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.     

Effect of a uniform magnetic field on nonlinear magnetocenvection in a rotating fluid spherical shell

Abstract

Dynamic interaction between magnetic field and fluid motion is studied through a numerical experiment of nonlinear three-dimensional magnetoconvection in a rapidly rotating spherical fluid shell to which a uniform magnetic field parallel to its spin axis is applied. The fluid shell is heated by internal heat sources to maintain thermal convection. The mean value of the magnetic Reynolds number in the fluid shell is 22.4 and 10 pairs of axially aligned vortex rolls are stably developed. We found that confinement of magnetic flux into anti-cyclonic vortex rolls was crucial on an abrupt change of the mode of magnetoconvection which occurred at Δ = 1 ～ 2, where A is the Elsasser number. After the mode change, the fluid shell can store a large amount of magnetic flux in itself by changing its convection style, and the magnetostrophic balance among the Coriolis, Lorentz and pressure forces is established. Furthermore, the toroidal/poloidal ratio of the induced magnetic energy becomes less than unity, and the magnetized anti-cyclones are enlarged due to the effect of the magnetic force. Using these key ideas, we investigated the causes of the mode change of magnetoconvection. Considering relatively large magnetic Reynolds number and a rapid rotation rate of this model, we believe that these basic ideas used to interpret the present numerical experiment can be applied to the dynamics in the Earth's and other planetary cores.     

Unsteady hydromagnetic flow in an annulus with porous Walls when the inner boundary starts moving from rest

Summary The problem of unsteady hydromagnetic flow in a porous annulus when the inner boundary starts moving from rest with a constant longitudinal velocity is considered. For the case of equal Reynolds number and magnetic Reynolds number Laplace transforms of the solutions for the axial components of velocity and magnetic field are obtained in terms of modified Bessel functions. The inversions are effected for the cases of very large and small Reynolds number when the pressure gradient vanishes.     

A Route to Magnetic Field Reversals: An Example of an ABC-Forced Nonlinear Dynamo

We are investigating numerically the nonlinear behaviour of a space-periodic MHD system with ABC forcing. Most computations are performed for magnetic Reynolds numbers increasing from 0 to 60 and a fixed kinematic Reynolds number, small enough for the trivial solution with a zero magnetic field to be stable to velocity perturbations. At the critical magnetic Reynolds number for the onset of instability of the trivial solution the dominant eigenvalue of the kinematic dynamo problem is real. In agreement with the bifurcation theory new steady states with non-vanishing magnetic field appear in this bifurcation. Subsequent bifurcations are investigated. A regime is detected, where chaotic variations of the magnetic field orientation (analogous to magnetic field reversals) are observed in the temporal evolution of the system.     

A note on short-term core-mantle coupling,geomagnetic secular variation impulses,and potential magnetic field invariants as Lagrangian tracers of core motions

This note summarizes recent studies of atmospheric excitation of short-term changes in the length of the day and polar motion which set useful limits on the timescales associated with angular momentum transfer between the Earth's core and mantle. It also speculates about the nature of the recently-discovered phenomenon of “impulses” or “jerks” in the geomagnetic secular variation, proposing that they might be manifestations of “loop” instability of the magnetic field within the core. Finally, it outlines novel properties of high magnetic Reynolds number flows that bear on the inverse problem of deducing core motions from geomagnetic secular variation data.     

准周期性磁结构的形成过程及其特征的数值分析

在入流马赫数ＭＡ为０．１－０．４范围内，选取不同的入流，逐一考察在可压缩导电介质中磁场重联的类型随磁雷诺数Ｒｍ的变化．大量的数值结果表明：在不同入流驱动下，磁雷诺数（Ｒｍ）均有临界值存在，如果等离子体系统逐渐趋于稳定的单Ｘ线重联；若间歇性的次级撕裂产生了重复出现的磁结构，而且Ｍａ越大产生间歇性次级撕裂的临界值越高，与ＭＡ之间基本上符合线性关系．此外还发现，当多重Ｘ线重联间歇性地出现时，有关物理量发生准周期性地振荡．     

Magnetic Helicity in fast dynamos

The behaviour of magnetic helicity in kinematic dynamos at large magnetic Reynolds number is considered. Hughes, et al . [ Phys. Lett. A 223 , 167-172 (1996)] observe that the relative helicity tends to zero in the limit of large magnetic Reynolds number. This paper gives upper bounds on the helicity, by relating the helicity spectrum to the energy spectrum. These bounds are confirmed by numerical simulation and the distribution of helicity over scales is considered. Although it is found that the total helicity becomes small in the limit of high conductivity, there can remain significant, but cancelling, helicity at large and small scales of the field. This is illustrated by considering the evolution of helicity in the stretch-twist-fold dynamo picture.     

