Kinematic turbulent dynamo in a shear flow

Abstract

We consider the turbulent dynamo action in a differentially rotating flow by making use of a kinematic approach when the effect of a generated magnetic field on turbulent motions is neglected. The mean electromotive force is calculated in a quasilinear approximation. Differential rotation can stretch turbulent magnetic field lines and break the symmetry of turbulence in such a way that turbulent motions become suitable for the generation of a large scale magnetic field. The presence of shear changes the type of an equation governing the mean magnetic field. Due to shear stresses the mean magnetic field can be generated by a turbulent dynamo action even in a uniform turbulence. The growth rate depends on the length scale of the mean field being faster for the field with a smaller length scale.     

Broken ergodicity,magnetic helicity,and the MHD dynamo

We consider an unforced, incompressible, turbulent magnetofluid constrained by concentric inner and outer spherical surfaces. We define a model system in which normal components of the velocity, magnetic field, vorticity, and electric current are zero on the boundaries. This choice allows us to find a set of Galerkin expansion functions that are common to both velocity and magnetic field, as well as vorticity and current. The model dynamical system represents magnetohydrodynamic (MHD) turbulence in a spherical domain and is analyzed by the methods similar to those applied to homogeneous MHD turbulence. We find a statistical theory of ideal (i.e. no dissipation) MHD turbulence analogous to that found in the homogeneous case, including the prediction of coherent structure in the form of a large-scale quasistationary magnetic field. This MHD dynamo depends on broken ergodicity, an effect that is enhanced when total magnetic helicity is increased relative to total energy. When dissipation is added and large scales are only weakly damped, quasiequilibrium may occur for long periods of time, so that the ideal theory is still pertinent on a global scale. Over longer periods of time, the selective decay of energy over magnetic helicity further enhances the effects of broken ergodicity. Thus, broken ergodicity is an essential mechanism and relative magnetic helicity is a critical parameter in this model MHD dynamo theory.     

A Quaternary geomagnetic instability time scale

Reversals and excursions of Earth's geomagnetic field create marker horizons that are readily detected in sedimentary and volcanic rocks worldwide. An accurate and precise chronology of these geomagnetic field instabilities is fundamental to understanding several aspects of Quaternary climate, dynamo processes, and surface processes. For example, stratigraphic correlation between marine sediment and polar ice records of climate change across the cryospheres benefits from a highly resolved record of reversals and excursions. The temporal patterns of dynamo behavior may reflect physical interactions between the molten outer core and the solid inner core or lowermost mantle. These interactions may control reversal frequency and shape the weak magnetic fields that arise during successive dynamo instabilities. Moreover, weakening of the axial dipole during reversals and excursions enhances the production of cosmogenic isotopes that are used in sediment and ice core stratigraphy and surface exposure dating. The Geomagnetic Instability Time Scale (GITS) is based on the direct dating of transitional polarity states in lava flows using the ⁴⁰Ar/³⁹Ar method, in parallel with astrochronologic age models of marine sediments in which oxygen isotope and magnetic records have been obtained. A review of data from Quaternary lava flows and sediments gives rise to a GITS that comprises 10 polarity reversals and 27 excursions that occurred during the past 2.6 million years. Nine of the ten reversals bounding chrons and subchrons are associated with ⁴⁰Ar/³⁹Ar ages of transitionally-magnetized lava flows. The tenth, the Gauss-Matuyama chron boundary, is tightly bracketed by ⁴⁰Ar/³⁹Ar dated ash deposits. Of the 27 well-documented geomagnetic field instabilities manifest as short-lived excursions, 14 occurred during the Matuyama chron and 13 during the Brunhes chron. Nineteen excursions have been dated directly using the ⁴⁰Ar/³⁹Ar method on transitionally-magnetized volcanic rocks and these form the backbone of the GITS. Excursions are clearly not the rare phenomena once thought. Rather, during the Quaternary period, they occur nearly three times as often as full polarity reversals.     

