JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 100, NO. B9, PAGES 17,615-17,636,SEPTEMBER 10, 1995
Dynamicsof differentiation in magma reservoirs
ClaudeJaupartand StephenTait
Institutde Physiquedu Globe, Paris, France
1919-1994
Abstract. In large magmachambers,gradientsof temperatureandcompositiondevelopdue to
coolingandto fractionalcrystallization.
Unstabledensitydifferencesleadto differentialmotions
betweenmelt andcrystals,anda majorgoal is to explainhow thismight resultin chemical
differentiation
of magma.Arrivingat a full description
of thephysicsof Crystallizing
magma
chambers
is a challengebecause
of thelargenumberof processes
potentiallyinvolved,themany
coupledvariables,andthe differentgeometricalshapes.Furthermore,perturbations
are causedby
the reinjectionof melt from a deepsource,eruptionto the Earth'ssurface,andthe assimilationof
countryrock. Physicalmodelsof increasingcomplexityhavebeendevelopedwith emphasison
threefundamentalapproaches.
One is, given that large gradientsin temperatureand composition
may occur,to specifyhow to applythermodynamic
constraints
sothatcoexistingliquid and solid
compositions
may be calculated.The secondis to leavethe differentiationtrendasthe solutionto
be found, i.e., to specifyhow coolingoccursand to predictthe evolutionof the compositionof the
residualliquidandof thesolid'forming.
Thethirdis to simplifythephysics
sothattheeffectsof
coupledheatandmasstransfermay be studiedwith a reducedsetof variables.The complex
shapesof magmachambersimply thatboundarylayersdevelopwith densitygradientsat various
anglesto gravity,leadingto variousconvectiveflowsandprofilesof liquid stratification.Early
studies
weremainlyconcerned
withdescribing
fluidflowintheliquidinterior
oflargereservoirs,
duetogradients
deveioped
atthemargins.
Morerecent
workhasfocused
ontheinternal
structure
andflow field of boundarylayersandin particularon the gradientsof solidfractionandinterstitial
melt compositionwhichdevelopwithin them.Crystalsettlingmay occurin a surprisinglydiverse
rangeof regimesandmay lead to intermittentdepositioneventsevenwith small crystal
concentrations.
Incorporatingthermodynamic
constraints
in the studyof the dynamicsof settling
hasonlyjust begun.Many dynamicalphenomenahavebeenfoundusingtheoreticalarguments,
laboratoryexperimentson analogsystems,andnumericalcalculations
on simplifiedchemical
systems.However,they haveseldombeenappliedto naturalsilicatemeltswhosephasediagrams
andimportantphysicalpropertiessuchas thermalconductivityand chemicaldiffusioncoefficients
remainpoorlyknown.Thereis a gapbetweenmodelpredictionsandobservations,
asmany
modelsaredesignedto explainlarge-scalefeaturesandmanyobservations
deal with the local
textureandmineralassemblages
of therocks.Thisreviewstresses
therelevanceto thegeological
problemof the work carriedoutin parallelin otherdisciplines,suchasphysics,fluid dynamics,
andmetallurgy.
Introduction
The studyof the physicsof the processes
that may take place
in magmachambershas been a strikingly active researchfield
duringthe last 20 yearsor so.The main purposeof this review is
to put the contributionof this work into somehistoricalcontext.
The issuesof how heat transfer and crystallization take place
have been discussedqualitatively, since the early days of
researchon igneousdifferentiation [Bowen, 1921, !928; Hess,
1960; Jackson,1961; Wager, 1963; Wager and Brown, 1968].
The macroscopicphysical framework necessaryto treat such
difficult physical problemswas not available then. In a sense,
many of the recentphysicalstudieshave tackledquantitatively
problemsthat had been outlined qualitativelymany years ago.
However, we shall also seethat the focushas shiftedaway from
The geologicalobservations
requirethe physicalprocesses
of
coolingand of separationof crystalsand residualliquids.The
tendencyhas been, however,to use the rocksto deducehow a
reservoiroperatesin a physicalsense.This approachavoidsthe
physicalproblemwhichhasits own logic.This reviewconcerns
what causesthe systemto evolvein sucha way asto producethe
observed differentiation trend, i.e., how cooling and
crystallization are likely to develop from given starting
conditions.We will not attemptan exhaustivesummaryof all
recentwork on magmadynamicsbecauseit coversa very wide
i'angeof phenomena
but will concentrate
on two central
questions.
First,howdo crystallization
andchemicalevolutionof
magmastake place, and second,what determinesthe rate of
coolingof a magmabody?Thesequestionsare stronglyrelated
because, on the one hand, chemical evolution of the magma
thoseearlyquestions,
as it hasbecomeclearthatpartially dependson wherecrystallisation
occursandhow separation
of
crystallized systems are exceptionally rich in new dynamic
phenomena.
Copyright1995 by the AmericanGeophysicalUnion.
Papernumber95JB01239.
0148-0227195/95JB-01239505.00
crystalsand residualmelt takesplace,while on the otherhand,
the way in which heat loss takes place determines how
crystallizationproceeds.This couplingof coolingand chemical
evolutionof the liquid, the phasechange,and the macroscopic
transportphenomenamakesthe physicalproblema difficult one
to treat from first principles.
17,615
17,616
JAUPART
AND
TAIT:
MAGMA
CHAMBER
DYNAMICS
contributeto the densityand diffuseat differentrates,a kind of
"staircase"stratificationcan develop,in whichlayersconvecton
time, in equilibrium with a precise mineral assemblage.The
main physicalidea invoked to explain magmaticdifferentiation
wasthe gq'avitational
settlingof crystalsfrom lessdenseliquid.
The qualitative physical picture of a magma chamber was
foundedon two principlepiecesof evidence:that of the overall
stratigraphicrelationsof mineralogicaland chemicalvariations
vertical scales that are much less than the overall thickness of the
and that of the cmnulate textures of the rocks. The textures were
The difficulty involved may be illustratedby the following
example.One early model for igneouslayeringwas doublediffusiveconvectivephenomena[McBirneyand Noyes, 1979;
Turner, 1980]. In fluids in which two or more components
liquid body and are separatedby thin diffusive interfaces. interpretedas indicating that the crystals were depositedas a
Various suggestions
have beenmadefor how suchlayeringin sediment.The physical history of the formationof a rock was
the liquid statemightbe translatedin the final rock [e.g., Kerr subdividedinto a phaseof deposition,one of enlargementof the
and Turner, 1982; Irvine, 1980]. This idea has not proved as
fruitful as might originally have been thought.The physical
reason,first pointedout by McBirney [1985] andMorse[ 1986],
is that in a crystallizingsystemtemperatureand composition
cannotbe variedindependently
becauseoneis constrained
by the
liquidusrelationship.In all the experiments,the liquidswere
superheated,
andlayeringoccursbecausea significantamountof
thermal buoyancyis available [e.g., Chen and Turner, 1981].
This is unlikely in a system constrainedto lie close to its
depositedcrystalswhen closeto or at the top of the cumuluspile
(so-calledadcumulusgrowth) and one of crystallizationof the
interstitialtrappedliquid [Wageret al., 1960].The mainphysical
agentof masstransportduringadcumulusgrowthwasthoughtto
be chemical
diffusion.
The fact that the cumulate rocks became
progressivelymore evolvedas a functionof stratigraphicheight
was taken to show that the whole volume of liquid in the
chamber was evolving chemically becauseof crystallization
[Morse, 1979a,b].It was thussupposedthat crystalsettlingwas
liquidus.
Researchon the dynamics of crystallizationhas been very
active because it has applications in many different fields
efficient
in the sense that it occurred at a much faster rate than
Petrogenetic and Geochemical Models
Bottom Crystallization With Chemical Diffusion
crystallizationof the body of liquid.
One additionalconsequence
of theseideasis the requirement
including metallurgy and the crystal growth industry. Thus thatthe partiallycrystallizedlayer at the floor of a reservoirnmst
severalcollectivebooksand reviewshave beenpublishedin the be thin, because the diffusive chemical flux is not large and
recentpast[Loper, 1987;Huppert, 1990;Davis et al., 1992].To cannot supply high temperature chemical components for
set the stagefor the presentdiscussion,we first summarizethe adcumulusgrowth over large volumes[Wager, 1963]. This led
basic framework adopted by petrological studies. This to important conclusions regarding the heat budget of
frameworkhasbeengraduallyadaptedto accomodate
new facts, crystallizationat the floor. Taking into accountthe t•ct that the
but its basictenetshave beenkept. We alsoincludea discussion bottom contact is initally cold, as shown by the common
of the respectiverolesof physical,geochemicaland petrological occurrenceof basalchill zones,the temperaturegradientthrough
models.This is importantbecausethe three approachesdo not a thick layer of adcumulaterocks nmst be directed downwm'd
deal with the same pieces of evidence and differ in their and small. Thus, if heat is removed by conductionthroughthe
predictiveabilities.For example,thereare few physicalmodels bottomcontact,the melt regionwhosetemperatureis closeto the
of igneous textures, and yet these constituteone of the key liquidus. where adcumulus growth occurs, is thick. This is
observationsusedby petrologists.Physicalmodelsare only able inconsistentwith the chemical budget considerationsoutlined
to addressgross features of igneousintrusions,and hence we above. Thus Wager [1963] proposed that heat must be
shall include a descriptionof these. For each mechanism,we transportedinto the overlyingmelt layer, whichimpliesthat the
explain its implicationsfor petrologicalanalysisand discussthe interior of the reservoir is undercooled. Morse [1986] has
evidencefor and againstit in the geologicalrecord.
recentlyelaboratedon this idea.
In this section,we review a seriesof modelsfor magmatic
differentiationwhich do not deal explicitly with the physicsof
the differential motionsbetweenmagmaand crystals.Most of
these models have been developed within a chenfical and
thermodynamicframework and have not adresseddirectly the
relationshipbetweenthe thermalregimeof mag-machambersand
their differentiation
behavior.
Cumulus Theory
For mostof this cemm'y,principallysincethe influential work
of Bowen [1928], the main emphasis has been on the
investigationof the thermodynamicsof the chemicalequilibria
between crystals and liquids in various igneoussystems.In the
small capsulesin which this type of experimentis carried out,
large thermalgradientscan generallybe avoided,andthe charge
is essentiallyhomogeneous.
This work hasfocusedon the liquid
compositions
and mineralassemblages
generatedasa functionof
temperaturefor a given startingcomposition.Perhapsas a result,
magma chambersbecameviewed in the samelight, that is, as a
body of liquid with essentially one compositionat any given
Cawthom and McCat2hy [ 1980, 1985] have arguedthat at the
floor of an intrusion. crystallization occursin situ, and have
stressed the continuous
variations
of trace elements over some
zones of the Bushyeld complex. For example, chromium
concentrationvariesin a monotonicfashionover a heightof 8 m
in magnetite layers of the Upper Zone of this complex.
