Proc. Nati. Acad. Sci. USAVol. 75, No. 1, pp. 34-39, January 1978Geophysics

On some global problems of geophysical fluid dynamics (A Review)t(gravitational differentiation/rotational pole/mantle convection)

A. S. MONINP. P. Shirshov Institute of Oceanology, Academy of Sciences of the Union of Soviet Socialist Republics, Moscow, Union of Soviet Socialist Republics

Contributed by A. S. Monin, September 28,1977

The development of the earth sciences during recent years hasbeen associated with a wide use of geophysical fluid dynamics(i.e., the dynamics of natural flows of rotating baroclinicstratified fluids), a discipline whose scope includes turbulenceand vertical microstructure in stably stratified fluids, gravitywaves at the interface, internal gravity waves and convection,tides and other long-period waves, gyroscopic waves, the hy-drodynamic theory of weather forecasting, circulations of theplanetary atmospheres and oceans, the dynamo theory of thegeneration of planetary and stellar magnetic fields, etc.

POTENTIAL VORTICITYOne of the basic notions in geophysical fluid dynamics, com-bining fluid rotation and stratification nonlinearly, is the po-tential vorticity

Q = p-1 rot u grad n,in which u is the absolute velocity of fluid motion, p the density,v the specific entropy; Q is the invariant of fluid particles in theiradiabatic motions (see, for instance, ref. 1). The evolution of theQ and q fields is the main object of study in the hydrodynamictheory of weather forecasting [2, 3].The similar object in magnetic field dynamics is the "mag-

netic field charge"X = p-1H grad I,

in whichH is the magnetic field intensity; the quantity X is alsothe adiabatic invariant of moving particles. The evolution ofthe If field should be the principal object in the dynamo theoryof the generation of magnetic fields of celestial bodies (1,4-6).More detailed equations of the hydrodynamic theory of the

geomagnetic field generation are considered in refs. 7 and 8,in which the motions inside the Earth are described as madeup of the mantle rotation (observed by the astronomicalmethods and usually called the earth's rotation), magnetohy-drodynamic flows in the liquid layer ("liquid core"), and thedisplacement and rotation of the internal solid core. The mo-tions of these three layers interact due to hydromagnetic stressesat the internal and the external boundaries of the liquid layerand the deformations of the gravity field with the displacementsof the internal core. The model suitable for the study of thedynamics of these three layers was considered in refs. 7 and 8.It contains three simplifications: (i) rheological-the mantleand the internal core are assumed to be absolutely solid, whichexcludes from consideration some types of internal motions inthem (elastic oscillations, tidal deformations, and convectivemotions in the mantle and the continental drift they produce);(ii) geometric-the mantle and the internal core are assumedto be spherically symmetric bodies, so that, in particular, theirflattening due to rotation (and hence the ability for precession)is not taken into account; (iii) dynamic-gravitational effects

of the moon, the sun, and other planets are not taken into con-sideration. These simplifications do not distort too much theclass of motions inside the earth that we are interested in; ifnecessary, the simplifications can be removed by the intro-duction of appropriate corrections. Equations of motion arewritten for each of the layers, with the right-hand parts con-taining volume forces associated with the presence of thegravity and magnetic fields and stresses of the viscous andmagnetic origin. A magnetohydrodynamic equation of themagnetic field evolution (induction equation) should be addedto the equations of motion. The energetics of the processes inthe layers under consideration can be represented by mutualtransformations of kinetic, magnetic, and internal energies. Theequation for kinetic energy density of each of the layers containsthe terms describing mutual transformations of kinetic andpotential energy in the gravity field and viscous dissipation ofkinetic energy. The equation for energy density of the magneticfield contains in its right-hand side the terms describing ohmicdissipation of the magnetic field energy (i.e., joule heat gen-eration) and mutual transformations of kinetic and magneticenergy owing to the action of Maxwell field stresses (pondero-motive forces). The thermodynamic equation for the densityof internal energy contains the terms describing the dissipationof viscous and magnetic stresses, heat flux generated by con-ductivity of the medium, external heat sources inside the earth(including radioactivity), and energy dissipation of the pre-cession and tidal motions. Integrating these equations over thevolumes of the mantle, the liquid layer, and the solid core (theindices introduced further correspond to this succession) resultsin nine expressions for kinetic K, magnetic M, and internal Eenergy of each of the three layers. A diagram of energy trans-formations is shown in Fig. 1 (potential energy of the liquidlayer P2 and energy of the geomagnetic field outside the earthMO are also introduced there). The diagram shows the estimatesof energy components (in joules/100 years) obtained in ref. 8.One of the most interesting elements of the diagram is the rateof transformation K2 -* M2 describing the geomagnetic fieldgeneration by the dynamo mechanism in the liquid layer.