A shell model for a large-scale turbulent dynamo

This article addresses the interesting and important problem of large-scale magnetic field generation in turbulent flows, using a self-consistent dynamo model recently developed. The main idea of this model is to consider the induction equation for the large-scale magnetic field, integrated consistently with the turbulent dynamics at smaller scales described by a magnetohydrodynamic shell model. The questions of dynamo action threshold, magnetic field saturation, magnetic field reversals, nature of the dynamo transition and the changes of small-scale turbulence as a consequence of the dynamo onset are discussed. In particular, the stability curve obtained by the model integration is shown in a very wide range of values of the magnetic Prandtl number not yet accessible by direct numerical simulation but more realistic for natural dynamos. Moreover, from our analysis it is shown that the large-scale dynamo transition displays a hysteretic behaviour and therefore a subcritical nature. The model successfully reproduces magnetic polarity reversals, showing the capability to generate persistence times which are increasing for decreasing magnetic diffusivity. Moreover, when the system reaches a statistically stationary dynamo state, where the large-scale magnetic field can abruptly reverse its polarity (magnetic reversal state) or not, keeping the same polarity (steady state), it shows an unmistakable tendency towards the energy equipartition for the turbulence at small scale.     

From stable dipolar towards reversing numerical dynamos

We are using a three-dimensional convection-driven numerical dynamo model without hyperdiffusivity to study the characteristic structure and time variability of the magnetic field in dependence of the Rayleigh number (Ra) for values up to 40 times supercritical. We also compare a variety of ways to drive the convection and basically find two dynamo regimes. At low Ra, the magnetic field at the surface of the model is dominated by the non-reversing axial dipole component. At high Ra, the dipole part becomes small in comparison to higher multipole components. At transitional values of Ra, the dynamo vacillates between the dipole-dominated and the multipolar regime, which includes excursions and reversals of the dipole axis. We discuss, in particular, one model of chemically driven convection, where for a suitable value of Ra, the mean dipole moment and the temporal evolution of the magnetic field resemble the known properties of the Earth’s field from paleomagnetic data.     

Small-scale magnetic buoyancy and magnetic pumping effects in a turbulent convection

We determine the nonlinear drift velocities of the mean magnetic field and nonlinear turbulent magnetic diffusion in a turbulent convection. We show that the nonlinear drift velocities are caused by three kinds of the inhomogeneities; i.e., inhomogeneous turbulence, the nonuniform fluid density and the nonuniform turbulent heat flux. The inhomogeneous turbulence results in the well-known turbulent diamagnetic and paramagnetic velocities. The nonlinear drift velocities of the mean magnetic field cause the small-scale magnetic buoyancy and magnetic pumping effects in the turbulent convection. These phenomena are different from the large-scale magnetic buoyancy and magnetic pumping effects which are due to the effect of the mean magnetic field on the large-scale density stratified fluid flow. The small-scale magnetic buoyancy and magnetic pumping can be stronger than these large-scale effects when the mean magnetic field is smaller than the equipartition field. We discuss the small-scale magnetic buoyancy and magnetic pumping effects in the context of the solar and stellar turbulent convection. We demonstrate also that the nonlinear turbulent magnetic diffusion in the turbulent convection is anisotropic even for a weak mean magnetic field. In particular, it is enhanced in the radial direction. The magnetic fluctuations due to the small-scale dynamo increase the turbulent magnetic diffusion of the toroidal component of the mean magnetic field, while they do not affect the turbulent magnetic diffusion of the poloidal field.     

Homogeneous planar and two-dimensional mean-field antidynamo theorems with zero mean flow

In an electrically conducting fluid, two types of turbulence with a preferred direction are distinguished: planar turbulence, in which every velocity in the turbulent ensemble of flows has no component in the given direction; and two-dimensional turbulence, in which every velocity in the turbulent ensemble is invariant under translation in the preferred direction. Under the additional assumptions of two-scale and homogeneous turbulence with zero mean flow, the associated magnetohydrodynamic alpha- and beta-effects are derived in the second-order correlation approximation (SOCA) when the electrically conducting fluid occupies all space. Limitations of the SOCA are well known, but alpha- and beta-effects of a turbulent flow are useful in interpreting the dynamo effects of the turbulence. Two antidynamo theorems, which establish necessary conditions for dynamo action, are shown to follow from the special structures of these alpha- and beta-effects. The theorems, which are analogues of the laminar planar velocity and two-dimensional antidynamo theorems, apply to all turbulent ensembles with the prescribed alpha- and beta-effects, not just the planar and two-dimensional ensembles. The mean magnetic field is general in the planar theorem but only two-dimensional in the two-dimensional theorem. The two theorems relax the previous restriction to turbulence which is both two-dimensional and planar. The laminar theorems imply decay of the total magnetic field for any velocity of the associated turbulent ensemble. However, the mean-field theorems are not fully consistent with the laminar theorems because further conditions beyond those arising from the turbulence must be imposed on the beta-effect to establish decay of the mean magnetic field. In particular, negative turbulent magnetic diffusivities must be restricted. It is interesting that there is no inconsistency in the alpha-effects. The failure of the SOCA with the two-scale approximation to simply preserve the laminar antidynamo theorems at the beta-effect level is a further demonstration of the restricted validity of the theory and shows that negative diffusivity effects derived by approximation methods must be treated cautiously.     

