Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , , Ra ff 0.25. − , whole = P β Solid Earth Discussions . Three domains P 4.8, and − and = ). Layering occurs when α Ra ), are capable of layering and more negative 38. Extrapolating to high 1995 . , 0 Ra dP/dT ≈ − = γ P and transitional behaviour in an inter- P and 0.1, and the fit for the boundary between Christensen − 4 . If there is an appropriate restoring density University, Main Building, Park Place, Cardi ; γ = 714 713 ff 10 β × 1982 1 2.5 , ) and the vigour of convection (as measured by the ≈ P Ra 1.05, and and less negative − Ra = α ) on mantle convection. We have undertaken 76 simulations of Olson and Yuen and J. H. Davies Ra 1,* where β αRa = P This discussion paper is/has been under review for the journal Solid Earth (SE). Please refer to the corresponding final paper in SE if available. School of Earth and Ocean Sciences, Cardi now at: University of Ottawa, Ottawa, Ontario, Canada flections of the boundary away fromof its the equilibrium deflections position. depend The on nature the and value magnitude of 1 Introduction Mantle convection has hadbeen known a for many dominant years that control(pressure-temperature mineral phase on slope changes Earth’s with of negativemantle surface Clapeyron phase convection slope evolution. ( change, Itthe has lateral temperature variations of convection produce laterally varying vertical de- These two curves converge at which is likely earlierIt in is Earth therefore likely history, that thisphase convection work change, in suggests the with a Archean Earthdomain. large would being have transitional at been domain. influenced least by in this the transitional domain, if not the layered the Phase Buoyancy parameter, Rayleigh number, isoviscous mantle convection in sphericalof geometry behaviour varying were found:mantle layered convection convection for for low high vening domain. The boundary betweencurve the layered and transitional domain wasthe fit transitional by a and whole mantle convection domain was We investigate the influenceringwoodite to on perovskite mantle and convectionlated ferro-periclase of with mantle the phase the transition, negative seismicderstanding which Clapeyron the discontinuity is slope influence at corre- of 660 km the depth. magnitude of In the particular, Clapeyron slope we (as focus measured on by un- Abstract 1 Wales, CF10 3AT, UK * Received: 21 July 2011 – Accepted: 27Correspondence July to: 2011 J. – H. Published: Davies 4 ([email protected]) AugustPublished 2011 by Copernicus Publications on behalf of the European Geosciences Union. Influence of the Ringwoodite-Perovskite transition on mantle convection in spherical geometry as a functionClapeyron of slope and Rayleigh number M. Wolstencroft Solid Earth Discuss., 3, 713–741,www.solid-earth-discuss.net/3/713/2011/ 2011 doi:10.5194/sed-3-713-2011 © Author(s) 2011. CC Attribution 3.0 License. 5 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ; : ; ). ρ (1) (2) (3) er- ∆ ff 1991 1993 2001 , , , Wolstencroft ect has been : density, ff ρ ) there has only Liu et al. ; 1997 Marquart et al. , 1991 Steinbach et al. ; , ; : acceleration due to gravity, ). Therefore, we can poten- 1996 1993 g , , 2001 , Bunge et al. ; Peltier ) undertook a similar study simulta- ; Weinstein 1995 ; 2010 ). The motivation of this work is to under- ( : hydrodynamic pressure, , 1995 , p 716 715 ). The resulting equations modelled are: the Machetel and Weber Shim et al. 1992 ; ; ect Earth’s mantle dynamics. Early simulations 1985 , ff , 2007 , ) of the phase change reaction (i.e. the slope dP/dT, 1985 1969 γ , , Machetel et al. Ricard Zhao et al. Machetel et al. ; ρH ; ; + Yanagisawa et al. T Ringwood 2 1994 ). ; : dynamic viscosity, 1992 1994 0 , ∇ b η , , , k = ˆ r = 1936 ) 1993 , Christensen and Yuen T ρg , cient, the buoyancy forces resulting from the phase boundary deflections 2008a ·∇ ffi , +∆ u Christensen and Yuen p : velocity, + Bernal , u 0 −∇ ∂t ∂T = ( u p 2 u Most work to date has focussed on 2-D, 2-D axisymmetric, and 3-D Cartesian ge- The mineral phase change in the olivine system from ringwoodite to ferro-periclase ∇ Tackley et al. Where lateral variation in density away from the reference state, the equation for the conservation of linear momentum η and the equation for the conservation of energy ρC numerical simulations we assumed theical mantle fluid, is with a constant viscous,Boussinesq material incompressible, approximation properties isochem- ( with infinite Prandtl number subject to the speculating on its possible consequences for Earth evolution. 2 Methods Appropriate assumptions were madethe to mantle focus behaves on asof a the the function objective negative of of Clapeyron both slope characterisingof ( the how the vigour phase of change convection and boundary the in magnitude Pressure-Temperature space). For example, in our ∇· simulations at varying vigoura of regime convection diagram. and We strengthparameterise constrain of them. the phase boundaries transition between Thiswhich to the allows will define various be extrapolation behaviours relevant of and tional to the means early to boundaries Earth simulate. to history After characterising very but the which high behaviour are rigorously vigour we currently conclude beyond by computa- equation for conservation of mass ometries ( Peltier and Solheim Our methodology is very similar; we characterise the behaviour of a large number of stand the role that suchlogical evolution a by phase investigating how change the mightspherical vigour have models of had of convection mantle on controls convection. the Earth’s behaviour thermal in and geo- Solheim and Peltier While there has been notable( work including this phase change in spherical geometry higher vigour ( and Mg-perovskite is known to havereaction), a negative and Clapeyron a slope (i.e. restoringspond is density an to increase. endothermic the Thismantle seismic reaction ( discontinuity is at widely believedtially 660 km to expect this corre- depth layering separating processsuggest the to that a upper under some andsuch conditions lower this that layering the breaksshown evolution down to can in be an be sensitive episodic to very manner the time-dependent. vigour of convection, This with layering a system e more likely to layer at act against the convective thermalence buoyancy. If are su the Clapeyron slopecan and overcome density di the local(Fig. convective 1). thermal buoyancy, resulting in layered convection contrast between the phases, the deflection is accompanied by buoyancy forces that been limited work inthe spherical slope geometry of to thements characterise phase of the our change, work influence and in of sphericaland the the geometry Davies vigour have value been of of presented convection previously ( on the behaviour. Ele- neously where they recently conclude that 3 domains of behaviour can be identified. 