GRAVITATIONAL DIFFERENTIATIONAs the second example of the use of the geophysical fluid dy-namics let us consider, following refs. 9-13, the problem ofgravitational differentiation of the interior of a sphericallysymmetric and initially homogeneous planet consisting of twocomponents: light "mantle" and heavy "core" ones. Thequestion in essence concerns the Earth's evolution-the for-mation of its core and mantle, the process giving the basiccontribution to the energy balance of the planet (14). The in-

Abbreviation: TME, tectono-magmatic epoch.t By invitation. From time to time, reviews on scientific and techno-

logical matters of broad interest are published in the PROCEED-INGS.

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FIG. 1. Diagram of the Earth's energy transformation.

ternal structure of such a planet at different stages of its evo-lution can be estimated with the aid of the hydrostatic equation,which, with neglect of rotation, has the form

dp= Gm

dr= _p; g=2= m = 4Jo

pr2dr.

Here and further, p is the pressure, p the density, g the accel-eration of gravity, r the radial coordinate, G the gravity con-

stant. Under barotropic approximation (assumed for solidplanets) the knowledge of the equation of state p = p(p) ofplanetary material is sufficient for integrating the hydrostaticequation. Taking into account that the density variations in theplanets of the solar system lie within a small interval of values2 < p < 15 g/cm3, let us approximate the equation of state ofeach of the planetary composing materials by parabolas

P = P1,2(P) = a,2Po(P); Po(P) = (P2 + 27rL2)

with the parameters pi, al, and L chosen from the availableinformation on the Earth's contemporary structure. The localequation of a planetary state is reduced to the form

2i7rGL22Ck1p = 272 (p2 a2ps2); a =

kFCa k=i arkThe solutions of the hydrostatic equation in every chemicallyhomogeneous layer are given by the general integral

1 arp=-(Asin.++Bcost); = L

The coefficients A and B can be found from the condition ofcontinuity of pressure and the acceleration of gravity at theinterfaces. Without loss of generality it can be put a2 = 1 andail > 1. Let the planetary "core" material concentration becl= c; then the "mantle" material concentration will beC2= 1 - c. At some stage of the differentiation process char-

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Table 1. Calculated values for various parameters of Earth during its evolution

+ri, r2, Pc, P , P, Pc, P 1, II,

x km km g/cm3 g/cm3 g/cm3 TPa TPa I/I. 1031 J

0 0 6393 11.34 0.230 - 1.12 0.89 00.2 2091 6386 12.38 10.86 7.43 0.289 0.204 1.09 0.92 0.320.4 2652 6381 12.93 10.45 6.96 0.323 0.183 1.06 0.94 0.730.6 3043 6376 13.38 10.05 6.48 0.351 0.163 1.03 0.97 1.110.8 3361 6372 13.75 9.65 6.00 0.375 0.144 1.01 0.99 1.490.863 3451 6371 13.86 9.52 5.84 0.382 0.138 1 1 1.611 3635 6368 14.08 9.25 5.50 -0.397 0.125 0.98 1.02 1.86

acterized by the fraction x of the already differentiated material(the core mass is cxM) the average concentrations of the mantleand core material in the mantle are (1- c)/(1 - cx) and (c -cx)/(1 - cx), respectively, and the equation of state for themantle material has the-parabolic form with-the parameter