Sq发电机电流的逐日变化和Sq指数

用中国地磁台站的资料,研究了S_q逐日变化的形态学特征,用理论模型计算了磁层环电流、部分环电流、场向电流、磁尾电流、Chapman-Ferraro电流的地磁效应.在消除了这些磁层电流体系的影响之后,得到了电离层潮汐风发电机电流产生的磁场S_q变化.对1973年的资料研究表明,S_q发电机电流的逐日变化主要表现在强度上,即使在磁扰期间,也可以分离出形态稳定的S_q变化.由此提出了一种新的地磁指数--S_q指数,用来描述S_q发电机电流强度的逐日变化.     

The initial temporal evolution of a feedback dynamo for Mercury

Various possibilities are currently under discussion to explain the observed weakness of the intrinsic magnetic field of planet Mercury. One of the possible dynamo scenarios is a dynamo with feedback from the magnetosphere. Due to its weak magnetic field, Mercury exhibits a small magnetosphere whose subsolar magnetopause distance is only about 1.7 Hermean radii. We consider the magnetic field due to magnetopause currents in the dynamo region. Since the external field of magnetospheric origin is antiparallel to the dipole component of the dynamo field, a negative feedback results. For an αΩ-dynamo, two stationary solutions of such a feedback dynamo emerge: one with a weak and the other with a strong magnetic field. The question, however, is how these solutions can be realized. To address this problem, we discuss various scenarios for a simple dynamo model and the conditions under which a steady weak magnetic field can be reached. We find that the feedback mechanism quenches the overall field to a low value of about 100–150 nT if the dynamo is not driven too strongly.     

南海南部约80ka以来的古地磁记录

晚更新世以来以一系列地磁漂移事件是区域地层对比和确定沉积物年代框架的重要工具.但是在海相沉积物中,识别这些地磁漂移事件多依赖相对磁场强度(RPI)的变化,在地磁方向异常方面鲜有报到,从而影响对这些事件可靠性的讨论.本文选择南海南部巽他陆架附近重力活塞钻孔BKAS2PC的沉积物,进行系统的岩石磁学和古地磁研究,获得该钻孔沉积记录的RPI和磁倾角变化信息.岩石磁学及扫描电镜结果表明沉积物的原生主要载磁矿物为单畴(SD)和假单畴(PSD)钛磁铁矿.在一些层位,沉积后发生的还原作用形成胶黄铁矿等铁硫化物.磁性矿物的浓度和粒度等参数呈现显著的两阶段变化特征,上部(约220 cm以上)含量低而粒度细,下部含量高但粒度相对较粗,整体上均在一个数量级范围内波动.样品的交变退磁特征显示当交变场超过60 mT时,受胶黄铁矿影响产生旋转磁化,剩磁强度反而上升.因此,在20～60 mT之间确定原生特征剩磁,并把RPI定义为NRM_((20-40)mT)/ARM_((20-40)mT).通过~(14)C限定,并与其他有良好年代控制的相对磁场强度曲线进行对比,建立了钻孔的年代框架.结果显示,钻孔沉积物记录了几次显著的地磁漂移事件,这为联合应用RPI与磁场方向异常构建海相沉积物年代学框架提供了新的依据.     