5 5 20 10 15 15 20 10 25 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ). ); Ito (4) (6) (5) (e.g. , the 1997 1985 ). The P ( ( ranging Ra γ 0.054, was , where this 2009 ) shows that , (Table 2). We = : temperature, Ra 7 T 2 , for this range of 1993 10 ( P Bunge et al. × ). TERRA uses di- Baumgardner . p k T k/ρHD 2000 ρC ( = to 8.49 3 = ∆ H 10 Tackley et al. Davies and Davies × ; usivity : density change across the phase ff : superadiabatic temperature drop T δρ Ra/Ra 1997 . Since the “660” Clapeyron slope has ∆ 1 , − , is given by H from 5.19 718 717 , is given by and the Phase Buoyancy parameter Ra . : thermal di Ra ) implemented in TERRA by is given by κ Ra H Ra erence (see Table 2). In fact at low P Ra ff Yang and Baumgardner : specific heat at constant pressure, ). Earlier simulations with numerical methods includ- Bunge et al. 1993 p ( ); ). Mineralogy experiments also suggest a thin loop ( ; C : radiogenic heat production per unit mass. 1990 0.831) and H , 1995 1992 1985 ( , − , (the equivalent phase buoyancy parameter, was varied, the ratio of 1 Wood − ; γ Tackley et al. : mantle thickness, ). . The simulations were undertaken using a benchmarked version cient of thermal expansion, . D erence, many simulations were undertaken with and without – and no P 0.0554 to and 5 ffi ff 1989 : mean density of the two phases. 3 − , η 1997 ρ 30 MPa K , and Baumgardner TD gHD − ∆ 2 : coe κkη κη : Clapeyron slope of the phase change, α gD Ra 2 αρ γ 2 to γδρ αρg Shearer and Masters − = αρ = H erence was found. ectively also assumes an infinitesimally thin phase loop. The sharp discontinuity ob- The phase change is implemented at a depth of 660 km depth using the sheet mass Using these equations we investigated the form of layered mantle convection for The basal-heated Rayleigh number The internal-heated Rayleigh number Non-dimensionalisation of these equations shows that the behaviour is controlled Since only The Phase Buoyancy Parameter, = ranges from ff : thermal conductivity and ff : unit vector in radial direction, ˆ ing the width of the loop suggest that the large scale dynamics are largely insensitive This method applies an appropriate bodythe force local at the temperature discontinuity and depth, phase dependentthis on change is parameters. an excellentlikely method boundary especially deflections, when ase in the our radial simulations. resolutionserved cannot The seismically resolve at sheet short the massloop periods anomaly ( suggests method that thisand phase Takahashi change does have a thin anomaly method of very large negative values, whetheror the set small to zero slope usually 410might km makes make phase little a di change di isdi included olution of around 15 kmof near around the 22 surface, km and mid-mantle, the whileof next the around very highest 88 lowest vigour km. vigour runs Using runs a aparameter only resolution resolution needed survey appropriate a possible. resolution to the A simulationfrom total helps make of this 76 large simulationsγ were undertaken with note that for a sub-set ofincluded the at simulations 410 a km positive depth Clapeyron slope equal phase to change 1.5 was MPa K mensional variables and the basicConvection was parameters isochemical, of with the free-slip simulationscomponent and are of isothermal listed internal boundary in heating. conditions, Tablefeatures Spatial 1. and of resolution a each was simulation. carefully This selected resulted to in the resolve highest the vigour run having a spatial res- temperature and velocity as theBunge free and variables, are Baumgardner presented in of TERRA ( where: across the shell, where change, and varying Ra Ra r k by only 3 non-dimensionalinternal parameters, heating the Rayleigh basalBunge number et heated al. Rayleigh number, P details of how TERRA solves the dimensional form of the equations with pressure, always constant in this work.to We describe therefore only our need experiments; one we of use the two Rayleigh numbers 5 5 25 20 15 10 20 10 15 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , (7) (8) Ra ect are ff 9 %. . P ≈ P Tackley ; and and H δρ/ρ Ra 1985 Ra of , , δρ Ra layered convection is P to these boundaries. The best β , are ultimately not important. Only αRa Christensen and Yuen γ = (i.e. low absolute value) whole mantle , P ). We should remind the reader that the P δρ P and more negative 720 719 , a whole mantle convection domain at low Ra P and high Ra 0.332) run a large number of simulations spanning small ). − 1985 , implies a simple linear relationship between our Clapeyron slope and a transitional domain at intermediate values of and more negative P 0.221 and δρ − 1 . ( Ra 25 0 . − 0 P on the behaviour of mantle convection with mineral phase changes. As . We have fit curves of the form − γ Ra Ra Ra 05 8 . . and 1 4 ). We assume a density contrast across the phase change − − Ra We now go on to compare these results with earlier work and discuss their possible Each simulation was initiated by a radially uniform, laterally small scale, random ) and the Phase Buoyancy Parameter ( = = Christensen and Yuen γ P been termed partially layered,the we wide avoid range this of termtwo behaviours values as displayed. of it To better doesranges constrain not of the accurately boundary represent wefit have curves at defining our boundaries are between the two end-member behaviours. In previous work, this transitional region has for the boundary between the layered regime andP the transitional regime, and domain at high and less negative 4 Discussion 4.1 Domains of convection modes As described in the Introduction thereof has been a long historymentioned of above investigating the our e work shows three domains of behaviour; a layered convection relationship. Without guidance of anwith alternative a relationship we simple argue relationship, it( which is best in to this keep case has a longimplications. history of usage in the field for the boundaryregime. between the We transitional notethat that regime the the and line form the fits of whole to the mantle the curves, data convection i.e. are simple not power perfect. law, might There not is be a the suggestion true form of the convection is preferred, whilepreferred at (Table 2, high Fig. 3). An intermediate domain of transitional behaviour is found especially cases where thethese simple investigations, each diagnostics case were was not classifiedTransitional cases as definitive were layered, (Fig. identified whole by mantle 2).pendent their or layering transitional. intermediate Following behaviour. radial structure and/or time de- 3 Results The results show that at low allows one to characterise eachis simulation. greatly reduced In at particular, the the phaseis absolute change not radial in advected a mass across well flux layered thislayer convecting boundary, system. at it Since the also heat develops depthsualised an of at additional thermal the various boundary times phase during change. the The simulations global to thermal better distinguish structure the was behaviour, also vi- to its width within reasonable1995 parameter values ( The constancy of ( individual values of parameters,the resulting including values of theimportant. controlling non-dimensional parameters, structure. The results were independentan of extended this length initial of condition time,achieved since until by they a monitoring were thermal the run quasi-steadystructure for surface state and heat was the flow. reached. radial absolute Forlation This mass each were was flux, simulation investigated. at the The variouscharacteristic radial