1. M M A ........... n nm W1 . ........ . REPORTS includingany outermost stable layer. We achievedan equilibrium state by balancing the Reynolds stress of the penetrative convec- tion rolls againstthe viscous shear of the mean zonal flow. The alternately directed jets of the mean zonalwind may be a resultof additional instabilities whenthe mean flowV is strong, as suggested by three-dimensional numerical simulations (29). Because penetra- tive convection inside the cylinder tangent to the inner sphere's equator requires a much larger temperature gradient to excite, the zon- al flow structure in lowerlatitudes 4 < 450 (determined from the sizeof the metallic in- nercore) is fundamentally different from that in higherlatitudes. The confinement of the zonal flow jets to the equatorial regions out- side the tangent cylinder suggests a rotation- ally dominated deep convection origin(15). Furthermore, the jovian zonal jetsare roughly symmetric about the equator andappear to be rather stable, indicating that they are con- trolled by rotation anddeepconvection with a long time scale.As a consequence of rapid rotation and spherical geometry, deep convec- tion can readily penetrate through the entire H-He envelope and produce a mean zonal wind with an amplitude that can be much larger thanthatof the corresponding nonaxi- symmetric (eddy) convective flows. Our re- sults on penetrative spherical rotating convec- tion have implications for the dynamics of Earth's fluid core and the sun'sconvection zone,places where theremaybe stably strat- ifiedlayers (30, 31). REFERENCES AND NOTES 1; D. H. Atkinson, J. B. Pollack, A. Seiff, Science 272, 842 (1996). 2. P. J. Gierasch and B. J. Conrath, J. Geophys. Res. 98, 5459 (1993). 3. T. Guillot,D. Gautier, G. Chabrier,B. Mosser, Icarus 112, 337 (1994). 4. T. Guillot,G. Chabrier, P. Morel, D. Gautier, ibid., p. 354. 5. W. B. Hubbard,Astrophys. J. 152, 745 (1968). 6. H. K. Moffatt, Magnetic Field Generationin Electrical- ly Conducting Fluids (Cambridge Univ. Press, Cam- bridge, 1978). 7. D. J. Stevenson and E. E. Salpeter, Astrophys. J. Suppl. Ser. 35, 221 (1977). 8. A. Seiff et al., Science 272, 844 (1996). 9. A. D. DelGenio and K. B. McGrattan,Icarus 84, 29 (1 990). 10. B. Straughan, Mathematical Aspects of Penetrative Convection (Longman Scientitic and Technical, Lon- don, 1993). 11. G. Veronis, Astrophys. J. 137, 641 (1963). 12. P. C. Matthews, J. FluidMech. 188, 571 (1988). 13. F. H. Busse, ibid. 44, 441 (1970). 14. K. Zhang, ibid. 236, 535 (1992). 15. F. H. Busse, Icarus 29, 255 (1976). 16. __, Astrophys. J. 159, 620 (1970). 17. Z.-P. Sun, G. Schubert, G. A. Glatzmaier, Science 260, 661 (1993). 18. G. A. Glatzmaier and P. Olson, Geophys. Astrophys. FluidDyn. 70, 113 (1993). 19. J. B. Manneville and P. Olson, Icarus, in press. 20. F. H. Busse and L. Hood, Geophys. Astrophys. Fluid Dyn. 21, 59 (1981). 21. R. L. Kirk and D. J. Stevenson, Astrophys. J. 316, 836 (1987). 22. Take the typical mean flow speed V0 = 0(100 m s-1), v = 10-6 m2 s-1, L = 0(107 m), and Ql = 1.76 x 10-4 S-1 [see, for example, (7) and F. M. Flaser, Icarus 26, 280 (1986)]. 23. A Boussinesq fluid spherical shell of constant ther- mal diffusivity K, constant thermal expansion coeffi- cient u-,and constant viscosity v that is rotating uni- formly with a constant angular velocity Ql was as- sumed. Stress-free and isothermal boundary condi- tions were also assumed. 24. We have concentrated on the case with the ratio of the innerto outer radius rl/ro = 0.35. Solutions with other values of rl/ro were obtained and show similar features. In our calculation, E is based on the thick- ness of the shell, E = v/2(ro - r,)2Q. 25. We have used a temperature gradient of the form dT 3r*"7 [ n rO* 3 dr (n + 3)(ro - r,)L (r) r* ] where r* = r/(rO - ri) and n, Cf, and ] are parameters. We have focused on the case with n = 0 and p = 0.6. Convection takes place when the Rayleighnum- ber R = ort9 g(ro - rj)4/(Kv) is sufficiently large, where g is the acceleration due to gravity;9- measures the magnitude of the driving temperature gradient in the model and determines the vigor of convection through R. The model only qualitatively simulates conditions in the "real" Jupiter. 