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Showman et al.: The Global Atmospheric Circulation of Saturn 11.1 INTRODUCTION

The Global Atmospheric Circulation of Saturn

Adam P. Showman, Andrew P. Ingersoll, Richard Achterberg, and Yohai Kaspi

Over the past decade, the Cassini spacecraft has provided an unprecedented observationalrecord of the atmosphere of Saturn, which in many ways now surpasses Jupiter as thebest-observed giant planet. These observations, along with data from the Voyager spacecraftand Earth-based telescopes, demonstrate that Saturn, like Jupiter, has an atmospheric circulationdominated by zonal (east-west) jet streams, including a broad, fast eastward equatorial jet andnumerous weaker jets at higher latitudes. Imaging from Voyager, Cassini, and groundbasedtelescopes also document a wide range of tropospheric features, including vortices, waves,turbulence, and moist convective storms. At large scales, the clouds, ammonia gas, andother chemical tracers exhibit a zonally banded pattern whose relationships to the zonal jetsremains poorly understood. Infrared observations constrain the stratospheric thermal structureand allow the derivation of stratospheric temperatures; these exhibit not only the expectedseasonal changes but a wealth of variations that are likely dynamical in origin and highlightdynamical coupling between the stratosphere and the underlying troposphere. In parallel tothese observational developments, significant advances in theory and modeling have occurredover the past decade, especially regarding the dynamics of zonal jets, and we survey these newdevelopments in the context of both Jupiter and Saturn. Highly idealized two-dimensionalmodels illuminate the dynamics that give rise to zonal jets in rapidly rotating atmospheresstirred by convection or other processes, while more realistic three-dimensional models of theatmosphere and interior are starting to identify the particular conditions under which Jupiter-and Saturn-like flows—including the fast equatorial superrotation, multiple jets at higherlatitudes, storms, and vortices—can occur. Future data analysis and models have the potentialto greatly increase our understanding over the next decade.

