A comparative analysis of kinematic dynamo models using perturbation theory

Abstract

By using perturbation methods an analytical study has been carried out of large-scale dynamo models, which previously were mainly investigated by numerical methods.     

Patterned ground formation and penetrative convection in porous media

Abstract

A theoretical explanation is advanced consisting of a five stage process for the formation of polygonal ground which consists of stone borders forming regular hexagons and soil centres. One of these stages, namely the onset of convection in a porous soil between temperatures of 0°C and approximately 4-6°C, is studied analytically. Darcy's law is employed but variable permeability is allowed for and a parabolic density dependence on temperature is assumed. It is found that the theoretical predictions of the aspect ratio agree very well with field studies when a constant upper surface heat flux condition is imposed and an upwardly stratified permeability is chosen. Field study data, which agree very well with the theory, are reported in detail.     

Ordovician system

Rocks in the Brungle‐Darbalara area of the Tumut Trough form two distinct domains: basement (mainly Bullawyarra Schist), of Cambrian‐Ordovician age, and an Ordovician ‐ Early Silurian sedimentary and volcanic cover sequence. These two domains are separated by a sharp discontinuity that marks an abrupt change in rock type, structure, metamorphic grade and deformation style. Cover sequences have undergone only one major penetrative deformation during the Late Silurian, involving sub‐greenschist facies metamorphism and upright folding. In contrast, the basement also underwent at least two older deformations at greenschist facies and contains distinct high‐strain zones subconcordant with the basement‐cover contact. The high‐strain zones, characterized by a ubiquitous south‐southeast trending mineral lineation, record a discontinuous history of ductile followed by brittle behaviour, consistent with an extensional origin.

The structural and metamorphic discontinuity separating basement from Silurian cover is characterized by widespread cataclasis and alteration and is interpreted as a major detachment fault associated with lithospheric extension and the development of the Tumut Trough in the Early Silurian. During the main period of movement on the detachment, which took place prior to intrusion of the Blacks Flat Diorite into the Bullawyarra Schist, mafic and serpentinized ultramafic rocks either were tectonically emplaced or intruded into the high strain zones. This preceded and accompanied extensional faulting of the cover and deposition of Silurian trough sediments and volcanics which unconformably overlie and onlap older units.

The development of the Tumut Trough, in the Brungle‐Darbalara area, bears many similarities with that of Cordilleran metamorphic core complexes. Such a model is consistent with environments suggested for the trough by previous workers. The south‐southeast extension direction parallels the trough‐bounding faults and implies an overall strike‐slip tectonic setting.     

The destabilising nature of differential rotation

Abstract

In a rapidly rotating, electrically conducting fluid we investigate the thermal stability of the fluid in the presence of an imposed toroidal magnetic field and an imposed toroidal differential rotation. We choose a magnetic field profile that is stable. The familiar role of differential rotation is a stabilising one. We wish to examine the less well known destabilising effect that it can have. In a plane layer model (for which we are restricted to Roberts number q = 0) with differential rotation, U = sΩ(z)1 _?, no choice of Ω(z) led to a destabilising effect. However, in a cylindrical geometry (for which our model permits all values of q) we found that differential rotations U = sΩ(s)1 _? which include a substantial proportion of negative gradient (dΩ/ds ≤ 0) give a destabilising effect which is largest when the magnetic Reynolds number R _m = O(10); the critical Rayleigh number, Ra _c, is about 7% smaller at minimum than at R_m = 0 for q = 10⁶. We also find that as q is reduced, the destabilising effect is diminished and at q = 10^?6, which may be more appropriate to the Earth's core, the effect causes a dip in the critical Rayleigh number of only about 0.001%. This suggests that we see no dip in the plane layer results because of the q = 0 condition. In the above results, the Elsasser number A = 1 but the effect of differential rotation is also dependent on A. Earlier work has shown a smooth transition from thermal to differential rotation driven instability at high A [A = O(100)]. We find, at intermediate A [A = O(10)], a dip in the Ra_c vs. R_m curve similar to the A = 1 case. However, it has Ra_c ≤ 0 at its minimum and unlike the results for high A, larger values of R_m result in a restabilisation.     

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.     

Transitions to chaotic thermal convection in a rapidly rotating spherical fluid shell

