Treatise on Geophysics : Volume 8 Core Dynamics

333 Pages·2015·40.198 MB·English

by  Olson, Peter

8.01 Core Dynamics: An Introduction and Overview
POlson,JohnsHopkinsUniversity,Baltimore,MD,USA
ã2015ElsevierB.V.Allrightsreserved.
8.01.1 Introduction 1
8.01.2 TheScientificJourneytotheCenteroftheEarth 1
8.01.3 StateoftheCore 4
8.01.4 TheSearchforaDynamoTheory 5
8.01.5 CoreDynamicsandtheGeomagneticField 9
8.01.6 CoreEnergetics 10
8.01.7 CoreDynamicsasaHeatEngine 12
8.01.8 ConvectionandDynamoAction 12
8.01.9 SimulatingtheGeodynamo 14
8.01.10 MantleEffectsWithintheCore 15
8.01.11 TheDynamicalInnerCore 16
8.01.12 FutureProspectsandProblems 17
8.01.13 AdditionalReferences 18
8.01.14 SummaryoftheChaptersinThisVolume 18
8.01.14.1 EnergeticsoftheCore 18
8.01.14.2 TheoryoftheGeodynamo 18
8.01.14.3 Large-ScaleFlowintheCore 19
8.01.14.4 ThermalandCompositionalConvectionintheOuterCore 19
8.01.14.5 WavesintheCoreandMechanicalCore–MantleInteractions 20
8.01.14.6 TurbulenceintheCore 20
8.01.14.7 RotationalDynamicsoftheCore 20
8.01.14.8 NumericalDynamoSimulations 20
8.01.14.9 MagneticPolarityReversalsintheCore 21
8.01.14.10 InnerCoreDynamics 22
8.01.14.11 ExperimentsonCoreDynamics 22
8.01.14.12 Core–MantleInteractions 23
References 23
8.01.1 Introduction (cid:129) Newapproachestoimagingthestructureofthelarge-scale
coreflow
TheinauguraleditionoftheTreatiseonGeophysicspublishedin (cid:129) Identification of shorter-period torsional oscillation fre-
2007 included for the first time a geoscience volume specifi- quencies,providingnewestimatesoftheaveragemagnetic
cally devoted to the dynamics in the Earth’s core. This Core fieldstrengthinsidethecore
Dynamics volume in the second edition of Treatise on Geo- (cid:129) Novel laboratory experiments including the von Ka´rma´n
physics continues that tradition, offering an in-depth discus- sodiumdynamoexperiment
sionofthedynamicalprocessesthatareactiveattheveryheart (cid:129) Application of broad-based scaling laws derived from
oftheEarth,someofwhichhaveimpactfarbeyondthecore numerical dynamos and laboratory experiments applied
itself.Intheyearssincethefirstedition,therehasbeenmuchin tothemodernandtheancientgeomagneticfield
the way of progress, plus some revisions, as is inevitable in
TheCoreDynamicsvolumeinthesecondeditionofTrea-
studying the most remote region of our planet. The overall
tiseon Geophysicsincludesupdatesofwhatappearedinthe
trend is toward a more dynamical perspective of the core, in
firsteditionplusaccountsoftheprogresssincethen,suchas
which energy production and dissipation are higher and the
theitemslistedearlierinthetext.Italsoincludesanewchapter
pulseofevolutionisstronger,comparedtoourthinkingjusta
onwavesinthecoreandanewlyauthoredchapteronouter
fewyearsago.Evidenceofthistrendisfoundinthemajornew
coreturbulence.
ideas, advances, concepts, and research directions that have
appearedsincethefirstedition,includingthefollowing:
(cid:129) Innercoreconvection,includingtheproposedtranslation 8.01.2 TheScientificJourneytotheCenter
instability oftheEarth
(cid:129) First-principles atomic structure calculations and high-
pressureexperimentsindicatinghigherelectricandthermal AslongasmanhasspeculatedabouttheinterioroftheEarth,it
conductivityinthecorethanpreviouslythought,alteringour hasbeenpresumedthereexistsacentralcore.Centuriesbefore
pictureofitspresent-daystateanditsevolutionaryhistory theriseofmodernscience,philosophersandtheologianshad
TreatiseonGeophysics,SecondEdition http://dx.doi.org/10.1016/B978-0-444-53802-4.00137-8 1
2 CoreDynamics:AnIntroductionandOverview
concluded that the Earth has a hot core at its center, with filled shell. Halley envisioned that both the crust and the
properties that differ from all other parts of our planet. For central region or core rotate in the prograde sense but the
nearly as long, it has been recognized that the Earth is also corerotatesslightlyslowerthanthecrust,causingthemagnetic
magnetic, but the origin of the Earth’s magnetism remained fieldtodriftsystematicallywestwardasseenatthesurface.Two
justasmysteriousasthenatureofthedeepinterior. importantandlong-lastingconceptswerethusborn:thebasic
Although the ancient Chinese made the first discoveries three-layermodeloftheEarth’sinterior(solidcrustandman-
relatedtogeomagnetism,scientificinquiriesabouttheEarth’s tle,liquidoutercore,andsolidinnercore)andtheassociation
core began in the West in the Middle Ages. In 1269, Petrus betweenthegeomagneticdriftandmotion ofthefluidouter
Peregrinus de Maricourt’s treatise Epistola de magnete offered corewithrespecttootherpartsoftheEarth’ssystem.Halley’s
explanationsformagneticattractionandrepulsion,theopera- modelimplicitlyassumedthatthemagneticfieldoriginatedin
tion of the compass, the properties of magnetized materials, a solid inner core (Evans, 1988), akin to Gilbert’s uniformly
andtheconceptofmagneticpoles(Arnold,1904).Peregrinus magnetized sphere. Subsequently, it was shown that Halley’s
alsoreportedanunsuccessfulsearchformagneticmonopoles– modelisatvariancewiththeferromagneticpropertiesofEarth
breaking naturally magnetized lodestones into ever smaller materials, which lose their permanent magnetization at the
fragments – and he even described in rudimentary terms the Curietemperatureatdepthsofafewtensofkilometersbeneath
ideaofamagneticfieldreversal.Gilbert(1600)wasthefirstto the surface. However, by then, the physical connection
demonstratethatthecompassneedleiscontrolledbyaforce betweenmagneticfieldsandelectriccurrentshadbeenestab-
originatingwithintheEarth,showingthatthepatternofmag- lished, providing an alternative explanation for the geomag-
netic field lines near a uniformly magnetized sphere netic field that relied on free electric currents rather than
approximates the known directions of the compass needle permanentmagnetization(Figure2).