discrete radial form thermal for times thermal a during structure layered the system and simu- as absolute opposed mass to flux whole mantle have convection a which 5 5 20 15 10 25 15 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , ) in 1 Ra 0.2, − − ) 2-D 2010 ( ). They = Yanagi- 4.4 and − β 1985 ) results to = ( 0.33, for the 2010 ( α − = 2010 Christensen and ( β 4.7 and er) they should be − ff = ), like us, also define ) and α ect resulting from the de- 12 and Yanagisawa et al. ff 2010 − ( 1994 0.38. The curves of ( = ects are of minor importance , the two curves will approach α ff Yanagisawa et al. ≈ − Ra , boundary deflection is known to P Christensen and Yuen Ra Yanagisawa et al. ects of the latent heat of the reaction, , where the ff , and 4 Ra in our work against 0 and 2.5 MPa K Ita and King , in fact they have only a limited number of 1 10 was assumed and they found − cient simulations to characterise accurately Ra × 722 721 β ffi Yanagisawa et al. 2.5 ). αRa ≈ = ), with increasing P erence in the Clapeyron slope assumed for the phase Ra 2010 ff ( ). The work of 1971 , 1995 . , . At the other end, at very high Ra Ra number where most of the previous data points lie, but that there are ) do not converge at low (where influence of latent heat would be expected to be irrelevant) this Ra Yanagisawa et al. 2010 Ra ) showing that Boussinesq, extended Boussinesq and compressible simu- ( Christensen . Therefore, since we are interested in how the behaviours might extrapo- Ra axis but never cross it. This is as one would expect since a mineral reaction with 1985 ( 0.2. The work presented here is similar to that of Schubert and Turcotte ciently similar that it is worthwhile to consider the results together (Fig. 5). We note − Ra ( erences at lower erence between the two sets of simulations is that while the internal heat genera- ffi We note that the two curves in our study converge at low Rayleigh number – we Therefore while we would not expect our and To repeat, this work here focusses on just the buoyancy e We do observe episodic behaviour in the transitional domain. It has been beyond = ff ff parameter space. As aEarth. result, The there models are are limitations without when depth applying or temperature these dependent outcomes viscosity, to do not have a positive Clapeyron slope cannot layer the flow with the4.3 resulting boundary deflection. Implications for Earth history 4.3.1 Limitations of modelling It is interesting to speculateearlier what this in research Earth implies history. fortions mantle were Before convective intentionally behaviour doing simple so, to allow we understanding would and like complete investigation to of emphasise the that the simula- simulations in this range. Ifthen it it is tightens correct considerably that therelationship the fit to two to high curves the should curves convergethe and at therefore low the extrapolation of this sawa et al. be identical (interpretationsu of the boundarythat cases most might of also theircurves, points di especially also as satisfy we ourstudy extrapolate has curves. to many data-points. high This gives further confidence inestimate our this point to be around for the boundary between layeredboundary and transitional, between and whole mantleprevious convection domain and boundaries transitional. andwell at our Figure higher data 4 points.di shows these We note that these curves agree a transitional regime and their fits to the two boundaries have change at 410 km depth;the 0 work and of 1.5 MPa K Cartesian work, where the form β also used the code TERRA anddi very similar input parameters to ourselves.tion The is biggest the same,There their was also temperature sometimes drop a across di the mantle is 150 K lower than ours. Yuen The earliest reference,layered to and our whole knowledge, mantle for convection a was curve from fit to the boundary between flection of the phase change boundary.ulations, By which undertaking to incompressible be convection self-consistent sim- we ignore the are e removing itsRa influence. While latent heatdominate is ( known to have an influence at low extend across the whole transitionalcloser domain to and the seems layered to domain.behaviour. occur for It parameter would values be interesting to constrain4.2 the boundary of this Fits to domain boundaries lations give similar resultsat reinforces high that latent heatlate to e high simplification is sensible. the limit of thiswhere project this to behaviour occurs undertake on su the regime diagram, but we do note that it does not 5 5 25 15 20 10 25 20 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , , 1 1 ). − − Hi- Ra ect ff Goes 2006 Abbott Green Litasov Katsura ; , ; ; Dziewonski , assuming ( 3.5 MPa K 7 1995 Weidner and 1995 − 2004 3 , ), while recent , ; 10 − , , super-adiabatic ≈ ) has pointed out 1 − 1998 1981 Ohtani and Litasov 2.0 to K , ) and volume change , ). Earlier in Earth his- − 5 2 orders of magnitude 1994 − ( Fei et al. 10 Ra 1998 2006 Nisbet et al. ; Nisbet et al. might be Liu , , × ; 2 erently. We note that present- ≈ Ra ff 2003 α Irifune et al. 2004 , , ; , 1 − s Steinberger and Calderwood 2 1989 Christensen ected di m ff , 6 − for base of upper mantle and slightly more ). We note that , with recent values for a dry mantle head- 724 723 1 10 1 − − ≈ Katsura et al. Dziewonski and Anderson K κ 2009 5 ). These simplifications could be expected to a − , cient of thermal expansion at around 660 km depth 10 Grove and Parman ffi Pa s, × ; 2010 Steinberger and Calderwood , 21 3.5 MPa K ) would suggest that mantle viscosity might decrease by ect of latent heat ( − ff Ito and Takahashi 10 2009 ; ). The mean absolute density, in contrast, is fairly well con- × ) of the phase changes. , 2008 5 Fukao et al. and , ; 2550 K ( ≈ ). The coe 2002 1 2008 ≈ 2010 η − , but clearly with significant uncertainty. , , for uppermost lower mantle ( , 9 2002 1 10 1981 − , Lee et al. , K ≈ Billen Hirose 5 ; Yanagisawa et al. ). Assuming a 200 K hotter mantle at say 3 Ga we might expect Earth to ; − ), therefore the negative Clapeyron slope could have played a dynamic role, ; ) from his experiments suggests that this transition might occur at around Ra 0.5 MPa K 10 − 1998 × 1994 2005 2004 2008 2002 , ( , , ). Seismological estimates in-situ of the slope of phase change at 660 km depth ). A hotter mantle would translate to a higher Rayleigh number. To illustrate , , Lebedev et al. Korenaga and Karato Krien and Fleitout around ing towards theet less al. negative value ( greater at 4.3.3 Phase Buoyancy parameter Mineralogical work places estimates of the Clapeyron slope somewhere between We note that the olivine component of the mantle probably makes up around 60 % of have a viscosity 2 orders of magnitude lower and therefore than 2 measurements for a “wet” mantle2006 have the more negativebased values on ( estimates of the deflectionthermal of perturbations the would boundary suggest and( a independent estimates Clapeyron of slope the around is probably slightly less than 2 erage mantle ( et al. the potential implications weas will a assume function that of therheology only time is changing is a parameter viscosity, field( in with the with it large being lower uncertaintiesapproximately an at but