zotero/storage/P8U8DFJ2/.zotero-ft-cache

REVIEWS OF GEOPHYSICS, SUPPLEMENT, PAGES 443-450, JULY 1995 U.S. NATIONAL REPORT TO INTERNATIONAL UNION OF GEODESY AND GEOPHYSICS 1991-1994

Dynamics of the core, geodynamo
Paul H. Roberts
Institute of Geophysics and Planetary Physics, University of California. Los Angeles

1. Introduction

standing affiliations with US Institutions. US theoreti­

cians have played a major role in elucidating fast dy­

T h e mechanism for generating the geomagnetic field namos, which amplify fields on the same time scales as

remains one of the central unsolved problems in geo­ the flows. In contrast, slow dynamos act on a diffusive

science." So states the report on the National Geo­ timescale, based on the magnetic diffusivity, n, of the

magnetic Initiative (NGI) prepared by the U.S. Geo- conductor. Interestingly, McFadden and Merrill [1993]

dynamics Committee, et al [1993], with advice from have recently derived 17 ~ 1 m 2 s"1 from the paleomag­

the NGI Workshop held in Washington D.C. in March netic data, but we shall take n = 3 m2 s""1. The diffu­

1992. All analyses of the geomagnetic data point to the sive time scale of the core is therefore about 104 years,

core as containing the source of the field and "The ba­ and the geodynamo problem is to understand how the

sic premise that virtually everyone accepts is that the geomagneticfieldis maintained over times that are sub­

Earth's magnetism is created by a self-sustaining dy­ stantially longer than this. Fast dynamo theory has no

namo driven by fluid motions in Earth's core" (NGI, obvious contributions to make, and will therefore not

p.135). Dynamical questions at once arise, such as be considered here. The core is a slow dynamo.

"What is the energy source driving those motions?" Ja­

cobs [1953] proposed that the solid inner core (SIC) is 2. C o r e D y n a m i c s ( M i c r o s c a l e )
the result of the freezing of the fluid outer core (FOC).

Verhoogen [1961] noticed that the release of latent heat

at the inner core boundary (ICB) during freezing would There has been increasing interest in the role played

help drive thermal convection in the FOC, and Bragin­ by small-scale motions in transporting and mixing ther­

sky [1963] pointed out that the release of the light al­ mal and chemical inhomogeneities in the core. When

loying elements during fractionation at the ICB would the heavy constituents (mainly Fe) of core fluid freeze

provide compositional buoyancy. These two sources suf­ onto the ICB, latent heat and the light constituents are

fice to supply the geodynamo with energy throughout released. Moffatt [1989] proposed that this light, hot

geological time, even in the absence of dissolved radioac­ fluid would congregate into "blobs" at the ICB that

tivity in the core [Braginsky and Roberts, 1994a; Kuang would, when large enough, break away from the ICB

et al, 1994]. Stevenson [1991] argues that potential dif­ and rise through the core, stirring it as it did so, and

ferences on the core-mantle boundary (CMB) of elec­ possibly retaining their identity until they reach the

trochemical origin may be partially responsible for the CMB, where some may remain to form a light layer

geomagnetic field.

(see §4 below). This idea has been pursued by Ruan

Whatever the driving mechanism, it is clear that the and Loper [1993], Loper and Moffatt [1993] and Moffatt

magnetohydrodynamics (MHD) of the core must be un­ derstood. This has proved to be a challenging task;

and Loper [1994]; see also Bush et al [1992,1994], Loper
et al [1994]

progress has been slow. The directional property of Braginsky and Meytlis [1990] argued that core tur­

the magnetic compass needle demonstrates that Corio- bulence is totally unlike classical turbulence of Kol-

lis forces play an essential role. Because the molecular mogoroff type, in which energy 'cascades' from large

diffusivities of heat and composition are so small, these to small eddies. Nor is it related to classical MHD tur­

sources of buoyancy must instead be transported across bulence, where a reverse cascade may create large-scale

the core by turbulence. The phenomena of interest arise magnetic fields by turbulent dynamo action, possibly

from slight deviations in the FOC from a well-mixed through a turbulent a-effect. [The a-effect is the cre­

adiabatic state, and theory must consistently disentan­ ation of a mean electromotive force (emf) parallel to the

gle these from the large "background." In short, it is far mean magnetic field.] They argue that the microscale

from obvious what equations best describe large scale fields are so tiny that they produce neither a significant

core MHD [Braginsky and Roberts, 1994a].