over the Earth’s surface (Figure 1). Three hundred and fifty Theliquid(i.e.,molten)stateoftheoutercorewasfirmly
years later, Sidney Chapman characterized Gilbert’s demon- establishedduringtheearlypartofthetwentiethcentury,but
stration as ‘the only successful experiment in the history of therootsoftheideacanbetracedbackintoantiquity.Several
geomagnetism!’ independentlinesofscientificevidenceappearedinthemiddle
Earlyintheeraofglobalexploration,navigatorsobserved ofthenineteenthcenturyinfavorofhightemperaturesinthe
that the Earth’s magnetic field slowly changes with time, a Earth’sdeepinterior,includingthesteepgeothermalgradient
property now called the secular variation. In an attempt to
explain the secular variation, Halley (1683, 1692) proposed
thatthegeomagneticfieldhasitsoriginneartheEarth’scenter,
inaregionseparatedfromthesolidcrustbyacavernous,fluid-
Figure2 EdmondHalley(1656–1742)interpretedthegeomagnetic
Figure1 TitlepagefromGilbert’s(1600)treatiseDeMagnete. secularvariation.
CoreDynamics:AnIntroductionandOverview 3
measured in deep mines and petrologic measurements that the era of seismic exploration of the core. Within a decade,
indicated very high temperatures are needed to form most Oldham identified seismic P- and S-waves (1899) and inter-
igneousrocks.However,theearlyestimatesoftheactualtem- preted the P-wave shadow as low velocity in a central core
perature variation through the deep Earth varied wildly, pre- (Oldham, 1906). Shortly thereafter, Gutenberg (1912) deter-
venting any firm conclusion about the state of matter in minedthelocationofthecore–mantleboundary,atadepthof
thecore. 2900 20km, consistent within his calculated uncertainty
(cid:1)
Towardthecloseofthenineteenthcentury,twocompeting withthepresent-dayvalue.
models ofthe state ofthe Earth’s deepinterioremerged.One Gutenberg’s original Earth model included rigidity
model assumed thatthe interior was solid (except small melt throughout the core, in spite of the fact that seismic shear
regionsbelowvolcanoes)andalsoelastic,withaveryhighshear wavetransmissionthroughthecorehadneverbeenconfirmed,
modulus,‘asrigidassteel,’accordingtoKelvin’s(1862)famous atestimonytothelastinginfluenceofKelvin’sideas.Indeed,
prescription.Thismodelwassupportedbyobservationsofthe the fluidity of the core was not settled until Jeffreys (1926)
amplitudesofthetides(Darwin,1879)andtheperiodofthe showeditwaspossibletoreconcileseismicwavespeedswith
Earth’sfreenutation,theChandlerwobble(Newcomb,1892). tidalandChandlerwobbleobservationsusinganEarthmodel
Thecompetingmodelheldthattheinteriorwaslargelyfluid,an withaliquidcoreofradius3471km,essentiallythesameasin
ideathatwaspopularwithgeologistsatthattime,althoughit the Gutenberg model. As Brush (1996) pointed out in his
had prominent adherents within the physics community as historyoftheexplorationoftheEarth’sinterior,Jeffreys’repu-
well, for example, Ritter (1878), Poincare´ (1885), Arrhenius tationwassomewhattarnishedbyhisrefusaltoacceptconti-
(1900),and,evenearlier,Franklin(1793). nental drift and the concept of mantle convection (Jeffreys,
Thetermsofthisdebateunderwentapermanentshiftwith 1929).Ironically,however,Jeffreyshimselfmadeseveralfun-
the publication by Wiechert (1897) of the first quantitative damentalcontributionstothetheoryofconvectioninviscous
model of the Earth’s structure (Figure 3). Wiechert’s Earth fluidsthatledtothebasicmodelformantleconvection,andhe
model was based on all available astronomical and geodetic also contributed importantly to the acceptance of the geody-
dataandfeaturedacentralmetalliccoresurroundedbyarocky namotheorybydemonstratingtheoutercoreisliquid.