11.1. Introduction1

The dynamics of Jupiter and Saturn have long been the2

subject of fascination. Although Galileo trained the tele-3

scope on both objects starting in 1610, the pace of at-4

mospheric discoveries over subsequent centuries was far5

slower for Saturn than for Jupiter because of the fact that6

Saturn is dimmer, smaller in Earth’s sky, and more muted in7

its cloud-albedo contrasts. The first description of Jupiter’s8

zonal banding occurred in 1630. Cassini and others dis-9

covered short and long-lived spots, the equatorial current,10

and other atmospheric features on Jupiter starting in the lat-11

ter decades of the 1600s, and ever more refined observa-12

tions have continued episodically since then (e.g., Rogers13

1995). In contrast, early observations of Saturn could not14

make out features on the planet’s surface, instead empha-15

sizing the discovery of Saturn’s moons and the nature of its16

rings (van Helden 1984). Cassini reported an equatorial belt17

on Saturn in 1676, and hints of non-zonal atmospheric fea-18

tures appeared a century later in the 1790s, but it took until19

the latter decades of the 1800s before spots could reliably20

be observed on Saturn (van Helden 1984). This disparity21

in pace of discovery between Jupiter and Saturn continued22

through the twentieth century, and even over the last few23

decades, the relative difficulty of observing Saturn relative24

to Jupiter means that Saturn has received much less atten-25

tion than its sister planet. Yet the Cassini mission, in or-26

bit around Saturn since 2004, has revolutionized the quality27

and quantity of observational constraints, which now rival 1

or exceed those available for Jupiter. This for the first time 2

places Saturn at the forefront of understanding giant planets 3

as a class. 4

The atmospheric circulations on Saturn and Jupiter are 5

dominated by numerous fast east-west (zonal) jet streams, 6

which interact with a wealth of vortices, waves, turbu- 7

lent filamentary structures, convective storms, and other 8

features in poorly understood ways. The jet profiles ex- 9

hibit qualitative similarities—on both planets, there exists 10

a broad, fast prograde (eastward) equatorial jet and numer- 11

ous narrower, weaker jets at higher latitudes. Nevertheless, 12

the zonal jets are considerably broader, faster, and fewer 13

in number on Saturn than Jupiter—peak wind speeds reach 14

∼500 m s−1 on the former but never exceed 200 m s−1 on 15

the latter. Both planets exhibit cloud banding that is modu- 16

lated by the zonal jets and, at large scales, is far more zon- 17

ally symmetric than the cloud pattern on Earth. Yet the de- 18

tailed relationship of the cloud-band structure to the zonal- 19

jet structure differs considerably between Jupiter and Sat- 20

urn. Moreover, despite the existence of many dozens of 21

vortices on both planets, Saturn lacks prominent large vor- 22

tices like Jupiter’s Gread Red Spot and White Oval. These 23

differences remain poorly understood. As case studies in 24

similarities and differences, comparative investigations of 25

the two planets therefore have great potential for insights. 26

Motivations for studying the atmospheric dynamics of 27

Jupiter and Saturn are several. Our understanding of Earth’s 28

1

Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHERE

circulation is well developed (see, e.g., Vallis 2006), but1

necessarily confined to the specific conditions relevant to2

Earth. The giant planets illustrate how an atmosphere’s cir-3

culation operates when there is no planetary surface, when4

the incident solar energy flux is weak (∼2 W m−2 on Saturn5

versus 240 W m−2 for Earth), when the energy flux trans-6

ported through the interior is comparable to the energy flux7

absorbed from the Sun, and when the background gas com-8

prises hydrogen rather than high-molecular-weight species9

like N2 or O2 (which, among other things, promotes larger10

atmospheric scale heights on Jupiter and Saturn than on11

Earth and implies that, opposite to the situation on Earth,12

moist air is denser than dry air at a given temperature and13

pressure). Moreover, as they lack many of the complexities14

of the Earth system, the giant planets serve as ideal lab-15

oratories for testing and understanding fundamental issues16

in geophysical fluid dynamics (GFD) such as the dynamics17

of zonal jets, vortices, and stratified turbulence. The gi-18

ant planets are dynamic and exhibit meteorological and cli-19

matic changes on timescales ranging from minutes to cen-20

turies. Most of the phenomena that are richly characterized21

in the observational record remain poorly understood; con-22

tinued observations, theory, and modeling will be necessary23

to understand even some of the zeroth-order aspects of the24

circulation. Finally, Saturn and Jupiter can serve as a proto-25

type for helping to understand the behavior of the numerous26

brown dwarfs and giant planets that are being discovered27

outside the solar system.28

The primary goal of this chapter is to survey observa-29

tions and theory of Saturn’s atmospheric dynamics near30

the close of the Cassini mission. Our scope is Saturn’s31

global atmospheric circulation, emphasizing the thermal32

and dynamical structure of the large-scale zonal jets, vor-33

tices, turbulence, and interior structure. We summarize the34

current dynamical state of Saturn—emphasizing observa-35

tions but including dynamical interpretation and analysis36

where appropriate—beginning with the troposphere (Sec-37

tion 11.2), followed by the stratosphere (Section 11.3). In38

Section 11.4, we summarize Saturn’s dynamics, beginning39

with basic balance arguments for jet structure, and proceed-40

ing to a summary of models for the formation of the zonal41

jets. Anticipating the Grand Finale stage of the Cassini Mis-42

sion, we end with a brief discussion of constraints provided43

by gravity data on the deep jet structure. Our review fol-44

lows the prior reviews of Ingersoll et al. (1984) and Del45

Genio et al. (2009), who summarized the state of knowl-46

edge after the Voyager flyby and nominal Cassini missions,47

respectively. It also complements other reviews of Jupiter48

and the giant planets generally, including Ingersoll (1990),49

Marcus (1993) Dowling (1995a), Ingersoll et al. (2004), and50

Vasavada and Showman (2005). Reviews of Saturn’s poles,51

stratospheric thermal structure, and convective storms can52

be found in the chapters by Sayanagi et al., Fletcher et al.,53

and Sanchez-Lavega et al. in this volume.54

11.2. Observations of the Troposphere 1

On Saturn the winds blow primarily east-west and are or- 2

ganized into alternating jet streams, each peaking at its par- 3