Fluid–particle interaction in turbulent open channel flow with fully-resolved mobile beds

The paper presents Direct Numerical Simulations of an open channel flow laden with spherical particles at a bulk Reynolds number of 2941. The transport of thousands of mobile particles is simulated propagating over a rough bed which consists of immobile particles of the same size in hexagonal ordering. An Immersed Boundary Method is used for the numerical representation of the particles. With 22 points per diameter even the viscous scales of the flow are resolved at this Reynolds number. The reference run contains just as many fixed as mobile particles with a relative density slightly above the nominal threshold of incipient motion. Further runs were conducted with decreased mass loading and decreased Shields number together with a simulation containing only immobile particles. The variation of the parameters defining the mobile sediment yields a strong modification of particle–fluid as well as particle–particle interactions yielding different structures in space and time. This is assessed by means of appropriate statistical quantities addressing the continuous and the disperse phase. The results are in qualitative agreement with experimental observations at higher Reynolds number.     

Alpha-effect in flux ropes and sheets

The alpha-effect is studied at large magnetic Reynolds numbers (R) for certain simple steady flows. The flux sheets created by a two-dimensional cellular flow sustain an of order R^−1/2 at large values of R. For an analogous helical axisymmetric motion the mean electromotive force gives a finite nonzero limit of as R → ∞, this being a consequence of the existence of an intense axial flux rope. The latter estimate may be typical of steady three-dimensional motion.     

Kinematic dynamo induced by helical waves

We investigate numerically the kinematic dynamo induced by the superposition of two helical waves in a periodic box as a simplified model to understand the dynamo action in astronomical bodies. The effects of magnetic Reynolds number, wavenumber and wave frequency on the dynamo action are studied. It is found that this helical-wave dynamo is a slow dynamo. There exists an optimal wavenumber for the dynamo growth rate. A lower wave frequency facilitates the dynamo action and the oscillations of magnetic energy emerge at some particular wave frequencies.     

CALCULATION OF THE TRAJECTORIES AND THE IMPINGING ACTION OF SOLID PARTICLES IN FLOWS AROUND BODIES

Trajectories and impinging action of spherical sand particles moving in the flows around a cylinder and in a plane cascade are calculated. Equations of motion, including more factors pertinent to the motion of particles, are applicable to flows at high particle Reynolds number. Erosion areas predicted from calcula- tion agree well with those from field observation in bydromachines. The results can also be used to estimate the intensity of erosion.     

Dynamos on stream surfaces of a highly conducting fluid

Abstract

This paper discusses dynamo action in generalisations of the Ponomarenko dynamo at large magnetic Reynolds number. The original Ponomarenko dynamo consists of a spiralling flow in which the stream surfaces are concentric cylinders of circular cross section, and the flow depends only on distance from the axis in cylindrical polar coordinates.

In this study, the stream surfaces are allowed to be cylinders of arbitrary cross section, and the flow is only required to be independent of the coordinate along the cylinder axes. For smooth flows alpha and eddy diffusion effects are identified, in terms of the geometry of the stream surfaces, and asymptotic formulae for growth rates in the limit of large magnetic Reynolds number are obtained. Numerical support for these results is presented using direct simulation of dynamo action in selected flows at high conductivity. Finally the case is considered when in spherical polar coordinates the flow is independent of the azimuthal coordinate and the stream surfaces, which are tori, have arbitrary cross sections.     

Fast dynamo action in the Ponomarenko dynamo

Abstract

An analysis of small-scale magnetic fields shows that the Ponomarenko dynamo is a fast dynamo; the maximum growth rate remains of order unity in the limit of large magnetic Reynolds number. Magnetic fields are regenerated by a “stretch-diffuse” mechanism. General smooth axisymmetric velocity fields are also analysed; these give slow dynamo action by the same mechanism.     

Mechanisms for magnetic field generation in precessing cubes

ABSTRACT

It is shown that flows in precessing cubes develop at certain parameters large axisymmetric components in the velocity field which are large enough to either generate magnetic fields by themselves, or to contribute to the dynamo effect if inertial modes are already excited and acting as a dynamo. This effect disappears at small Ekman numbers. The critical magnetic Reynolds number also increases at low Ekman numbers because of turbulence and small-scale structures.     

Opening of the Gulf of Aden and Afar by progressive tearing

A new detailed aeromagnetic survey of the Republic of Djibouti and surrounding area reveals a wealth of new information which can be correlated with other data, in particular geologic and tectonic maps. Oceanic magnetic anomalies are identified from the Gulf of Aden westward to the Ghoubbet-Asal rift in Afar. Identification of the anomalies, together with a reinterpretation of earlier magnetic profiles, indicates that rifting started earlier in the east and provides clear evidence for the westward propagation of a crack through the lithosphere at an approximate velocity of 3 cm y^?1. The crack tip is now thought to lie somewhere close to lake Asal and should continue its motion further to the northwest. Some first consequences of this non-rigid model of plate opening are discussed and independent support from a number of sources is obtained.     