mantle. Wiechert is often given credit for being the first to Thefinalpieceofthemainradialstructureofthecorewas
attribute both chemical and physical differences to the core providedbyLehmann(1936),whodiscoveredtheinnercore
and mantle and the first to conclude that the core–mantle boundary, which she placed at 4970km depth, or 1400km
boundary, the most significant discontinuity in the planet’s radius (the currently preferred radius is about 1220km)
interior,representsachangefromsilicatestoironandadensity (Figure 4). Following Lehmann’s discovery, seismologists
jump.Inanycase,thereislittledoubtthathisworklaunched havesucceededindemonstratingthecrystallinenatureofthe
inner core material. The study by Dziewonski and Gilbert
(1971)ofnormalmodeovertonesexcitedbythe1964Alaska
earthquake provided an estimate of its average rigidity, and
subsequentinvestigationshavedeterminedthattheinnercore
Figure3 EmilWiechert(1861–1928)constructedthefirstquantitative
Earthmodelwithacore. Figure4 IngeLehmann(1888–1993)discoveredtheinnercore.
4 CoreDynamics:AnIntroductionandOverview
Table1 Chronology Table2 Knownphysicalproperties
Year Person(s) Event Property Notation Units Value
1000 Chinese Discoveredlodestonesouth– Coreradius(mean) r m 3.480 106
northorientation Innercoreradius(mean) ro m 1.22 (cid:3)106
1269 P.Peregrinus Definedmagneticpoles Outercorethickness di m 2.26(cid:3)106
1600 W.Gilbert PublicationofDeMagnete Core–mantleboundary(CMB) A m2 1.52(cid:3)1014
o (cid:3)
1634 H.Gellibrand Discoveredgeomagneticsecular area
variation Innercoreboundary(ICB)area A m2 1.87 1013
11688230 EH..H(cid:1)aellresyted,A.Ampere RInetleartperdetmedagsneectuislamrvtoareialeticotnric Coerleli–pmticaitnytleboundary eoo nd 2.5(cid:3)(cid:3)10(cid:4)3
currents Corevolume V m3 1.77 1020
1831 M.Faraday Introduceddiskdynamo Innercorevolume V m3 7.6 (cid:3)1018
1834 C.F.Gauss Measuredmagneticintensity Outercorevolume Vi m3 1.70(cid:3) 1020
1836 C.F.Gauss Sphericalharmonicanalysis Coremomentofinertia Io kgm2 9.2 (cid:3)1036
1897 E.Weichert IroncoreEarthmodel Outercoremass M kg 1.83(cid:3)5 1024
1906 R.Oldham Observedcoreseismicwaves Innercoremass Mo kg 9.68 (cid:3)1022
1906 B.Brunhes Reverselymagnetizedrocks Coredensity(mean) ri kgm(cid:4)3 1.09(cid:3)104
11991129 BJ..LGaurtmenobrerg DPreotepromseindesdeclfo-sreusrtaadiniuinsgfluid ICnonreer–mcoarnetldeebnosiutynd(amryeagnr)avity rgoi kmgsm(cid:4)(cid:4)23 11.02.968(cid:3)(cid:3)104
dynamos ICBgravity gi ms(cid:4)2 4.40
1936 I.Lehmann Discoveredinnercore Core–mantleboundary P GPa 136
o
1933 T.Cowling Antidynamotheorems pressure
1942 H.Alfve´n Magnetohydrodynamicwaves ICBpressure P GPa 323
i
1946 W.Elsasser FirstMHDdynamotheory P-wavevelocitybelowCMB vp kms(cid:4)1 8.07
1952 F.Birch Compositionofthecore P-wavevelocityaboveICB vp kms(cid:4)1 10.36
1953 J.Jacobs Present-dayinnercoregrowth Poissonratio,innercore n nd 0.44
P
1955 E.Parker ao-Dynamoeffect Angularvelocityofrotation O rads(cid:4)1 7.292 10(cid:4)5
1958 A.Hertzenberg,G.Backus Laminarkinematicdynamos Freecorenutationperiod T s 3.71 (cid:3)107
1961 J.Verhoogen Innercorefreezingascore Magneticdipolemoment mc Am2 7.8 (cid:3)1022
d (cid:3)
energysource Magneticdipoletilt y deg 10.8
d
1963 F.LowesandI.Wilkinson Laboratorydynamo Magneticintensity,CMB(rms) B mT 0.42
CMB
1963 J.B.Taylor Rotationaldynamoconstraint Magneticintensity,outercore B mT 2–4
rms
1966 M.Steenbecketal. a2-Dynamoeffect (rms)
1971 A.Dziewonskiand Innercorerigidity Magneticdipoleintensity,CMB Bdip mT 0.263
CMB
F.Gilbert (rms)
1976 S.Braginsky AsymptoticdynamomodelZ
1995 G.Glatzmaierand Self-consistentreversing
P.Roberts dynamomodel
1995 A.KageyamaandT.Sato Self-consistentcompressible transport properties (which are generally less well known),
dynamomodel andFigure5showsitsbasicradialstructure.