Cawthornand McCarthy [1980, 1985] considered
an essentially
flat solidification front moving at a constantvelocity with a
diffusionboundarylayer developingin the melt aheadof it. In
the case of a compatible trace element, the initial solid takes a
large amount of this element, as dictated by the partition
coefficient, and a diffusive boundarylayer developswhich is
depleted in this element. This leads to a decrease of the
concentrationin the solid rock until a steady state is reached
such that the solid has the same trace element concentration
the melt. The observations
are inconsistent
with known
as
values
for the diffusion coefficientof the speciesstudied,and hence
someform of convectionis called for [McCarthy et al., 1985].
This model relies on the assumptionthat the interfacebetween
solidand melt canbe treatedas a flat boundary,suchthatthereis
little gradientof interstitialmelt fractionbelow it.
JAUPART AND TAIT: MAGMA
Reinjection
One striking feature of large igneous intrusions is the
repetitionof sequencesof layers, in which the proportionsof
constituentminerals vary, on a wide range of length scales
[Parsons, 1987]. Large-scalecyclic layeringoccurson length
CHAMBER
DYNAMICS
17,617
A large number of studies have dealt with the diffusive
transportof a given chemical speciesdue to gradientsof other
intensive thermodynamic variables. One such variable is
temperature,which givesrise to the Sorereffect [Hildreth, 198I;
Walker et al., I981: Lesher, 1986]. Other variables are the
concentrationsof the other chemical speciesinvolved [Baker,
1990, 1992; Kress and Ghiorso, 1993; Trial and $•era, 1994;
this type of layering,Jackson[ 1961] developeda sophisticated
Liang et al., 1994; Kressand Ghiorso, 1995]. The effectsdepend
conceptualmodel involving an interactionin a closed system
on the magnitude of gradientswhich are present,which cannot
between convectionand crystallization.He proposedthat the
be specified a priori. In realistic conditions with thermal
build up of crystalsin a sublayerin the lower partof the magma
boundary layers evolving due to heat conductionor convective
scale of 50 m. in ultramafic
zones at the base of intrusions. For
chambermight isolate it from the main body of liquid. This
sublayer then crystallized separately, until eventually the
concentration of crystals became sufficient to suppress
convection and an abrupt sedimentation event occurred,
depositingonecycliclayer.The explanationthathasbeenmuch
more favored in the recentliteratureis that of reinjectionof the
chamber with more primitive melt that interrupts the
crystallizationsequence.
Originalgeologicalexampleswere the
Rhum Intrusion [Brown, 1956] and the Muskox Intrusion [Irvine
and Smith, 1967], but this interpretationhasnow been extended
to others.
Assimilation
With the adventof traceelementand isotopegeochemistry,it
has become clear that wall rock assimilation may play an
importantrole [Allbgre and Minster• 1978; DePaolo, 1981].
ChangingSr and Nd isotopicratiosin cumulaterocksprovide
unambiguousevidence for the mixing of melts coming from
sources with different compositions and ages. Present
interpretationshave fractional crystallization and assimilation
occurringsimultaneously,with the magmachambermelting its
own hostrocks [DePaolo, 1985].
GeochemicalModels of Igneous Intrusions
The presentconceptualframeworkfor the chemicalevolution
of magma reservoirs includes fractional crystallization,
assimilation,reinjection,and venting. Detailed modeling of the
pathsin compositionspacethat are followedby liquids hasbeen
carried out, generally concentrating on trace elements and
isotopes[O'Hara, 1977; Palacz, 1984; Stewart and DePaolo,
1990]. Major element trends can be deduced from phase
diagrams, when they are available [Ghiorso, 1985; Nielsen,
1988, 1989; Ghiorso and Sack, 1994]. In these models,
breakdown,
the mass fluxes due to Sorer diffusion
and cross
diffusion are small [Carrigan and Cygan, 1986: Lesher and
Walker, 1988]. Such eflkcts, however, are important on a small
scaleand may be responsibletbr someof the tkaturesof igneous
textures.
In many "parameterized" differentiation models, a key
assumptionis that of a homogeneous
system,in which eachpart
of the systemsimultaneouslyundergoesthe sameevolution.This
is the major premise that more recent work on convection and
the dynamics of boundary layers has called into question.The
emphasishas now shifted to studiesof the physicsof partially
crystallizedlayers, as anticipatedby Hess [ 1972].
Drilling throughthe partially solidified crust of basalticlava
lakes at Kilauea volcano, Hawaii, has provided us with an
opportunity to study directly how a large body of melt
differentiates.A seriesof studieshave given us accessto profiles
of solid Iraction, interstitialmelt compositionand temperatureas
a function of time and have indicated that several processesare
simultaneouslyactive [Richter and Moore, 1966; Wright et al.,
1976: Heir., 1980: Helz and Thornbet, 1987: Heir., 1987; He& et
al., 1989]. For our presentpurposes,it is only usefulto mention
three. One is that crystal settling is essentially limited to the
coarsephenocrystswhich were presentin the lava when it was
erupted.The major crystalphaseswhich formed when the lake
cooled, olivine, augire and plagioclase, did not settle to any
appreciableextent.A secondresultis that low-densitymelt from
the floor cumulatepile risesthroughthe lake interiorandmixes
with the melt at the base of the growing upper crust. A third
result is that the boundary layers contain mineral assemblages
and coexisting interstitial liquids spanning the whole
crystallizationinterval betweenthe solidusand the liquidus.
Importance of Physical Models
parametersincludethe amountsof fractionationand assimilation,
which may be allowed to vary as a I•nction of time (and hence
stratigraphicheight in the cumulatelayer). In the following, for
the sake of simplicity, we shall refer to such models as
"parametefized."
Purposesof PhysicalModelsfor IgneousDifferentiation
Chemical evidence on igneous intrusions is rapidly
accumulating, which causes a dilemna. On the one hand,
building a physical model from first principles in order to
reproducesuchvastamountsof datais at presentimpossible.On
the other hand, a complex sequenceof eventsfor any given
Discussion:Differentiation in Large Magma Chambers
magma chamber implies a large number of adjustable
Differentiation of a magma chamber involves large-scale parameters,
whichvirtuallyensuresa satisfactory
fit to the data.
relative motionsof solid and liquid, which mustbe studiedwith Thus it hasbeenarguedthat it is pointlessto try andunderstand
specificmethods.Experimentscarriedout with naturalmagmas the physics of each processindividually. Setting aside the
in petrologicalcapsulescannot be used to studythe importance obviouspointsthat the advanceof scientificknowledgerequires
of such processes in a physically realistic manner. The
characteristic length scales inherent in such phenomena
determine,lbr example, the magnitudesof the buoyancy and
viscous forces acting in a convective flow and hence the
dynamic regime. Whereas laboratoryexperimentswith natural
magmatic liquids establish equilibrium thermodynamic
constraintswhere length scalesdo not have to be specified,they
give no informationon dynamicphenomena.
suchfundamentalstudiesand that extrapolatingknowledgefrom
known intrusionsto othersituationsrequiresan understanding
of
the physicsinvolved,there are two main reasonswhy physical
models are needed.
Parameterizedchemicalmodelsmay not be unique, and some
aspectsof them may be criticizedon physicalgrounds.In other
words,suchmodelsguaranteeconsistencywith the data, as they
arebasicallysetup asinverseproblems,but thereis no guarantee
17,618
JAUPART
AND TAIT'
MAGMA
of compatibilitywith physicallaws. For example,considera
case of adcumulusgrowth, such that interstitial melt between
touching crystals evolves chemically to produce a totally
crystallizedrockessentially
madeof a singlemineralphase.This
requiresefficientchemicalexchangebetweenthe cumulatepile
and the overlying reservoirof liquid. The point that chemical
diffusionwouldbe ineffectiveovera largethickness
of partially
solidified material was appreciatedby the proponentsof the
cumulustheory, who concludedthat adcumulateswere evidence
of thin partially-solidified
layers.A physicalmodelis requiredto
demonstrate
that this is a correctinference.Otherkey elements
of petrogeneticmodelshavenot beenstudiedfrom a physical
viewpoint.For example,despitetheenormous
weightattached
to
the ideaof crystalsettling,not muchconsideration
wasgivento
howthismightactuallytakeplacein a convecting
magma.One
thing madeclear by the physicalstudiesis that in a reservoirof
largedimensions,
manyprocesses
whichmightseemplausible
at
first sightare foundto be unstable.
Another reason to develop physical models is because
parameterizedmodels are seldom able to specify the actual
mechanisms
at work. For example,the amountof assimilationis
oftenfoundto varyasa functionof timein an evolvingchamber
CHAMBER
DYNAMICS
Noyes,1979; Campbellet al., 1978]. This is clearlyinconsistent
with crystalsettling.
Evidence
From
Lava
Series
Another problem has been the comparisonbetweenintrusive
and extrusive rocks that gives direct insights into the
compositionof melt in the reservoirbothas a functionof depth
andas a functionof time. Many volcanicdepositsgive evidence
that magmachambersare chemicallystratified[e.g.,Larsenand
Thorarinsson,1977; Hildreth, 1981; Bogaardand Schmincke,
1985; Huijsmans and Barton, 1989; Druitt et al., 1989]. This
violatesthe assumptions
behindmostgeochemicalmodels.
General Features of Igneous Differentiation
We show here that the characteristicsof igneousintrusions
vary systematicallyas a functionof a magmachamberthickness.
Also, the same internal features are repeated in different
intrusions of similar overall bulk composition and size,
indicating that the physical processesof differentiation are
reproducible. Such regularities in the rock record are best
assessed
from a physicalpoint of view.
[DePaolo,1985;Stewartand DePaolo, 1990].The meltingof
The degreeof internaldifferentiationof igneousintrusionsis
countryrockmay occurduringor soonafteremplacement,
with
largest in basaltic systems,and is related to the size of the
a large volume of magmaslowly gettingincorporatedin the
reservoir. Figure 1 shows the compositionsof plagioclase
primaryliquid.Alternatively,it may occurcontinuously
whilst
feldspar, a ubiquitous phase, in several mafic intrusionsof
the reservoiris differentiating.
It is the efficiencyof mixing
similar bulk compositionswhich span almost 3 orders of
whichvariesin thefirstcase,whileit istheefficiency
of melting
magnitude in vertical thickness. A general effect of
which varies in the second one.
differentiation is that the anorthite content of plagioclase
decreases.