A p ~~1-Cxa(3ai; ~=ai(1 - C) + c(1 - X

The radial distributions of density and pressure for an arbitraryplanet of massM at the stage x contain five unknown param-eters aip,, L/a1, fi, and the radii of the core and the entireplanet, ri and r2. The mass fixation of the core cxM and themantle (1- cx)M, as well as the moment of inertia 5 yield threeequations, the simultaneous solution of which makes it possibleto find the constants a,, ps, L (see ref. 9). For the contemporarystate of Earth, M = 5.98 X 102 g, r2 = 6371 km; the dimen-sionless moment of inertia S1 = 0.3308; r, = 3451 km; the rel-ative core mass cx = 0.3218. It has been assumed that the con-temporary earth's mantle consists of Ringwood pyrolite, andthat Fe2O, according to ref. 15, is the core material. In thiswaythe values obtained were a, = 1.681; L= 4017 km; p, = 3.42g/cm3; c = 0.373; and the Contemporary value of the evolu-tional parameter x = 0.863. Knowing the parameters of tihemodel, one is able to calculate the structure of any planet ofmass Mj with the "core" material concentration CG at any stageof the gravitational differentiation process 0 < x < 1. Theabove-mentioned algorithm was applied, apart from Earth, tothe terrestrial planets: Mercury, Venus, Mars, and the Moon(10-13); the parameters Cj were chosen so that the knownplanetary radii are obtained.t Besides, for all the planets themoments of inertia 9 and released potential energy II werecalculated at different values of the evolutional parameter x.The calculation results for the Earth are presented in Table 1.It is seen from the table that as x grows the core radius r1 nat-urally grows, pressure Pi and densities p1+ and Pi- at the coreboundary decrease, and pressure and density in the core center(pc and Pc) increase noticeably. The Earth's moment of inertiafor the whole history decreases by 14%. Only an insignificantcontraction (the Earth's radius decrease) equal to 25 km for thewhole history of the Earth's evolution takes place. The potentialenergy released by the present time [4.6 billion (= 109) years]II = 1.6 X 1031 J is 80% in excess of radiogenic heat estimatedin ref. 16, yet their sum is insufficient for a complete meltingof the Earth.To obtain the dependence on time of all the calculated pa-

rameters, it is necessary to know the law x(t). The law can beconstructed, as a first approximation, if, following ref. 15, it isassumed that the reaction of a heavy component deposition atthe core-mantle boundary is a surface one and that its rate is

* The use of the two-component model does not allow an accuratecomputation of the Moon's evolution; for this purpose the intro-duction of a third, lighter, crustal material is required. Here the dataare presented on the evolution of the quasi-Moon, a planet with lunarmass and the lunar concentration of iron.

proportional to the average concentration of core material inthe mantle: -

cM-= 47rkr12 C - CXdt 1 -Cx'

in which k if the coefficient of proportionality, assumed to beconstant. Integrating this equation simultaneously with theremaining equations of the model gives x(t) for all the planetsof interest here, and the assumption-of their simultaneous for-mation makes it possible to determine the coefficient k fromthe earth's age (4.6 billion years at x = 04863), which turns outto be equal to 3.34 g/cm2 year (10,11).

Table 2 contains tie results of thecomputations of the stateand evolution parameters for the terrestrial planets, giving onlythe values corresponding to their present evolutional age. FromFig. 2, which shows the evolutional curves-x(t), it is easily seenthat for Earth x* = 0.863, for Venus x* = 0.920, and for Mars,Mercury, and the Moon x* - 1. Table 2 also contains the timestm of the maximum value of dx/dt, which can apparently beidentified, as a first approximation, with the time of the highesttectonic activity in the planetary interiors (for Earth t1-= 3.25billion years, which corresponds to the-Gothic tectono-mag-matic epoch); these times are marked with circles on the curves.The values of t o in Table 2 correspond to x: t 1, i.e., to the timeof decay of the gravitational differentiation process. Proceedingfrom these data, it is believed that tectonic processes will con-tinue for some 1.9 billion years more on Earth and for some 1.3billion years more on Venus, whereas on Mars, Mercury, andthe Moon these processes ceased 0.5, 4 and 2.5 years ago, re-spectively. Note also a sharp decrease of the released gravita-tional energy II as the planetary dimensions diminish (H -

M5/3). From this it follows that radiogenic heat sources (the totalpower of which is -M) play an essential role in the heat balanceof minor planets.