1996 Z.SongandP.Richards Innercoresuperrotation Themodelofapredominantlyironcorewasfirmlyinplace
2001 A.Gailitis,U.Muller,and Firstlaboratoryfluiddynamos bythemiddleofthetwentiethcenturyandwaswellsupported
others byevidencefromseismology(Bullen,1954)andmineralphys-
2006 U.Christensenand Scalinglawsforplanetary
ics(Birch,1952).Oneearlyargumentthatwasoftencitedin
J.Aubert dynamos
supportofanironcorewasBirch’slaw(Birch,1964),alinear
2007 VKSteam vonKa´rma´nreversinglaboratory
relationship between density and bulk sound velocity with a
dynamo
coefficient proportional to the mean atomic weight of the
2010 T.Alboussiere, Innercoretranslation
M.Monnereau,and material. Application of Birch’s law revealed that the mean
others atomicweightoftheoutercoreandinnercoreisbothslightly
less thaniron butis far toolarge tobeexplained by aphase
transformation of lower mantle material. Although it is now
isalsoanisotropicandheterogeneous.Table1givesachronol- recognizedthatthetheoreticalbasisforBirch’slawisweak,it
ogyofimportantmilestonesinthisscientificjourney. was historically important because it seemed to demand a
metallic,ratherthananoxide-richorsilica-richcomposition.
Othermetalsmightalsobepresentinthecore.Theabundance
8.01.3 StateoftheCore ofnickelinironmeteoriteswashistoricallyusedtoarguethat
thecorecontainssubstantialFe–Nialloy,butsincemanyofthe
AfullreviewofthecompositionofthecoreisfoundinVolume physicalpropertiesofnickelareindistinguishablefromironat
2 of this treatise. Here, we provide a brief summary of the coreconditions,unambiguousdetectionofnickelinthecoreis
major constituents of the core, for purposes of this chapter. problematic.
Table2listssomeofthewell-knownphysicalpropertiesofthe Thepresenceoflighterelementsisvitallyimportantforthe
core, Table 3 lists some important thermodynamic and dynamicsofthecore.AsdescribedinVolume2ofthistreatise,
CoreDynamics:AnIntroductionandOverview 5
Table3 Thermodynamicandtransportproperties are basically consistent with a homogeneous mixture of iron
and the lighter alloying elements listed in the preceding text
Property Notation Units Range
(DziewonskiandAnderson,1981).Regionsthatdeviatefrom
thisapparenthomogeneityincludingathinlayeratthebaseof
Core–mantle T K 4100 400
o (cid:1) the outer core will be described later. Unfortunately, it has
boundary
temperature proven to be difficult to choose between the candidate light
ICBtemperature T K 5500 600 elements in the core on the basis of their seismic properties
i (cid:1)
Outercore T K 4700 500 alone.Somedilutionofthesolidinnercorebylighterelements
(cid:1)
temperature isalsoindicated,asthepredicteddensityofsolidironisafew
(mean) percent greater than what the seismic properties indicate
Adiabatic (cid:4)dT/ Kkm(cid:4)1 0.8(cid:1)0.2 (Masters and Gubbins, 2003; Shearer and Masters, 1990).
temperature dr
ad The actual density change at the inner core boundary is
gradient,CMB
Adiabatic dT/ Kkm(cid:4)1 1.0 0.3 600–900Mgm(cid:4)3 (Cao and Romanowicz, 2004), of which
(cid:4) (cid:1) aboutone-thirdisduetosolidification.Therestislikelydue
temperature dr
ad
todifferencesinlightelementconcentrationbetweentheinner
gradient,ICB
Densityjump,ICB Dri kgm(cid:4)3 750(cid:1)150 coreandoutercore.Thissmalldensitydifferencehasprofound
Lightelement C % 8 3 implications for the driving mechanism for flow in the core
o (cid:1)
concentration, and also for the power source of the geodynamo (Buffett,
outercore 2003). A related issue is the abundance of radioactive heat
Lightelement Ci % 3(cid:1)2 sourcesinthecore.Amongthepossibleradioisotopes,40Kis
concentration, the most likely to be energetically significant, because of its
innercore
low-pressure affinityforironsulfides,suggestingitmayhave
Thermalexpansivity a K(cid:4)1 1.2(cid:1)0.5(cid:3)10(cid:4)5 partitionedintothecoreduringtheEarth’saccretion.However,
Lightelement a nd 0.8 0.2
C (cid:1) theamountofpotassiuminthecoreisstilldebated(Bouhifd
expansivity
SLapteecniftichehaeta,t CLp JJkkgg(cid:4)(cid:4)11K(cid:4)1 81500(cid:1).520106 e2t0a0l3.,)2.0In07a;dGdeitsisomnatnonpaontdasWsiuomod,ss,o2m00e2u;rRaanmiuamMcuornthteynetthaal.s,
(cid:1) (cid:3)
crystallization beenproposedforthecore,whichcouldslightlyaugmentthe
Thermalconductivity k Wm(cid:4)1K(cid:4)1 100 30 amount of internal heat production. As mentioned earlier in
Thermaldiffusivity k m2s(cid:4)1 5 3(cid:1) 10(cid:4)6 the text, the temperature distribution in the core appears to
Compositional D m2s(cid:4)1 1(cid:1)10(cid:3)(cid:4)9(cid:1)2 follow anadiabat. Based on melting point temperature mea-
(cid:3)
diffusivity surements(Boehler,1996)andshockwavedata(Nguyenand
Kinematicviscosity, n m2s(cid:4)1 1(cid:3)10(cid:4)6(cid:1)2 Holmes, 2004), it is estimated that the temperatures at the
outercore
core–mantleboundaryandinnercoreboundaryareapproxi-
Kinematicviscosity, ni m2s(cid:4)1 1(cid:3)1010(cid:1)3 mately4100and5500K,respectively,asshowninTable3.
