proton exchange or if it can undergo protonexchange without dissociation, we moni-tored the signal at mass 48 (dashed line).This mass corresponds to DCOOD+ fromDCOOD monomer and to (DCOOH)H+from doubly proton-exchanged dimer. Thefast arrival times in the mass-48 spectrumindicate that the signal arises mostly fromcontaminant DCOOD monomer in the in-cident beam scattering inelastically fromthe acid, and not from (DCOOD)2 reac-tions with the acid leading to thermallydesorbing DCOOD or (DCOOH)2. Thethree spectra demonstrate that only directlyscattered dimers survive intact, whereastrapped dimers undergo both dissociationand proton exchange before the monomersdesorb from the acid.

These experiments reveal that reactionswith H2SO4 nearly always accompany thethermal accommodation of formic acidmonomers and dimers on the surface ofsulfuric acid. We expect chemical reactionsto follow trapping if H2S04 molecules with-in the collision zone can reorient rapidlyenough to hydrogen bond to the formic acidmonomer or dimer before thermal motionspropel the molecules back into the gasphase (16). Subsequent proton transferwould then occur either within an interfacethat is a few molecules thick or be delayeduntil the formic acid molecules diffusedeeper into the acid. The observation ofproton exchange in collisions between for-mic acid molecules and sulfuric acid impliesthat solvation and protonation may oftenbe intermediate steps in the trapping anddesorption of protic gas species.

REFERENCES AND NOTES

1. S. K. Chaudhuri and M. M. Sharma, Ind. Eng. Chem.Res. 30, 339 (1991); D. R. Hanson and E. R. Lovejoy,Science 267, 1326 (1995).

2. J. E. Hurst et al., Phys. Rev. Lett. 43, 1175 (1979); C.T. Rettner, E. K. Schweizer, C. B. Mullins, J. Chem.Phys. 90, 3800 (1989); M. E. Saecker and G. M.Nathanson, ibid. 99, 7056 (1993).

3. S. T. Govoni and G. M. Nathanson, J. Am. Chem.Soc. 116, 779 (1994).

4. See also J. H. Hu et al, J. Phys. Chem. 99, 8768(1995); E. D. Guldan, L. R. Schindler, J. T. Roberts,ibid., p. 16059; K. B. Eisenthal, Acc. Chem. Res. 26,636 (1993).

5. M. Eigen, Angew. Chem. Int. Ed. Engl. 3,1 (1964); K.Ando and J. T. Hynes, J. Mol. Liq. 64, 25 (1995); andreferences therein.

6. The basicity of formic acid, as gauged by the aciddissociation constant K of the protonated base, isK(formic acid-H4) 108.7. Formic acid is much lessbasic than water because K(H2O-H-) = 100. SeeM. Liler, Reaction Mechanisms in Sulfuric Acid (Ac-ademic Press, New York, 1971), p. 256.

7. Uptake measurements indicate that roughly 60% ofthe impinging formic acid molecules dissolve in andremain within the acid during the 0.05-s observationtime of the surface (K. M. Fiehrer and G. M.Nathanson, in preparation).

8. R. A. Cox, J. Am. Chem. Soc. 96,1059 (1974).9. S. A. Lednovich and J. B. Fenn, AlChE J. 23, 454

(1977).10. Some formic acid molecules in solution may decom-

pose into CO + H20. We could detect only a very

noisy signal for CO desorption, in part because of alarge background at the CO+ mass due to residualN2. See K. W. Smith, R. M. Noyes, P. G. Bowers, J.Phys. Chem. 87,1514 (1983).

11. We expect that proton exchange of DCOOD leads toDCOOH and not HCOOD. A search for double pro-ton exchange revealed no evidence of desorbingHCOOH at mass 46 after correction for signal fromdesorbing DCOOH and DCOOD dissociatively ioniz-ing into DCOO+.

12. The lower limit of 3:1 is imposed by the noise in theDCOOD spectrum. The ratio of the TD intensities ata 45° exit angle should reflect the angle-integratedTD ratio because the TD channels typically follownearly identical, cosine-like angular distributions.

13. J. Chao and B. J. Zwolinski, J. Phys. Chem. Ref.Data 7, 363 (1978).

14. Enhanced nonpairwise, cooperative effects are ex-

pected to increase the basicity of the dimer over themonomer. R. Zhang and C. Lifshitz, J. Phys. Chem.100, 960 (1996); A. E. Reed, L. A. Curtiss, F. Wein-hold, Chem. Rev. 88, 899 (1988).

15. At lower impact energies, the monomer ion/dimerion ratio increases as more dimers become trappedand dissociate into monomers.