WANDERING ROTATIONAL POLEOur third example refers to the problem of the wandering ofEarth's rotational pole, which has become classical. Let usconsider this question following our recent work (17). Thepresent paleomagnetic and paleoclimatic data give an idea onlyof relative displacements of the pole with respect to the Earth'ssurface area from which samples serving as indicators have beentaken. The problem has become more precise due to the suc-cesses of mobilism, which assumes the displacement of lithos-pheric plates with respect to each other. Lack of coincidenceof the polar wandering trajectories constructed relative to dif-ferent plates gives forcible arguments in favor of mobilism,leaving open the question of the absolute displacement of thepole and hence the plates themselves. A possibility of consid-erable displacements of the Earth with respect to the axis fixedin the stellar space is closely related to inelastic properties of themantle, because polar shifts over the Earth's surface must beaccompanied by the corresponding displacements. of theequatorial bulge; the main reason for such movements is an

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Table 2. State and evolution parameters of the terrestrial planets

XX tMI t.osr*, r2, ri, Pc, P1 +, P1-, Pc, P1, 1044 Y/M. H 109 109

No. Planet M/M1 km c % Fe km km g/cm3 g/cm3 g/cm3 TPa TPa g-cm2 r22 1031 J yr yr

1 Earth 1 6371 0.373 32.6 6371 3451 13.86 9.52 5.84 0.382 0.138 8.029 0.3308 1.610 3.25 6.462 Venus 0.815 6050 + 0.358 31.3 6051 3342 12.54 8.83 5.35 0.298 0.108 5.950 0.3337 1.154 2.94 5.93

53 Mars 0.10766 3394 i 0.183 16 3393.4 1615 6.99 6.47 3.85 0.0377 0.209 0.274 0.3712 0.0167 1.65 4.03

24 Mercury 0.0543 2439 i 0.792 69.3 2438.8 2144 6.76 5.89 3.50 0.0303 0.0038 0.0703 0.3639 0.00748 0.47 0.66

25 Quasi- 0.0123 1738 0.149 13 1680 759 6.02 5.91 3.52 0.0075 0.0046 0.0079 0.3778 0.000228 0.86 2.13

Moon

irregular distribution of the Earth's masses with respect to theequatorial bulge (the existence of the continents and the oceans)(6, 18).

It is possible to calculate the proper motion of the poles withthe aid of Liouville equation (dM/dt) + w XM = 0 expressingthe angular momentum M conservation law for the Earth ro-tating with an angular velocity c and written in the dynamicframe of reference rigidly associated with the Earth as a whole,so that the function m(t) = wi describes polar wandering (therotation velocity w is assumed to be approximately constantduring the Phanerozoic period). Considering the Earth as aviscoelastic Maxwell body with relaxation time T small com-pared to the typical time of polar wandering, its approximateangular momentum can-(6, 18) be written in the form

-M UC (m _2Q dm + Me, Q =19 (A7 C-A

()dt 4 pgR CHere C is the moment of inertia with respect to the rotation axis,Q the dimensionless effective viscosity of the mantle [q is thedimensional viscosity, R the Earth's radius, (C - A)/C thedynamic contraction; at v =o102 Pa-s (1 Pa-s = 10 poise) Q105], and M' the vector with the Cartesian components I'd wj.It is the additional inertia tensor created by the distribution ofthe continents and the oceans, which is determined by theequation

Fj = -N {E Sk(k)nj (k)--

SninjdS};N = (pc - po)r4dr,

in which n is the unit vector of arbitrary direction (from theEarth's center), n(k) the direction to the center of gravity of thekth continental block, S(k) the area of this block (Sc the total areaof all the blocks), S the Earth's surface area (dS its differential),and pc(r) and po(1) the typical vertical density profiles beneath

3 4t, billion years

FIG. 2. Evolutional curves x(t) of the terrestrial planets. Numbersfor the planets are as in Table 2. The broken line indicates thepresent.

the continents and the oceans. Preserving in Liouville equationonly terms with the large factor Q and with the excitationfunction M', it can be reduced to the form dm/dt = M'/2QC,or, taking into account the expression for I'qj, to the form

dmn |s(k)n (k)(m * n (k)) C(m * n)ndS},dt k Sin which k = wN/2QC, n(k) = m(t) + p(k(t), p(k)(t), thedesignated relative vectorial coordinates of the centers ofgravity of the continental blocks counted from the paleopoles(according to Munk (ref. 18), N = 1.78-1039 cm g s; then K =0.784.1023/n cm g s). If the continental block is only one wehave T. Gold's problem on polar wandering under the actionof a "beetle" crawling over the Earth's surface. If the continentsdo not move, so that all n(k) do not depend on time, we have theproblem of G. Darwin, M. Milankovitch, I. Burgers, and D.Inglis on the wandering of poles towards their equilibriumposition (for the contemporary distribution of the continentsit was determined by M. Milankovitch and W. Munk). Ourequations give a problem on polar wandering under the actionof several crawling "beetles" whose movement is predeter-mined only with respect to the wandering poles.