order higher an of temperatures.Magmatic activation magnitude products energy for Mantle also every of suggest 100 500mates that KJ degrees varying mol the increase from mantle in 100 was K temperature. such hotter to as 300–500 in K the how hotter Archean, wet at with 3 the Ga esti- komatiite depending source upon interpretations region was, and what is representative of av- et al. Wang strained from global radial seismologicaland models Anderson at just over 4.15 Kg m the detail of the conclusionsvalid here; as hopefully more the sophisticated broaddiscussions models trends should are in investigated also this in consider spacenet the other will systems; future. mineral remain and reactions, More also both the sophisticated e in the olivine and gar- temperature drop of tory workers expect a hotterthe mantle, formation due to era, the and dissipationsumption the of that the gravitational higher energy mantle radioactivity. was from 1975 hotter Limited earlier observations in Earth support history this ( as- that the slope oftemperatures, the Clapeyron in curve that for case thisrose in reaction these might regions not the be2070 K. convection negative This would at temperature-dependence not higher tothat be upwellings the layered. and phase downwellings transitionday might leads estimates be of to a mantle the temperature at possibility 660 km depth might be around 1880 K ( ( 4.3.2 Rayleigh number Applying a single number likesince a the Rayleigh number properties is are clearly spatiallythe fraught variable for and discussion the not actual we constant. Earth, e.g. Accepting estimate mean this, viscosity that to advance present day mantle at least for average andis cold also regions an of uncertainty theably regarding mantle, lying the from density between early contrast 7.0 in % across Earth and this history. phase 9.3 % There change, ( prob- et al. plates or continents and thus can not display behaviours such as slab-rollback ( 5 5 10 25 25 15 20 15 10 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | ; , , P 2007 . This ected. , ff P Grand et al. Fukao et al. Parman ; ective value of ff Anderson and Bass 1998 , ). We also note that the ); and also observations 2001 , 2002 1984 , ). Such events have been sug- , University) for computational resources. Condie 1998 ff , 726 725 Condie ). Phase-change induced mantle avalanches Ernst and Buchan ; 2008 Creager and Jordan , ; 2008 ), while it has been argued that the isotopic peaks may , 1997 Rudge , 2009 , University) and Helix (Cardi approximately 2 orders of magnitude greater and similar ff Frimmel ; values would suggest that we are today either in the transitional MW would like to acknowledge the support of NERC (UK) for his stu- Ra P / 2007 ). Clearly there is the potential for multiple observations to be a , Ra ect not just magmatic outputs, but also core-generated magnetic fields ff 1991 , van der Hilst et al. ) who argue for a piclogitic transition zone) our methodology of not making this Hawkesworth et al. ) ; Larson 1986 The authors would like toment thank and D. maintenance Rhodri of Davies the and code the used wider in TERRA this group study. for the develop- to high Rayleigh number (convectivetional vigour) domain and we possibly suggest also that thehistory it layered domain and is will therefore likely be that of forrealistic interest the understanding during simulations transi- Earth early to Earth evolution. bebecome This undertaken available. work in encourages the more future as moreAcknowledgements. computational resources dentship (NER/S/A/2005/13131). We would(UK) and also ARCCA like (Cardi to acknowledge the support of HECToR and Mg-Perovskite transition at 660domain, km a depth. layered convection These domain and are:rating a the a transitional domains domain. whole converge The mantle at boundariestional convection the sepa- domain low (which near-critical includes Rayleigh number, episodicslope. while behaviour) the is By transi- very extrapolating broad power at law realistic fits Clapeyron of these well constrained domain boundaries Future work to better constrain therealistic input simulations, parameters, are Earth encouraged history by and the undertake work more to date. 5 Conclusions We discover 3 domains ofa negative behaviour Clapeyron for slope a phase spherical change simulating geometry the convecting ringwoodite mantle to ferro-periclase with In such a scenariotion it in is its earlier possibile history that as Earth previously might suggested ( have had episodic mantle convec- evidence presented for episodicity is controversial;tion zircon ( peaks might reflect preserva- not be statistically robustcould ( initiate superplumes/superevents ( If we speculate asexpect it to to be where at Earthwould a suggest, was in on a thisthe simple regime deeper interpretation, diagram that regions 3 Earth of Gaearly would the Earth ago, have history, transitional we most the domain might likelywe mantle occupied in look operated the in at a past. ourfrom layered results, a convection It mode. we layered/transitional is regime Therefore, would possible as to predict that a that in dominantly over very Earth whole mantle history convection the regime. mantle evolved Pearson et al. ( of stagnant slabs which1992 might reflect some resistance at this boundary4.3.5 ( Earth evolution gested to a 1997 should be reduced by athe similar proportion proportion. of Since olivine there in is the some uncertainty transition regarding zone (see for example tions of subducting slabs descending from the upper to the lower mantle ( the mantle, therefore when applying this work to the mantle( the e correction in the simulations makes it simpler for others4.3.4 to use this Present-day work. earth Using the estimates above forter the we Rayleigh mark number and Earth’s the currentwhose Phase position size Buoyancy on suggests parame- the an domain approximateapproximate diagram sense (Fig. of 6) the with uncertaintyregime a of large or the Earth parameters. just The inlayered regime. the Seismological whole evidence seems mantle to strongly convection support regime this and – with very observa- unlikely to be in the 5 5 25 15 20 10 20 25 15 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 4 and SiO 4 2 , 2009. SiO 726 2 -Fe 4 715 SiO ects, Earth Planet. 2 724 ff ects of depth-dependent viscosity, 725 ff 724 726 , doi:10.1016/j.epsl.2008.11.027 721 725 , 723 725 720 , 724 723 723 728 727 719 721 , 725 723 using MgO as an internal pressure standard and its 718 715 , 4 724 Rayleigh number: E 718 8 discontinuity, Observatory, 59, 268, 1936. , 1986. 717 SiO ◦ 723 2 raction, Science, 279, 1698–1700, 1998. 725 ff 726 724 ,597, 2002. 721 725 , ects of phase transitions on mantle convection, Ann. Rev. Earth Pl. Sc., 23, 718 ff , 714 717 726 , doi:10.1038/320321a0 715 724 for upwellingdoi:10.1029/2001JB000 of plumes from the lower mantle, J. Geophys. Res., 107, B2078, Science, 323, 49–50, 2009. S., Uchida, T., Katsura,determined by T., in and situ X-ray Ohtaka, di O.: Theform postspinel of governing phase equations, boundary initialGeophys. conditions, in Res., boundary 99, conditions, Mg 15919–15938, and 1994. equation of state, J. plate motions, Nature, 451, 981–984, 2008. gradients and tectonics, Geology, 3, 15–18, 1975. Planet. Sci. Lett., 219, 173–187, 2004. Annual. Rev. Earth Pl. Sc., 37, 19–46, 2009. Convection in the Earth, GSA Today, 7, 1–7, 1997. 