On the magnetic field diffusion in mhd modeling of the inner coma of comet halley

Abstract

Some approaches of one-dimensional time-dependent magneto-hydrodynamic modeling of the structure of the inner coma of comet Halley are considered. The influence of the magnetic field diffusion on this structure is studied. The solution of Cravens (1989) approach containing classic magnetic diffusion is compared with an approach containing a specific diffusion, caused by non-instantaneous mass-loading of new ions. A case with no magnetic field is also considered. Common features of all the solutions are obtained. Special attention is paid to the sharp velocity jump, synchronized with a local density pick. Some differences between two types of magnetic field diffusion are discussed. A possible connection is supposed between this consideration and the large-scale shock fitting modeling of the solar plasma-comet interaction.     

Maximally-efficient-generation approach in the dynamo theory

Abstract

We propose a method of derivation of global asymptotic solutions of the hydromagnetic dynamo problem at large magnetic Reynolds number. The procedure reduces to matching the local asymptotic forms for the magnetic field generated near individual extrema of generation strength. The basis of the proposed method, named here the Maximally-Efficient-Generation Approach (MEGA), is the assertion that properties of global asymptotic solutions of the kinematic dynamo are determined by the distribution of the generation strength near its leading extrema and by the number and distribution of the extrema.

The general method is illustrated by the global asymptotic solution of the α²-dynamo problem in a slab. The nature of oscillatory solutions revealed earlier in numerical simulations and the reasons for the dominance of even magnetic modes in slab geometry are clarified.

Applicability of the asymptotic solutions at moderate values of the asymptotic parameter is also discussed. We confirm this applicability using comparisons with complementary asymptotic expansions and numerical simulations. In particular, this justifies application of the MEGA solutions to estimation of the generation threshold.     

The Karlsruhe Dynamo Experiment. A Mean Field Approach

At the Forschungszentrum Karlsruhe an experiment is in preparation which it is hoped, in view of the geodynamo and other cosmic dynamos, that a homogeneous dynamo will be demonstrated and investigated. This experiment is discussed within the framework of mean-field dynamo theory. Results are presented concerning kinematic cylindrical mean-field dynamo models reflecting some features of the experimental device, as well as results of detailed calculations of the -effect that apply to arbitrarily high magnetic Reynolds numbers. On this basis estimates of the excitation conditions of the dynamo are given and predictions concerning the geometrical structure of the generated magnetic fields are made.     

Reducing the non-axisymmetry of a planetary dynamo and an application to saturn

Abstract

If a conducting fluid shell is undergoing spin-axisymmetric differential rotation and overlies the dynamo generating region of a planet then it is capable of greatly reducing the non-spin-axisymmetric components of the generated field, provided the appropriate magnetic Reynolds number is large. The model, closely related to the electromagnetic skin effect, is quantified and applied to Saturn. The observed small dipole tilt (～ 1°) of Saturn's magnetic field can be explained because of the presence of a stably stratified conducting layer overlying the dynamo region. This layer is a predicted consequence of the thermal evolution, arises because of the limited solubility of helium in metallic hydrogen (Stevenson, 1980), and appears to be required by the Voyager infrared observations indicating depletion of helium from Saturn's atmosphere. The much larger dipole tilt angles of Jupiter and the Earth indicate the absence of any such stable, differentially rotating layer with a large magnetic Reynolds number.     

Dynamo in Asymmetric Square Convection

Linear and nonlinear dynamo action is investigated for square patterns in nonrotating and weakly rotating Boussinesq Rayleigh-Bénard convection in a plane horizontal layer. The square-pattern solutions may or may not be symmetric to up-down reflections. Vertically symmetric solutions correspond to checkerboard patterns. They do not possess a net kinetic helicity and are found to be incapable of kinematic dynamo action at least up to magnetic Reynolds numbers of , 12 000. There also exist vertically asymmetric squares, characterized by rising (descending) motion in the centers and descending (rising) motion near the boundaries, among them such that possess full horizontal square symmetry and others lacking also this symmetry. The flows lacking both the vertical and horizontal symmetries possess kinetic helicity and show kinematic dynamo action even without rotation. The generated magnetic fields are concentrated in vertically oriented filamentary structures. Without rotation these dynamos are, however, always only kinematic, not nonlinear dynamos since the back-reaction of the magnetic field then forces the solution into the basin of attraction of a roll pattern incapable of dynamo action. But with rotation added parameter regions are found where stationary asymmetric squares are also nonlinear dynamos. These nonlinear dynamos are characterized by a subtle balance between the Coriolis and Lorentz forces. In some parameter regions also nonlinear dynamos with flows in the form of oscillating squares or stationary modulated rolls are found.