ticular latitude. At large scales, the cloud structure is zon- 4

ally banded—to a much stronger degree than on Earth—but 5

also contains numerous vortices, waves, storms, and various 6

cloud features at small scales (Figure 11.1). Viewed from a 7

non-rotating reference frame, cloud features near the equa- 8

tor exhibit periods of about 10 h 10 min. At latitudes of 9

35–40 in each hemisphere, the recurrence period is about 10

10 h 40 min, and at higher latitude the periods vary within 11

this range up to the pole. 12

These observations indicate that rotation plays a crucial 13

role in the atmospheric dynamics of Saturn. The importance 14

of rotation can be characterized using the Rossby number, 15

which is the ratio of the advection force to the Coriolis force 16

in the horizontal momentum equation. The advection force 17

per mass has characteristic magnitude U2/L, and the hor- 18

izontal Coriolis force per mass has characteristic magni- 19

tude fU , where U is the characteristic wind speed, L is 20

the characteristic horizontal length scale of the circulation 21

(e.g., the jet width), f = 2Ω sinφ is the Coriolis parameter, 22

Ω is the planetary rotation rate (2π over the rotation pe- 23

riod), and φ is latitude. Thus, the Rossby number is given 24

byRo = U/fL. The cloud measurements described above 25

suggest a characteristic rotation period of order 10.5 hours, 26

with zonal speed differences between the cloud bands of 27

typically ∼100 m s−1 (Figure 11.1 and 11.2). Inserting ap- 28

propriate values of f ≈ 2 × 10−4 s−1, U ≈ 100 m s−1, 29

and L ≈ 107 m (relevant to Saturn’s zonal jets), we ob- 30

tain Ro ≈ 0.05. Thus, on Saturn—as well as on Jupiter, 31

Uranus, Neptune, and Earth’s atmosphere and oceans— 32

the large-scale circulation exhibits small Rossby number. 33

This estimate implies that, for the large-scale flows on the 34

giant planets, advective forces are weak compared to the 35

Coriolis force. Since the pressure-gradient force is the 36

only other significant force in the horizontal momentum 37

equation, the smallness of Ro implies that the dominant 38

balance in the horizontal momentum equation is between 39

the Coriolis force and the pressure-gradient force—called 40

geostrophic balance (see, e.g., Holton and Hakim 2013, 41

Chapter 2). 42

Although the observed differential rotation is evidence 43

of wind, we do not know the precise wind speeds relative 44

to the planetary interior—simply because Saturn’s interior 45

rotation rate is not well determined. The other giant planets 46

have internally generated magnetic fields that are tilted with 47

respect to the rotation axis, and those fields are presumably 48

locked to the electrically conducting fluid interiors, at least 49

on time scales of years to decades, so the daily wobble of 50

the field gives us a good estimate of the internal rotation pe- 51

riod. Saturn has an internal field as well, but it is not tilted. 52

Thus far, the instruments on Cassini and other spacecraft 53

have been unable to detect a wobble and therefore unable to 54

provide an exact period from which to measure the winds. 55

Voyager flew past Saturn in 1980 and measured magnetic 56

2


the absorbing gas. In MT3, high-altitude features appearbright against the dark background of absorbing gas.Saturn’s appearance in UV3 will expose any ultraviolet-absorbing aerosols and is strongly affected by gas scatter-ing. In UV3, high-altitude features that absorb UV lightappear dark against a bright background, since there is lessgas above them to scatter light toward the spacecraft. Thesuite of filters is expected to reveal features at pressurelevels between tens and hundreds of mbar.[22] The CB2 map contains more fine-scale structure than

the others in Figures 5a and 5b, such as the internal structureof larger vortices, the presence smaller vortices and patchyclouds, and the convective storm and its associated clouds.In images using filters sensitive to higher features, thecontrast between major latitude bands increases, but thereis less fine-scale detail. However, when MT images areviewed at full spatial resolution, the bands are found tocontain extended cloud filaments that bend and fold due tointeractions between jets, or between jets and vortices. Ingeneral, there are no major features (e.g., vortices) that areunique to the higher-sounding wavelengths. An importantexception occurs near the equator, where there is relativelysharp detail in MT2 and MT3 (and inverted in brightness in

UV3) that is distinct from cloud textures within CB2 at thesame location. The presence of distinct and different cloudmorphologies in the CB2 and MT2 images allowed thedirect measurements of vertical wind shear reported inPorco et al. [2005]. The convective storm is not visible inMT2, MT3, or UV3, suggesting that it does not penetratebeyond the deeper levels sensed.[23] Saturn’s banding is correlated with the profile of

zonal winds, but not in a way that obviously implies the‘‘belt/zone’’ model, in which bright anticyclonic regions(zones) signify the upwelling branches of meridional circu-lations and clear cyclonic regions (belts) are sites ofsubsidence [Smith et al., 1981]. Figures 5a and 5b showthat narrow bands with less cloud/haze scattering occur justsouthward (i.e., on the cyclonic sides) of the eastward jetmaxima at 49.5!S, 60.5!S, and 74.5!S. The two broadregions in between these eastward jets are relatively uniformin brightness, despite the change in sign of vorticity acrossthe westward jet. The region in between the eastward jets at33!S and 49.5!S conforms more to the belt/zone model,with more scattering from anticyclonic latitudes and lessfrom cyclonic. The band just south of 60.5!S is unusuallybright in BL1 and UV3, suggesting low aerosol opacity andenhanced Rayleigh scattering. Finally, the polar spot is darkat all wavelengths except UV3, where it is absent.

4. Vortices

[24] We have analyzed the characteristics and behavior ofvortices by measuring their sizes, shapes, and spatial distri-bution on the HRMs and monitoring their evolution on theAMs.Avortexwas noted if it was present in three consecutiveAMs or in both HRMs. There were many small, shorter-livedfeatures, but these could not be distinguished from imageartifacts. We manually measured the center location, east-west extent, and north-south extent of each vortex using adisplay tool that allows zooming and adjustment of brightnessand contrast. We estimate the uncertainty in the centerlocation to be <2 pixels based on frame-to-frame repeatabilityand repeated measurements on the same frame. Our approachto determining the center location is similar to that of Li et al.[2004]. For symmetric vortices, we estimated the center pixel;for asymmetric vortices, we estimated the centroid of the areaof greatest contrast.