innercore
Electricconductivity s A2kg(cid:4)1m(cid:4)3s3 1–2 105
Magneticdiffusivity l m2s(cid:4)1 1 0(cid:3).5
(cid:1) 8.01.4 TheSearchforaDynamoTheory
Untilratherlateinthetwentiethcentury,coredynamicswasa
the abundance of the various candidate light elements has rathernarrowlydefinedsubject,limitedtoahandfuloftopics
beenamatterofintensecontroversy.Decadesofhigh-pressure drawn from classical mechanics, such as rotational and tidal
measurements and theory have convincingly demonstrated deformation,pursuedbyasmallnumberoftheoreticalphys-
Birch’s interpretation that the outer core is less dense than icists and applied mathematicians, G. Darwin, H. Poincare´,
pureironatinsituconditions,evenallowingfortheexpected andH.Jeffreys,amongthem.Thefullrangeofcoredynamics,
density decrease due to melting, and therefore requires the thesubjectofthisvolume,hasreceivedwidespreadstudyonly
addition of light elements to reduce the density by 6–10%. sincetheadventofthemoderndynamotheoryfortheoriginof
Candidatelightelementsfrequentlyproposedtoreconcilethis thegeomagneticfield.
density deficit include oxygen, sulfur, silicon (MacDonald, AfterthetimeofHalley,relativelylittleattentionwaspaid
2003;Poirier,1994),and,lessfrequently,hydrogenandeven to the origin of the geomagnetic field, until well into the
carbon.Sulfurhasaknownaffinityforironatlowpressures, twentieth century. Gauss (1832, 1939) conjectured that geo-
andhigh-pressurestudiesindicatethattheoxygenissolublein magneticsecularvariationwasaconsequenceofsolidification
iron at core conditions (Alfe et al., 2003). Both sulfur and ofthecrustbutevidentlydidnotspeculatemuchontheorigin
oxygenareknowntoaffectthephasediagramofironsubstan- of the main field (Figure 6). Zollner (1871) constructed a
tially, including the melting point. Somewhat less is known modelforgeomagneticsecularvariationthatincludedseveral
about the high-pressure effects of silicon in the core (Georg aspects of the present-day dynamo theory, including electric
etal.,2007)andstilllessabouthydrogenandcarbon. currentsinducedinaliquidcoreandinteractionwiththesolid
Mostdetailedinformationonthepresent-daystructureof mantle. However, his ideas evidently were not taken up by
thecorecomesfromseismology(seeVolumes1and4ofthis others, and the subject continued to languish in obscurity.
treatise). The variation of seismic wave velocity and density Eveninthemiddledecadesofthetwentiethcentury,leading
withdepththroughthefluidoutercoreshowninFigure5(b) theoristsshowedonlypassinginterestinthegenerationofthe
6 CoreDynamics:AnIntroductionandOverview
CMB
ICB
(a)
3) 15 420
-
m
mg Vp 360 12
or r g
1- s 10 300 P 10
elocity or density (km 5 Inner core Outer core antle Vs Pressure (GPa) 112284000 Inner core Outer core Mantle 468 2-y (ms)Gravit
mic v M 60 2
s
ei
S 0 0 0
0 2000 4000 6000 0 2000 4000 6000
(b) Radius (km) Radius (km)
Figure5 (a)CutawayviewshowingthemainlayersoftheEarth’sinterior,includingthesolidmantle(yellow),theliquidoutercore(orange),thesolid
innercore(red),andthecore–mantleboundary(CMB)andtheinner–outercoreboundary(ICB).(b)SeismicEarthmodelPREM.Reproducedfrom
DziewonskiAMandAndersonDL(1981)PreliminaryreferenceEarthmodel.PhysicsoftheEarthandPlanetaryInteriors25:297–356.