Sucha decreaseis very pronounced
as onegoesup
Inconsistencies
With the CumulusTheory
the stratigraphicsequencein the Bushveldand Skaergaard
Somefeaturesof layeredigneousrocksappearinconsistent intrusions, which are approximately 9 km and 3 km thick,
with the cumulustheory.In the Skaergaard,
thereis a sharp respectively.In the 300-m-thick Palisadessill, differentiationof
discontinuitybetweenthe rocksthat are supposed
to have the melt was muchweaker.Finally, in the thin (40 m) Dippin
formed by sedimentationonto the floor of the intrusionand the
sill, thereis no significantvariationof plagioclase
composition.
Thesefeaturesare apparenton a large scalebut are mademore
complexon a smallerscale.Anotherimportantpointshownby
walls.Olivinecrystals
maybe foundin thelattereventhough Figure 1 is that in casesin whichbothfloor androof sequences
Upper Border Group and Marginal BorderGroup that are
thoughtto haveformedby growthof crystals
stickingontothe
theyaremuchdenserthanthe meltfromwhichtheygrew.A are preserved, both show the same trend of differentiation;
majorcumulusphaseof maficrocksis plagioclase
whichseems however,the floor sequenceis typically 6-7 times thickerthan
likelyto belessdense
thanmanymaficmagmas
[McBirney
and the roof sequence.
PALISADES
1.0
BUSHVELD(9 km )
SKAERGAARD
(3.2 km )
SILL (350 rn )
DIPPIN SILL (40 rn )
0.8
i
0.t5
.
0.4
0.2
0
J
I
30
I
? •
J..
30
_1
!,
t
50
70
90
Anorthite
I i 1i
,
30
50
70
90
30
50
70
90
mol. %
Figure1. The stratigraphic
variations
of plagioclase
composition
for intrusions
spanning
a largesizerange.
Differentiation
becomes
morepronounced
thelargertheintrusion.
Bothroofandfloorsequences
of thePalisades
SillandtheSkaergaard
Intrusion
arepreserved
andshowthatthefloorsequence
isthickerthantheroofsequence,
typicallyby a factorof 6. References
areWagerandBrown[1968],McBirney[1989],Shirley[1987],andGibb
and Henderson[ 1978].
JAUPART AND TAIT: MAGMA
CHAMBER
DYNAMICS
17,619
10kin
,•
In Figure 2, we compare the vertical distribution of
incompatible trace elements in three of the same intrusions.
Starting from the floor, concentrations remain essentially
constant over a large vertical extent and increase markedly
toward the top. This indicates that as crystallization and
differentiation proceeded,liquid/crystal separationwas very
efficient and residual liquid becameprogressivelyenriched in
Fe-oxides in
incompatibletrace elements.The final concentrationbuildup
occurswhen the melt was sufficiently enrichedto precipitate
5km -specifichostminerals.
BANDED
Mafic intrusions exhibit similar mineral assemblagesand
overall stratigraphicrelations.This point was emphasizedby
WagerandBrown[1968] andJackson[1970] andimpliesthatas
far as the main differentiationtrendis concerned,essentiallythe
Elements
deposi,s
• ..... 1
samesequence
of processes
wasrepeated.For example,Figure3
showsthe stratigraphyof the Bushveldand Stillwaterintrusions
U1.,'rRAMAFICS
L'LTRAMAFICS
and demonstrates
that major changesof mineral compositions
occur at similar heightsin the sequence.Furthermore,major
01an ---preciousmetal-bearingsulphidehorizonsare foundat almostthe
samepositions.A very similar sequenceseemsto exist in the
BUSHVELD
STILLWATER
much younger Sept-Iles mafic complex, Quebec, which has
similardimensions[Loncarevicet al., 1990]. In comparison,
the Figure 3. Comparative stratigraphyof the Bushveld and
much thinner Palisades sill was never able to produce dunites
Stillwaterintrusionsemphasizingsomelarge-scalefeaturesof
and extreme concentrationsof preciousmetals.Furthermore,the
themineralogicsequences
from [Naldrettet al., 1987].
onsetof mineralogicallayering occursat similar distancesfrom
Platinum
Group
I$œRIF"
!
Plagioclase
in• •
ine
in - ':'•'•'•••!:
the lower
contact
in intrusions
of different
thicknesses.
For
example,a layer of increasedolivine contentis observedat 11 m
from the bottom in the 600-m-thick Lambertville sill [Jacobeen,
1949], at 12 m in the 350-m Palisadessill [Walker, 1940] and at
9 m in the 43-m Dippin sill [Gibb and Henderson, 1978].
Another example is that in large intrusions, rocks highly
enriched
in olivine
are first found at distances between
100 and
300 m from the floor contact in several different complexes:
Stillwater [Jackson, 1961], Bushveld [Vermaak, 1976], and
Muskox [Irvine, 1970]. These observations indicate that
differentiationstartsat some specificdistancefrom the contact,
independentlyof the size of the intrusions.
Structure of Boundary Layers
Model Thermodynamic Systems
Physical models cannot realistically hope to incorporatethe
same level of chemical and thermodynamicdetail that exists in
natural silicate systems,and it is legitimate to ask what is the
PALISADES SILL
SKAERGAARD
BUSHVELD
1.0
.
_
0.6
-,.
0.4
-I
,ô
o
o
I
I
lOO
200
,,
1 ,I
100
20o
I
300
Zr concentration (ppm)
i
2
6
10
best kind of simplified analogue.This dependson the problem
which is being posed.
Systemsinvolving both binary eutecticswithout solid solution
and a singlesolid solutionloop have beenused.Natural magmas
exhibit
a mixture
of these features
in the sense that
several
different solid phases form, while each phase exhibits some
extent of solid solution. Magmatic differentiation trends are
recordedboth by the varying amountsof mineralsphasespresent
in the rocks and by the so-called "cryptic" variation of the
compositionsof the various solid solutions.In binary systems
with just a solid solution loop, all nucleationtakes place at the
initial temperature and further crystallization is achieved by
growth at different compositions.The solid compositionmay
adjustby reequilibrationwith liquids if solidificationconditions
permit. In binary eutectic systemswithout solid solution, each
one of the two solid phases has a fixed composition and the
chemical evolution of the liquid can be directly predictedas a
function of fraction crystallized. Enrichmentor depletion of the
final solid with respectto the initial liquid can be measuredfor
either componentof the binary.
The origin of modal layering, that is, the formation of solids
with variable proportionsof different mineral phases,and the
conditionsfor adcumulusgrowth can be studiedwith a simple
eutecticsystem.It will certainlybe desirablein the future to have
some solid solution in order to see how this other degree of
treedom affects crystallization conditions.One may reasonably
expect that as far as the fluid dynamics of crystallization are
concerned,this will not changethe basicprinciplesat work and
will only affect the specificdetailsof the chemicalevolution.We
discussbelow observationsin the boundarylayers of lava lakes
which shedsomelight on this issue.
Quiescent Case
Th (ppm)
Before evaluatingthe effects of differential motion between
Figure 2. Stratigraphicvariationsof incompatibletraceelements magmaandcrystals,which entailsboth heatandmasstransfer,it
concentrationsfor three of the same intrusionsas in Figure 1. is useful to consider static conditions. This illustrates the initial
Referencesare Cawthorn [1983], McBirney [ 1989] andShirley conditionswhen motionsstartand allows a simplediscussionof
[19871.
severalfeaturesof coolingand crystallizationin a large chamber.
17,620
JAUPART AND TAIT: MAGMA
CHAMBER DYNAMICS
crystalsize, as is usually the case,thermodynamicequilibrium
may be achievedby diffusion between a crystal and the melt
surroundingit but cannotbe achievedover the whole boundary
layer. The simplestapproximationis that at every position,melt
and crystals are in thermodynamicequilibrium at the local
conditions. Thus the temperature gradient implies one of
chemicalcomposition.
For a •ven bulk startingcomposition,
the
This is probably the most important physical fact.
local value of liquid compositionlies on the liquidus and is
Thermodynamicconstraintsdictate that mineral assemblages determinedby the local temperature.The crystal content and
differ in bulk compositionwith the melt andhencethat gradients solidcompositionare alsoknownusingthe phasediagram.Hills
et al. [1983], Roberts and Loper [1983], and Bennon and
of melt compositionare set up when crystallizationoccurs.In
principle,one may envisagethe growthof a totally solidlayer, b•cropera[1987] have developeda so-called"mixture"model
with chemical diffusion in the melt supplyingthe required along theselines, where the systemof melt plus crystalscan be
elementsto the solid. However, this seldomoccursin practice studiedas a singlematehalwith•effectiveproperties
depending
anda two-phasesystemdevelopswith the solidphaseascrystals on temperature and crystal content. Experiments on the
disseminated
throughthe undercooledlayer.For binarysystems conductivecooling of simple binary systems,such as aqueous
with and without solid solution, this has been demonstrated
solutionsof simple salts,have shownthe validity of the theory
theoreticallyandexperimentallywhenthe coolingrateis abovea
and of the assumptionof local thermodynamicequilibrium
certain critical value [Mullins and Sekerka, 1964; Loper and [Huppert and Worster, 1985; Tait and Jaupart, 1992a]. In these
Roberts, 1978, 1981; Hills et al., 1983; Caroli et al., 1985;
calculationsand experiments,it may be seenthat the local solid
Worster, 1986]. For silicate melts, this is shown by direct tYactionincreasescontinuouslyfrom zero at the liquidus to one
observation[Helz, 1987]. Models for sucha mixed systemhave at the eutectictemperature.
been derivedusing variousapproximations.
In magma chambers, therefore, a thermal boundary layer
should contain the whole liquid line of descentof the initial
By definition,thereis a large gradientof temperatureacrossa
thermal boundary layer and, to a lesser extent, a gradient of
magma.Suchcharacteristics
havebeenobservedin basalticlava
pressure.If the boundarylayer is much thicker than the typical lakes. The summary of Helz [1987] statesthat the order of
appearanceof the phasesis simply relatedto the temperatureat
the local positionin the boundarylayer.The extentto whichthe
Wer
phasecompositions
reflectlocal equilibriumvariesaccordingto
the phase. Moving from the hottest to coldest parts of the
boundarylayer, as the interstitialliquid becomesmore evolved,
the olivinegrainsreequlibrateandhaveprogressively
moreironrich compositions.Diffi•sion is less efficient in plagioclase
grainswhich becomezonedin consequence,
equilibriumbeing
maintained only between the surfacesof the grains and the
interstitial liquid. Pyroxenesshow intermediatebehavior and
reequilibratepartially.Thus,in thisnaturalboundarylayer,local
equilibrium for the phases,the mineral compositions,and the
interstitialliquid compositionsis nearly attained.Someof the
interstitial liquids are rhyolitic in composition,even at an early
After its emplacement,magma loses heat to the surrounding
country rock which is initially effected through the growth of
cold thermalboundarylayersat the marginsof the body (Figure
4).