turbulent or—effect, nor an enhancement in the mean

We shall concentrate below on the research of U S field diffusivity. Nevertheless, the turbulent diffusivi­

scientists, even when it was carried out abroad. We ties of the mean thermal and chemical inhomogeneities

shall add the work of foreign scientists who have long are enormously greater than their molecular counter­

parts, at least in some directions. Because of the strong

influence of Coriolis and Lorentz forces on motions of

Copyright 1995 by the American Geophysical Union.

all scales, the turbulence is highly anisotropic, forming

'plate-like' eddies that have their long dimensions par­

Paper number 95RG00735.

allel to the rotation axis (Oz) and to the mainly zonal

8755-1209/95/95RG-00735$15.00

(^—)direction of the prevailing toroidalfield;the short

443

444

ROBERTS: DYNAMICS OF THE CORE, GEODYNAMO

dimension is in the s—direction, away from the rotation larity reversal mechanism. Some MC instabilities are of

axis. Turbulent diffusion is represented by one tensor, short time scale, of the order of 103 years. These are the

the same for both heat and composition. The elements so-called ideal instabilities, where "ideal" refers to the

of that tensor corresponding to diffusion in the z and fact that, unlike the so-called resistive instabilities, they

<j> directions are large, of the same order as the molec­ do not rely on the finite resisitivity of the fluid. Ideal

ular magnetic diffusivity, 17; turbulent diffusion in the and resistive instabilities are the counterparts of sim­

s—direction is comparatively weak. Braginsky-Meytlis ilar instabilities that arise in laboratory plasmas but,

theory has recently been taken further by Braginsky and because of the importance of Coriolis forces in the core,

Roberts [1994a]; it still contains ad hoc elements.

they evolve there on longer time scales (see above).

It is the highly dispersive character of rotating flu­ London [1992a, b] examined MC waves and instabili­

ids that led to this unusual picture of core turbulence. ties, supposing that the prevailing magnetic field, B, is

The effect of that dispersion on the Moffatt mecha­ zonal and proportional in strength to distance, s, from

nism has recently been studied by St Pierre [1994a, the rotation axis, Oz. Assuming a geostrophic dynam­

b] who argues, on the basis of computer simulations, ical balance of the kind used in atmospheric dynamics,

that a blob released at the ICB will be stretched, lami­ he developed a uniform approximation for waves that

nated in plates, and absorbed into its surroundings be­ have a short wavelength in the s—direction, i.e. away

fore it can rise far into the FOC; see also St Pierre from the rotation axis. He showed [London, 1992b] that

and Roberts [1994]. It is difficult in the laboratory to these waves propagate in a westward direction. In a

mimic core conditions in which the effective diffusivities later work [London, 1993], he generalized to other zonal

of heat and composition are (see above) the same. Ex­ fields; see also London [1994].

periments have however been performed by Cardin and Stablefieldconfigurations may become unstable when

Olson [1992].

the fluid is top heavy, and there is much interest there­

fore in MAC waves and instabilities, where the added

3. Core Dynamics (Macroscale)

'A* stands for Mrchimedean' (i.e. buoyancy) forces. Simple examples of MC and MAC instabilities have

Nearly all existing models of the geodynamo are ax­ isymmetric. Since the axisymmetric part of the ge­ omagnetic field cannot, according to Cowling's theo­ rem, be self-maintained, the emf created by the nonaxisymmetric components of fluid flow and magnetic field must be retained. For simplicity, it is usually parameterized by an a—effect. Since turbulent induc­ tion is unimportant (see §2), the a—effect is created by asymmetric waves/instabilities of global scale. Recent work on axisymmetric geodynamo models is reported in §5 below; here we describe studies of waves/instabilities.
Viewed from the inertial frame, a contained rotat­ ing fluid is filled with vortex lines parallel to the ro­ tation axis that impart the "elasticity" that inertial waves require. In a non-rotating electrically conducting fluid, the "elasticity" of the lines of force of the pre­ vailing magnetic field is responsible for Alfven waves. In a rapidly rotating conductor, the Alfven and inertial waves are replaced by 'fast* and 'slow' waves. The for­ mer resemble the inertial waves and have a timescale of the order of a day; the latter act on timescales of order r8 = 2QjAopR2/B%1 where Q « 7 x 10"5s""1 is the angu­ lar velocity of Earth, fio « 4w x 10"7H m"1 is the mag­