55, 2008. plumes: evidence from large igneous provinces, J. Geodyn., 34,Komabayashi, 309–342, 2002. T., Walter,transformation M., boundary and in Funakoshi, Mg geophysical implications, K.: J. Geophys. Res., Experimentally 109, 2004. determined postspinel transition zone, J. Geophys. Res., 97, 4809–4822, 1992. Int., 25, 297–356, 1981. tion?, Earth Planet. Sci. Lett., 163, 97–108, 1998. 321–328, 65–87, 1995. Sci. Lett., 154, 295–306, 1998. phys. Res., 90, 10291–10300, 1985. Cambridge, New York, 2001. 3031–3049, 1984. observations, Earth Planet. Sci. Lett., 278, 50–54, Stat. Phys., 39, 501–511, 1985. heating mode and an1997. endothermic phase change, J. Geophys. Res., 102, 11991–12007, J. Geophys. Res., 99, 13835–13850, 1994. spherical mantle convection at 10 717 Comput. Phys., 9, 207–215, 1995. 2008. Ito, E. and Takahashi, E.: Postspinel Transformations in the System Mg Hirose, K.: Phase transitions in pyrolitic mantle around 670-km depth: Implications Irifune, T., Nishiyama, N., Kuroda, K., Inoue, T., Isshiki, M., Utsumi, W., Funakoshi, K., Urakawa, Ita, J. and King, S.: The sensitivity of convection with an endothermic phase change to the Hawkesworth, C., Cawood, P., Kemp, T., Storey, C., and Dhuime, B.: A matter of preservation, Green, D. H.: Genesis of Archean peridotitic magmas andGrove, constraints T. and on Parman, Archean S. geothermal W.: Thermal evolution of the Earth as recorded in komatiites, Earth Goes, S., Capitanio, F. A., and Morra, G.: Evidence of lower-mantle slab penetration phases in Grand, S. P., Hilst, R. D. v. d., and Widiyantoro, S.: Global Seismic Tomography: A Snapshot of Fukao, Y., Obayashi, M., Nakakuki, T., and Deep Slab Project, A.: Stagnant slab: A review, Frimmel, H. E.: Earth’s continental crustal gold endowment, Earth Planet. Sci. Lett., 267, 45– Ernst, R. E. and Buchan, K. L.:Fei, Maximum Y., size Van and Orman, distribution in J., time Li, and J., space of van mantle Westrenen, W., Sanloup, C., Minarik, W., Hirose,Fukao, Y., K., Obayashi, M., Inoue, H., and Nenbai, M.: Subducting slabs stagnant in the mantle Condie, K. C.: Episodic continental growth and supercontinents: a mantle avalanche connec- Christensen, U.: E Christensen, U. R.: Dynamic phase boundary topography byChristensen, latent U. heat R. e and Yuen, D. A.: Layered convection induced by phase transitions, J. Geo- Condie, K. C.: Mantle plumes and theirCreager, record K. C. in and Earth Jordan, T. history, H.: Cambridge Slab University penetration into Press, the lower mantle, J. Geophys. Res., 89, Davies, D. R. and Davies, J. H.: Thermally-driven mantle plumes reconcile multiple hot-spot Anderson, D. L. and Bass, J. D.: Transition region of the Earth’s upper mantle, Nature, 320, Dziewonski, A. and Anderson, D. L.: Preliminary reference Earth model, Phys. Earth Planet. Baumgardner, J. R.: Three dimensional treatment of convective flow in the Earth’s mantle, J. Abbott, D., Burgess, L., and Longhi, J.: An empirical thermal history of the Earth’s upper mantle, Bunge, H. P., Richards, M. A., and Baumgardner, J. R.: A sensitivity study of three-dimensional References Bunge, H. P. and Baumgardner, J. R.: Mantle convection modeling on parallel virtual machines, Bernal, J. D.: Hypothesis onBillen, the M. 20 I.: Modeling the dynamics of subducting slabs, Annu. Rev. Earth Pl. Sc., 36, 325–356, 5 5 25 30 20 15 10 25 20 15 30 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | , 4 718 SiO 2 726 716 and its , 2004. 4 723 723 724 SiO raction study 2 ff 726 726 715 , 2010. 715 715 715 723 715 doi:10.1029/2003JB002438 , 2008. ects in phase-transition modulated thermal- doi:10.1029/2009jb006505 ff 724 730 729 715 715 ractometry, Phy. Earth Planet. In., 136, 11–24, 2003. ff ect of water on mantle phase transitions, in: Water in ff 715 718 714 ects and mantle convection patterns, Science, 264, 1904–1907, 725 ff doi:10.1029/2007JB005100 721 , J. Geophys. Res., 109, B02209 4 724 SiO 723 2 , P., Plank, T., Dalton, H., and Leeman, W. P.: Constraints on the depths and y, T. S., and Shen, G.: The post-spinel transformation in Mg ff ffi 715 715 724 of mantle thermal convection, Geophys. Res. Lett., 20, 1119–1122, 1993. 1994. convection – a model of Earth’s mantle, J. Geophys. Res. (Solid Earth), 99, 6997–7018, 76, 1424–1432, 1971. Nominally Anhydrous Minerals, 62, Rev. Mineral.of Geochem., America, 397–419, Mineralogical 2006. Society Res., 87, 3993–4002, 1982. and continent growth seen in osmium isotopes, Nature, 449, 202–205, 2007. Nature, 355, 791–796, 1992. relation to the 660-km discontinuity, Nature, 411, 571–574, 2001. ture, 446, 900–903, 2007. continental crust correlation, Earth Planet. Sci. Lett., 274, 179–188, 2008. phys. Res., 113, B02403, mantle phase boundaries, J. Geophys. Res., 105, 5679–5693, 2001. temperature of the Archean291–307, 1995. mantle: a review of the evidence from komatiites, Lithos, 30, Soc. A, 354, 1425–1447, 1996. Geophys. Res. Lett., 19, 321–324, 1992. 1969. Y., Yoshino, T., Walter, M. J.,system Ito, (Mg,Fe) E., and724 Funakoshi, K.: Olivine-wadsleyite transition in the determined by high P-T in724 situ X-ray di scopic scale, J. Geophys. Res., 115, B03403, M. J., Ito, E., Urakawa, S., Funakoshi, K., and Utsumi, W.: Post-spinel transition in Mg Some Geophysical Implications, J.724 Geopys. Res.-Sol. Ea., 94, 10637–10646, 1989. spherical mantle convection with anPhys. endothermic Earth phase Planet. change In., at 88, the 43–51, 670 1995. km discontinuity, at the 410- and 660-kilometer discontinuities, Science, 296, 1300–13–2, 2002. 1994. mantle due to phase transitions, Science, 252, 1836–1839, 1991. mic phase-change at 670 km, Nature, 350, 55–57, 1991. temperatures of basaltic magma generationthermobarometers on for Earth mafic and magmas, other Earth terrestrial Planet. planets Sci. using Lett., new 279,of 20–33, postspinel 2009. transformation inEarth a Planet. peridotite Sci. mantle: Lett., 238, implication 311–328, for 2005. the 660-km discontinuity, Steinbach, V., Yuen, D. A., and Zhao, W.: Instabilities from phase transitions and the timescales Solheim, L. P. and Peltier, W. R.: Avalanche e Schubert, G. and Turcotte, D. L.: Phase transitions and mantle convection, J. Geophys. Res., Shim, S.