In mostcircumstances,
i.e., for normal"cold"countryrock,the
countryrock/magmainterfaceis below the solidustemperature:
thusthe boundarylayer spansthe whole crystallizationinterval.
o
o
Floor
Partially crystallized
layer
(mush)
\
\
ß
\,
\:
stageof evolution.
Departures from local thermodynamic equilibrium may be
expected but are very difficult to treat theoretically. Attempts
have been limited
to the definition
of the smallest
number
of
variableswhich allow a tractableset of equations[Loper, 1987;
rock
Hills and Roberts,1993] and to simpleparameterizations
of local
diffusion between crystals and surroundingmelt [Toramaru,
Tcf
Ts
T•
1991]. Using expressionsfor the kinetic ratesof nucleationand
crystal growth, Brandeisand Jaupart [1987a,b] and Spohn et
Temperat
ure'
al.[ 1988] have calculatedthe distributionof crystal sizes.This is
Figure 4. Showsqualitativelythe thermalstructureof boundary useful becausecrystal size not only dictates the efficiency of
crystalsettlingbut is also an independentvariablewhich may be
layers that are formed at the contactswith the country rock
colder than the solidus temperature.The coldest part of the measured. At any given time in the partially crystallized
boundarylayers contain solid rock, while the remainderspans boundarylayer, crystal size increasestoward the contactwith
increases.As
the temperatureinterval betweensolidusand liquidus.Thermal countryrock, while crystalcontentsimultaneously
cooling proceeds,the mean crystal size increasesand the final
convection leads to a higher heat flow through the roof than
throughthe floor and henceto an asymmetryin the thicknesses result in fully solidified rock will be an increaseof crystal size
of the two thermal boundarylayers. This can lead to a thicker with increasing distance from the margin. Model predictions
rock sequenceat the basethan at the roof. Two complicating have been comparedsuccessfullywith grain size data in several
factors are illustrated. One is the variation of liquidus sills and dikes [Brandeis and Jaupart, 1987a,b' Spohnet al.,
1988' Hort and Spohn,1991]. During solidificationat the floor
temperaturewith pressure,and henceheightin the chamber,and
the other is the possibilitythat the contacttemperaturesat the of a magmareservoir,for example,the largestcrystalsare lying
floor and roof are different.
in a high crystallinityregion closeto the margin:thosecrystals
.......
,
JAUPART AND TAIT: MAGMA
CHAMBER
with the largest settling velocities are already at the floor and
have nowhere
DYNAMICS
17,621
• Liquid
density
Temperatu
e
to settle to.
"Slurry" and "Mush" Models
When relative motionsbetweenmelt and crystalsare allowed,
there are two main typesof theoreticalmodels.Both are identical
in the motionlessstate and only differ in dynamic situations.In
"mush" models [Roberts and Loper, 1983; Hills et al., 1983;
Drew, 1983; Worster, 1991, 1992], the crystalsstay fixed with
respectto each other, and melt is allowed to move with respect
to them in responseto buoyancy forces. The variables for such
models are solid (or liquid) fraction, temperature, and melt
composition. This type of model applies, for example, when
crystallization takes the form of dendrites forming an
interconnected network of solids attached to the cooling
boundary.This is appropriateto many situationsin metallurgy
and to many aqueoussolutionsof simple salts which have been
usedin laboratoryexperiments.In the geologicalcase,it appears
valid for the coolingof spinifex-texturedkomatiiteflows [ Turner
et al., 1986]. It is also valid for the coldestpart of the boundary
layer where crystals start forming an interconnectednetwork.
This certainlyoccursat solidfractionshigherthan60%, whichis
the packing limit for a random spatial distribution of equal
spheresbut may, in fact, occurat lower solidfractionsas crystals
may be arrangedin chain structures.In "slurry" models [Loper
and Roberts,1987], crystalsandliquid may move,as a wholeor
independentlyof eachother.These modelsrequirethe additional
specificationof crystal sizes. A slurry may be involved in bulk
convective motions involving both crystals and melt.
Interestingly,one of the earliest slurry modelsis that of Malkus
[ 1973] who applied it to the coolingof Earth'score and included
crystal settling.
Liquid Density
Density varies as a function of both temperature and
composition, which may lead to two different kinds of
convectivemotions,driven by unstablethermal gradientsand
unstablecompositionalgradients.Thus the crucial issueis how
the densitiesof naturally occurringmelts tend to evolve as they
cool and differentiate. A conceptthat hasproved useful is that of
fractionation density [Sparks and Huppert, 1984]. This is the
densityof the chemicalcomponentsthat are incorporatedinto a
mineralphasebut consideredas a melt. This is an elegantway of
avoidingthe problemof the jump in densitythat occursbecause
of the change of phase. One can see directly,that if the
fractionationdensityof a mineralis superiorto the densityof the
melt from which it is crystallizing,the residualmelt mustbe less
dense,and vice-versa.An examplein which residualmelt is less
denseis given in Figure 5.
In natural magmas, the predominant effect of fractional
crystallization is to increase in the SiO2 content of the melt,
which tends to reduce density. In basaltic melts, density can
initially increasewith differentiationbecauseof an early trendof
iron enrichmentfrom primitive to ferrobasalts.The key issue
concernsthe existenceand positionof the point at which Fe-Ti
oxides start to precipitate, which is controlledby the oxygen
fugacityof the melt as well asits bulk composition[Justeret al.,
1989; Snyder et al., 1993]. Most basic and ultrabasic intrusions
have Fe-Ti
oxide minerals.
Atler
Fe-Ti
oxides saturate in such
tholeiiticsystems,the Fe/Mg ratio of the melt typicallycontinues
to increase
whereas
the absolute
Fe content
of the melt and its
densitydecrease.The initial volatile contentof the melt is also
o•
I
-I-
!
.,
o
,.
o o
.,
o
,,,
o
-
,.
,,, o -
Fully
crystallized
rock
I
Figure 5. Schematicsectionthrough a boundarylayer formed
when the lower contactis below the solidustemperature.A steep
temperature gradient is created by thermal diffusion. The
partially solidified region betweensolidusand liquiduscontains
the whole liquid line of descent. In this case the stabilizing
thermal effect on density is overwhelmedby the destablizing
effect of composition, and the bulk profile of density in the
interstitial liquid is unstable. There is also a thin, unstable
boundary layer just above the mush created by chemical
diffusion.
very important. Figure 6 from [Snyder et al., 1993] showsthat
for a particular basaltic liquid, the density maximum is
suppressed
for an initial water contentlargerthan approximately
0.5 wt %. Basaltsin subduction-relatedsettingsseemgenerally
to containmore than this amount[Sissonand Layne, 1993]. Even
mid-ocean ridge basalts which are among the dryest mafic
magmas quite commonly have close to this amount of water
[Byerset al., 1984; Dixon et al., 1988] as well as other volatiles
suchasCO2 andhalogens.
We concludethat crystallizationthe boundarylayer of magma
chamberswill in most circumstancesreleaselight residualmelt,
becausethe compositionaleffect that tendsto reducethe density
dominates the opposing thermal effect. Hence the interstitial
liquid will be convectively unstablein boundary layers at the
floor and sidewalls.
Boundary Layer Instabilities
Calculations show that unstable density gradients are
generatedboth within boundarylayers and at their edgesdue to
2,1'
0.o,• - -
•
• 2.62.5
:2,4 ....
...
,
MgO (wt-•)
Figure 6. The densityof residualmelt as a functionof chemical
differentiationfor a tholeiitic mafic liquid after Snyderet al.
[1993]. The density maximum that is present under dry
conditionsis eliminatedif the initial water contentis greaterthan
approximately0.5 wt.%.
JAUPART
17,622
AND
TAIT:
MAGMA
diffusion.Convectiontakesdifferent forthsdependingon the
locationof the boundarylayer.Along horizontalmargins,at the
roof andfloor, say,convection
will occuras a setof plumesof
smalldimensionsoriginatingfrom the boundarylayer.Along a
vertical or sloping margin, convectionwill take the form of a
sidewall current which may be either turbulent or laminar
dependingon the dimensionsand viscositiesinvolved. Research
has looked into these phenomenaindependently,whereasall
must be expectedto occur in a real magma chamber.However,
fortunately,
theseboundary
layerscontribute
in differentwaysto
the thermal and compositional evolution of the reservoir. In
terms of heat removal, the most efficient interface is that which
CHAMBER
DYNAMICS
intimate relation is not always appreciated,the "cumulus"theory
restson the existenceof thermal convection!It may thereforenot
come as a surprise that the existence or absence of thermal
convection has been hotly debated [Carrigan, 1987; Marsh,
1989; Huppert and Turner, 1991; Marsh, 1991; Davaille and
Jaupart, 1993b].
Temperature Difference Driving Convection
The Rayleigh number defines the potential for thermal
convection in a layer of liquid subjected to a temperature
difference
AT:
liesat theroofiThus,for the purposes
of determiningthecooling
rate of a magma reservoir, accurate understandingof this
Ra =
g otATd3
(1)
KV
boundary layer must be obtained. On the other hand, for the
purposesof lookingat the cum.ulatesequencewhichgrowsat the
where c• is the coefficient of thermal expansion,r is thermal
floor of a sheetlikeintrusion,attentionmustbe paid mostlyto in diffusivity, d is the thickness of the liquid layer, and v is
situ crystallizationin the boundarylayer [Jaupartand Brandeis, kinematic viscosity. The Rayleigh number may be calculated
1986], with additional effects of crystal settling from the once appropriatescaleshave been specifiedfor the variables. In
reservoirinterior.To understand
how the chamberliquidinterior magma chambers,temperaturedifferencesimply changesof melt
may becomechemically stratified,one must focus attentionon viscosityand rheologicalchangesdue to the presenceof crystals.
the sidewalls,althoughboundarylayer instabilitiesat the roof Thus there are large variations of physical properties, which
andfloor may contributesomewhatto the process.
makes it difficult to select the proper scales.For example, it is
clear that the overall temperaturedifferencebetweenthe magma
and its countryrock, which may take valueslarger than 500øC, is
Thermal
Convection
not relevant as magma is chilled againstthe colder countryrock.