been analyzed by Kuang and Roberts [1991,1992], Lan,
Kuang and Roberts [1993]. Fearn and Kuang [1994] and
Kuang [1994] stress the importance of the conductivity of the boundaries on the instabilities.
Bergman and Madden [1993] studied core convection, paying particular attention to the steady mean poloidal circulation in the core, for which they argued equato­ rial upwelling would occur. Such a circulation has a profound effect on the functioning of an ocu—dynamo; see §5. Compositional buoyancy is important for driv­ ing core convection in the considerations of Kuang et al [1994], and Bergman et al [1994]. The surface of the inner core is probably constitutionally supercooled, so that a mushy layer exists there. If no magnetic field is present, chimneys form in such a layer through which the light fluid, released during fractionation inside the layer, is ejected into the FOC. Bergman et al investi­ gate how this mechanism is affected by the prevailing magnetic field.
For simplicity, many investigations of core dynamics and the geodynamo ignore the SIC, by assuming that the entire core is fluid. At first sight, this unrealism seems not too serious: the SIC is only 4% of the vol­ ume of the core and 5% of its mass. Nevertheless, the

netic permeability, p « 104kg m~3 is the core density, SIC may have a disproportionate effect on core flows

R « 3.5 x 106m is the radius of the core and B<f> is a char­ and field generation. It has long been known [Stewart-

acteristic strength of the (zonal) field. If B<f, « 30mT, son, 1966] that, because of the rapid rotation of Earth,

TS « 750years, which is similar to timescales observed differential rotation between inner core and mantle, in a

in the secular variation.

non-magnetic core, exerts a profound influence on the

Slow waves are sometimes called 'MC waves', because dynamics of the FOC. Ruzmaikin [1993] and Holler-

the primary dynamical balance is between Magnetic bach [1993] pointed out that the same is likely to be

and Cbriolis forces. In some circumstances MC waves become MC instabilities; these are much studied in the hope of deriving constraints on the structure and strength of the field in the core. It has also been argued that MC instabilities play a significant role in the po­

true in corresponding MHD situations. The dynamics of the FOC has a different character inside and outside the tangent cylinder (TC), that is the circular cylinder drawn around the rotation axis and tangent to the SIC at its equator. As Stewartson showed, the TC is itself

ROBERTS: DYNAMICS OF THE CORE, GEODYNAMO

445

surrounded by a thin "shear layer" in which the flows and especially topographic coupling, mechanisms. Their

inside and outside the T C adjust themselves to one an­ reductio ad absurdum argument is based on an inverse

other. Hollerbach [1993] showed how an axisymmetric problem: assuming that core-mantle coupling is elec­

magnetic field alters the structure of this layer. Holler- tromagnetic, they seek the time-varying toroidal field,

hack and Proctor [1993] observed that the significance of BT(R)> at the CMB that creates an electromagnetic

the T C and its adjustment layer may be even greater for torque that best fits the length of day data. They make

the asymmetricfields;see also Hollerbach [1994]. Glatz­ three demands which they find cannot be simultane­

maier and Olson [1993] studied non-magnetic convec­ ously met: (a) Br(R) does not exceed the upper limit

tion in a rotating sphere and showed that the amplitude provided by dynamo theory (see also Levy and Pearce

of the convective motions is greatest outside the TC; see [1991] who argue that B T ( R ) is less than lOmT, and

also Cardin and Olson [1994a]. In contrast, for the cor­ is probably less than lmT), (b) the poloidal electric

responding MHD situation, where a zonal magnetic field currents which generate that toroidal field and which

was imposed, Olson and Glatzmaier [1993, 1994] and leak into the mantle do not exceed bounds on the elec­

Glatzmaier and Olson [1994] found that the convection tricfieldinferred from measurements at Earth's surface

was strongest inside the TC, the Taylor columns outside [Lanzerotti et al, 1992, 1993, 1994], (c) the ohmic dis­

that cylinder being suppressed by the Lorentz force; see sipation in the mantle caused by those currents does

also Jones et al [1994], Cardixt and Olson [1994b] and not exceed the heat flux from the Earth. They con­

§5 below.

clude that magnetic stresses cannot be the main factor

in core-mantle coupling. Their treatment offluxdiffu­

4. Effects of t h e M a n t l e o n C o r e M H D

sion in the analysis leading to their conclusion merits further study. Love and Bloxham [1994b] have recently

proposed a second application of their idea.