4.1. Number and Size Frequency Distribution

[25] The number of vortices counted in the AMs in-creased with time, primarily as a result of the threefoldincrease in spatial resolution as the spacecraft approachedSaturn. Even the final AMs contain only !65 vortices,compared to 138 in the HRMs. The size frequency distri-butions in Figure 6 suggest that the population of vorticeswith east-west diameters <1000 km cannot accurately becounted in the final AM. Therefore the AMs cannot revealhow the total number of vortices over all sizes varied withtime. However, a comparison of the AM and HRM histo-grams suggests that the number of mid to large vorticesevolved but remained similar between the two observations.

4.2. Vortex Characteristics

[26] We have attempted to classify vortices into familiesbased on their brightness and morphology at 750 nm (CB2

Figure 5b. Similar to Figure 5a, but maps were con-structed from images acquired using the three ISS filterscentered in progressively stronger CH4 absorption bands:(top) MT1 (619 nm), (middle) MT2 (727 nm), and (bottom)MT3 (889 nm).

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ring of bright cloud material at 88.8!S. The dark spot isreminiscent of the infrared hot spot described by Orton andYanamandra-Fisher [2005]. The polar cloud ring is slightlyoff center from the pole (not due to viewing geometry) andcontains a small segment of arc with increased width.

[17] We measured the latitudinal profile of zonal wind bytracking the displacement of cloud features on the pair ofHRMs. The time separation is 10 hours 30 min, giving aprecision of 1.4 m s!1 for a displacement of one map pixel atthe equator. The combination of errors due to image naviga-tion, feature tracking, and foreshortening at higher latitudes isestimated to be <20 pixels (consistent with the low dispersionof the measurements shown below). Features were identifiedand tracked by eye using custom IDL software that blinks themapped images on a monitor and allows the user to fine-tunetiepoint locations on a pair of static zoom windows. Trackedfeatures include discrete clouds and long-livedmorphologicalfeatures (e.g., kinks) within cloud bands or streaks. Vortices,diffuse clouds/hazes, and features that exhibited nonzonalmotionswere avoided in order to derive the ambient flowwiththe highest accuracy. At any given location, cloud featuresappear to translate with a single wind speed; no evidence ofmultilevel cloud decks or vertical wind shear was found in theCB2 images.[18] Figure 4 shows a total of 458 wind measurements,

including 347 on the HRMs from our study and 111 on the

Figure 2. Polar stereographic projection of Saturn’s south-ern hemisphere on 18 September 2004, during Cassini’s firstrevolution of the planet. Themap shown here is the first of theHRM pair used for polar wind measurements. The spatialresolution of the raw 750-nm images is"50 km pixel!1 in theimage plane. Data within 10! latitude of the pole are takenfrom a single mapped image.

Figure 3. Profile of Saturn’s zonal winds measured onCassini images overlain on a segment of the cylindrical mapshown in Figure 1.

Figure 4. Plot of the 458 Cassini zonal wind measure-ments from this study and Porco et al. [2005]. The thinsolid curve has been manually fit to the Cassini points.Voyager (thick shaded curve) [Sanchez-Lavega et al., 2000]and HST (dashed curve) [Sanchez-Lavega et al., 2002]profiles are shown for comparison. The box near the polebounds the velocities of features on a circumpolar cloudring "3! in diameter.

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Fig. 11.1.— Cassini images of Saturn’s southern hemisphere. Left: A cylindrical projection mosaic comprised of CassiniISS images using the MT2 filter, centered in a methane absorption band at 727 nm wavelength and showing the equatorto ∼85S latitude and 180–360W longitude. The image is overlain with the zonal-wind profile obtained from cloudtracking (plotted such that 0 m s−1 in System III is at the center of the panel). Right: Polar stereographic projection ofCassini ISS images in the CB2 filter, which is centered at 750 nm, in the continuum between methane absorption bands.From Vasavada et al. (2006).

Fig. 11.2.— Mean zonal wind profile for the 2004–2009 time period. The black curve is from clear filters that sense cloudsin the 350–700 mbar pressure range. The red curve is from methane band filters that sense clouds in the 60–250 mbarpressure range. From Garcıa-Melendo et al. (2011).