geomagneticfield.Forexample,ChapmanandBartels’(1940) (Figure 8). Although Larmor’s suggestion was primarily
treatiseGeomagnetismdevotesportionsofjustsevenpages(out intendedforapplicationtotheSun(hispaperreferstoHale’s
of1050total)tothistopic.Theyrejectedpermanentmagneti- discovery of magnetic fields in sunspots), the idea seemed
zation,ohmicdecayoffreeelectriccurrents,andgyromagnet- equally applicable tothe Earth. However,itdid notresult in
ismasprimarycauses.Theyalsodismissedtheself-sustaining immediateprogressonthegeodynamo,perhapsbecauseofan
dynamomechanism,concluding,asdidSchuster(1911),that influential paper by Cowling (1933), who showed that elec-
the “difficulties which stand in the way of basing terrestrial tromagneticinductionbyaconductingfluidcannotmaintaina
magnetism on electric currents inside the Earth are steadyaxisymmetricmagneticfield.Thiswasthefirstofseveral
insurmountable”(Figure7). antidynamo theorems that cast a shadow of doubt on the
Evidently, Chapman and Bartels were responding to the validity of the self-sustaining dynamo concept. In retrospect,
suggestion in a short paper by Larmor (1919), proposing itseemsthatCowling’stheoremwasoverinterpreted.Asteady
that,becausethecirculationofaconductingfluidinthepres- axisymmetricdynamoisprobablyanunphysicalsituationand
enceofaseedmagneticfieldwouldinduceanelectricfield,ifa is certainly not applicable to the Earth. Nevertheless, many
suitable path for electric currents was created in the fluid, a theoristsofthateraconcludedthatCowling’stheoremimplied
stronger magnetic field might be maintained indefinitely. In that a general nonexistence proof of fluid dynamos would
short, Larmor had proposed a self-sustaining fluid dynamo eventuallybefound.
CoreDynamics:AnIntroductionandOverview 7
Figure8 JosephLarmor(1857–1942)proposedaself-sustainingfluid
dynamoforthecore.
these early papers thathave stood the test oftime include the
Figure6 CarlFriedrichGauss(1777–1855)fatherofgeomagnetism. derivationofthemagneticinductionequationforincompressible
flow,representationofthemagneticfieldintermsofitspoloidal
and toroidal parts, amplification of toroidal field through the
interactionoftoroidalshearflowwithapoloidal(i.e.,dipolar-
type) field, selection rules for interaction between toroidal
magneticfieldsandpoloidalflows,identificationofoutercore
convectionasthemainsourceofkineticenergyfortheflow,and
definitionsofseveralofthekeydimensionlessparametersthat
govern self-sustaining fluid dynamos, including the ratio of
Lorentz to Coriolis forces, now called the Elsasser number. In
addition, these early papers offered an explanation for the
observedgeomagneticwestwarddrift,basedontheconservation
ofangularmomentumandcore–mantleinteraction(Figures9
and10).
Themainshortcomingofthesepioneeringpaperswasthat
theyfailedtoadequatelyprovetheexistenceofself-sustaining
fluiddynamos,evenkinematicones.Elsasser’s(1946)attempt
atatheoreticaldemonstrationfellshortofcompleteness,and
theearlynumericaleffortsbyBullardandGellman(1954)to
constructkinematicdynamosintermsofaseriesofspherical
harmonicshavesubsequentlybeenshowntodivergewhenthe
seriesisextended(Gubbins,1973;Lilly,1970).Thefirstwork-
ingtheoreticalexamplesofkinematicfluiddynamoswereby
Backus(1958)andHertzenberg(1958).Althoughthesewere
based on quite unrealistic flows (e.g., the Backus dynamo
assumedperiodsofmotionalternatingwithperiodsofstasis),
they succeeded in demonstrating the existence of fluid
dynamosand,withthis,thelimitationsofCowling’stheorems.
Figure7 HenriPoincare´(1854–1912)developedthetheoryofrotating, Several other examples of kinematic dynamos followed on
precessingfluids.
their heels, in which the flow was assumed to consist of
large-scale,laminar-typemotionsamenabletoanalyticorsim-
Thelogjamstartedtobreakinthe1940s,beginningwitha ple numerical investigation (see Chapter 8.03), including an
series of papers by Elsasser (1946, 1950) and Bullard et al. important experimental dynamo by Lowes and Wilkinson
(BullardandGellman,1954;Bullardetal.,1950),thefirstquan- (1963) that involved both fluid and solid conducting parts.
titative efforts to build a full magnetohydrodynamic (MHD) Although these idealized dynamos provided only limited
theory for the main geomagnetic field. Accomplishments in insightintothedynamicsofthegeodynamo,theynevertheless
8 CoreDynamics:AnIntroductionandOverview
kinematic models, following the introduction of mean-field
dynamo concepts. The first mean-field theory for dynamo
action was an early model by Parker (1955), who proposed
that polodial magnetic field is induced in the core by the
statisticalactionofsmaller-scaleconvectivevorticesactingon
the large-scale toroidal magnetic field. Parker used the term
cyclonictodescribethekinematicsofconvectiveflowsinwhich
theradialvelocitycorrelateswiththeradialvorticity,aconse-
quenceoftheEarth’srotation.Thetermnowusedtodescribe
suchmotionsishelicity,definedastheinnerproductofvortic-
ityandvelocityvectors.