The core is only one component of the coupled core- Diffusion offluxplays an important role in the study

mantle system. Each component profoundly affects, of Braginsky and Le Mouel [1993], who are particularly

and is affected by, the other. Strictly, the core cannot interested in the inductive effects of high shears in a

be considered in isolation from the mantle but, when it "A—layer" at the top of the core. Kuang and Bloxham

is, the mantle is replaced by a set of conditions on the [1993] analyze how magnetic field in the upper core af­

CMB. The resulting theoretical simplification is enor­ fects topographic core-mantle coupling. Theyfindthat

mous, but sometimes is an over-simplification. In par­ the field may change the strength of the coupling by

ticular, to suppose that the form, and the physical state, of the CMB are uniform in space and unvarying in time is simplistic. Larson and Olson [1991] argue that vari­

several orders of magnitude but, for parameters appro­ priate to the core, the stress is of order 10~1N m~2,

ations in the convective regime in the mantle, and in which is adequate to account for the decadal variations

particular the changing configuration of mantle plumes, in Earth's rotation. Angular momentum exchange be­

control the rate of geomagnetic field reversals. It has tween core and mantle is also discussed by Bloxham and

recently been realized that lateral variations in the tem­ Kuang [1994].

perature of the CMB will have a strong effect on core Malkus has long urged that precessional driving of

motions and therefore on core-mantle coupling; see Sun the core is an important and, possibly, the dominant et al [1994]. A new type of geodynamo is also possible; source of energy for core motions and the geodynamo;

see §5. In this section we shall ignore lateral variations e.g. see Malkus [1994]. Interest in this idea has been

on the CMB, apart from topography.

revitalized by the discovery that flows with elliptical

The assumption (§1) of an adiabatic well-mixed core streamlines, somewhat similar to flows driven by the

becomes suspect near the CMB, and several authors luni-solar precession, are unstable. Malkus has pro­

have argued that a layer of comparatively light fluid vided experimental demonstrations of the instability in

exists adjacent to the CMB. Braginsky [1993] has chris­ an elliptically distorted cylinder of fluid. Experiments

tened this "the hidden ocean of the core" and has ar­ have also been performed by Vanyo [1991], Vanyo et

gued that waves propagating in this stable layer may be al [1992, 1994b] and Wilde and V anyo [1994]; see also

partially responsible for the short period geomagnetic Vanyo et al [1994a], Vanyo and Lods [1994]. So far,

secular variation. It may also strongly affect core-man­ all studies have been non-magnetic, but it is hoped

tle coupling, particularly topographic coupling. Waves that they will provide stepping stones to the corre­

in a stratified layer at the top of the core have been sponding MHD situations. The a—effect created by

studied by Bergman [1993], who developed a theory of precessionally-driven flows has already been estimated

magnetic Rossby waves based on a generalization of by Barenghi et al [1994]. The effects of the SIC on the

Laplace's tidal equation in which the Lorentz force is forced nutation of the Earth have been studied theoret­

included and the induction equation is added. He also ically, and the results have been compared with obser­

developed /?—plane solutions analytically and showed vational data by Mathews et al [1991a, b] and Herring

that the magneticfieldcan release equatorially trapped et al [1991]. Cognate issues are analyzed by de Vries

Rossby waves.

and Wahr [1991].