-H., Du Olson, P. and Yuen, D.: Thermochemical plumes and mantle phase transitions, J. Geophys. Pearson, D. G., Parman, S. W., and Nowell, G. M.: A link between large mantle melting events Shearer, P. M. and Masters, G. M.: Global mapping of topography on the 660-km discontinuity, Ohtani, E. and Litasov, K. D.: The e Parman, S. W.: Helium isotopic evidence for episodic mantle melting and crustal growth, Na- Ricard, Y.: Physics of Mantle Convection, in: Treatise of Geophysics, 7, Elsevier, 2007. Rudge, J. F.: Finding peaks in geochemical distributions: A re-examination of the helium- Nisbet, E. G., Cheadle, M. J., Arndt, N. T., and Bickle, M. J.: Constraining the potential Peltier, W. R.: Phase-transition modulated mixing in the mantle of the Earth, Philos. T. Roy. Ringwood, A. E.: Phase transformations in the mantle, Earth Planet. Sci. Lett., 5, 401–412, Peltier, W. R. and Solheim, L. P.: Mantle phase transitions and layered chaotic convection, Korenaga, J. and Karato, S.: A new analysis of experimental data on olivine rheology, J. Geo- Katsura, T., Yamada, H., Nishikawa, O., Song, M., Kubo, A., Shinmei, T., Yokoshi, S., Aizawa, Krien, Y. and Fleitout, L.: Accommodation of volume changes in phase transition zones : Macro- Katsura, T., Yamada, H., Shinmei, T., Kubo, A., Ono, S., Kanzaki, M., Yoneda, A., Walter, Marquart, G., Schmeling, H., Ito, G., and Schott, B.: Conditions for plumes to penetrate the Machetel, P., Thoraval, C., and Brunet, D.: Spectral and geophysical consequences of 3-D Machetel, P.and Weber, P.: Intermittent layered convection in a model mantle with an endother- Larson, R. L.: Geological consequencesLebedev, S., of Chevrot, superplumes, S., Geology, and 19, van 963–966, der 1991. Hilst, R. D.: Seismic evidence for olivine phase changes Liu, M.: Asymmetric phase e Liu, M., Yuen, D. A., Zhao, W., and Honda, S.: Development of diapiric structures in the upper Lee, C.-T. A., Lu Litasov, K., Ohtani, E., Sano, A., Suzuki, A., and Funakoshi, K.: In situ X-ray di 5 5 30 10 25 20 15 10 30 15 25 20 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 718 1 1 − − 1 − m m 3 1 kg K 6 6 T − − 1 W kg 5 K − ∆ − 10 10 1 2 12 − × × − − αρ 10 715 = × 10 ects of multiple phase 5 1 % 4 % 480 370 and some geophysical ρ × . . . . . ects of an endothermic ff 4 ff 4500 kg m 2 9 6 1000 J K ∆ 715 SiO 2 740 -Fe δρ/ρ , 4 725 723 SiO 719 , 2 715 722 724 δρ/ρ , α 721 , 731 732 p 715 C 715 0 718 ρ , 715 724 , 718 723 cient of thermal expansion, ffi 715 Common input parameters. ParameterInternal heating, H 5 Value Reference density – Eq. (2), Density jump across 660 kmDensity phase jump change across – 410 Eq. km (6), phaseGravitational change acceleration, gVolume coe Specific heat at constant volume, 10 ms Thermal conductivity, k 4 W m Temperature at outer shell boundaryTemperature at inner shell boundaryBoundary conditions (velocity)Inner radius of spherical shellOuter radius of spherical shellViscosity structurePressure Equation of stateThermal Equation of state 300 K 2850 K Free slip 3 6 Incompressible Isoviscous 92, 151–195, 2000. variable viscosity infinite Prandtl number thermal convection, Geophys. Astrophys. Fluid Dyn, vection, Phys. Earth Planet. Int., 72, 185–210, 1992. and internal heat generation, Geophys. Res. Lett., 20, 101–104, 1993. Avalanches and Thermal Pulses, EOS Trans, AGU, 89(53), 2008a. stagnant slabs inEarth 3-D Planet. spherical Int., 183, mantle 342–352, convection 2010. models at Earth-like conditions, Phys. ment on “Postspinel transformations inimplications” the by system E. Mg Ito and E. Takahashi, J. Geophys. Res., 95, 12681–12685, 1990. from Global Tomography, Nature, 386, 578–584, 1997. tinuity, J. Geophys. Res., 103, 7431–7441, 1998. duced layering at 660 km2008b. in early Earths mantle, Geophys. Res. Abstr., EGU2008-A, 00228, transitions in a threephys. dimensional Res., 99, spherical 15877–15901, model 1994. of convection in Earth’s mantle, J. Geo- Nature, 361, 699–704, 1993. tle with constraints from1461–1481, 2006. mineral physics and surface observations, Geophys.wellings, J. J. Geophys. Int., Res., 100, 167, 15477–15488, 1995. phase change at 670 km depth in a spherical model of convection in the Earth’s mantle, Yang, W. S. and Baumgardner, J. R.: Matrix-dependent transfer multigrid method forZhao, strongly W., Yuen, D. A., and Honda, S.: Multiple phase transitions and the style of mantle con- Weinstein, S. A.: Catastrophic overturn of the Earth’s mantle driven by multiple phase changes Wolstencroft, M. and Davies, J. H.: Time Dependent Layering in Earths Mantle: Mantle Yanagisawa, T., Yamagishi, Y., Hamano, Y., and Stegman, D. R.: Mechanism for generating Wood, B. J.: Postspinel transformations and the width of the 670 km discontinuity: A com- Weidner, D. and Wang, Y.: Chemical- and Clapeyron-induced buoyancy at the 660 km discon- Wolstencroft, M. and Davies, J. H.: The influence of convective vigour on phase change in- Table 1. van der Hilst, R., Widiyantoro, S., and Engdahl, E. R.: Evidence for Deep Mantle Circulation Tackley, P. J., Stevenson, D. J., Glatzmaier, G. A., and Schubert, G.: E Tackley, P. J., Stevenson, D. J., Glatzmaier, G. A., and Schubert, G.: E Steinberger, B. and Calderwood, A. R.: Models of large-scale viscous flow in the Earth’s man- Tackley, P. J.: On the penetration of an endothermic phase transition by upwellings and down- 5 30 15 25 20 10 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | 660: P 1 1 1 1 1 1 1 1 1 1 1 2 1 1 2 2 2 2 1 1 2 T T T T 2 1 1 2 2 1 1 2 2 1 1 1 1 2 2 2 T T T T T T T T T Classification Classification 6 6 6 5 4 4 4 3 6 5 4 4 4 3 4 4 4 3 6 5 4 4 4 3 4 4 4 3 4 4 4 3 4 4 4 3 7 6 6 6 6 6 6 6 6 6 6 6 6 6 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × × Ra Ra 660 660 0.415 5.19 0.415 1.11 0.111 7.76 0.415 5.19 0.111 1.56 0.443 9.74 0.111 5.19 0.443 5.19 0.111 9.74 0.443 1.11 0.111 5.19 0.443 5.19 0.111 1.11 0.554 9.74 0.111 5.19 0.554 5.19 0.221 1.56 0.554 1.11 0.221 5.19 0.554 5.19 0.221 9.74 0.111 8.49 0.221 5.19 0.111 4.00 0.221 1.11 0.111 2.00 0.221 5.19 0.138 7.79 0.332 9.74 0.152 8.66 0.332 5.19 0.166 4.00 0.332 1.11 0.166 1.56 0.332 5.19 0.166 5.00 0.388 1.56 0.194 7.79 0.388 5.19 0.221 8.66 0.388 9.74 0.221 8.00 0.388 5.19 0.221 7.79 0.388 1.11 0.221 6.77 0.388 5.19 0.221 5.99 0.415 9.74 0.0554 7.76 P P − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − : basally heated Rayleigh number, ) ) Ra 1 1 − − 734 733 4.0 4.0 4.0 5.0 5.5 6.0 6.0 6.0 7.0 8.0 8.0 8.0 8.0 8.0 15.0 15.0 2.0 4.0 15.0 4.0 16.0 4.0 16.0 4.0 16.0 4.0 16.0 4.0 20.0 4.0 20.0 8.0 20.0 8.0 20.0 8.0 8.0 8.0 8.0 12.0 12.0 12.0 12.0 14.0 14.0 14.0 14.0 14.0 14.0 15.0 − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − − ) Cl660 (MPa K ) Cl660 (MPa K 1 1 − − 026 1.5 027 1.5 028 1.5 029 1.5 030 1.5 031 1.5 032 1.5 033 1.5 034 1.5 035 1.5 036 1.5 037 0.0 038 0.0 039 0.0 040 0.0 041 0.0 042 0.0 043 0.0 044 0.0 045 0.0 046 0.0 047 0.0 048 0.0 049 0.0 050 0.0 001 1.5 002 1.5 003 1.5 004 1.5 005 1.5 006 1.5 007 1.5 008 1.5 009 1.5 010 1.5 011 1.5 012 1.5 013 1.5 014 1.5 015 1.5 016 1.5 017 1.5 018 1.5 019 1.5 020 1.5 021 1.5 022 1.5 023 1.5 024 1.5 025 1.5 Case Cl410 (MPa K Case Cl410 (MPa K Continued. Cases modelled with case-specific parameters and outcome. Cl410: Clapeyron slope Table 2. at 410 km, Cl660: Clapeyron slope at 660 km, Table 2. buoyancy parameter for the 660two phase layer convection, change T Layering transitional status: behaviour. 1 whole mantle convection, 2 Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | illustrates a on the right R R Pv Pv (B) (A) 2 1 1 1 2 1 1 1 1 1 1 1 1 T T T T T T T T T T T T T Classification 6 6 6 5 5 5 5 5 4 4 4 4 4 4 4 4 3 4 4 4 3 4 3 4 3 4 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 10 × × × × × × × × × × × × × × × × × × × × × × × × × × Ra ∆ρ ∆ρ A B 660 0.221 5.00 0.221 4.00 0.221 1.56 0.221 7.00 0.221 5.00 0.221 2.00 0.277 5.00 0.277 2.00 0.332 8.00 0.332 7.00 0.332 6.00 0.332 5.00 0.332 4.00 0.332 2.50 0.360 5.19 0.388 1.11 0.388 5.19 0.415 5.19 0.415 2.50 0.415 1.11 0.415 5.19 0.443 1.11 0.443 5.19 0.554 1.11 0.554 5.19 0.830 1.11 P − − − − − − − − − − − − − − − − − − − − − − − − − − ) 1 − 23 736 735 8.0 8.0 8.0 8.0 8.0 8.0 B

