Non-axisymmetric α2Ω-dynamo waves in thin stellar shells

Linear α²Ω-dynamo waves are investigated in a thin turbulent, differentially rotating convective stellar shell. A simplified one-dimensional model is considered and an asymptotic solution constructed based on the small aspect ratio of the shell. In a previous paper Griffiths et al. (Griffiths, G.L., Bassom, A.P., Soward, A.M. and Kuzanyan, K.M., Nonlinear α²Ω-dynamo waves in stellar shells, Geophys. Astrophys. Fluid Dynam., 2001, 94, 85–133) considered the modulation of dynamo waves, linked to a latitudinal-dependent local α-effect and radial gradient of the zonal shear flow. These effects are measured at latitude θ by the magnetic Reynolds numbers R _α f(θ) and R _Ω g(θ). The modulated Parker wave, which propagates towards the equator, is localised at some mid-latitude θ_p under a Gaussian envelope. In this article, we include the influence of a latitudinal-dependent zonal flow possessing angular velocity Ω_*(θ) and consider the possibility of non-axisymmetric dynamo waves with azimuthal wave number m. We find that the critical dynamo number D _c?=?R _α R _Ω is minimised by axisymmetric modes in the αΩ-limit (Rα→0). On the other hand, when Rα?≠?0 there may exist a band of wave numbers 0?m?m ^? for which the non-axisymmetric modes have a smaller D _c than in the axisymmetric case. Here m ^? is regarded as a continuous function of R _α with the property m?→0 as R _α→0 and the band is only non-empty when m??>1, which happens for sufficiently large R _α. The preference for non-axisymmetric modes is possible because the wind-up of the non-axisymmetric structures can be compensated by phase mixing inherent to the α²Ω-dynamo. For parameter values resembling solar conditions, the Parker wave of maximum dynamo activity at latitude θ_p not only propagates equatorwards but also westwards relative to the local angular velocity Ω_*(θ _p ). Since the critical dynamo number D _c?=?R _α R _Ω is O (1) for small R _α, the condition m ^??>?1 for non-axisymmetric mode preference imposes an upper limit on the size of |dΩ_*/dθ|.     

On the frontal condition for finite amplitude α2Ω-dynamo wave trains in stellar shells

Abstract

In a previous paper, Bassom et al. (Proc. R. Soc. Lond. A, 455, 1443–1481, 1999) (BKS) investigated finite amplitude αΩ-dynamo wave trains in a thin turbulent, differentially rotating convective stellar shell; nonlinearity arose from α-quenching. There asymptotic solutions were developed based upon the small aspect ratio ε of the shell. Specifically, as a consequence of a prescribed latitudinally dependent α-effect and zonal shear flow, the wave trains have smooth amplitude modulation but are terminated abruptly across a front at some high latitude θ_F. Generally, the linear WKB-solution ahead of the front is characterised by the vanishing of the complex group velocity at a nearby point θ_f; this is essentially the Dee–Langer criterion, which determines both the wave frequency and front location.

Recently, Griffiths et al. (Geophys. Astrophys. Fluid Dynam. 94, 85–133, 2001) (GBSK) obtained solutions to the α²Ω-extension of the model by application of the Dee—Langer criterion. Its justification depends on the linear solution in a narrow layer ahead of the front on the short O(θ_f—θ_F) length scale; here conventional WKB-theory, used to describe the solution elsewhere, is inadequate because of mode coalescence. This becomes a highly sensitive issue, when considering the transition from the linear solution, which occurs when the dynamo number D takes its critical value D _c corresponding to the onset of kinematic dynamo action, to the fully nonlinear solutions, for which the Dee—Langer criterion pertains.

In this paper we investigate the nature of the narrow layer for α²Ω-dynamos in the limit of relatively small but finite α-effect Reynolds numbers R _α, explicitly ε^½ ? R ² _α ? 1. Though there is a multiplicity of solutions, our results show that the space occupied by the corresponding wave train is generally maximised by a solution with θ_f—θ_F small; such solutions are preferred as evinced by numerical simulations. This feature justifies the application by GBSK of the Dee—Langer criterion for all D down to the minimum D _min that the condition admits. Significantly, the frontal solutions are subcritical in the sense that |D _min| ≤ |D _c|; equality occurs as the α-effect Reynolds number tends to zero. We demonstrate that the critical linear solution is not connected by any parameter track to the preferred nonlinear solution associated with D _min. By implication, a complicated bifurcation sequence is required to make the connection between the linear and nonlinear states. This feature is in stark contrast to the corresponding results for αΩ-dynamos obtained by BKS valid in the limit R _{2 α} ? ε^½, which, though exhibiting a weak subcriticality, showed that the connection follows a clearly identifiable nonbifurcating track.     