Love and Bloxham [1994a] have recently investigated The exchange of the z—component of angular mo­

a new idea which may lead to the abandonment of mag­ mentum between core and mantle is accomplished via

netic core-mantle coupling in comparison with other, geostrophic motions in the core; these are zonal flows

446

ROBERTS: DYNAMICS OF THE CORE, GEODYNAMO

that depend only on distance s from the rotation axis, therefore be strong. It used to be said that an appeal to

Oz, and on time t. By analyzing the field extrapolated an invisible zonal field is a return to armchair science,

downwards to the CMB, Jault and Le Mouel [1988] esti­ but galaxies are transparent to observation. Their fields

mated the geostrophicflowin the recent past and could are predominantly toroidal and seem to be produced by

therefore monitor the angular momentum of the core an aw—mechanism; see §7 of Krause et al [1993]. It is

as a function of time. They showed that its variations in principle possible to detect a zonal field in Earth's

are roughly equal but opposite to those of the angular core through the electric fields it creates outside the

momentum of the mantle over the same period, as deter­ core, in particular the potential difference between the

mined by changes in the length of day; the net angular two ends of a trans-oceanic cable [Lanzerotti et al, 1992,

momentum of the core-mantle system as a whole is con­ 1993, 1994]. In practice, the obscuring, long period, in­

stant. Jackson ei al [1993] have developed this theme ductive effects of ocean currents have so far prevented a

and have used their analysis of the core geostrophic flow convincing demonstration [Runcorn and Winch, 1991).

to predict, with encouraging results, variations in the The axisymmetric force balance in an MHD dynamo

length of day.

is not easily understood. Many studies of 2D "inter­

mediate" dynamo models have been launched to elu­

5. G e o d y n a m o Modeling

cidate it. These are so named because, while they do not address the full MHD problem, they take a

Dynamo models that solve the induction equation alone are called 'kinematic', and several such geodynamos models have been integrated. The main chal­ lenge today is to solve the fully dynamic dynamo prob­ lem, sometimes also called 'the MHD dynamo problem' or 'the fully self-consistent dynamo problem', in which the induction equation is solved and the equation of motion for the fluid. This nonlinear problem raises formidable difficulties. Because of Cowling's theorem, a true MHD dynamo model should be 3D, but a super­

step beyond kinematic models. An a—source is in­

voked to maintain the axisymmetric field. Whether an

a2—, a w - or a2w—dynamo results depends on the dy­

namical balance. In an a2—dynamo the primary bal­

ance is geostrophic, i.e. between Coriolis and pressure

forces; the magneticfieldstrength, B, is determined by

a secondary balance, e.g. between the Lorentz and vis­

cous forces, which gives B ~ (fiopi/rj)1/2/R)

where v

is core viscosity. In a strong field dynamo, the mag­

netic field plays a role in the primary balance and

computer is then required to integrate it numerically. therefore B = ^(B^BM)

~ (2f2f7/i0/?)1/2 ~ 2.4mT,

Axisymmetric (2D) models can be solved on worksta­ a relation confirmed by Benton [1992]. Benton ar­

tions, but the magnetic field will decay to zero unless gued further that a typical zonal flow velocity would

the emf generated by the omitted asymmetricfieldsand be (2Qn2/R)1/3

- 7 x 10"*4m s""1, which is similar to

flows is reintroduced in some way, through an a—effect. the speed with which some features of the geomagnetic

Axisymmetric a—effect models are of two extreme field drift westward.

types, a2— and aw—dynamos, together with a range St. Pierre [1993b] demonstrated that, when a strong

of a2w—models between them. In an a2—model, zonal field branch exists, weak field solutions are likely to be

field creates meridional field and vice versa; in an aw- nonlinearly unstable. Although his plane layer model is

model, the a-effect creates meridional field from zonal geometrically too simple to represent the geodynamo,

field, but the zonalfieldis created by an w—effect, i.e. by it is a convective MHD dynamo of similar physical

the inductive effects of zonal shearing motions. Some­ type. It clearly demonstrates the existence of a strong

times aw—models are called "strong field dynamos" field branch, one that also operates subcritically, i.e. at

since the zonal field, which is locked inside the con­ smaller thermal forcing than that at which kinematic

ductor, is large compared with the observed merid­ dynamo action is first possible. The model of St. Pierre

ional field, in contrast to the "weak field" dynamos is fully 3D, as is the spherical 3D model of Glatzmaier

of a2—type where the strength, BM , of the meridional and Roberts [1994] described below.

field is characteristic of the strength of the entire field. The axisymmetric force balance in intermediate mod­

A strong field dynamo functions only if the product of els is so dominated by magnetic and Coriolis forces that

a and w, as measured by the so-called "dynamo num­ inertial forces are often omitted. One of two extreme

ber" , D, exceeds in magnitude a certain marginal value, scenarios arise, or perhaps some intermediate scenario.

