SS and CI. It implies that SCR generation is not isolated stochastic phenomena characteristic exclusively for chromospheric and/or coronal structures. In fact, this process may have global features and involve large regions in the Sun’s atmosphere.     

Studying correlations between the coronal hole area,solar wind velocity,and local magnetic indices in the Canadian region during the decline phase of cycle 23

Geomagnetic disturbances in the Canadian region are compared with their solar and heliospheric sources during the decline phase of solar activity, when recurrent solar wind streams from low-latitude coronal holes were clearly defined. A linear correlation analysis has been performed using the following data: the daily and hourly indices of geomagnetic activity, solar wind velocity, and coronal hole area. The obtained correlation coefficients were rather low between the coronal hole areas and geomagnetic activity (0.17–0.48), intermediate between the coronal hole areas and the solar wind velocity (0.40–0.65), and rather high between the solar wind velocity and geomagnetic activity (0.50–0.70). It has been indicated that the correlation coefficient values can be considerably increased (by tens of percent in the first case and about twice in the second case) if variations in the studied parameters related to changes in the ionosphere (different illumination during a year) and variations in the heliolatitudinal shift of the coordinate system between the Earth, the Sun, and a spacecraft are more accurately taken into account.     

Fast damping of acoustic waves in solar coronal loops as a result of their radiation

The problem of the observed fast damping of longitudinal waves in solar coronal magnetic loops is studied. According to some data, the radiation effect, which plays a key role in the cooling of coronal loops that are observed in the extreme UV wavelength range, is used to explain this phenomenon. The dispersion relation for slow magnetosonic modes of a cylindrical magnetic tube has been obtained with regard to the radiation effect. It has been indicated that the radiation actually results in the fast damping of the slow magnetosonic modes of coronal magnetic loops.     

The self-similar,non-linear evolution of rotating magnetic flux ropes

We study, in the ideal MHD approximation, the non-linear evolution of cylindrical magnetic flux tubes differentially rotating about their symmetry axis. Our force balance consists of inertial terms, which include the centrifugal force, the gradient of the axial magnetic pressure, the magnetic pinch force and the gradient of the gas pressure. We employ the “separable” class of self-similar magnetic fields, defined recently. Taking the gas to be a polytrope, we reduce the problem to a single, ordinary differential equation for the evolution function. In general, two regimes of evolution are possible; expansion and oscillation. We investigate the specific effect rotation has on these two modes of evolution. We focus on critical values of the flux rope parameters and show that rotation can suppress the oscillatory mode. We estimate the critical value of the angular velocity _crit, above which the magnetic flux rope always expands, regardless of the value of the initial energy. Studying small-amplitude oscillations of the rope, we find that torsional oscillations are superimposed on the rotation and that they have a frequency equal to that of the radial oscillations. By setting the axial component of the magnetic field to zero, we study small-amplitude oscillations of a rigidly rotating pinch. We find that the frequency of oscillation is inversely proportional to the angular velocity of rotation ; the product being proportional to the inverse square of the Alfvén time. The period of large-amplitude oscillations of a rotating flux rope of low beta increases exponentially with the energy of the equivalent 1D oscillator. With respect to large-amplitude oscillations of a non-rotating flux rope, the only change brought about by rotation is to introduce a multiplicative factor greater than unity, which further increases the period. This multiplicative factor depends on the ratio of the azimuthal speed to the Alfvén speed. Finally, considering interplanetary magnetic clouds as cylindrical flux ropes, we inquire whether they rotate. We find that at 1 AU only a minority do. We discuss data on two magnetic clouds where we interpret the presence in each of vortical plasma motion about the symmetry axis as a sign of rotation. Our estimates for the angular velocities suggest that the parameters of the two magnetic clouds are below critical values. The two clouds differ in many respects (such as age, bulk flow speed, size, handedness of the magnetic field, etc.), and we find that their rotational parameters reflect some of these differences, particularly the difference in age. In both clouds, a rough estimate of the radial electric field in the rigidly rotating core, calculated in a non-rotating frame, yields values of the order mV m⁻¹.     

Earth-flattening procedure for the propagation of Rayleigh wave

Summary The propagation of Rayleigh waves in the earth is investigated in the period range of about 60 to 590 seconds. It has been shown that a set of earth-flattening approximations can be used to transform the heterogeneous spherical earth into plane-layered earth on which the dispersion computations by matrix method can be applied effectively to describe the fundamental mode of spheroidal oscillations involving the crust and the mantly only.     

径向分层TI孔隙介质井孔中激发的模式波的数值研究

横向各向同性介质是地层中普遍存在的一种各向异性介质.本文对径向分层TI孔隙介质包围井孔中激发的斯通利波和弯曲波的传播特性进行了理论计算,发现模式波在低频时更多的是反应原状地层的信息,而随着频率的增加侵入带参数逐渐起控制作用;Biot理论描述的地层衰减比速度更容易受井壁附近地层参数的影响.利用灵敏度曲线定量研究了不同频率下地层各个参数对相速度和衰减系数的贡献大小,主要结果显示模式波的衰减受水平渗透率影响明显,而垂直渗透率的变化对模式波几乎无影响;斯通利波对水平向传播的横波速度比弯曲波的灵敏度高.从单极子和偶极子声源在井孔中激发的全波波形也可发现,声波测井仪器较宽的声源频带和合适的源距设置有利于对不同径向深度上的地层声学参数进行成像.     

Convection in a rotating,laterally heated annulus pattern velocities and amplitude oscillations

Abstract

The velocities of the wave patterns relative to the rotating annulus have been measured with either increasing or decreasing positive radial temperature gradients and different rotation rates, with the fluid in thermal equilibrium and in contact with a rigid lid. The pattern velocities are dependent on initial conditions except in the unique areas of the stability diagram, where the velocities observed with either increasing or decreasing ΔT, overlap. The pattern velocities change discontinuously with each wave number transition, with a particularly large discontinuity at the transition from two to one wave. The frequency of the amplitude oscillations of the waves has been measured also. It has been found that the period of the oscillation of the three wave pattern is inversely proportional to the period of the pattern velocity, which means that in this case the ratio of the frequency of amplitude oscillation and the frequency of the pattern revolution is incommensurate.     

On the Ultra Long Propagation of Felt Ground Motion Due to the <Emphasis Type="Italic">M</Emphasis><Subscript><Emphasis Type="Italic">w</Emphasis></Subscript> 8.3 Deep-Focus Sea-of-Okhotsk Earthquake of May 24, 2013

This study uses macroseismic data and wave equations to solve the problem of ultra long propagation of felt ground motion (over 9000 km from the epicenter) due to the Sea-of-Okhotsk earthquake. We show that the principal mechanism of this phenomenon could be excitation of a previously unknown standing radial wave as a mode of the Earth’s free oscillations, ₀S₀, due to the superposition of an incident and a reflected spherical P wave in the epicentral area of the Sea-of-Okhotsk earthquake. The standing wave generates slowly attenuating P waves that travel over the earth’s surface that act as carrying waves; when superposed on these, direct body waves acquire the ability to travel over great distances. We show previously unknown parameters of the radial mode ₀S₀ for the initial phase of earth deformation due to the large deep-focus earthquake. We used data on the Sea-of-Okhotsk and Bolivian earthquakes to show that large deep-focus earthquakes can excite free oscillations of the Earth that are not only recorded by instrumental means, but are also felt by people, with the amplification of the macroseismic effect being directly related to the phenomenon of resonance for multistory buildings.