Compositionalconvectionweakly affectsthe thermalregime In the definition of the Rayleigh number, the thicknessof the
of crystallization[ Tait and Jaupart, 1989, 1992a]. Thus how the liquid layer is raisedto the power three, and hencethe size of the
interior of a magmachambercools and crystallizesdepends systemis the most important parameterconcerningthe existence
critically on the existence of thermal convection. The overall or absenceof convection. In a large reservoir, therefore, some
coolingtime of a reservoirwill alsodependon heattransportin form of natural convection seemsinevitable. At high values of
the roof rocks, whether or not they melt, whether or not Ra, when convection is active, the important length scale is the
hydrothermalconvectionoccurs,their thermalconductivity,etc. thicknessof the unstableboundarylayer, and it is sufficient for
The thermalregimeof the magmaalso bearson the importance many purposesto studythe local dynamicsof boundarylayers.
of crystalsettling.In the absenceof thermalconvection,crystals
Most knowledge of thermal convection pertains to constant
nucleateand grow only in boundary layers, and the interior of
viscositysystemsand can only be extrapolatedto the magmatic
the reservoiraway from the boundarylayersremainsat its initial case with caution. In general terms, one expectsthe coldest part
temperature. With thermal convection, on the contrary, the of the boundary layer, which is very viscous,to remain stable,
whole magma reservoiris being cooled by the motion of cold and the key question is to define which part of the overall
plumes, and crystals may nucleate and grow over the whole temperaturedifference is available to drive convection.On the
magma volume (Figures 7 and 8). Thus, in fact, althoughthis basisof thisgeneralprinciple,Turneret al. [ 1986], Brandeisand
..
ß:* "ill!??•*..................
....
,::::':-:':
......
:.";-4
.... -....•....... '.......½::-'
;:';---h*.'x,.,,**..
-.:<
.........
'*...../"?.
..... ,. •.
Figure 7a A setof thermalplumesgenerated
by sudden
coolingat theupperboundaryof a layerof siliconeoil
Notethesmalldimensions
of theplumesin comparison
withtheoverallthickness
of thelayerof liquid.
JAUPART AND TAIT: MAGMA CHAMBER DYNAMICS
Conductivecooling
Convectivecooling
17,623
Assuming that partially crystallized magma behaves like a
slurry, it is possible to determine the characteristics of
convection at the roof of a cooling chamber [Davaille and
Jaupart, 1993b]. The viscosity contrast across the actively
convecting melt takes a typical value of about 10, and the
temperaturescalefor convectionis determinedby the viscosity
function
ATv -
dg
(2)
dT
Temperature
Temperature
Figure 7b. This contrastsqualitatively some aspectsof the
thermalhistoriesof bodiesof liquid that are cooledby thermal
conduction and convection. The left-hand panel shows
conductionin which the boundarylayers slowly thicken with
time and the center of the liquid layer stays at the initial
temperaturefor a significantportionof the coolinghistory.The
right-handpanelshowsconvection,in whichthe stirringeffectof
convectionkeepsthe boundarylayersthin and rapidly transmits
coolingto the centerof the liquid.
Marsh [1989], Worster et al. [1990], and Kerr et al. [1990] have
relied on the assumptionthat convectionis driven by the amount
of kinetic undercooling,i.e., the temperaturedifferenceaheadof
the partially crystallized layer, which takes a typical value of a
few degrees. This assumption was supported by laboratory
experimentson various systemswith dendritic mushy layers.
However, in such conditions, convective breakdown cannot
affect the partially crystallizedlayer simply becausethe crystals
are interconnected.In most casesof petrologicalinterest,thick
thermal boundary layers develop with crystals suspendedin
where T is temperatureand la is the magmaviscosityand where
all variablesare evaluatedat the temperatureof the interior.
Evidence
for Thermal
Convection
The occurrence of thermal convection in cooling magma
bodies is supportedby observationsin the molten region of
Hawaiian lava lakes [Wright and Okamura, 1977]. Cooling
occursfirst by conduction,and after a finite time, it is observed
that temperaturebegins to fluctuate. The magnitudeof these
fluctuationsvaries systematicallyas a function of depth in the
thermal boundary layer. This magnitudeis zero in the coldest
part of the thermal boundarylayer where the crystalcontentis
highest and increaseswith depth to a maximum value of about
20øC (Figure 9). These observationsare similar to what happens
in variable viscosity convection. The unstable boundary layer
involves melt with crystal contentsgoing from about 10%, the
value in the lake interior, to about 22% [Davaille and Jaupart,
1993b]. In this case,the slurry approximation,suchthat crystals
do not form an interconnectednetwork, is justified. Later in the
evolution of the magma body, the crystal content is high
everywhere,and the slurry approximationis probablynot valid.
Other evidence for the existence of thermal convection is that in
fluid.
several large sills and intrusions,rock sequenceswhich have
A seriesof recentpapershave addressedthe generalvariable crystallized from the roof are much thinner than those which
viscosityproblem,and scalinglaws for the unstabletemperature formed at the floor (Figure 1). Thermal convectionactsto keep
difference and for the convective heat flux are available [Smith, the upper thermalboundarylayer thin (Figure 4) [Worsteret al.,
1990].
1988; Ogawa et al., 1992; Davaille and Jaupart, 1993a].
Temperalure
TEMPERATURE
STRUCTURE
OF CONVECTION
Figure 8. In the coldestpartof the partiallysolidifiedboundarylayer,the crystalsmay form a rigid network,or
mush,whereasin the outerparta slurrymayexist.In a purelyconductivestate,crystalsthat sedimentinto the main
bodyof melt wouldbe expectedto remeltasfall into thehotterinterior(right-handpanel).In the convectivestate,
thermalplumesfall from the slurrypartof the boundarylayer andhencewill containcrystals.This may lead to
nucleationandgrowthof crystalsin the mainbodyof melt.
17,624
JAUPART AND TAIT: MAGMA CHAMBER DYNAMICS
where Ts is the melting temperatureof pure solid (composition
Cs).Equationshowsthat, in the mushylayer, thereis only one
independent thermodynamic variable, and hence doublediffusive convectionis not active. The densitydistributionin a
mush cooled from below and in which the residual liquid is
(compositionally)lessdensethan the startingliquid is shownin
Figure 5.
•, 1050
- .•l•nm'a
½rys•ass
e'
[- 1100
_
u.11150
300
e.e 9.1m
e--.. e,e'-e4ß \e,.e'
_
Onset of Compositional Convection
e....,,'*'.
ß.(' • 10.7
m
I
I
350
400
450
TIME (Days)
Figure 9. The structure of the upper boundary layer of a
Hawaiian lava lake after Wright and Okamura [ 1977], showing
the magnitude of temperaturefluctuationsthat were observed
that are associated with the onset of thermal
convection
in the
melt.
Implications for Magma Chambers
One consequenceof the formation of a mush, is that two
independentconvectiveinstabilitiesare possible[Worster, 1992;
Chen and Chen, 1991' Tait and Jaupart, 1992b]' that of the thin
chemicalboundarylayer just aheadof the mush and that of the
interstitialliquid (Figure 5). A local Rayleigh numbercriterion
for the former instability can be written
Ra =
g Ap]153
Dg
= Ra(crit)
(5)
where 15is the thicknessof the boundarylayer, Ap] is the
difference in fluid density acrossthe boundarylayer, D is the
chemicaldiffusivity,andg is themeltviscosity;
15is proportional
to the mush thicknessbefore instability occurs,and hence this
local criterionmay be rewrittenin termsof the mushthicknessh
[Tait and Jaupart, 1989]. A similar critical Rayleigh number
thattheheatflux outof theconvecting
magmatakeslargevalues criterionfor the onsetof instabilityof the interstitialfluid is
andmay be enoughto melt the overlyingcountryrock [Ahemet
g Ap2 II o h
The implications of the probable existence of thermal
convectionin magmachambersare essentiallytwofold. One is
al., 1981;Huppertand Sparks,1988].Thusassimilation
may
Rap=
= R% (crit)
(6)
indeed be achieved as the reservoir cools down and its amount is
estimated.One obvious feature of this processis that the rate of
melting decreaseswith time, as the reservoirbecomescolderand
more differentiated. The other implication pertains to where
crystallizationoccurs.Thermal convectionoperatesthroughthe
motion of plumes, which carry cooled magma downward, and
hence also small crystals. In such a situation, the reservoir
interior is well-mixed in the thermal sense, but the flow field is
where h is the mushthickness,K is the thermaldiffusivity, Ap2 is
the density difference acrossthe mushy layer, and II o is a
representative
permeability.In the caseof magmas,thechemical
boundarylayer becomesunstablefirst. Thus one expectsa first
phaseof weak compositionalconvectiondriven by the small
compositiondifferencein the chemicalboundraylayer lying at
the top of the mush,followedby a muchstrongeroneinvolving
madeup of plumelikeupwellings
and'downwellings
which- interstitial
meltin thewholemush.
Oncethissecond
instability
essentially extend over the whole thicknessof liquid. Thus
crystalsnucleatedat the roof may endup at the floor, wherethey
may mix with crystals grown in situ in different conditions
[Brandeis and Jaupart, 1986]. Another important fact is that
plume motions are intrinsically intermittent,which implies that
the record of crystallizationat the floor may be quite complex.
hastakenplace,the thin boundarylayerat the top of the mushis
destroyedandonly themushylayermodeof convectionremains.
Flow Pattern of Compositional Convection
The key idea for understandingconvectionin the mushis that
of porosityfluctuations.If chemicaldiffusionis neglectedin the
transportof solute,compositionalconvectionwill createporosity
fluctuationsbecausethe effect on porosityof advectiondepends
Compositional Convection
on the signof the verticalvelocity(W) [Flemings,1974;Fowler,
When coolingis from below at the floor of a magmachamber, 1985; Tait and Jaupart, 1992a]. Dissolutionandprecipitationare
an unstable density gradient can result if the residual liquid the means by which the solutebudget is closed.As fluid rises
producedby crystallizationis sufficientlydepletedin the heavy throughthe temperaturegradient,it heatsup, and downwelling
component.The essenceof the physicsmay be illustratedwith a fluid is cooled. The condition of local equilibrium requiresthe
binary system,for which one can write the liquid density(p) as
composition of the fluid to adjust by melting crystals in
upwellingsand crystallizingin downwellings.Near the edge of
(3)
p = po[ ]-a (T-To)+ • (C-Co)]
an upwelling, W is small, cooling dominates,and porositytends
to decrease,albeit less rapidly than in downwellings. At the
where T is the temperature and C is the concentrationof the centers of upwellings, W is largest and here advection can
heaviercomponent;
c•,thethermalexpansion
coefficient,and
dominateand porositycan increase(Figure 10). Thus dissolution
its compositionalanalogue,are positive constants,and Po is a is most efficient at the center of an upwelling and increasingly
referencedensityat the temperatureTOandcompositionCO. It is less so towardsthe edge. Horizontal gradientsof permeability
common that the compositional term dominates the thermal develop, which lead to different flow ratesin downwellingsand
term. In several simple binary systems, the liquidus can be upwellings.
approximatedas a straightline of constantslopeF, as is often
Fully Developed Compositional Convection
the casefor aqueoussolutionsusedin laboratoryexperiments:
We now present a synthesisof laboratory experiments and
T- Ts = r (C-Cs)
(4) theoreticalstudiesto documentthe developmentof convection
JAUPART AND TAIT: MAGMA
[Copley et.al., 1970;Sarazin and Hellawell, 1988; Beckermann
and Viskanta, 1988; Chen and Chen, 1991; Nellson and
Incropera, 1991; Tait and Jaupart, 1992a,b; Tait et al., 1992;
Ambergand Homsy, 1993]. As convectiondevelopswithin the
mush,porosityfluctuationsgrow and lead to flow focusing.The
initial planform is an array of hexagonal cells with linear
upwellings along the edges [Tait et al., 1992]. The pattern
changes by the edges of the hexagons getting choked with
crystals (Figure 10). This processdoes not necessarilygo to
completion,but when it does,the ultimate form is that of a set of
vertical channelsor "chimneys"devoid of crystalsat the nodes
of the hexagons,whereresidualmelt flows rapidly upward.The
process of chimney formation has been observed in several
metallic alloys and aqueoussolutionsand dependsstronglyon
the microscopic structure of the mushy layer [Huppert and
Hallworth, 1993].