D M ; for an a2—model to function the a—effect magnetic At one extreme is the model—Z state [Braginsky, 1975, Reynolds number, Ra, a dimensionless measure of a, 1991,1994] which relies on the coupling of core to man­ must be large enough. While a2—dynamos are usually tle and in which the geostrophic motions in the core

steady, aw—dynamos tend to be oscillatory, but they are large. At the other extreme is the Taylor state

too may become steady, and more efficient (as judged [Taylor, 1963] in which core-mantle coupling is insignif­

by a smaller value of D M ) , when a sufficiently strong icant, but in which a certain integral demand (the Tay­ meridional flow is present. Meridionalflowis produced lor constraint) must be satisfied. Sometimes models of

by Lorentz forces or by core-mantle coupling; see also either type can exist under the same conditions of exci­

Bergman and Madden [1993].

tation. Model—Z is energetically the more expensive to

Zonal shearing motion is comparatively easily excited run, because of core-mantle friction, and the external

in rotatingfluids,for example by pole-equator temper­ fields it produces therefore tend to be smaller than in

ature differences; the w—effect and the zonal field may the corresponding Taylor-type model. There are there-

ROBERTS: DYNAMICS OF THE CORE, GEODYNAMO

447

fore two contenders for the geodynamo, a strong field of anisotropic aw—models; see also Kono and Roberts

(model—Z) mechanism and a very strong field (Taylor- [1994]. A general method for solving weakfieldMHD

type) mechanism. In trying to decide between these, models when conditions for kinematic dynamo action

it is usually supposed for simplicity that core-mantle are only marginally exceeded, has been explored by

coupling is viscous — it is the existence of this cou­ Kono and Roberts [1991, 1992].

pling rather than its precise nature that is significant. Lateral variations in the temperature of the CMB

St. Pierre [1993a] has examined the stability of Taylor bring about concomitant changes in the electrical con­

states.

ductivity of the lower mantle so that new current paths

This then is the background against which much of are allowed and old ones forbidden. The axisymmetry

the recent work on intermediate geodynamos may be assumed in most geodynamo modeling is destroyed and

viewed. Hollerbach and Ierley [1991] analyzed an in­ with it the applicability of Cowling's theorem [Busse,

termediate dynamo of a2—type and showed that, as 1992]]. A zonal shear can readily create zonal magnetic

Ra exceeds its marginal value, Ram > the solution is at field from meridional field through the w—effect, but first viscously controlled. As Ra is further increased, a it is incapable, in an axisymmetric system, of creating second critical value, iZaT, is reached at which Taylor meridional field from zonal field. This, however, is no states appear. When Hollerbach et al [1992] carried longer true when longitudinal inhomogeneities destroy

out a parallel study for an aw—model, they uncovered the axial symmetry. A zonal shear can then produce

a more complex situation. Despite very simple choices zonal field from meridional field and vice versa. This

of a and ut they found that, as the dynamo number D fact enabled Busse and Wicht [1991] and Wicht and increases beyond D m , the solution is at first viscously Busse [1993] to construct new, simple models of dy­ controlled but that, as D increases through a second namo action that make use of the broken symmetry

critical value DXi oscillations arise in which the Taylor and which work through zonal shear alone. balance is struck during part of each cycle but in which An unusual approach to the geodynamo problem was

viscous coupling is essential during the remainder.

initiated by Ruzmaikin et al [1993]. They divide the

Braginsky and Roberts [1994b] continued earlier in­ fluid domain into fixed cells, each of which randomly

vestigations of one particular model. They observed a amplifies or destroys field by dynamo action; nonlin-

transition from Taylor-type behavior to model—Z—type earity, diffusion and correlations between cells are then

behavior as D increases. An au;—dynamo model inte­ added. An initially smooth field becomes intermittent,

grated by Glatzmaier and Roberts [1993] developed an the field concentrating mainly in a few cells, the loca­

interesting bifurcation as D was increased. Against the tion of which changes with time, a phenomenon they

background of an approximately steady dipole compo­ liken to the motion of geomagnetic field anomalies.