Abstract

Numerical simulations of thermal convection in a rapidly rotating spherical fluid shell heated from below and within have been carried out with a nonlinear, three-dimensional, time-dependent pseudospectral code. The investigated phenomena include the sequence of transitions to chaos and the differential mean zonal rotation. At the fixed Taylor number T _a =10⁶ and Prandtl number Pr=1 and with increasing Rayleigh number R, convection undergoes a series of bifurcations from onset of steadily propagating motions SP at R=R _c = 13050, to a periodic state P, and thence to a quasi-periodic state QP and a non-periodic or chaotic state NP. Examples of SP, P, QP, and NP solutions are obtained at R = 1.3R _c , R = 1.7 R _c , R = 2R _c , and R = 5 R _c , respectively. In the SP state, convection rolls propagate at a constant longitudinal phase velocity that is slower than that obtained from the linear calculation at the onset of instability. The P state, characterized by a single frequency and its harmonics, has a two-layer cellular structure in radius. Convection rolls near the upper and lower surfaces of the spherical shell both propagate in a prograde sense with respect to the rotation of the reference frame. The outer convection rolls propagate faster than those near the inner shell. The physical mechanism responsible for the time-periodic oscillations is the differential shear of the convection cells due to the mean zonal flow. Meridional transport of zonal momentum by the convection cells in turn supports the mean zonal differential rotation. In the QP state, the longitudinal wave number m of the convection pattern oscillates among m = 3,4,5, and 6; the convection pattern near the outer shell has larger m than that near the inner shell. Radial motions are very weak in the polar regions. The convection pattern also shifts in m for the NP state at R = 5R _c , whose power spectrum is characterized by broadened peaks and broadband background noise. The convection pattern near the outer shell propagates prograde, while the pattern near the inner shell propagates retrograde with respect to the basic rotation. Convection cells exist in polar regions. There is a large variation in the vigor of individual convection cells. An example of a more vigorously convecting chaotic state is obtained at R = 50R _c . At this Rayleigh number some of the convection rolls have axes perpendicular to the axis of the basic rotation, indicating a partial relaxation of the rotational constraint. There are strong convective motions in the polar regions. The longitudinally averaged mean zonal flow has an equatorial superrotation and a high latitude subrotation for all cases except R = 50R _c , at this highest Rayleigh number, the mean zonal flow pattern is completely reversed, opposite to the solar differential rotation pattern.     

An east–west‐trending Quaternary tunnel valley in the south‐eastern North Sea and its seismic–sedimentological interpretation

A combination of a dense reflection seismic grid and up to 50‐m‐long records from sediment cores and cone penetration tests was used to study the geometry and infill lithology of an E–W‐trending buried tunnel valley in the south‐eastern North Sea. In relation to previously known primarily N–S‐trending tunnel valleys in this area, the geometry and infill of this 38‐km‐long and up to 3‐km‐wide valley is comparable, but its E–W orientation is exceptional. The vertical cross‐section geometry may result from subglacial sediment erosion of advancing ice streams and secondary incision by large episodic meltwater discharges with high flow rates. The infill is composed of meltwater sands and reworked till remnants on the valley flanks that are overlain by late Elsterian rhythmic, laminated, lacustrine fine‐grained sediments towards the centre of the valley. A depression in the valley centre is filled with sediments most likely from the Holsteinian transgression and a subsequent post‐Holsteinian lacustrine quiet‐water setting. The exceptional axis orientation of this tunnel valley points to a regional N–S‐oriented ice front during the late Elsterian. Copyright © 2012 John Wiley & Sons, Ltd.     

Formal definition and dating of the GSSP (Global Stratotype Section and Point) for the base of the Holocene using the Greenland NGRIP ice core,and selected auxiliary records

The Greenland ice core from NorthGRIP (NGRIP) contains a proxy climate record across the Pleistocene–Holocene boundary of unprecedented clarity and resolution. Analysis of an array of physical and chemical parameters within the ice enables the base of the Holocene, as reflected in the first signs of climatic warming at the end of the Younger Dryas/Greenland Stadial 1 cold phase, to be located with a high degree of precision. This climatic event is most clearly reflected in an abrupt shift in deuterium excess values, accompanied by more gradual changes in δ¹⁸O, dust concentration, a range of chemical species, and annual layer thickness. A timescale based on multi‐parameter annual layer counting provides an age of 11 700 calendar yr b2 k (before AD 2000) for the base of the Holocene, with a maximum counting error of 99 yr. A proposal that an archived core from this unique sequence should constitute the Global Stratotype Section and Point (GSSP) for the base of the Holocene Series/Epoch (Quaternary System/Period) has been ratified by the International Union of Geological Sciences. Five auxiliary stratotypes for the Pleistocene–Holocene boundary have also been recognised. Copyright © 2008 John Wiley & Sons, Ltd.     

云南丽江台OSG-066重力潮汐观测结果及应用

基于云南丽江台超导重力仪OSG-066超过5 a的连续重力潮汐观测资料，获取高精度潮汐参数并构建地方重力潮汐模型，为丽江地区精确重力潮汐改正提供参考。研究9个全球海潮模型在丽江台的重力影响改正有效性，用时域内回归分析法和频域内小波分析法分别研究大气重力导纳值的变化特征，并利用观测潮汐数据估算自由核章动本征参数。结果表明，9个海潮模型在丽江台的重力影响改正效果基本一致，NAO.99b模型的改正精度较高；大气重力导纳值在时域和频域内均显示出较为明显的季节性变化特征，且与降雨量变化存在负相关关系。自由核章动本征周期为431.5(411.2, 454.0)恒星日，品质因子为 -2 796。