As the initial information about the relative movement ofplates p(k)(6,X) = f8(k)(t),X(k)(t)l (X is the eastern longitude, 0 thecolatitude in the paleopole system), Gorodnitsky and Zonen-shain's (19) paleogeographic reconstructions were used. Thus,there were relative trajectories of 14 paleostable blocks for thePhanerozoic period (570 billion years). Under the fixed presentposition of the continents the equilibrium position of thenorthern pole was at a point with coordinates 0 = 62°, X = 1900,which is in quite good agreement with the results of the previousauthors. Given the relative trajectories of the continental blocks,the integration of our equations was performed at differentvalues of the parameter K corresponding to the mantle's ef-fective viscosity from the interval of 1018 to 1024 Pass. For theoptimum choice of k (and hence effective viscosity) a varia-tional principle related to the least-action principle was used:the value of K delivering the minimum total kinetic energy ofthe absolute displacements of continental blocks was sought.Such a value was found to be K =0.133, which corresponds toviscosity ii = 5.9-1022 Pass.North pole absolute trajectories in the contemporary geo-

graphic coordinate system are shown in Fig. 3. The minimumtotal energy trajectory (solid line) indicates that the pole shiftedfrom a position close to the contemporary one approximatelyalong the 180° meridian and returned back along a somewhatwestern trajectory slightly turning to the zero meridian side,so that it looks as though a second loop started recently. The loopis 860 long, and this result can be interpreted from the point ofview of the large-scale cellular convection in the Earth's mantle(15, 17, 20). In fact, under axisymmetric convection in a uni-cellular regime the continents should crowd around the subsi-

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i,|.:I - i

1as Al-;.

40c

50}.150- / /

f / i/ i

60C 140' / .'

FIG. 3. Absolute displacements of the north pole (in the contemporary geographic system of coordinates) under three values for the Earth'seffective viscosity. Values for k are on the right of the trajectories.

dence pole and the convection axis tends to become perpen-dicular to the rotation axis; in a bicellular regime with closedcells the continents drift apart to the subsidence equator, andthe convection axis tends to coincide with the rotation axis.Oscillations between these regimes with their axis of symmetrypreserved should result in periodic displacements by 900 of therotation poles from the convection poles to its equator and back.The loop in Fig. 3 shows a good fit to the oscillation pattern ofthe convection regimes in the Earth's mantle (with the Phan-erozoic sequence bicellular-unicellular-bicellular regime).Knowing the absolute polar trajectory, it is not difficult to

construct absolute trajectories of all the continental blocks underconsideration. This procedure has shown that instead of thetendency towards the northern components of relative dis-placements, there appears another regularity on the absolutetrajectories-rapid displacements along very smooth trajectoriesduring the Lower Paleozoic and looplike "marking time"during the Meso-Cenozoic that might be completed by now;this pattern corresponds quite well to the oscillations betweenthe unicellular and the bicellular convection regimes.

TECTONO-MAGMATIC PROCESSESThe oscillations between the unicellular and the bicellularconvection during the Phanerozoic period make possible anassumption that such oscillations occurred during the Pre-cambrian time too. An attempt was made in ref. 20 to use suchoscillations for establishing tectonic periods in the Earth's his-tory, which naturally divides itself into epochs of high and lowintensities of tectono-magmatic processes measured by thequantity of volcanic and metamorphic rocks of the corre-sponding age in the Earth's continental crust. The histogramconstructed by Dearnley (21) to show the ages of such rocks(Fig. 4) reveals four maxima with the ages of 2.6, 1.9, 1.0, and0.4-0.25 billion years.The tectono-magmatic processes observed at the Earth's