fields, radio emissions, and modulations of the charged par-1

ticle distribution around the planet that pointed to a period2

that was close to the longest periods determined by tracking3

clouds in the atmosphere. Accordingly, the System III rota-4

tion period of 10 h 39 min 24 s was chosen as the reference5

frame from which to measure the longitudes and drift rates6

of phenomena on Saturn (Desch and Kaiser 1981). This 1

longitude system is the official standard, even though the 2

electromagnetic phenomena on which it was based have not 3

kept pace but have wandered in ways that are uncharacter- 4

istic of the planet’s interior. In recent years, several authors 5

have attempted to obtain improved estimates of the interior 6

3


rotation period. Anderson and Schubert (2007) and Read1

et al. (2009b) used theoretical arguments combined with the2

observed wind field to suggest rotation periods that are 5–3

6 minutes shorter than the System III period, and Helled4

et al. (2015) used the measured low-order gravitational co-5

efficients and the shape of the planet to suggest a rotation6

period of 10 h 32 min 45 s± 46 s. If these estimates are cor-7

rect, then the winds measured relative to the interior would8

be shifted westward (by a latitude-dependent value) relative9

to those plotted in Figure 11.2.10

On an oblate planet like Saturn, where the rotational flat-11

tening (1 − Rp/Re) is 9.8%, where Rp and Re are the po-12

lar and equatorial radii, there are two ways to define the13

latitude. Planetocentric latitude φpc is the angle of a line14

from the center of the planet relative to the equatorial plane.15

Planetographic latitude φpg is the angle of the local verti-16

cal relative to the equatorial plane. If we approximate the17

planet’s shape, e.g., on a constant-pressure surface, as an el-18

lipse rotated about its short axis, then the relation between19

φpg and φpc is tanφpg = (Re/Rp)2 tanφpc. Thus |φpg|20

is always greater than |φpc| except at the poles and equator,21

where they are equal. Both kinds of latitude are used in the22

literature and this review.23

11.2.1. Zonal Velocity24

Figure 11.2, from Garcıa-Melendo et al. (2011), shows25

the zonal mean zonal wind as a function of planetocentric26

latitude, measured in the System III reference frame. The27

curves are time averages from 2004 to 2009, but at high and28

mid latitudes the variations from year to year are generally29

less than the uncertainty of the measurement, which falls in30

the range 5 to 9 m s−1, depending on the latitude. Depar-31

tures from the zonal mean—the eddies—do not show up on32

this figure. They have been averaged out, but at least on a33

large scale the eddy winds are small.34

The two curves in Figure 11.2 refer to different alti-35

tudes. In both cases the winds are obtained by tracking36

small clouds in images separated by one Saturn rotation pe-37

riod. The black curve uses images in the CB2 and CB338

filters, centered at 752 and 959 nm, where the main sources39

of opacity are the clouds themselves. Generally this band-40

pass senses clouds at the 350–700 mbar pressure range, but41

clouds outside this range may show up at certain times and42

places. The red curve uses images in the MT2 and MT343

filters, centered at 727 and 890 nm, where methane, one44

of the well-mixed gases in the atmosphere, limits the depth45

one can see. Thus the red curve shows the motion of clouds46

and haze at the 60–250 mbar pressure range, depending on47

latitude. This range spans the tropopause—the temperature48

minimum where the pressure scale height (the e-folding49

scale) is of order 30 km, so the clouds contributing to the50

red curve are ∼40 km higher than those contributing to the51

black curve.52

One notable feature of the zonal wind profile is the high53

speed in the equatorial band—at least 360 m s−1 faster than54

the minimum speeds at higher latitudes. These differential55

speeds are two times larger than those on Jupiter and are 1

7–8 times larger than the difference between the easterlies 2

and westerlies on Earth. Nevertheless, they are comparable 3

to the speed differential on Uranus, and less than that on 4

Neptune. These differences are not well understood. 5

The four high-latitude eastward jets, separated by four 6

high-latitude westward jets (eastward jet minima) in each 7

hemisphere are another notable feature. Both in terms of 8

their speeds and their numbers, these jets are more like 9

Jupiter’s jets, although the latter are somewhat more numer- 10

ous and somewhat less speedy. Away from the equator, the 11

winds are remarkably steady in time and remarkably con- 12

stant in altitude. There is a general tendency for the profiles 13

at the zonal jet minima to be more rounded than the pro- 14

files at the zonal jet maxima, which are sharper. The zonal 15

wind must go to zero at the pole, and Figure 11.2 hints at 16

the extremely rapid drop in winds speed within one degree 17

of the south pole. This is the south polar vortex, like the eye 18

of a hurricane, with 150 m s−1 winds circling around the 19

pole at −89 latitude (Dyudina et al. 2008; O’Neill et al. 20

2015, 2016). The circulation direction is cyclonic, meaning 21

that it is in the same direction that the planet is rotating as 22

seen looking down from above. In the southern hemisphere 23

a cyclonic vortex is clockwise. A cyclonic vortex exists 24

at the north pole as well (Antunano et al. 2015), although 25

Figure 11.2 doesn’t show it because the north pole was in 26

darkness when the data were taken. Hurricanes on Earth 27

are also cyclonic, although they form in the subtropics and 28

drift around, unlike the polar vortices on Saturn (Dyudina 29

et al. 2008). See the chapter by Sayanagi et al. on polar 30

phenomena. 31

The final notable feature is the vertical variation near the 32

equator. From 10 to 25 in each hemisphere, the wind is 33

slightly stronger at the higher altitude. From 2 to 10, the 34