Compositional convection causes the bulk liquid in the
reservoir to evolve chemically. This may be estimated with
various approximations of how the compositional budget is
closed[Turner et al., 1986; Woodsand Huppert, 1989]. Detailed
numerical calculations are not yet available over long time
intervals becauseof the necessityto resolve both small-scale
gradientsof porosity and permeability, as well as large-scale
chemicalevolution [Nellson and Incropera, 1991]. As we shall
CHAMBER
DYNAMICS
see, numerical calculations have been more extensive for
sidewall cooling becausethey are more amenableto the nature
and length scaleof the flow.
A crucial effect of compositional convection is that flow in
upwellings is considerably faster than that in downwellings.
Thus thermodynamicconditionsmay be far from equilibriumin
the upwellings. In the extreme case of chimneys, which are
devoid of crystals, the melt rises without reacting with the
cumulate layer (Figure 11). The compositional flux that is
carried by convection causes the body of overlying melt to
differentiate and hence its liquidus temperatureto decrease.The
effect of this, all else being equal, is to make the mush thicken
more slowly (Figure 12a). Compositionalconvectioncarries a
relatively low heatflux and so verticalprofilesof temperaturedo
not differ greatly from those that would be observed due to
conductionalone. In consequence,the greaterthe compositional
flux, the thinneris the mushfor given thermalconditions(Figure
12b). The residual liquid flowing out of the mush is not on the
liquidus becauseit has been heated up whilst rising through
high-permeabilitychannels.This fluid is mixed into the body of
overlying liquid and hence will tend to generate a path of
evolutionin temperature/composition
spacethatis differentfrom
the liquidus.That is to say that in the absenceof other effects,
this type of convectionwill causethe overlyingliquid to become
Figure 10. Photographs
showingthe development
of porosityfluctuationsin the mushformedin an experiment
with aqueousNH4C1 solution.A cellularpatterndevelopsinitially, with upwellingoccurringalongthe marginsof
hexagonalcells.This ultimatelybecomesfocused,andonly cylindricalchimneysremainthat form at the nodesof
the hexagonalcells.
17,625
17,626
JAUPART
AND TAIT'
MAGMA
CHAMBER
DYNAMICS
Figure 10. (continued)
superheated
(Figure 13) (seealsoMorse [1986]). This is contrary of the basal zone is taken to be where olivine becomes the main.
to the assumptionof many petrologicalmodelsthat the systemis constituentof the rock [Zientek et al., 1985]. Figure 14 showsan
homogeneousat all times, with crystalsdistributedthroughout enlargedportion of a simplified phasediagram for such a mafic
the liquid.
system and also the structureof the conductiveboundary layer
prior
to the onset of compositional convection. Basal zones
Evidence From Intrusions
shouldrecordthe structureof this boundarylayer. Right adjacent
The onset of convective differentiation occurs at some finite
to the contact, the initial liquid can be fully crystallizedin situ
time, when unstabledensity gradientshave built up over a before the onset of convection. If negligible mass transport
criticalthickness.Thusoneexpectsto seea transitionin the rock occurs,the same final rock compositionshould be found at all
sequencefrom early formed units to later units which formed levels. As we move up the stratigraphicsequence,however, the
when compositionalconvectionwas active. Studiesof layered rocks becomeprogressivelyenrichedin pyroxene and olivine,
intrusionshaveusuallyfocusedon the cyclicunits,withoutmuch which contain the high melting point componentsof the melt
attention being paid to their relationshipto underlying basal (Figure 14). This progressionmay be interpretedasrecordingthe
zones.The first event discussedin any detail is the formationof advection of fresh melt from the uncrystallized interior of the
the first olivine cumulatelayer as a resultof reinjection[Irvine reservoir,which providesthe requiredflux of high meltingpoint
and &nith, 1967; Wilson, 1982; Raedekeand McCallurn, 1984]. components.Sucha convectivecirculationis a prime candidate
This model requiresthe first crystalon the liquidus,olivine, to as a mechanismof adcumulusgrowth [Kerr and Tait, 1986; Tait
settledirectly onto the floor. However, crystallizationrequires and Jaupart, 1992b].
By continuity,the downwardflow of melt from the overlying
cooling and hence some boundary layer growth prior to
reinjection and settling. Thus olivine should settle onto a reservoirrequiresan upward flow of the residualmelt. A related
cumulatelayer containingmineralsformedat temperaturebelow question is to find field evidence for this upward flow. An
the liquidus. Cooling from the bottom is demonstratedby the important observationis that adcumulaterocks appear to be
existenceof chill zones and hornfels,showingthat the magma homogeneousover large distances. Thus, if they are due to
downward flow from the reservoir interior, the return flow must
lost heat to the underlying rock.
We now look in more detail at the internal stratigraphyof have been localized in narrow zones. The focused flow structures
basalzonestaking the Stillwater intrusionas an example[Page, of mushylayer convectionhave the requiredproperties.Both the
1979]. Adjacentto the basalcontactwith countryrock, the rocks Bushveld and Stillwater intrusions show vertical or subvertical
are fine-grained. Moving up the stratigraphy, they become structureswhich crosscutthe horizontallylayeredrocks,suchas
coarser-grained,indicating that the cooling rate was decreasing, iron-rich pegmatitesderived from very evolved melts [Viljoen
and pass through a sequenceof plagioclase/pyroxenebearing and Scoon, 1985; Scoon and Mitchell, 1994]. The rocks in these
rocks to thosecontainingmainly pyroxene(Figure 14). The top structurescrystallized from more differentiated melts than did
JAUPART AND TAIT: MAGMA CHAMBER DYNAMICS
17,627
;½.•;
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•..•:•: .........•%:........:
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'":.•'•:':•.."•:<"'q•:.•!"
½•;:•D• .;'½'"•%•••,
',.•'•':•2"•';•
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"'••5-%:;.•
"•
'•"•4 • %';•':• .;5•.;.?'•.'•'•
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z/•.'....
....................
•
::•:.•*•-..•-•/;.:..•.•.•.:½•-;.'•;..
.......
.• ......;•:•
½ ,..
..........:':.....
." ½::•:':'""
; ¾."•' '•'X-':
::•'?¾:-:•"::':•'•
"•"•
.,..•
.....:......:,.•.::•
.:•.-'•.-..:..:
...-.
. ½..•&.••,?.• ...
.....
:'
..:,..;
......,..:,•
-•..
Figure11.Fullydeveloped
compositional
convection
inwhich
cylindrical
plumes
arerising
fromchimneys
inthe
mushyregion.The lower boundaryof the tank is cooled,while the othersare insulated.The flow patternmay be
contrastedwith that of thermalconvectionin Figure 7.
the hostrockswhichthey cut, andfurthermore,the higherup in
the overall stratigraphythey are found, the more differentiated
are their compositions.
The stratigraphic
sequence
of an intrusionrecordsa temporal
sequenceof events in the chamber. The liquid part of the
reservoirevolveschemicallyat a small rate becauseof its large
size, which leads to the gradual variation of composition
documented
above(Figure 1). At the floor,the rateof thickening
of the crystal pile diminisheswith time, in part becausethe
coolingrateis decreasing,
andin partbecausethe liquidusof the
melt is decreasingwith time. This implies that stratigraphic
gradientsin the rockcomposition
cannotbe simplyinterpretedin
termsof ratesof processessuchas differentiationor assimilation
in the liquid interior.For example,a steepgradientof isotopic
composition, such as that found in the Bushveld complex
[Sharpe, 1985] may not necessarilyimply a rapid change,such
as the arrival of a new batch of magma. It may also be
interpretedas recordingprogressiveassimilationat a time when
the mushwas growingat a very slowrate (Figure 12).
Anotherpoint concernsvolatile species.The presenceof very
evolved (rhyolitic) melt compositionsin the cold parts of the
boundarylayers of basaltic lava lakes implies that in the case
wherethepressureis highenoughto havelargerinitial dissolved
volatilecontentsin the melt,volatilespecieswill be considerably
enricheddeep in a magmaticmushylayer. Thus fluids may be
generatedvery early in the historyof crystallizationand are not
necessarilyto be associatedonly with the latest stages of
differentiationof the whole mamabody. Suchfluids may not be
expectedto remain in situ becauseof their large buoyancyand
shouldpervadethe rocks. Fluids are indeed presentthroughout
the cumulate layers of the Stillwater and Bushveld complexes
[Boudreau et al., 1986; Mathez et al., 1989].
A final implication is that the liquid part of the chambercan
differentiate with crystallization occurring principally at the
margins.Thus the liquid may evolve chemically with few if any
crystalsin suspension.This possiblyexplainswhy very evolved
aphyric magmascan be erupted,with successiveeruptedliquids
following a differentiationtrend.The melt will haveondergone
crystallization
not only of the phaseor phasesthat ar• •rl the
liquidusof the mainbodyof meltbutalsoof all of the phases
that are crystallizing deep in the mush. A parameterizedmodel
by Langmuir[1989] showssomeof the consequerlces
of this
type of remixing for the chemicalevolutionof a melt re•ierv0ir.