10.0 10.0 12.0 12.0 12.0 12.0 12.0 12.0 13.0 14.0 14.0 15.0 15.0 15.0 15.0 16.0 16.0 20.0 20.0 30.0

− − − − − − − − − − − − − − − − − − − − − − − − − − e temperatur Average ) Cl660 (MPa K 1 − A Pv Temperature 660 km

R 051 0.0 Pressure 052 0.0 053 0.0 054 0.0 055 0.0 056 0.0 057 0.0 058 0.0 059 0.0 060 0.0 061 0.0 062 0.0 063 0.0 064 0.0 065 0.0 066 0.0 067 0.0 068 0.0 069 0.0 070 0.0 071 0.0 072 0.0 073 0.0 074 0.0 075 0.0 076 0.0 Case Cl410 (MPa K Illustration of the layering mechanism modelled. The left hand side figure shows a Continued. Illustration of the layering mechanism modelled. The left hand side figure shows a Fig. 1. schematic version of the phaseupper diagram of left the region olivine (labelled component(labelled - with with Ringwoodite R) is Pv) while stable incold below Perovskite the downwelling and the impinging Ferropericlase phase on ischange the boundary can stable phase still line. in change. be the the The lighterto region The Ringwoodite fact the phase left. that right is As the shown hand a by materialringwoodite result the side below phase letter there the A is Part producing on a phase A the downward ahand phase deflection side illustrates diagram buoyancy of illustrates the force a that boundary, and which thelayering leads with potentially same to hot mechanism layering. the upwellings. also lighter can Part work B in reverse, on potentially the leading to right cold downwelling impinging onchange the can phase still change. be the The lighterto Ringwoodite fact the phase left. that is As the shown a by materialringwoodite result the below phase letter there the A is producing on phase a a the downwardhand phase buoyancy deflection side diagram of force illustrates the and that boundary, potentially which thelayering leads with same layering. to hot mechanism the upwellings. Part also lighter can work in reverse, potentially leading to schematic version of the phaseupper diagram of left the region olivine component (labelled(labelled – with Ringwoodite with is R) stable Pv) while in below the Perovskite the and phase Ferropericlase boundary is stable line. in The the region right hand side Part Fig. 1. Table 2. Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | (D)