16. I. Benjamin, M. A. Wilson, A. Pohorille, G. M.Nathanson, Chem. Phys. Lett. 243, 222 (1995).

17. We thank F. Weinhold for discussions concerninghydrogen bonding and K. Fiehrer for the formicacid uptake measurement. This work was support-ed by NSF (CHE-9417909) and Presidential YoungInvestigator and Dreyfus Teacher-Scholar Awardsto G.M.N.

18 March 1996; accepted 20 May 1996

The Morphogenesis of Bands and Zonal Windsin the Atmospheres on the Giant Outer Planets

James Y-K. Cho and Lorenzo M. Polvani

The atmospheres of Jupiter, Saturn, Uranus, and Neptune were modeled as shallowlayers of turbulent fluid overlying a smooth, spherical interior. With only the observedvalues of radius, rotation rate, average wind velocity, and mean layer thickness as modelparameters, bands and jets spontaneously emerged from random initial conditions. Thenumber, width, and amplitude of the jets, as well as the dominance of anticyclonicvortices, are in good agreement with observations for all four planets.

Despite vast differences in chemical com-position, thermodynamic properties, physi-cal size, rotation rate, and orientation, theatmospheres of the four Jovian planets ex-hibit a remarkable similarity in their band-ed appearance and the associated strongzonal (east-west) winds. This unexpectedsimilarity is at present a major unansweredquestion (1, 2). Here we address this ques-tion with a single unifying dynamicalframework to determine how many of theobserved large-scale features of the Jovianatmospheres can be captured by a very sim-ple physical model.We assumed that the Jovian atmo-

spheres can be modeled with a nearly invis-cid, hydrostatically balanced, thin layer ofturbulent fluid under the influence of grav-itational and Coriolis forces. The motion ofsuch a fluid (3) is governed by the shallow-water equations

avat + v * Vv + fk x v = -gVh (1)

ahat +V

- (hv) = 0 (2)

where v is the horizontal velocity, t is time,h is the height of the fluid, f = 2fQsin (p isthe Coriolis parameter, g is the gravitationalProgram in Applied Mathematics and Department of Ap-plied Physics, Columbia University, New York, NY 10027,USA.

acceleration, fl is the rotation rate of theplanet, up is the latitude, and k is the unitvector normal to the surface of the sphere.For all four planets, h is taken starting fromjust below the visible cloud decks at anapproximately 1000-mbar level; this is thelevel at which the planetary radius is com-monly measured. Equations 1 and 2 weresolved in spherical geometry with the use ofa high-resolution, pseudospectral, parallelcode (4). Similar equations have been usedto model latitudinally confined features,principally Jupiter's Great Red Spot, in an-nular and channel geometries (5). In con-trast, we extend the shallow-water model tocomprise the entire planetary surface andapply it to all four planets.

The computations presented here are ini-tialized with a random turbulent flow. Theinitial vorticity of this flow (Fig. IA) is thesame for all four planets, and the results areinsensitive to the scale of the initial vorticitystructures, provided it is chosen to be small.These computations, performed at a grid res-olution of 0.70, are essentially inviscid sincemore than 97% of the initial energy is con-served throughout the evolution.

The advantage of using this simple modelis that only five parameters need to be spec-ified (Table 1): fl, g, the planetary radius a,the characteristic velocity scale U, and themean height of the fluid layer H. The overallamplitude of the initial energy spectrum iscontrolled by U; the Rhines scale (6) L3 is

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set by U, a, and 51; and the deformationradius L[) is determined by g, H, and Ql (7).Using for each planet the parameters in Ta-ble 1, we numerically integrated the equa-tions starting from the initial conditionshown in Fig. lA for 300 planetary rotations,well beyond the time when a stationary statewas reached in all cases.

Latitudinal bands spontaneously self-or-

ganized for all four of the planets without theuse of any kind of forcing. Studies in restrict-ed (8) and nonspherical (9) geometries haveused forcing to obtain and sustain bands, andthe only unforced study in spherical geome-try (10) did not obtain bands because of theinfinite LD in that model (4).

The formation of a globally banded pat-tern from random initial conditions is ap-

parent in the potential vorticity field (11)after only 20 planetary rotations for theJupiter parameters (Fig. iB). Robust zonalbands persist for long times (Fig. IC), longafter the flow pattern has become station-ary. Several large, coherent vortices arespontaneously produced and persist embed-ded in the bands, a feature not produced inprevious studies.

For Neptune as well, zonal structuresappear early and eventually become station-ary (Fig. ID), but the large-scale pattern isdifferent from that in Fig. 1C. Only threebands appear in the case of Neptune: Themain one is very broad and centered aroundthe equator, implying that over a large frac-tion of the spherical surface, the potentialvorticity is well homogenized. This homog-enization has previously been assumed (12)whereas here it is shown to be a natural endstate of the turbulent shallow-water dynam-ics. The striking difference between Figs.IC and 1D is a direct consequence of thefact that the ratio L ja is much greater forNeptune than it is for Jupiter. The ratioL,ja is at least five times as large as L,Ja forboth planets; this shows that L la and notL1Ja, controls the number of bands (4),which is roughly 7ra/LL.