high-altitude winds are weaker, and within the narrow jet 35

inside ±2, the high-altitude winds are stronger. The equa- 36

torial winds are also variable in time. Garcıa-Melendo et al. 37

(2011) point out that the equatorial winds were 450 m s−1 38

at the time of the Voyager encounters in 1980 and 1981 39

(Sanchez-Lavega et al. 2000), and ranged up to 420 m s−1 40

as measured by Hubble in 1990 (Barnet et al. 1992). Garcıa- 41

Melendo et al. (2011) conclude that there was a real slow- 42

down of the wind speed at the equator. Nevertheless, Choi 43

et al. (2009) showed by tracking features in 5-µm images 44

from Cassini VIMS—which sense as deep as ∼2 bars— 45

that the near-equatorial winds reach speeds of ∼450 m s−1, 46

similar to the Voyager wind measurements. This suggests 47

that any real slowdown in the winds may have been con- 48

fined to the lower-pressure levels of the upper troposphere 49

(significantly above the level where VIMS 5-µm images 50

sense). Moreover, a stratospheric oscillation in temperature 51

has been observed from Earth-based telescopes since 1980 52

(Orton et al. 2008) and implies an oscillation in the winds 53

via the thermal-wind equation (see Section 11.3), which 54

may have some connection to the oscillation in equatorial 55

jet speeds seen in Figure 11.2. 56

4


11.2.2. Clouds and Temperatures1

The clouds that we see in the clear filters CB2 and CB32

are thought to be crystals of ammonia. From spectroscopic3

observations, we know that ammonia vapor is close to sat-4

uration at these levels, so it is likely that ammonia is con-5

densing. Solid particles do not give as clear a spectroscopic6

signature as the vapor, so it is difficult to say what other sub-7

stances are present in the cloud particles. What condenses8

below the ammonia cloud base depends on composition and9

temperature, and both are uncertain. One must rely on mod-10

els based on plausible assumptions, which we now describe.11

Figure 11.3, from Atreya (2006), is a cartoon showing12

a possible cloud structure for Saturn for three different as-13

sumptions about the mixing ratios of condensable gases rel-14

ative to hydrogen and helium, which are the major con-15

stituents. One takes the ratios O/H, N/H, S/H, and Ar/H16

on the Sun, determined spectroscopically, and multiplies17

(enriches) them all by a single factor, either 1, 5, or 10.18

Then one allows the reactive elements to combine with hy-19

drogen to form H2O, NH3, and H2S. The Ar and He stay20

in atomic form, and the remaining hydrogen becomes H2.21

Even with 10-fold enrichment, the minor constituents make22

up less than 2% of the molecules in the gas. One assumes23

Fig. 11.3.— Cloud structure for 1, 5, and 10-fold enrich-ment of H2O, NH3, and H2S relative to solar composition.An enrichment factor of 1 means taking the solar elemen-tal ratios of O/H, N/H, and S/H and allowing the mixtureto cool to planetary temperatures. Higher enrichment fac-tors are applied uniformly to all elements relative to hydro-gen and helium. Even with an enrichment factor of 10, thenumber of H2 + He molecules in the gas is still more than98%. From Atreya (2006), calculated using updated solarcomposition data from Grevesse et al. (2005).

the atmosphere is convecting up to the tops of the ammo- 1

nia clouds, which means temperature T and pressure p fol- 2

low an adiabat—a moist adiabat in this case to take into 3

account the latent heat released when the vapors condense. 4

The particular adiabat is chosen to match the observed T 5

and p at the top of the clouds, which is about as deep as 6

we can see with remote sensing instruments. In the fig- 7

ure the clouds are labeled and color-coded by their com- 8

position, and T , p values are given along the sides. For a 9

rising parcel, the less volatile substance, water, condenses 10

out first—at higher temperatures, and the more volatile sub- 11

stance, ammonia, condenses out last—at lower tempera- 12

tures. The location of cloud base is fairly certain provided 13

the composition is known. The cloud density is much less 14

certain, since it assumes that none of the condensate falls 15

out of the cloud and none is carried upward from where 16

it condenses. Despite these uncertainties, the three-cloud 17

structure is generally accepted. Enrichment factors up to 10 18

times the solar abundances are supported by the C/H ratio 19

implied by the methane abundance (Fletcher et al., 2009, 20

2012). Methane, which doesn’t condense at Saturn atmo- 21

spheric temperatures, is easier to measure above the clouds 22

by remote sensing and is therefore a good measure for the 23

planet as a whole. 24

Temperature profiles obtained from radio occultations 25

and infrared spectra are shown in Figure 11.4. They show 26

that the temperature is close to an adiabat below the 300- 27

400 mbar level, presumably indicating that convection is 28

occurring, but becomes sigificantly stratified at higher lev- 29

els (Li et al. 2013). The two techniques agree reasonably 30

well, and can only sense to levels near∼1 bar, below which 31

we have few observational constraints. The temperatures 32

are fairly steady deeper than the ∼300-mbar level, but ex- 33

hibit greater spatial and temporal variations in the strato- 34

sphere. 35

11.2.3. Inferences From Dynamical Balance 36

Given the observations of zonal winds at cloud level and 37

temperatures in the overlying layers, basic dynamical argu- 38

ments can be used to infer the zonal winds above the cloud 39

deck. On planets that rotate rapidly, with small Rossby 40

number, there exists a dynamical link between winds and 41

temperatures. Specifically, combining geostrophic bal- 42

ance, hydrostatic equilibrium, and the ideal-gas law leads to 43

the thermal-wind equation for a shallow atmosphere (e.g., 44

Holton and Hakim 2013, p. 82). In the meridional direction, 45

this reads: 46

∂u

∂ log p=R

f

(∂T

∂y

)p

(11.1)