Helicalflowshavetheimportantpropertyoftwistingeast–
west-oriented toroidal magnetic field lines into meridional
planes,thusinducingapoloidalmagneticfieldfromtheorig-
inaltoroidalone.Thismechanismforinducingpoloidalfrom
toroidalmagneticfieldwasrecognizedasakeyingredientthat
wasmissingfrommanyofthefailedeffortstoproducekine-
maticdynamos.Itbecameaparticularlypotentconceptstart-
ing in the 1960s, with the introduction of mean-field
electrodynamics, a formal approach for calculating the large-
scale induction properties of complex, small-scale flows (see
Chapter 8.03). Mean-field electrodynamics is implicit in the
earlyworkofParker(1955),buttheforminwhichitisused
today came later, from astrophysics (Steenbeck and Krause,
1969; Steenbeck et al., 1967). The basic idea is to represent
Figure9 WalterM.Elsasser(1904–91)pioneerinthedynamotheory thefluidvelocityandthemagneticfieldasconsistingofamean
ofgeomagnetism. plusafluctuatingpart,thelatterparthavingzeroaverageover
some appropriately chosen length or timescales. Under the
rightconditions,theinteractionbetweenthesmall-scaleveloc-
ityandmagneticfieldsgeneratesalarge-scaleelectricfieldthat
isparalleltothelarge-scalemagneticfield.Theproportionality
betweentheinducedelectricfieldandthelarge-scalemagnetic
fieldisrepresentedbythecoefficienta,andthenamegivento
thistypeofinductionisthe‘a-effect.’Dynamoactionoccursif
thea-coefficientissufficientlylargetoovercometheinhibiting
effectsofmagneticdiffusion.
Roberts (1972) produced an extensive set of numerical
calculationsthatshowedhowself-sustainingkinematicdyna-
mos could be generated in conducting fluid spheres using
variousdistributionsofthea-parameter,incombinationwith
different types of large-scale flows. The nomenclature intro-
duced by Roberts for the large-scale flows included o for
toroidal shear flows and m for meridional (poloidal) flows.
Combinationsoftheseparametersproducedanassortmentof
dynamos,forexample,a2-dynamos,inwhichboththetoroidal
and poloidal magnetic fields are induced by the small-scale
motion;ao-dynamos,inwhichthepoloidalfieldisinducedby
thesmall-scaleflowthroughthea-effect,butthetoroidalfield
isinducedbytheo-effect;andaom-dynamos,whereallthree
effects are active. One advantage of this formalism is that
kinematicdynamosexhibitingawidevarietyofcharacteristics
could easily be constructed, without explicitly specifying the
Figure10 EdwardC.Bullard(1907–80),leadingtwentieth-century
details of the fluid motion, in essence by lumping all of the
geophysicist,thefirsttoattemptnumericalsolutionofthedynamo
flow properties into a few parameters. It was subsequently
problem.
shown that the a-effect is proportional in many rotating sys-
temstothefluidhelicity(Moffatt,1978;Ra¨dler,1978),sothat
werevaluablemilestones,helpingtodefinesomeofthecon- the kinematics of these dynamos could be related, at least
ditionsnecessaryformagneticfieldgenerationinthecore. indirectly,torealfluidmotions.
Justasthesesuccesseswerebeingregistered,thedirectionof Withthesuccessesofmean-fieldelectrodynamics,effortsto
dynamo research began to shift away from large-scale finddynamosdrivenentirelybylarge-scaleflowswanedinthe
CoreDynamics:AnIntroductionandOverview 9
1970s,andaroundthissametime,additionalimpetusforthe convectiveflowssubjecttotheLorentzforcesequilibratehad
study of mean-field dynamos was provided by experimental toawaittheadventof3Dnumericalmodels.
and theoretical developments on thermal convection in rap- Full 3D, spherical MHD simulations were pioneered by
idlyrotatingfluids.Asdiscussedearlier,itisgenerallyaccepted astrophysicists Gilman and Miller (1983) for application to
that the most important fluid motions in the outer core for the Sun and magnetic stars and by Zhang and Busse (1988)
maintainingthegeodynamoareconvection–flowsdrivenby forapplicationtotheEarth.Twoinfluentialandhighlypubli-
destabilizing thermal and compositional buoyancy forces. cized numerical dynamos were produced nearly simulta-
ConvectioninthecoreissurelyaffectedbytheCoriolisaccel- neously, oneby Glatzmaier and Roberts (1995)andanother
eration. Because of the small viscosity of liquid iron com- by Kageyama and Sato (1995). Both of these models were
pounds, theEkmannumberinthecoreisexceedinglysmall, driven by thermal convection, although the former used the
perhapsassmallas10(cid:4)15(theEkmannumberistheratioof Boussinesq approximation, whereas the latter included fluid
viscous to the Coriolis effects). In addition, the geomagnetic compressibility. Quickly thereafter, these models were
secularvariationindicatesthatthefluidvelocitiesinthecore extendedtoincludethebuoyancyderivedfromthegrowthof
areoftheorder10–20kmyear(cid:4)1.Assumingalengthscaleofa the inner core, for example, the study by Glatzmaier et al.