Numerical simulations of MHD dynamos

The generation of magnetic fields in space plasmas and in astrophysics is usually described within the framework of magnetohydrodynamics. Turbulent helical flows produce magnetic fields very efficiently, with correlation length scales larger than those characterizing the flow. Within the context of the solar magnetic cycle, a turbulent dynamo is responsible for the so-called alpha effect, while the Omega effect is associated to the differential rotation of the Sun.We present direct numerical simulations of turbulent magnetohydrodynamic dynamos including two-fluid effects such as the Hall current. More specifically, we study the evolution of an initially weak and small-scale magnetic field in a system maintained in a stationary regime of hydrodynamic turbulence, and explore the conditions for exponential growth of the magnetic energy. In all the cases considered, we find that the dynamo saturates at the equipartition level between kinetic and magnetic energy, and the total energy reaches a Kolmogorov power spectrum.     

S_q发电机电流的逐日变化和S_q指数

用中国地磁台站的资料,研究了S_q逐日变化的形态学特征,用理论模型计算了磁层环电流、部分环电流、场向电流、磁尾电流、Chapman-Ferraro电流的地磁效应.在消除了这些磁层电流体系的影响之后,得到了电离层潮汐风发电机电流产生的磁场S_q变化.对1973年的资料研究表明,S_q发电机电流的逐日变化主要表现在强度上,即使在磁扰期间,也可以分离出形态稳定的S_q变化.由此提出了一种新的地磁指数——S_q指数,用来描述S_q发电机电流强度的逐日变化.     

Grain size dependent potential for self generation of magnetic anomalies on Mars via thermoremanent magnetic acquisition and magnetic interaction of hematite and magnetite

Early in the history of planetary evolution portions of Martian crust became magnetized by dynamo-generated magnetic field. A lateral distribution of the secondary magnetic field generated by crustal remanent sources containing magnetic carriers of certain grain size and mineralogy is able to produce an ambient magnetic field of larger intensity than preexisting dynamo. This ambient field is capable of magnetizing portions of deeper crust that cools through its blocking temperatures in an absence of dynamo. We consider both magnetite (Fe₃O₄) and hematite (α-Fe₂O₃) as minerals contributing to the overall magnetization. Analysis of magnetization of magnetic minerals of various grain size and concentration reveals that magnetite grains less than 0.01 mm in size, and hematite grains larger than 0.01 mm in size can become effective magnetic source capable of magnetizing magnetic minerals contained in surrounding volume. Preexisting crustal remanence (for example ∼250 A/m relates to 25% of multi-domain hematite) can trigger a self-magnetizing process that can continue in the absence of magnetic dynamo and continue strengthening and/or weakening magnetic anomalies on Mars. Thickness of the primary magnetic layer and concentration of magnetic carriers allow specification of the temperature gradient required to trigger a self-magnetization process.     

The weak taylor state in an αω-dynamo

Abstract

A spherical αω-dynamo is studied for small values of the viscous coupling parameter ε ～ v^1/2, paying attention particularly to large dynamo numbers. The present study is a follow-up of the work by Hollerbach et al. (1992) with their choice of α-effect and Archimedean wind including also the constraint of magnetic field symmetry (or antisymmetry) due to equatorial plane. The magnetic field scaled by ε^1/2 is independent of ε in the solutions for dynamo numbers smaller than a certain value of D _b (the Ekman state) which are represented by dynamo waves running from pole to equator or vice-versa. However, for dynamo numbers larger than D _b the solution bifurcates and subsequently becomes dependent on ε. The bifurcation is a consequence of a crucial role of the meridional convection in the mechanism of magnetic field generation. Calculations suggest that the bifurcation appears near dynamo number about 33500 and the solutions for larger dynamo numbers and ε = 0 become unstable and fail, while the solutions for small but non-zero ε are characterized by cylindrical layers of local maximum of magnetic field and sharp changes of geostrophic velocity. Our theoretical analysis allows us to conclude that our solution does not take the form of the usual Taylor state, where the Taylor constraint should be satisfied due to the special structure of magnetic field. We rather obtained the solution in the form of a “weak” Taylor state, where the Taylor constraint is satisfied partly due to the amplitude of the magnetic field and partly due to its structure. Calculations suggest that the roles of amplitude and structure are roughly fifty-fifty in our “weak” Taylor state solution and thus they can be called a Semi-Taylor state. Simple estimates show that also Ekman state solutions can be applicable in the geodynamo context.     

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.     