where u is the zonal wind, p is pressure, R is the specific 47

gas constant, f = 2Ω sinφ is the Coriolis parameter, Ω is 48

the planetary rotation rate, φ is latitude, T is temperature, 49

y is northward distance, and the derivative on the righthand 50

side is taken at constant pressure. This equation can only 51

be applied away from the equator since geostrophy breaks 52

down at the equator. The equation implies that, away from 53

5


Temperature (K) Temperature (K)

Fig. 11.4.— Temperature profiles (abscissa, in K) versus pressure, measured by Voyager and Cassini by two differentmethods. The nadir observations use upwelling thermal radiation to infer temperature as a function of pressure. Theoccultations use the spacecraft’s radio signal passing tangentially through the atmosphere to infer density, from whichtemperature and pressure are derived. The profiles are close to adiabatic below the 300 mbar level. From Li et al. (2013).

the equator, vertical gradients of the zonal wind are pro-1

portional to meridional temperature gradients. Given the2

known winds at the cloud level from cloud tracking (Fig-3

ure 11.2), and given observations of temperature and its4

meridional gradient in the layers above the clouds, we can5

therefore integrate Equation (11.1) to estimate the zonal6

winds above the clouds.7

The top panel of Figure 11.5, from Read et al. (2009a),8

shows temperatures derived from Composite Infrared Spec-9

trometer (CIRS) observations from Cassini (Fletcher et al.10

2007, 2008), with an interpolation between 6 and 35 mbar11

where the Cassini CIRS instrument has no spectral sensi-12

tivity. The axes are latitude and log-pressure, with pressure13

increasing downwards. The contours show that the temper-14

ature increases upward above the 80 mbar level. The lower15

panel of Figure 11.5 depicts the zonal-mean zonal wind16

inferred for Saturn’s upper troposphere and lower strato-17

sphere by integrating the thermal-wind equation (11.1). The18

integration adopts as a lower boundary condition the zonal-19

mean zonal winds obtained from visually tracking clouds20

in the 350-700 mbar pressure range. At pressures greater21

than several mbar, the temperatures are correlated with the 1

winds such that the equatorward flanks of eastward jets— 2

the anticyclonic regions—are colder than the surrounding 3

regions (on an isobar), and the poleward flanks of eastward 4

jets—the cyclonic regions—are warmer than the surround- 5

ing regions. Given the thermal-wind equation, this correla- 6

tion implies that the change of zonal wind with altitude is 7

opposite to the direction of the wind—the winds are decay- 8

ing with altitude. Figure 11.5 indicates that they decay to 9

an average speed of about 40 m s−1, which is the average 10

speed of the stratosphere at the 1-2 mbar level. 11

This result is not new, but it has not been fully explained. 12

The IRIS instrument on Voyager observed the same corre- 13

lation of thermal gradients with the zonal jets during the 14

encounters with Jupiter (e.g., Conrath and Pirraglia 1983; 15

Gierasch et al. 1986). The problem is that there is no obvi- 16

ous radiative or thermodynamic heat source that would pro- 17

duce temperature gradients that correlate with the jets. The 18

IRIS team therefore proposed a mechanical origin. They 19

postulated that, in the upper troposphere above the clouds, 20

the net zonal acceleration due to eddies acts as a drag force 21

6


in the opposite direction from the zonal jets. Such a zonal1

eddy force would—in statistical steady state—be balanced2

by the Coriolis force acting on the meridional wind. In other3

words, the postulated eddy accelerations would induce a4

meridional circulation.5

Specifically, this force balance predicts that, for the Cori-6

olis acceleration to balance the eddy acceleration, the re-7

sulting meridional circulation would be poleward across8

eastward jets and equatorward across westward jets.1 This9

configuration implies that the meridional flow converges on10

the poleward flank of eastward jets, leading to downward11

1For poleward motion, the Coriolis force induces an eastward acceleration,whereas for equatorward motion, it induces a westward acceleration. Ifthere were an eastward jet with a westward eddy-induced acceleration, theCoriolis force must be eastward in order to balance the eddy acceleration.This implies a poleward meridional flow. Likewise, if there were a west-ward jet with an eastward eddy acceleration, the Coriolis force must bewestward to achieve steady state. This implies equatorward meridionalflow.Showman et al.: The Global Atmospheric Circulation of Saturn 3 OBSERVATIONS OF THE TROPOSPHERE

Pres

sure

(mba

r)Pr

essu

re(m

bar)