) and layering

e (MPa/K) e 660 km Clapeyron Slop Clapeyron km 660 Ra 0 -25 -30 -5 -10 -15 -20 1e+09 1e+09 700 0 -700 illustrates the case for a layered system. 1e+08 1e+08 (C) Whole-Transitional ). Key defines the symbols used to Layered-Transitional P shows the constant thermal gradient of a purely 1e+07 1e+07 C (A) 738 737 1e+06 1e+06 24 shows the whole mantle convection thermal structure, illustrating the AverageTemperature ion Total RadialMass Flux Rayleigh Number Rayleigh 100000 100000 (B) Transitional D 10000 10000 AB Layered Convection Layered 1000 1000 0

-0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.1 -0.2

Whole Mantle Convect Whole Mantle Buoyancy Parameter Buoyancy Criteria for defining whether convection is layered. Layering status of the experiments as a function of convective vigour ( Criteria for defining whether convection is layered. A shows the constant thermal strength of theindicate phase the change nature (Buoyancy ofwhole the Parameter, and convection. transitional The cases, solid whileThe line the equivalent is dashed Clapeyron a line slope power-lawaxis. divides fit for the attempting layered our and to parameters transitional divide is cases. the shown on the right hand side vertical Fig. 3. shows a cross-section andand a red radial hotter. surface The through visualisationchange the demonstrates in clearly thermal colour that anomaly across this the field. case phase has Blue change both is and a some colder large passage than degree of of the material layering, radial across. with average dramatic This case is classified transitional. In this case the solidleads line to shows an that additional the thermal absolute boundary radial mass layer, illustrated flux will by be a a step minimum in at the the dashed phase line, change, across which the also phase change. large temperature gradients at itsthe boundaries. two boundaries. The solid For line whole represents mantle the convecting it absolute peaks radial in mass mid-mantle. flux, which is zero at Fig. 2. conductive regime. The dashed line in Part Fig. 2. gradient of a purelyconvection thermal conductive structure, regime. illustrating thesolid large The temperature line dashed gradients represents at line its thewhole in boundaries. absolute mantle The Part convecting radial it B mass peaksthis shows flux, in case the mid-mantle. which the solid C whole is line illustrateschange, mantle zero shows the which that at case the also for the absolute a leads two radialdashed layered to mass boundaries. system. line, flux an across In will additional For the be thermalthe phase a thermal minimum boundary change. at anomaly layer, D the illustrated field. shows phase isation by a demonstrates Blue a cross-section clearly is step and that colder in achange this than in the radial case colour surface the across has through radial the bothclassified average phase transitional. a and change large and red degree some hotter. passage of of The layering, material visual- with across. dramatic This case is

Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

e (MPa/K) e Slop Clapeyron km 660 e (MPa/K) e Slop Clapeyron km 660 0 -30 -5 -10 -15 -20 -25 0 -30 -5 -10 -15 -20 -25 ion 985) erent parameters and the 2010) 1e+09 1e+09 ff 1e+09 1e+09 is study) his study) Transitional ) and the domain boundary lines a et al. 2010) 1e+08 1e+08 1e+08 1e+08 2010 ( Layered Convection nagisawa et al. 2010) anagisawa et al. 2010) 1e+07 1e+07 anagisawa et al. 2010) 1e+07 1e+07 Whole Mantle Convect hristensen and Yuen 1 ion (Yanagisawa et al. 26 740 739 Whole-Transitional (Th erences in parameters between our and previous 1e+06 1e+06 1e+06 1e+06 ff Layered-Transitional (T Transitional (Yanagisaw Yanagisawa et al. Rayleigh Number 100000 100000 100000 100000 Rayleigh Number Rayleigh Layered Convection (Y Whole-Transitional (Ya Layered-Transitional (Y 10000 10000 10000 10000 Whole Mantle Convect Layered-Transitional (C 1000 1000 0 1000 1000 0

-0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 -0.1

-0.6 -0.7 -0.8 -0.1 -0.2 -0.3 -0.4 -0.5

Buoyancy Parameter Buoyancy Buoyancy Parameter Buoyancy Data points from the study of Domain boundary curves from previous studies and our data points. We note that there erences of geometry and/or slight di Domain boundary curves from previous studies and our data points. We note that there ff Fig. 5. fit through the datado points of not this satisfy study. our While lines. we note This a could reasonable agreement, be all the the result points of the slightly di measure of subjectivity in defining the behaviour category of a simulation. simulations Fig. 4. are di Fig. 4. are differences of geometrysimulations and/or slight differences in parameters between our and previous

Discussion Paper | Discussion Paper | Discussion Paper | Discussion Paper |

e (MPa/K) e Slop Clapeyron km 660 0 -25 -30 -5 -10 -15 -20 1e+09 1e+09 1e+08 1e+08 1e+07 1e+07 Layered-Transitional Transitional 741 ction 1e+06 1e+06 Layered Convection Layered Rayleigh Number 100000 100000 Whole-Transitional 10000 10000 Whole Mantle Conve 1000 1000 0

-0.1 -0.2 -0.3 -0.4 -0.5 -0.6 -0.7 -0.8 Buoyancy Parameter Buoyancy Figure of Earth crudely represents an estimate of where the present-day Earth might Fig. 6. fit on abetween Rayleigh the number 3 regimes versus foundevolved in Buoyancy over this Parameter Earth work. plot. history. The arrow Noteinto, shows the The it the whole route probably lines mantle that moved convection the mark from domain Earth the the by might transitional present-day. have boundaries domain, to near to, or