D

o)a,@I

0)

4>

I onU/

._

1, >-

Fig. 1. (A) The initial vorticity, 4-= k*Vxv, used in our computations for all four planets (Table 1). (B) Thepotential vorticity q after 20 planetary rotations for Jupiter parameters. (C) Potential vorticity q after 240planetary rotations for Jupiter parameters. (D) Potential vorticity q after 240 planetary rotations forNeptune parameters. Red indicates positive values, and blue indicates negative values.

4

3

2

10

-1

-2

-3

-40 50 100 150 200 250 300

Time (planetary rotations)

Fig. 3. The skewness of the vorticity 4 as a func-tion of time. The initially zero value becomes neg-ative for all four planets, showing the dominanceof anticyclonic vortices.

0 200 400U (m/s)

90

60

30

0

-30

-60

-90

B_

~~~~~~~~~~~. .............

-400 -200 0 200U (m/s)

-400 -200 0

90D

60

30

0O

-30 -

-60 -

- -90 -200 -400 -200 0 200

U (m/s) U (m/s)

Fig. 2. The observed zonal wind profiles of (A) Jupiter (solid) and Saturn (dashed) and (B) Uranus (solid) and Neptune (dashed) from (15). The correspondingprofiles for (C) Jupiter (solid) and Saturn (dashed) and (D) Uranus (solid) and Neptune (dashed) from our computations after 300 planetary rotations.

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Jupiter--SaturnUranus.

Neptune

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_g.............. .......................

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Table 1. Physical parameters used in our model.Values from (1, 15).

Plnt a 27r/f I g U HPlanet (1 01 m) (hours) (m/s2) (m/s) (1 03 m)

Jupiter 7.1 9.9 23 50 20Saturn 6.0 10.7 9 300 40Uranus 2.6 -17.2 9 300 35Neptune 2.5 17.9 11 300 30

ing as a tracer for the flow, and is the dynamicallysignificant quantity to view. See, for instance, B. J.Hoskins, M. E. McIntyre, A. W. Robertson, Q. J. R.Meteorol. Soc. 111, 877 (1985).

12. B. A. Smith et al., Science 246, 1422 (1989); L. M.Polvani, J. Wisdom, E. DeJong, A. P. Ingersoll, ibid.249,1393 (1990); M. Allison and J. T. Lumetta, Geo-phys. Res. Lett. 17, 2269 (1990).

13. Anticyclones are eddies with negative vorticity in thenorthern hemisphere and positive vorticity in thesouthern hemisphere. Cyclones are the converse.

14. M.-M. McLow and A. P. Ingersoll, Icarus 65, 353(1986).

15. R. Beebe, Chaos 4, 113 (1994).16. This work is supported by NSF. The computations

were performed on the Cray C90 at the PittsburghSupercomputing Center. We are grateful to M. Alli-son for thoughtful suggestions on the manuscriptand to A. Simon and R. Beebe for the zonal winddata in Fig. 2.

26 March 1996; accepted 3 June 1996

Alternating potential vorticity gradients(Fig. 1) indicate the presence of strong zonaljets, as in the observations: Jupiter and Saturnhave multiple jets and a prograde (eastward)equatorial wind (Fig. 2A), whereas Uranusand Neptune have large retrograde (west-ward) equatorial winds (Fig. 2B). Our shal-low-water computations (Fig. 2, C and D)capture the approximate number, width, andamplitude of the observed zonal winds for allfour planets. Precise, quantitative agreementis neither sought nor expected, given the sim-plicity of this model. The important point isthat the values in Table 1 alone are sufficientto determine the gross features of the zonalwinds. One feature that the model seems un-able to reproduce is the direction of the equa-torial jets for Jupiter and Saturn, indicatingthat a more sophisticated model is necessaryfor those two planets. Furthermore, our modelpredicts that more anticyclones than cyclones(13) are to be found on all four planets. Thisasymmetry is depicted by the skewness of thevorticity field (Fig. 3). The negative bias isobservationally well established for Jupiter(14) but is not as robustly determined for theother planets.

In conclusion, our study strongly sug-gests that, however different the Jovianplanets may be, their characteristic bandedappearance is a direct consequence of theintrinsic shallow-water dynamics they allshare.

REFERENCES AND NOTES

1. A. P. Ingersoll, Science 248, 308 (1990).2. P. J. Gierasch, J. Geophys. Res. 98, 5459 (1993).3. P. S. Laplace, Mem. IAcad. R. Sci. Paris 88, 75

(1775); H. Lamb, Hydrodynamics, (Dover, New York,1932); J. Pedlosky, Geophysical Fluid Dynamics(Springer-Verlag, New York, 1979).

4. J. Y-K. Cho and L. M. Polvani, Phys. Fluids 8,1531(1996).

5. P. S. Marcus, Nature 331, 693 (1988); T. E. Dowlingand A. P. Ingersoll, J. Atmos. Sci. 46, 3256 (1989).