surface are, undoubtedly, a reflection of the deep processes.According.to the modem plate tectonics theory, the basis of thedeep processes is convection in the Earth's mantle; as assumedby 0. G. Sorokhtin, V. P. Keondjian, and A. S. Monin, this is

density convection penetrating the entire mantle and createdby the gravitational differentiation of heavy (iron) and light(silicates) materials at the lower boundary of the mantle, wherethe mantle is in contact with the melted external layer of theEarth's core. From fluid dynamics it is known that slow laminarconvective motions are arranged horizontally into cells. It isnatural to suppose that the alterations of the tectono-magmaticepochs (TME) apparent at the Earth's surface can be createdthrough the transformations of the forms of the convective cellsin the Earth's mantle.The historic sequence of the forms of convection in the

Earth's mantle could be the following. It reached intensitysufficient for breaking the protogenic lithosphere cooled by heatemission to the outside to form the first rifts and plate subduc-tion zones and make a start for magmatic outflows, mantle

150

*'W100M.E

0

50

-4 -3 -2 -1 0Billion years

FIG. 4. Histogram of the ages of volcanic and metamorphic rocks[after Dearnley (21)]. Tectono-magmatic activity is given in terms ofrelative amounts of volcanic and metamorphic rocks in the Earth'scontinental crust.

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degassing, and hydrospheric condensation, probably Asey:-as the Catarchean time during the second half-billion years ofthe Earth's existence. Evidence in favor of this was found insouthwest Greenland in the form of the most ancient volcanic(granitoid gneiss) and sedimentary (limonite) rocks, with agesof about 3.8 billion years (this may be their metamorphizationage, and their formation may be still older). During the Belo-zerskaya TME in the Early Archean (3.5 billion years) and theKolskaya TME in the Middle Archean (3 billion years) the firstislets of the continental crust with plagiogranites and granitemigmatites were formed (during the 3.5- to 3-billion-year pe-riod convection might be bicellular). The maximum intensityin the unicellular convection was reached, probably, during theKenoranskaya TME in the Late Archean (2.6 billion years). Thisis the first maximum on Dearnley's histogram (Fig. 4); at thattime within the framework of the primary supercontinent thecores of all future continental platforms were formed.

After that, there might appear a form with two closed cellsthat broke the primary supercontinent and existed during thewhole Lower Proterozoic until the Baltic TME (1.9 billion years,the second maximum on Dearnley's histogram). Then again aunicellular convection developed that combined all the ancientcontinents into the secondary supercontinent, the Megagea ofH. Stille, and reached the greatest intensity during the Karel-skaya TME (1.7 billion years), which marked the completionof the formation of the ancient continental platforms.

After the Karelskaya TME the character of the Earth's crustaldevelopment changed: bicellular convection might be formed,in the Lower Riphean with closed cells and in the Middle Ri-phean, after the Gothian TME that created in the Earth's crusta new system of mobile belts (the "great renovation" of theEarth's crust structural plan, the beginning of the Neogean),with open cells (and a tendency towards the formation of twosupercontinents near the subsidence poles on the rotationequator). It is believed that such a bicellular convection did notexist very long relatively and by the Middle Riphean it had beenreplaced by the unicellular one that reached the maximumintensity during the Grenville TME (1 billion years, the thirdmaximum on Dearnley's histogram). The possible formationat that time of the Tertiary supercontinent is attested by theconsolidation and adjoining to the Epikarelian platforms ofgeosyncline belts initiated during the Early Neogean.The Middle Riphean unicellular convection existed, proba-

bly, until the Delhi TME (850 million years) and was replacedby the bicellular convection with closed cells before the Ka-tanginskaya (Early Baikal) TME (650 million years) and then,possibly, the one with open cells before the Salairskaya (LateBaikal) TME (520 million years), as a result of which theGondwana supercontinent was formed near one of the subsi-dence poles (whereas the continental platforms of the northernhemisphere probably did not manage to gather around thesecond subsidence pole).