Turbulent transport of magnetic fields. V. Distribution of magnetic energy in a simple α2-dynamo

Abstract

In this paper we analyse the stationary mean energy density tensor T_ij = B_iB_j for the x ²-sphere. This model is one of the simplest possible turbulent dynamos, originally due to Krause and Steenbeck (1967): a conducting sphere of radius R with homogeneous, isotropic and stationary turbulent convection, no differential rotation and negligible resistivity. The stationary solution of the (linear) equation for T_ij is found analytically. Only T_rr , T _θθ and T _φφ are unequal to zero, and we present their dependence on the radial distance r.

The stationary solution depends on two coefficients describing the turbulent state: the diffusion coefficient β≈?u²?τ_c/3 and the vorticity coefficient γ ≈ ?|?×u|²?τ_c/3 where u(r, t) is the turbulent velocity and _c its correlation time. But the solution is independent of the dynamo coefficient α≈??u·?×u?τ_c/3 although α does occur in the equation for T_ij . This result confirms earlier conclusions that helicity is not required for magnetic field generation. In the stationary state, magnetic energy is generated by the vorticity and transported to the boundary, where it escapes at the same rate. The solution presented contains one free parameter that is connected with the distribution of B over spatial scales at the boundary, about which T_ij gives no information. We regard this investigation as a first step towards the analysis of more complicated, solar-type dynamos.     

Migration of sources of small earthquakes in the Garm region and variations in velocity of the Earth’s rotation

The spatial-temporal variations in localization of the sources of earthquakes with H ≥ 14 km are reviewed for the Garm region. The uneven distribution of such earthquakes is related to the block structure: their amount is higher in the weakened zones rather than in blocks. Three weakened zones are characterized by higher activity of deepened seismicity, which varies in time and increases before the earthquakes with K ≥ 12.5. The temporal variations in distribution of earthquake sources with depth allow a suggestion of the relation of the velocity of the Earth’s rotation and activity of deepened seismicity.     

A Review of the Seismicity in 2002

A total of 16 strong earthquakes with Ms≥7.0 occurred in the world in 2002 according to the determination of the Chinese Seismic Station Network (Table 1 ). The two strongest earthquakes were Sumatra earthquake (Ms7.8, November 2) and Alaska earthquake ( Ms 7.8 November 4) . Fig. 1 is the distribution of strong earthquakes that occurred in 2002. The global seismicity pattern in 2002 was similar to the ones since 1999. The frequency and strength apparently decreased in 2002 compared with the seismicity in 2001.     

A Review of the Seismicity in 2000

1. A SURVEY OF THE GLOBAL SEISMICITYAccording to the rec()rding of the seismic fletwork o[ China, 20 large earthquakes with M,     

Moment tensor inversion of small to moderate earthquakes in the Capital Region in 2004

The moment tensor solutions of 51 small to moderate earthquakes occurred in the Capital Region in the year of 2004 are obtained by inverting the broadband waveform data. Accordingly, other source parameters, such as scalar seismic moments, moment magnitudes, double-couple （DC） components and compensated-linear-vector-dipole （CLVD） components, are determined as well as fault parameters and stress-axis parameters. The inverted results are evaluated by groups of numerical tests.     

A Review of the Status of Seismicity in 1994

A total of 48 earthquakes with M_s ≥5.0 occurred in China in 1994 (29 on the Chinese mainland and offshore, 19 in Taiwan). Among them 9 earthquakes were of M_s ≥6.0 (4 on the mainland and offshore, 5 in Taiwan). The M_s 7.3 earthquake that occurred in Taiwan Straits on September 16 was the greatest one offshore, which was generally included in the mainland area according to the previous statistics. The most powerful earthquakes in Taiwan were the 2 with M_s =7.0 that occurred on May     

Macrodynamics of α2 dynamos

Abstract

Two distributions of the α-effect in a sphere are considered. The inviscid limit is approached both by direct numerical solution and by solution of a simpler nonlinear eigenvalue problem deriving from asymptotic boundary layer analysis for the case of stress-free boundaries. The inviscid limit in both cases is dominated by the need to satisfy the Taylor constraint which states that the integral of the Lorentz force over cylindrical (geostrophic) contours in a homogeneous fluid must tend to zero. For a small supercritical range in α, this condition can only be met by magnetic fields which vanish as the viscosity goes to zero. In this range, the agreement of the two approaches is excellent. In a portion of this range, the method of finite amplitude perturbation expansion is useful, and serves as a guide for understanding the numerical results. For larger α, evidence from the nonlinear eigenvalue problem suggests both that the Taylor state exists, and that the transition from small to large amplitude can require a finite amplitude (oscillatory) instability in accord with the findings of Soward and Jones (1983). However, solutions of the full equations have not been found which are independent of viscosity at larger values of α.     