Toroidal flux oscillation as possible cause of geomagnetic excursions and reversals

It is proposed that convection driven dynamos operating in planetary cores could be oscillatory even when the oscillations are not directly noticeable from the outside. Examples of dynamo simulations are pointed out that exhibit oscillations in the structure of the azimuthally averaged toroidal magnetic flux while the mean poloidal field shows only variations in its amplitude. In the case of the geomagnetic field, global excursions may be associated with these oscillations. Long period dynamo simulations indicate that the oscillations may cause reversals once in a while. No special attempt has been made to use most realistic parameter values. Nevertheless some similarities between the simulations and the paleomagnetic record can be pointed out.     

Energy geodynamo parameters compatible with analytical,numerical, paleomagnetic models and observations

A hydromagnetic dynamo is only possible at a sufficiently powerful convection. In the Earth’s core, it is probably the nonthermal convection very much in excess of its critical level with the molecular transporr coefficients. However, in the case of medium- or large-scale fields, the critical energy level caused by the turbulent tranport coefficients is likely to be slightly below the actual level. This probably explains both the 22-year success of this type of simplified geodynamo models and the energy scaling laws for hydromagnetic fields, which generalize these models. Also the review of energy-dependent analytical and observational estimates of vortex fields, hydromagnetic scale sizes, and velocities in the core is presented. These typical parameters are partly in a new way linked to the observed and more ancient magnetic variations. New, albeit, simplified and self-evident, substantiation is given to the paleomagnetic hypothesis about the predominance of the axial dipole under a certain time averaging. In (Pozzo et al., 2012) and more recent works, it is shown that the adiabatic heat flow and electrical conductivity in the Earth’s core are severalfold higher than the generally accepted estimates. Here, the dynamo supporting Braginsky’s convection (Braginsky, 1963) (under the crystallization of the heavy fraction of a liquid onto the solid core) started less than 1 Ga ago, whereas the more ancient geodynamo was supported by the compositional convection of another type. The known mechanisms implementing this convection, which differ by the scenarios of magnetic evolution, are reviewed. This may help identify the sought mechanism through the most ancient paleomagnetic estimates of the field’s intensity and through the numerical models. The probable mechanisms of generation and their absence for the primordial and recent magnetic field of the studied terrestrial planets are discussed.     

Past and present magnetism of the Moon

The characteristics of the remanent magnetism of lunar samples suggests that it was acquired in a magnetic field on the Moon. The most likely origin of the field is a dynamo process in a molten, electricallyconducting core, but generation of a transient magnetic field during large meteorite impacts cannot be entirely ruled out. The magnetizing process may be thermoremanence, acquired when the rocks cooled through, the Curie point of the constituent iron grains which carry the remanent magnetization, or it may involve shock at the time of a meteorite impact, with or without a partial thermoremanence arising from heating.Evidence from absolute and relative determinations of the ancient field strength from the sample magnetizations strongly favours a global lunar field. This is implied by a trend which shows the field rising to a maximum value of 100 T between about 3.9–3.7 by ago and then decaying to 5–10 T until3.1 by. Such a systematic variation of field with time is not expected to be derived from magnetizations acquired in transient, impact-generated fields varying randomly in intensity.Contributory evidence for a dynamo field is provided by measurements of present lunar surface fields, the present very small dipole moment of the Moon and accumulating evidence of variation of the axis of the lunar field with time. Although there is no direct evidence for the existence of a lunar core the relevant observations are consistent with the presence of a core of up to 400 km, in radius. There are some difficulties associated with the lunar dynamo mechanism and its energy source but the evidence for a lunar dynamo is accumulating, with important implications for the structure and thermal history of the Moon.     

Impact of the geomagnetic field and solar radiation on climate change

Recent studies have shown that, in addition to the role of solar variability, past climate changes may have been connected with variations in the Earth??s magnetic field elements at various timescales. An analysis of variations in geomagnetic field elements, such as field intensity, reversals, and excursions, allowed us to establish a link between climate changes at various timescales over the last millennia. Of particular interest are sharp changes in the geomagnetic field intensity and short reversals of the magnetic poles (excursions). The beginning and termination of the examined geomagnetic excursions can be attributed to periods of climate change. In this study, we analyzed the possible link between short-term geomagnetic variability (jerks) and climate change, as well as the accelerated drift of the north magnetic pole and surface temperature variations. The results do not rule out the possibility that geomagnetic field variations which modulate the cosmic ray flux could have played a major role in climate change in addition to previously induced by solar radiation.