fewhundredkilometersforthesemotions,theRossbynumber (1999) was based on the theory for thermochemical convec-
implied for these motions is also rather small (the Rossby tion in a compressible fluid proposed by Braginsky and
numberistheratioofvorticityinthefluidmotiontoplanetary Roberts (1995). Since then, numerical dynamos have spread
vorticity).Busseetal.(Busse,1970;BusseandCarrigan,1976) around the globe, with a wide variety of competing dynamo
developed theoretical and experimental techniques to study modelsnowinuse(seeChapter8.10).Furtherexperimental
the structure of convection in this so-called rapidly rotating confirmation of the dynamo theory came in the form of the
limit.Theydemonstratedthatrapidlyrotatingconvectiontakes first successful self-sustaining, laboratory fluid dynamos by
theformofsmall-scalecolumnsorvorticesthatarenearlytwo- Gailitisetal.(2003),Mu¨lleretal.(2006),andBerhanuetal.
dimensional(2D)andalignedparalleltotheaxisofrotation, (2010)usingliquidsodium(seeChapter8.13).
asdiscussedinChapter8.13.Moreover,columnarconvection
is helical, with negative helicity in the northern hemisphere
and positive helicity in the southern hemisphere (see Jones 8.01.5 CoreDynamicsandtheGeomagneticField
etal.,2000,andChapter8.05),andsoiscapableofdynamo
actionthroughthea2-mechanism.Thus,thestructureofrotat- The study of the geomagnetic field is a rich topic in its own
ing convection provides another important piece of the core rightandisthesubjectofVolume5inthistreatise.Extensive
dynamicspuzzle. descriptionsofthegeomagneticfieldandpaleomagneticfield
Whilealloftheseadvancesinunderstandingthekinematics canalsobefoundinMerrilletal.(1998)andinGubbinsand
ofdynamoactionweretakingplace,onlyincrementalprogress Herrero-Bervera(2007),andthefulltheoryofthegeomagnetic
was being made on the more difficult problem of dynamo fieldisgiveninBackusetal.(1996).Here,itisappropriateto
equilibration. Dynamo equilibration involves the back- brieflylistsomeofthemainfeaturesofthegeomagneticfield
reactionofthemagneticfieldontheflow,throughtheLorentz that weseek toexplainin termsofthe core’s dynamics. First
force.TheLorentzforceisnonlinearinthemagneticfield,and and foremost is the persistence of an internally generated
its action in the context of internally generated fields was a geomagnetic field, not just the modern field, but a field sus-
little-understoodfacetofMHDs.Themainfocusofeffortsto tained throughout most if not all of the Earth’s history. The
understanddynamoequilibrationmechanismsinvolvedathe- main geomagnetic field that originates in the core is at least
oremprovedbyTaylor(1963),showingthat,forsmallEkman 3.4Ga, according to the rock record (Tarduno et al., 2010),
andRossbynumbers,thetorqueexertedbytheLorentzforce andquitepossiblyisasoldasthecoreitself.Thepresent-day
must vanish on cylinders coaxial with the rotation axis. This dipolemoment,7.8 1022Am2,isprobablysomewhatlarger
(cid:3)
so-called Taylor constraint imposes some restrictions on the than the long-term average value, which may be around
configurationandthestrengthoftheinternalmagneticfieldin 6 1022Am2.Significantly,thereislittleevidenceforasecular
(cid:3)
such a dynamo. It was widely assumed that the Taylor con- trendinthedipolemomentovergeologictime,althoughthere
straintappliestothegeodynamo,andtherefore,itdetermines isabundantevidenceoffluctuations,asdescribedinthesuc-
thestrengthandthesymmetryofthegeomagneticfieldinside ceeding text. For reference, the free decay time of the dipole
thecore.Analternativemodelofthefieldequilibrationprocess fieldinthecoreisonly30–50ky.Theexistenceofanancient
was proposed by Braginsky (1976), the so-called model Z, field,thelackofevidenceofadecreasingdipolemoment,and
whichassumedanearlyuniformmagneticfieldconfiguration theinadequacyofpermanentmagnetizationasasourceforthe
in the core interior plus thin magnetic layers just below the fieldarethreefactsthatdemandtherebearegenerationmech-
core–mantleboundary. anism,thatis,adynamotheory.
The stumbling block for all magnetic field equilibration Thedominanceofthedipolecomponentisevidentinthe
theories has been the lack of a full understanding of the present-day field, where its energy exceeds that in any other
Lorentzforceinself-sustainingdynamos.Thenonlinearchar- sphericalharmoniccomponent,andthisremainsthecaseeven
acteroftheLorentzforcehasprecludedthedevelopmentoffull when the surface field is extrapolated to the core–mantle
analyticsolutions,exceptinafew,highlyidealizedtheoretical boundary. The dipole dominance becomes even stronger if
cases,suchasweaklynonlineardynamoactioninhorizontally time averages of the geomagnetic field are considered. The
infiniteplanelayers.Convincingdemonstrationsofhowdyna- characteristic time constants of the nondipole terms in the
mos in spherical geometry driven by fully developed spherical harmonic representation of the field are measured