Convection
Generated
at Sidewalls
A vertical or sloping boundary differs from the case of a
horizontal boundary in that there is no stable conductive state
and henceno stability criterionanalagousto the critical Rayleigh
number. The situation is inherently unstable. Although the
fundamentalphysicalprinciplesare the same,theseflows have a
different logic becauseof the different orientationof the density
gradientswith respectto gravity. We briefly discussthe flows
that occurwhen light residualfluid is being producedby cooling
at a vertical wall. The major characteristicof these flows is to
generatea thin boundarylayer of fluid that movesparallel to the
17,628
JAUPART AND TAIT: MAGMA CHAMBER DYNAMICS
'•o6
--'
Conduclion/
!
......I convection
/
Composi•ion&l
conveclion
2
I
I
0
,I
0
,
200
, ,l
400
600
Ts
Time (rains)
T,
Ti
Temperature
Figure 12. (a). The thicknessof the mushylayer formedby coolinga liquid from below. The solidcurve showsthe
resultsin purely conductiveconditionsas the viscosityof the solutionwas too high to allow convectionto take
place.The growth is proportionalto the squareroot of time. The dashedcurveshowsthe growthof the mushfor
the same experiment as that shown in Figure 10. After the initial conductivephase,compositionalconvection
considerablyslowsthe growth of the mushbecauseit is causingthe liquidusof the overlying solutionto decrease
with time. Imposed thermal conditionswere the samefor both experiments.(b) The solid lines show temperature
profilesin the lower boundarylayer for threedifferenttimes.The verticaldashedline showshow the heightof the
mushwill increaseunderconductiveconditions(T L is the liquidustemperatureof the initial liquid). The decrease
of the liquidustemperaturethat occursunderconvectiveconditionsleadsto a thinnermushfor a given temperature
profile.
wall. Upon reachingthe upperor lower boundaryof the system,
this fluid spreadsout horizontally and then the slow vertical
return flow takes place outside the boundary layer over the
whole of the remainingsurfacearea of the system.The major
consequence of this is that vertical thermal and/or chemical
stratificationbuilds up in the reservoirof fluid.
Early analysesdelimited the regimesthat are possiblefor the
purelydiffusivecase,i.e., withoutmushylayersforming[Nilson,
1985; Spera et al., 1989; Jarvis, 1991]. Different regimesare
possiblebecausethermal diffusivity is very much greaterthan
chemical diffusivity and because the temperature and
composition are here taken to have opposing effects on the
density of the fluid [Nilson et al., 1985]. A thin, buoyant
chemical boundary layer is embeddedin a thick, densethermal
boundary layer. Depending on the numerical values of the
diffusivitiesand on the relative sizesof the buoyancyforcesthat
result from temperatureand composition,one of three possible
regimes will result. These are a thermally dominatedregime in
which all of the flow is downward becauseeven the depleted
buoyant fluid is draggeddown by viscouscoupling with the
coldestfluid in the thermal boundarylayer. A compositionally
dominated regime is also possible in which the buoyant fluid
closestto the wall dragsupward the densercold fluid. Finally,
there is a so-called counterflow regime in which the
compositionallylight part of the boundarylayer flows upward
while the thermally heavy part flows downward. Figure 15
shows an example of such a flow and the induced chemical
stratificationin the liquid part of the reservoir.
The
formation
of
a mush
at
a sidewall
modifies
the
quantitative aspects of such flows, as it leads to vertical
percolationof light residual fluid in the permeablepart of the
wall. Thermal downflow can only occur outside the mushy
region.Experimentalwork hasbeenlargelyqualitative[Huppert
et al., 1986a; Thompsonand Szekely,1988; Leitch, 1987] and
has shown the rapid buildup of compositionalstratification
(Figure 16). Numerousnumericalstudieshave alsobeencarried
out andare ableto reproducethe main featuresof boththe flows
andtheirchemicaleffects[SzekelyandJassal,1978;Maplesand
Poirier, 1984; Vollet et al., 1989; Oldenburgand Spera, 1991].
Numerical studiesare made possiblebecausetheseflows have
largercharacteristic
lengthscalesthanin the caseof horizontal
crystallizingmushylayers.
3O
•
,
I
_
I
,
I
,
,
I
/!
-.
,
,0i' ,,,,, ,
24
26
28
NH,•CI CONCENTRATION
(wt•)
Figure 13. The evolutionof the overlyingreservoirof liquid in
the phasediagram for aqueousNH4C] solutionsfor the same
experiment featured in Figure 10. Note that although
crystallizationis taking place in the lower boundarylayer, the
overlyingsolutionbecomesincreasinglysuperheated
becauseas
residualfluid risesup throughthe thermal boundarylayer in the
chimneys, it is heated above its liquidus by horizontal
conduction
of heat.
JAUPART
AND TAIT:
MAGMA
CHAMBER
DYNAMICS
17,629
O' 90
STILLWATER
40'
BASAl.
SEQUEN('E
Z
60
E
01+I,
/.
()1
+Opx
+I, /-A
Opx
+sp
. !,,
•.,_____ !{
l Olivine
- richrocks
_•
ß Pyroxene
- rich
rocks
•]]•Feldspar
+pyroxene
r-]Quartzbearing
mafic rocks
Country rocks
Tem pe ra I u re
Figure 14. (left) An enlargedportion of the phasediagramforsterite-anorthite-silica
at 10 kbar. The predicted
structureof the conductiveboundarylayer prior to the onset of compositionalconvectionfor such a systemis
given, showingcoexistingmineral phasesfor an initial liquid compositionlying in the olivine field. (right) A
simplifiedprofile of the mineralogicvariationsin the BasalZone of the StillwaterComplex,modifiedfrom Page
[1979].
dimensionwith height due to entrainmentof ambientfluid by
eddies, whereasin the case of laminar flow, horizontal growth
occursonly by moleculardiffusion. In the caseof the Laacher
See magma chamber, flow is likely to have taken place in a
laminar regime [Tait et al., 1987].
Perhapsthe major impact of these studiescomes from the
conclusion that evolved melt is collected at the top of the
chamberalmost immediately after cooling and boundarylayer
flow begin.We contrastthis with a mechanismfor generating
evolved melt by "homogeneous"cooling of the entire chamber
stratification.
and crystal settling. A layer of evolved melt at the top of a
An interestingaspectof the dynamicsof boundarylayersat the chamber can be generated by the sidewall boundary layer
sidewallsof crystallizingreservoirsis whetheror not flow takes mechanismin a time that is vastly shorterthanthe characteristic
place in a predominantlylaminar or turbulentregime, because timescaleof coolingfor the wholebodyof liquid.
the stratification that results, in terms of the form of the vertical
An important aspect of the dynamic behavior still to be
adressedfor sidewall flows concernsthe possibleinteractions
profile of a chemicalcomponent,is not the same.In the caseof
turbulent flow, the boundary layer increases in horizontal betweentheseand flows generatedfrom the horizontalboundary
A common feature of volcanic eruptionsis that the chemical
composition of the lava changes with time as an eruption
proceeds.One interpretationof suchdatais that the reservoirthat
is beingtappedby the eruptionis verticallyzonedin composition
becauseof fractionalcrystallisation[Michael, 1983; Wornerand
Schmincke,1984; Bogaardand Schmincke,1985]. Althoughlack
of knowledgeof parameterssuchas reservoirgeometrymake a
quantitativecomparisonwith chemicaldata extremelyhard, the
process of sidewall compositional convection is the best
candidate as a mechanism for producing this type of
17,630
JAUPART
AND TAIT:
MAGMA
Stream
function
CHAMBER
DYNAMICS
Composition
Figure 15. The flow patternand compositionisoplethsformedby cooling,crystallizationand releaseof light
residual fluid at a vertical sidewall [from Jarvis, 1991]. The dashedlines show the presenceof a thermal vortex
thatis rotatingin the oppositesenseto the boundarylayerflow, asnegativethermalbuoyancyis alsoreleased.
layers at the floor and the roof in crystallizing systems.The
effects of variable viscosity are also significant but do not
dynamic regime [Tonks and Melosh, 1990; Solomatov and
change
thequalitative
picture
[Speraetal., 1982;Jarvis,1991].
convective
flow nearthebounda?y
is required,andit is obvious
Dynamics of Crystal Settling
Stevenson,
1993].Someknowledge
•)f thelocalstructure
of the
from the previoussectionsthat this is not easily specified.For
thermalconvectionflows in magmaticconditions,it is likely that
crystals settle almost as fast as in the absence of convection
Views on crystal settlinghave come arounda full circle. This
[Martin and Nokes, 1989; Solomatovet al., 1993]. However, if
processwas first thoughtto be dominant,was then neglected, compositionalconvectionis generatedby crystallizationat the
and has been reevaluated recently. The first level of
floor, crystalsmay be kept in suspension
in the chamberinterior
approximationis that crystalsare passivetracersand do not by the strongupward currents.
modify the dynamicsof a givenlarge-scaleconvectiveflow. The
Regardlessof the details of such models, the contribution of
second'level of approximationrequiresspecificationof the crystalsettlingto the growthof a cumulatepile is measuredby
behaviourof particlescloseto the solidmargins.
the amountof crystalswhich are kept in suspension,
which is
Clearly, high flow velocities act to keep crystals from necessarilylimited by the heat budget of the reservoir. To
sedimenting,and this was the basis of early models where crystallize, cooling must occur and latent heat must be released.
crystals remain suspendedand well-mixed in the chamber The balance between the two may be achieved in several
interior.The chamberthen evolvesonly in temperatureand
differentregimeswhich lead to differentkindsof size layering
crystalcontent:the bulk composition
is not changing. [Hort et al., 1993;Jarvisand Woods,1994]. One generalresult
Eventually, crystals grow and the intensity of convection
decreases,
and sedimentation
occurswhenthe settlingvelocityof
the crystalexceedsthe localfluid velocity[Huppertand Sparks,
is that crystalcontentstayssmallin the reservoir.