6. P. B. Rhines, J. Fluid Mech. 69, 417 (1975).7. The values of LD - H/2S1 are the least reliable of the

parameters in Table 1, because of the poor knowl-edge of the vertical structure of the atmospheres ofthese planets. However, the number of bands in ourcomputations is insensitive to the precise value of LD;the number is controlled by LP .Uaff.

8. G. P. Williams, J. Atmos. Sci. 35, 1399 (1978).9. M. E. Maltrud and G. K. Vallis, J. Fluid Mech. 228,

321 (1991).10. S. Yoden and M. Yamada, J. Atmos. Sci. 50, 631

(1993).11. The potential vorticity q-(; + f)/h is conserved

following the motion of each fluid element, thus serv-

A Magnetic Signature at lo: Initial Report fromthe Galileo Magnetometer

M. G. Kivelson, K. K. Khurana, R. J. Walker, C. T. Russell,J. A. Linker, D. J. Southwood, C. Polanskey

During the inbound pass of the Galileo spacecraft, the magnetometer acquired 1 minuteaveraged measurements of the magnetic field along the trajectory as the spacecraft flewby lo. A field decrease, of nearly 40 percent of the background jovian field at closestapproach to lo, was recorded. Plasma sources alone appear incapable of generatingperturbations as large as those observed and an induced source for the observedmoment implies an amount of free iron in the mantle much greater than expected. Onthe other hand, an intrinsic magnetic field of amplitude consistent with dynamo actionat lo would explain the observations. It seems plausible that lo, like Earth and Mercury,is a magnetized solid planet.

Jupiter's moon lo has repeatedly surprisedplanetary scientists. First, lo's orbital posi-tion was unexpectedly found to controldecametric radio emission from Jupiter's ion-osphere (1). Early explanations suggestedthat the emissions were generated by mag-netic field-aligned currents linking lo andJupiter (2). These ideas were refined andlinked to Alfv6nic disturbances generated bythe interaction of the flowing plasma of Ju-piter's magnetosphere with an electricallyconducting lo (3, 4). After the discoveries ofa large cloud of neutral sodium surroundinglo (5) and of a torus of ionized sulfur encir-cling Jupiter at the distance of lo's orbit (6),Voyager 1 found volcanic plumes distributedon the surface of the moon (7). The Voyager1 magnetometer detected magnetic pertur-bations of -5% of the ambient jovian mag-netic field (-1900* nT) as it crossed lo'smagnetic flux tube about 11 R1,, (radius of lo,1821 km) below lo (8), thereby confirmingthe presence of a field-aligned current flow-ing several thousand kilometers away fromthe spacecraft and carrying more than 106 Ainto the jovian ionosphere.

M. G. Kivelson, K. K. Khurana, R. J. Walker, C. T. Russell,Institute of Geophysics and Planetary Physics, Universityof California, Los Angeles, Los Angeles, CA90095-1567, USA.J. A. Linker, Science Applications International Corpora-tion, San Diego, CA 92171, USA.D. J. Southwood, Department of Physics, Imperial Col-lege of Science, Technology, and Medicine, London,SW7 2BZ, UK.C. Polanskey, Jet Propulsion Laboratory, Pasadena, CA91109, USA.

The Galileo spacecraft flew by lo on 7December 1995; its closest approach wasat 17:45:58 UT (universal time) at analtitude of 898 km (9). Particles and fieldsdata from the pass recorded on the space-craft tape recorder will be analyzed in theearly summer of 1996. However, surveydata (10) read out directly from the mag-netometer's ( 1) internal memory werereturned in late December 1995. All threecomponents of the background jovianfield measured on Galileo's trajectorythrough the plasma torus followed predic-tions based on a recent extension (12) ofVoyager-epoch magnetic field models ( 13)but in the wake of lo (that is downstreamin the flow of torus plasma corotating withJupiter), the field magnitude decreased by695 nT in a background of 1835 nT (Fig.1). Perturbations of the field along thespacecraft's trajectory were principally an-tiparallel to the model jovian field (Fig.2). The field rotated slightly, but thebending was not what would be producedif the field had been pushed outwardaround lo but rather that caused by a fieldpulled inward toward lo. Indeed, the per-turbations along the spacecraft trajectoryare quite well represented by a model inwhich Jupiter's field is merely added to thefield of an lo-centered dipole with mo-ment aligned with the local field of Jupiter(hence antiparallel to Jupiter's dipole mo-ment) (Fig. 3).

As the local corotation speed is greaterthan the Keplerian speed, the jovian plas-

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