Subsequently, the bicellular form seems to have been re-placed by the unicellular one, so that one of the old subsidencepoles in Gondwanaland was preserved, while the other, in thenorthern hemisphere, was replaced by the uplift pole that setthe northern continental platforms in motion towards Gond-wanaland. During the Caledonian TME (with the maximumat about 400 million years; see the first peak of the double fourthmaximum on Dearnley's histogram) they came into collisionand formed Laurasia and then, during the Gertsinskaya TME(with the maximum at about 260 million years during the Early

Pernmian; see the seeond peak of the fourth maximum in Fig.4) they united with Gondwanaland to form the fourth super-continent in the Earth's history-Pangea of A. Wegener. Afterthat a bicellular convection developed again, which brokePangea during the Kimmeriyskaya TME and is continuing nowto move Pangea's fragments apart.The assumed scheme outlined above includes 9 convective

form successions in the Earth's mantle, dividing its tectonichistory into 10 epochs (a bicellular Lower Archean epoch mightbe identified additionally). An extra support for the Phanerozoicpart of this scheme can be given by the bicellular form of thecontemporary geoid with two poles of negative anomalies (nearNew Guinea and in the North Atlantic) and a wide zone ofpositive anomalies along the equator, corresponding to thesepoles.

1. Monin, A. S. (1974) "On the equations of geophysical fluid dy-namics," Izv. Acad. Sci. USSR, Atmos. Oceanic Phys. 10,119-126.

2. Monin, A. S. (1972) Weather Forecasting as a Problem in Physics(Nauka, Moscow).

3. Monin, A. S. & Gavrilin, B. L. (1976) "Hydrodynamic weatherprediction," in Theoretical Applied Mechanics, ed. Koiter, W.T. (North Holland, Amsterdam).

4. Monin, A. S. (1971) "On the description of slow magnetohydro-dynamic processes," Dokl. Akad. Nauk SSSR 200,21-93.

5. Gavrilin, B. L. & Monin, A. S. (1972) "On possibilities of thecalculation of the geomagnetic field evolution," Dokl. Akad.Nauk SSSR 205, 1349-1351.

6. Monin, A. S. (1974) Earth's Rotation and Climate (Radok-Radhakrishnan, Delhi).

7. Monin, A. S. (1973) "On the Earth's internal rotation," Dokl.Akad. Nauk SSSR 211, 1037-1100.

8. Gavrilin, B. L. & Monin, A. S. (1974) "On the rotation of theEarth's internal layers," Izv. Acad. Sci. USSR, Phys. Solid Earth,Eng]. Ed., No. 5,293-296.

9. Keondjian, V. P. & Monin, A. S. (1975) "Model of gravitationaldifferentiation of the planetary interiors," Dokl. Akad. NaukSSSR 220,825-829.

10. Keondjian, V. P. & Monin, A. S. (1975) "Model of the evolutionof the terrestrial planets," Dokl. Akad. Nauk SSSR 223, 599-602.

11. Keondjian, V. P. & Monin, A. S. (1977) "Calculations of the ev-olution of the planetary interiors," Tectonophysics 41, 227-242.

12. Keondjian, V. P. & Monin, A. S. (1976) "Calculation of the evo-lution of the planetary interiors," Izv. Akad. Nauk SSSR, Physicsof the Earth 4,3-13.

13. Keondjian, V. P. & Monin, A. S. (1976) "On the evolution of theterrestrial planets," Gerlands Beitr. Geophysik, Leipzig 85,169-174.

14. Monin, A. S. (1977) History of the Earth (Nauka, Leningrad).15. Sorokhtin, 0. G. (1974) The Global Evolution of the Earth

(Nauka, Moscow).16. Lubimova, E. A. (1974) Thermics of the Earth and the Moon

(Nauka, Moscow).17. Keondjian, V. P. & Monin, A. S. (1977) "On polar wandering due

to continental drift," Dokl. Akad. Nauk SSSR 233, 316-319.18. Munk, W. H. & MacDonald, G. I. (1960) The Rotation of the

Earth (Cambridge Univ. Press, London).19. Gorodnitsky, A. M. & Zonenshain, L. P. (1977) "The Paleozoic

and Mesozoic reconstructions of the continents and the oceans,"Geotectonics 11,83-94.

20. Monin, A. S. & Sorokhtin, 0. G. (1977) "On tectonic periods inthe Earth's history," Dokl. Akad. Nauk SSR 234, 413-416.

21. Deamley, R. (1966) "Orogenic fold-belts and hypothesis of Earthevolution," Phys. Chem. Earth 7, 1-114.

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