Parity coupling in α2-dynamos

Abstract

The modal α²-dynamo of Hollerbach and Ierley (1991) is extended to include both parities, dipolar and quadrupolar. Two choices of α are considered. As before, the solutions approach the Taylor state, and the subsequent equilibration is independent of the viscosity in the asymptotic limit. The first choice of α yields stable steady-state pure-parity solutions of either type, and may yield some insight into the question of parity selection. The second choice of α yields rather complex time-dependent mixed-parity solutions, and demonstrates the extent to which parity coupling can affect the evolution of time-dependent solutions.     

A Study on the Tectonic Characteristics of Shallow Faults in the East of Zhengzhou City

Study on fault activity is a fundamental part of earthquake prediction and earthquake relief in big cities.In the active fault exploration in Zhengzhou,the spatial distribution,geological features and activity of the Huayuankou fault,the Shangjie fault and the Xushui fault were determined using the seismic prospecting method.New understanding about the characteristics of the faults was gained.This provides reliable basic data for future earthquake forecast and earthquake relief work in Zhengzhou.In addition,we proposed some ways to identify fault activity through analyzing the characteristics of the activity of a fault and raised an effective method for exploring active faults in big cities and exploring concealed faults in regions covered with thick overburdens.     

A study of the role of ion–molecule chemistry in the formation of sporadic sodium layers

Over two campaigns in 1998 and 1999, multiple sporadic sodium events were observed by the Arecibo Observatory sodium density lidar while simultaneously monitoring the plasma density using the incoherent scatter radar. In this paper, we test the theoretical explanation proposed by Cox and Plane (1998) where Na⁺ in a plasma layer is neutralized via an ion–molecule mechanism to form a sporadic sodium layer. A particular challenge is to interpret observations made in a Eulerian frame of observation where the spatial and temporal characteristics of events cannot easily be separated. The reaction scheme in the original mechanism is modified to include the reactions NaO⁺+N₂→Na⁺·N₂+O and NaO⁺+O₂→Na⁺+O₃, following the results of theoretical quantum calculations. Six unique case studies of sporadic sodium layers are presented here, and excellent agreement between simulation and observations was obtained for five of them.     

Nonlinear free thermal convection in a spherical shell:A variable viscosity model

Introduction The velocity field of surface plate motion can be split into a poloidal and a toroidal parts.At the Earth′s surface,the toroidal component is manifested by the existence of transform faults,and the poloidal component by the presence of convergence and divergence,i.e.spreading and subduc-tion zones.They have coupled each other and completely depicted the characteristics of plate tec-tonic motions.The mechanism of poloidal field has been studied fairly clearly which is related to …     

The discovery of TiO2-Ⅱ,the α-PbO2-structured high-pressure polymorph of rutile,in the Suizhou L6 chondrite

We report the discovery of TiO₂-Ⅱ in the unmelted rock of the shocked Suizhou L6 chondrite.Natural TiO₂-Ⅱ was previously found in ultrahigh-pressure metamorphic and mantle-derived rocks,terrestrial impact structures,and tektite.Our microscopic,Raman spectroscopic,electron microprobe and transmission electron microscopic investigations have revealed:(1) All observed TiO₂-Ⅱ grains are related with ilmenite and pyrophanite;(2) TiO₂-Ⅱ occurs as needle-and ...     

Study on the method for comprehensive discrimination of small earthquakes

IntroductionThe present-day digital seismic observation technique provides us a large amount of accurate seismic records of high-precision, wide-band, and large dynamic range and conditions for higher-solution and higher-speed discrimination of earthquakes. But the problem we face is how to use the modern theory and method for digital signal processing in fast and precise extraction of the characteristic parameters from the large amount of digital seismic records. A basis or the important prob…     

Source parameters of small and moderate earthquakes in the area of the 2009 L’Aquila earthquake sequence (central Italy)

The main goal of this study is to provide moment tensor solutions for small and moderate earthquakes of the 2009 L’Aquila seismic sequence (central Italy). The analysis was performed by using data coming from the permanent Italian seismic network run by the Istituto Nazionale di Geofisica e Vulcanologia (INGV) and the “Cut And Paste” (CAP) method based on broadband waveform inversion. Focal mechanisms, source depths and moment magnitudes are determined through a grid search technique. By allowing time shifts between synthetics and observed data the CAP method reduces dependence of the solution on the assumed velocity model and on earthquake location. We computed seismic moment tensors for 312 earthquakes having local magnitude in the range between 2.7 and 5.9. The CAP method has made possible to considerably expand the database of focal mechanisms from waveform analysis in the lowest magnitude range (i.e. in the neighborhood of magnitude 3) without overlooking the reliability of results. The obtained focal mechanisms generally show NW–SE striking focal planes in agreement with mapped faults in the region. Comparisons with the already published solutions and with seismological and geological information available allowed us to proper interpret the moment tensor solutions in the frame of the seismic sequence evolution and also to furnish additional information about less energetic seismic phases. Focal data were inverted to obtain the seismogenic stress in the study area. Results are compatible with the major tectonic domain. We also obtained a relation between moment and local magnitude suitable for the area and for the available magnitude range.