26. A. P. Ingersoll et al., J. Geophys. Res. 86, 8733 (1981). 27. The linearized Navier-Stokes equation and the heat equation for penetrative convection in a rotating spherical shell are solved. The heat equation is solved analytically in terms of Bessel functions whereas the Navier-Stokes equation is solved nu- mericallyby the spectral method. 28. Re = (DIVIt)/v, where D is the typical length scale of convective eddies. Take DIVI1) = 0(103 m2 S-1) [B. Fegley and K. Lodders, Icarus 11 0, 117 (1994)] and v = 10-6 m2 s-1 (7), we obtain Reli >> 1 for a moderate value of -q,. 29. Z.-P. Sun and G. Schubert, Phys Fluids 7, 2686 (1995). 30. J. A. Jacobs, The Earth's Core (Academic Press, New York, 1975). 31. J. P. Zahn, in Lecture Notes in Physics, D. Gough and J. Toomre, Eds. (Springer-Verlag, Berlin, 1990), vol. 388, pp. 225-232. 32. The work of K.Z. was supported by the Institute of Geophysics and PlanetaryPhysics, University of Cal- ifornia,Los Angeles. 18 April1996; accepted 3 July 1996 An Archean Geomagnetic Reversal in the Kaap ValleyPluton, South Africa Paul W. Layer,* AlfredKr6ner, Michael McWilliams The Kaap Valley pluton in South Africa is a tonalite intrusion associated with the Archean Barberton Greenstone Belt. Antipodal paleomagnetic directions determined from the central and marginal parts of the pluton record a geomagnetic reversal that occurred as the pluton cooled. The age of the reversal is constrained by an 40Ar/39Ar plateau age from hornblende at 3214 ? 4 million years, making it the oldest known reversal. The data presented here suggest that Earth has had a reversing, perhaps dipolar, magnetic field since at least 3.2 billion years ago. The behaviorof Earth's magneticfield is preserved in the geologicrecord and can be deciphered with paleomagnetic techniques. With these techniquesone can determine the locationof the magnetic pole relative to the rock unit at the time the rock cooled through its magnetic blocking temperature. Knowledgeof ancient pole positions and magnetic polarities has been used to con- structmodels of plate motion (superconti- nent positions and plate velocities) and the geomagnetic dynamo (reversal frequency and intensity). The usefulness of any paleo- magnetic pole is determined by the stability of its magnetization (as determined by, for example, stepwise demagnetization, reversal tests, fold tests, or contact tests) and the abilityto determine the time when magne- tization wasacquired. Fewrecords of Earth's P. W. Layer, Geophysical Institute, Universityof Alaska, Fairbanks,AK 99775, USA. A. Kr6ner, Institut fur Geowissenschaften, Johannes Gutenburg-Universit5t, 55099 Mainz, Germany. M. McWilliams, Department of Geophysics, Stanford University,Stanford, CA 94305, USA. *To whom correspondence should be addressed. geomagnetic field from before 3 billion years ago (Ga) exist. Two early Archean paleopole positionsfor rocksas old as 3.45 Ga have been reported (1), but each study yielded only unipolar directions, with few stability tests.Here,we usedpaleomagnetic techniques to investigatean Archean to- nalite pluton,andourresults, when coupled with the results of a detailed geochrono- logic study (2), indicate a 3.2-Gapaleomag- netic pole constrained by reversal and con- tact tests. Well-documented and dated pa- leopolesarenecessary to construct apparent polar-wander paths, and from these poles minimum average Archeanplate velocities can be calculated (3). The Kaap Valley pluton is a circular intrusion 30 km in diameterthat formsa valleysurrounded by the moremountaitous Barberton Greenstone Belt to the north, east, and south (Fig. 1). It is overlain to the west by the earlyProterozoic Transvaal Su- pergroup. The TransvaalSupergroup and related rocks form a thick sequence with an age range from2552 + 11 millionyears ago (Ma) at the baseto 2432 ? 31 Ma nearthe SCIENCE * VOL. 273 * 16 AUGUST 1996 943