nent, an oscillatory quadrupole field causes the merid­ Roberts [1992] introduced a "mapping method" that has

ional field lines to bunch up alternately in one hemi­ been successfully tested against axisymmetric [Naka-

sphere and the other. The role of the dipole and jima and Roberts, 1994a] and asymmetric [Nakajima

quadrupole families of solutions of the geodynamo equa­ and Roberts, [1994b] dynamo models; see also Nakajima

tion in geomagnetic field reversals is an oft recurring et al [1993a].

theme, and was raised again in a novel way by Hoffman The resources of the NSF Pittsburg

Supercomputing

[1991]. Questions of parity coupling in a2—models also Center were enlisted to generate the first 3D time-

arose in the work of Hollerbach [1991].

dependent, fully self-consistent numerical solution of

In integrating a kinematic ao;—geodynamo model, the MHD equations that describes thermal convection

Braginsky [1964] found that the fields induced outside and magnetic field generation in a low-viscosity rap­

the TC differed substantially from those generated in­ idly-rotating spherical shell with a solid conducting in­

side it. Dynamic (intermediate) models have recently ner core. The resulting solution, reported by Glatz­

been studied by Hollerbach and Jones [1993a]. They maier and Roberts [1994], serves as a crude simulation

find that most dynamo action takes place outside the of the geodynamo, crude because because the trunca­

TC, a conclusion that may depend on their, choices of a tion was too severe and because geophysicially realis­

and o> since it was not confirmed by the recent 3D inte­ tic values for some parameters were not numerically

grations of Glatzmaier and Roberts [1994]. The model accessible (e.g. v was several orders of magnitude too

of Hollerbach and Jones was used to benchmark that large, though still apparently not very influential). The

of Glatzmaier and Roberts [1993]; the agreement was heat flux from the core was taken to be 4 x 1013W and

nearly perfect. Hollerbach and Jones [1993b, 1994] ar­ the integration was continued over approximately three

gued that the SIC plays a potent role in the reversal magnetic diffusion times, during which the field showed

mechanism; its electromagnetic inertia diminishes chaos no signs of disappearing. Field generation takes place

in the FOC. Glatzmaier and Roberts [1994] agreed. The mainly within and near the T C . The pattern and am­

effects of conducting boundaries were investigated by plitude of the radial magnetic field at the CMB is qual­

Hirsching and Busse [1993].

itatively similar to that of the Earth. The toroidal field

Although the emphasis of the subject has moved to­ energy is rather larger than the poloidalfieldenergy but

wards MHD models, kinematic geodynamos are still be­ the maximum amplitudes attained by the two fields are

ing profitably studied. In particular, Hagee and Ol­comparable (~ 0.05T); the maximum fluid velocity is

son [1991] have suggested an interesting connection be­ of order 4 x 10~3m s - 1 . An irregular exchange of field

tween the observed secular variation and certain types between hemispheres takes place, similar to that found

448

ROBERTS: DYNAMICS OF THE CORE, GEODYNAMO

in the 2D model of Glatzmaier and Roberts [1993]. Its an inviscid drop in a bounded rotating fluid, Phys. Fluids

timescale is about 10% of the magnetic diffusion time of the FOC. Excitingly, the dynamo sometimes reverses its polarity spontaneously. Preliminary to doing so, the poloidal field in the SIC has to reverse; if it does not do so, the reversal is aborted (as in geomagnetic excur­ sions). It is hard not to be excited by such similarities

A4, 1142-1147, 1992. Bush, J.W.M., H.A. Stone and J. Bloxham, Axial drop mo­
tion in rotating fluids, J. Fluid Mech., t o appear, 1994. Busse, F.H., Theory of the geodynamo and core-mantle
coupling, in Chaotic Processes in the Geological Sciences, edited by D.A. Yuen, pp. 281-292, Springer, Heidelberg, 1992.

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haps the answer to the challenging sentence that opened ductivity variations, Geophys. Astrophys. Fluid Dynam.,

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(Received June 13, 1994; revised January 18, 1995; accepted January 23, 1995.)