As the focusof researchchangedto boundarylayers,wherein
situnucleationandgrowthcontributea largeamountof crystals,
1980].Sucha modelis applicable
to a well-stirred
reservoir crystalsettlingwas questionedas a mechanismresponsiblefor
where turbulenceis high even closeto the boundaries.However,
the most important featuresof magma chambers.It was not
in most cases,and especiallyin reservoirscooled from above, thought, for example, to be a significantagent to explain
flow velocities take small values at the floor and do not allow
layering.However,morerecentexperiments
demonstrate
that as
suspension.This emphasizesthat the flow field must be well
soonasthecrystal
content
exceeds
a fewpercent,
theinteraction
known, especiallyin the vicinity of the solid margins.Theory, between
theflowfieldandthecrystals
is strong
[HupPert
etal.,
numerical calculations, and laboratory experiments have 1991;Koyaguchi
etal., 1993;Sparks
etal., 1993].Theflowfield
established
howCrystals
settlein relatively
simpleflowfields, becomescomplicated,and the historyof settlingmay become
i.e., thosethat are dominatedby large-scaleeddies[Maxey and
Riley, 1983; Marsh and Maxey, 1985; Weinsteinet al., 1988;
Martin and Nokes,1989]. The mainresultis thatcloseto a solid
boundary, the flow velocity decreasesto zero and hence is
locally smaller than the crystal settling velocity. Thus
sedimentation
occursevenin an activelyconvectingsystem.The
application of these studies to magmatic systemshas been
criticizedon the groundsthat they are not in the ielevant
chaotic,with periodsof steadysedimentation
interspersed
with
periodsof catastrophic
depositionas the velocityof convection
dropsto smallvalues.An initiallyhomogeneous
convecting
layer may separateinto two layerswith differentbulk densities,
onedevoidof crystalsandthe otherwith a largerconcentration
of crystals.
Theformerlayerhasa smalleffectiveviscosity
and
convectsrapidly, while the other layer is more viscousand
convects at a smaller rate and hence with a smaller rate of heat
JAUPART AND TAIT: MAGMA
,.,1
Composition (CO - C)
Figure 16. The verticalprofilesof composition
thatdevelopedin
experimentsin which aqueoussolutionsof simple salts were
cooled at a vertical [after Leitch, 1987] or sloping boundary
[after Huppert et al., 1986a]. Fluid depleted in the heavy
componentthat enterspreferentiallythe crystalsaccumulatesat
the top of the tank due to the buoyantboundarylayer flow. In the
experimentswith a slopingboundary,the profilesgiven are those
that formed both when flow occurred beneath a cooled,
downward facing boundary and above an upward facing
boundary.
loss.One consequence
is that a temperaturedifferencebuildsup
betweenthe two layers,which may lead to a densityreversaland
an overturn of the layered system [Sparks et al., 1993]. Thus
crystalsettlingmay, in fact, be responsiblefor large-scaleflow
phenomenaand for intermittent depositionof crystals at the
margins.Researchin this area has barely begun,and one may
expectsignificantdevelopmentsin the future.
Open System Behavior
CHAMBER DYNAMICS
17,631
reinjectedliquid is the less denseof the two, a buoyantplume
forms, whereaswhen the reinjectedliquid is the denserof the
two, the tendencyis to form a layeredsystem.
When the reinjectedliquid formsa buoyantplumethat rises
into the chamber,the characterof the mixing that occursdepends
above all on the Reynolds number of the flow. The basic
possibilitieswere mappedout by Huppert et al. [1986b]. At low
Reynoldsnumber,a laminar plume is formed which risesup to
the top of the chamberand spreadsout to form a discretelayer
and mixing with the residentliquid is limited. On the otherhand,
a high Reynolds number plume will becometurbulentand as it
riseswill entrain the residentliquid leadingto intimate mixing.
When sucha turbulentplume reachesthe top of the chamber,its
mean composition will be somewhere between the initial
compositionsof the reinjectedandresidentliquids.It will spread
out and generatea downwardreturnflow and lead to the build up
of stratificationsimilar, from a fluid dynamicpoint of view, to
the sidewall boundary layer flows discussed earlier. The
characteristic "convex up" form of the profile of vertical
stratification generated by a turbulent plume in a finite box
[Baines and Turner, 1969] will result in this case.
Sparkset al. [ 1980] thoughtthat this mechanismmight explain
the tbrmation of mixed magmasobservedat mid-oceanridges.
The extensive mixing that can be associatedwith a turbulent,
buoyant plume may result in the scavengingoLtrace elements
from a large body of melt. This has been proposed as a
mechanismfor the formation of stratigraphichorizonsin large
mafic intrusions that are rich in precious metals such as the
Merensky Reef [Campbell et al., 1983]. Note that the
stratificationthat is establishedby thesebuoyantflows is such
that the less differentiated and hotter magma will be uppermost
in the chamber. This situation does not seem to be common, as in
eruptive sequences it is generally found that cooler, less
differentiated melt is the first to be erupted. Furthermore, it is
probable that these flows are limited to a restricted
compositional range. One circumstance in which turbulent
injection of buoyant primitive magma seems plausible is in
tholeiitic systemsfor which it is widely thought that a density
maximum occurs in the differentiation sequence around the
compositionof fen'obasalt[&Tyderet al., 1993].
When new magma that is denserthan the residentliquid enters
a chamber and the Reynolds number of the flow is low, a twolayer system will form. Several studieshave addressedthe fluid
dynamic behavior of thesetwo-layer systemsand how they may
eventually break down such that the two layers become mixed
The issue of how crustal magma reservoirsare fed by melts
ascendingfrom a deeperlevel chamberor a mantle sourceis a
fundamentalone. The possibilitythat magma reservoirsreceive
periodic reinjections of new melt has therefore been much
debated.Initially, this was not considereda key issue,probably
becauseof the enormousinfluenceof the early Skaergaardwork,
which suggestedthat this chamberhad essentiallycrystallizedas
[Huppert
andSparks,
1980;HuppertandTurner,1981].Both
a closedsystem.However, the recognitionof cyclic layering in
layers undergo thermal convection, with rapid heat transfer
large intrusionsand some observationsof magma mixing in
volcanicsuiteshave led to a numberof studiesof reinjection. acrossthe interfaceheatingthe upperlayer andcoolingthe lower
Indeed, one may arguethat fluid dynamic studiesof reinjection layer. Fractional crystallization takes place within the lower
layer causingthe compositionof the liquid to evolve and hence
are more completethan thoseof closedsystems,and thereis now
a tendencyto attributea great many observationsto reinjection its densityto steadilydecrease.At somepoint the densityof the
lower layer becomesequal to that of the upper layer, and the
as a wide rangeof behaviorsseemto be possible,asa functionof
the different parametersof the problem.The work that has been interfacebreaksdown leadingto rapidmixing of the two liquids.
done on the fluid mechanicsof reinjectionflows has paid very Mixing of the two liquids is delayed with respect to the
little attentionto how the new liquid is accommodatedinto the replenishment event both in time and in the sense that
finite volume of the preexistingreservoir.The two possibilities, considerableseparatechemicalevolutionof the liquids can take
generallyspeaking,are first that a volumeof liquid equivalentto place prior to mixing.
A numberof variationson this basicthemehave subsequently
that reinjectedcan be ejectedfrom the chamberby eruptionand
secondthat the volume of the chambercould be increasedby been carried out with the mixing taking place at a different
deformation of the walls.
moment or in different geometries according to the flow
responsible. At low input rate, the incoming liquid becomes
Reinjection
rapidly cooled and crystallized, releasing light liquid more or
The most thndamental division of such flows comes from the
less continuously and preventing the formation of a two-layer
relativedensitiesof theresidentandreinjectedliquids.When the
system[Huppertet al., 1982b].If theresident
liquidis stratified
17,632
JAUPART AND TAIT: MAGMA CHAMBER DYNAMICS
in density, a two-layer system forms, but the final mixing is
restricted in vertical extent. Campbell and Turner [1989)]
studiedthe effect on mixing of injecting a denselayer of liquid
but with some appreciable amount of initial momentum. The
incoming liquid formed a turbulentjet into which some of the
residentliquid was entrainedand mixed, beforespreadingout on
the floor of the chamber.Huppert et al. [ 1982a] and Thomaset
al. [1993] consideredcircumstances,thoughtto be relevant to
calc-alkaline systemsin which gas bubblesare exsolvedin the
lower layer, which generates a density reversal. Continuous
mixing of the two liquids also occurs when there is a large
viscosity contrast between the two layers, driven by strong
viscouscouplingat the interface.
Replenismentphenomenamay be responsiblefor large-scale
cyclic mineralogicallayering in the cumulatesequenceof large
mafic intrusions[e.g., Brown, 1956; Irvine and Smith, 1967;
Campbell, 1977; Raedekeand McCallurn, 1984; Wilson, 1982].
The tendencyhas been to analyze how a reinjectionevent could
lead to the formation of a specificmineralogicalsequencein one
cyclic layer [e.g., Irvine 1975; Raedekeand McCallum, 1984;
Tait, 1985]. Brandeis [1992] has shown, however, using an
overall massbalancefor the whole sequenceof cyclic layers in
the specific case of the Stillwater Complex, that such models
require more restrictive assumptionsthan had previouslybeen
realized on the amounts and compositionsof the reinjected
liquids.
Eruption
The effects of eruption on the internal structureof magma
chambers has not been studied in much detail. Most research has
looked at how the eruption processinducesmixing in the
volcanicconduit.For example,startingfrom a reservoirmadeof
two superimposedlayers of two different magmas, a basalt
overlain by a less denseand more viscousgranitic magma, say,
withdrawal from the chamber leads to the lower layer being
entrained into the volcanic conduit and mixed with the upper
layer liquid [Freundt and Tait, 1986; Blake and Ivey, 1986;
Spera, 1984]. Once the eruption has stopped, the layering
remains unperturbed.With a continuouslystratified reservoir,
however, the eruption processacts to homogenizeat least the
upperpart, which leadsto a differentcompositional
profile in the
chamber and may induce a different crystallization sequence
[Speraet al., 1986].
Conclusion
This brief overview has dealt with results which, in the main,
have been obtained over the last 10 years and shows that the
door to an extremely rich physicalworld has been opened.The
fluid dynamicsof differentiationin magmachambersis a mature
field, suchthat the main conceptsare sufficiently developedto
be used in the interpretation of petrological and geochemical
data. The key lesson is perhapsthat over a large volume, it is
extremely difficult to prevent motions. Most static models are
found to be unstable to small disturbanceswhich are always
present in natural systems.In fact, many dynamic models are
also found to be unstable.Thus the ultimate test for a physical
model is that of stability. As a consequence,it is of paramount
importanceto specify the model in such a way as to allow a
stabilityanalysis.
Another conclusionis that physical modelshave not yet been
able to answer several important petrological questions, for
example, how specific textures are generated.The reasonsare
partly that the questions are too difficult for our present
modelingabilitiesand partly that comprehensive
phasediagrams
are not availablefor many meltsof geologicalinterest.
Models have now beendevelopedto a quite sophisticated
level
and may well correctlydescribethe essentialphysics.However,
cautionmust be exercisedwhen making directcomparisonswith
the geological record becauseaccurate determinationsof the
physicalpropertiesof melts are too few. For example,we still
rely on a restricted number of thermal conductivity
determinations[Murase and McBirney, 1983; Snyder et al.,
1994].
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(ReceivedSeptember16, 1994;revisedApril 10, 1995;
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