Fig. 11.5.— Top: Saturn’s zonal-mean temperature versus latitude and pressure from Cassini CIRS observations takenin 2004-2006, during Saturn’s northern spring. Analysis is from Fletcher et al. (2007). Note the temperature minimumaround 80 mbar and the increase in temperatures toward the south pole at all levels above the 6-mbar level. The instrumentis not sensitive to the regions from 6–35 mbar and the temperatures have been interpolated across this pressure range.Bottom: Zonal-mean zonal winds versus latitude and pressure obtained by integrating the thermal-wind equation using thetemperature structure in the top panel, and assuming the zonal winds at 500 mbar correspond to the cloud-tracked windprofile. From Read et al. (2009a).

fied (specific entropy increases with altitude), the down-682

welling advects high-entropy air downward from above,683

leading to warmer temperature on constant-pressure sur-684

faces. Similarly, the meridional flow diverges on the685

equatorward flank of eastward jets, leading to upward686

motion, which advects low-entropy air from below and687

produces cooler temperatures on constant-pressure sur-688

faces. In other words, this scenario explains the temper-689

ature anomalies observed by Voyager and Cassini, and in690

thermal-wind balance, the resulting zonal jets must decay691

with altitude. Note that the poleward flank of eastward jets692

exhibit cyclonic vorticity and the equatorward flanks of693

eastward jets exhibit anticyclonic vorticity. Based mostly694

on differences in Jupiter’s cloud colors and morphology,695

the amateur astronomers called the cyclonic and anticy-696

clonic regions belts and zones, respectively. With a west-697

ward eddy acceleration on the zonal jets, the belts are re-698

gions of downwelling and the zones are regions of up-699

welling.700

3.4. Chemical Tracers701

Although one cannot measure upwelling and down-702

welling directly—the velocities are too small—one can703

detect these motions using chemical tracers. If a substance704

is removed from the air at high altitudes, either by con-705

densation or by chemical reactions, then finding it above706

that altitude means that it was brought there by an updraft.707

Conversely, if a substance is severely depleted at some lo-708

cation, then those parcels were probably brought there by709

a downdraft. If one knows the rate of the chemical reac-710

tion, one can often estimate the speed of the updraft or711

downdraft.712

Figure 11.6, from Fletcher et al. (2011), shows some713

of the tracers of vertical motion. The data are from the714

Cassini VIMS instrument and are from spectra in the 4.6–715

5.1 µm atmospheric window. A window is where the gases716

of the atmosphere are especially transparent, and photons717

in this spectral range are sampling the 1–3 bar pressure re-718

gion. Clouds are the main source of opacity, and the solid719

and dotted curves are from two different models of the720

clouds. Ammonia (upper right graph) is generally abun-721

dant at low altitude and is depleted by precipitation at high722

10

Fig. 11.5.— Top: Saturn’s zonal-mean temperature ver-sus latitude and pressure from Cassini CIRS nadir-viewingobservations taken in 2004-2006, during Saturn’s northernspring. Analysis is from Fletcher et al. (2007). Note thetemperature minimum around 80 mbar and the increase intemperatures toward the south pole at all levels above the6-mbar level. The instrument is not sensitive to the regionsfrom 6–35 mbar and the temperatures have been interpo-lated across this pressure range. Bottom: Zonal-mean zonalwinds (in Voyager System III) versus latitude and pressureobtained by integrating the thermal-wind equation using thetemperature structure in the top panel, and assuming thezonal winds at 500 mbar correspond to the cloud-trackedwind profile. Warm colors represent eastward wind, andcool colors represent weaker and/or westward wind. FromRead et al. (2009a).

motion.2 Because the upper troposphere is stably strati- 1

fied (specific entropy increases with altitude), the down- 2

welling advects high-entropy air downward from above, 3

leading to warmer temperature on constant-pressure sur- 4

faces. Similarly, the meridional flow diverges on the equa- 5

torward flank of eastward jets, leading to upward motion, 6

which advects low-entropy air from below and produces 7

cooler temperatures on constant-pressure surfaces. In other 8

words, this scenario explains the temperature anomalies ob- 9

served by Voyager and Cassini, and in thermal-wind bal- 10

ance, the resulting zonal jets must decay with altitude. Note 11

that the poleward flank of eastward jets exhibit cyclonic 12

vorticity and the equatorward flanks of eastward jets ex- 13

hibit anticyclonic vorticity. Based mostly on differences 14

in Jupiter’s cloud colors and morphology, the amateur as- 15

tronomers called the cyclonic and anticyclonic regions belts 16

and zones, respectively. With a westward eddy acceleration 17

on the zonal jets, the belts are regions of downwelling and 18

the zones are regions of upwelling. 19

11.2.4. Chemical Tracers 20

Although one cannot measure upwelling and down- 21

welling directly—the velocities are too small—one can de- 22

tect these motions using chemical tracers. If a substance 23

is removed from the air at high altitudes, either by con- 24

densation or by chemical reactions, then finding it above 25

that altitude means that it was brought there by an updraft. 26

Conversely, if a substance is severely depleted below the al- 27

titude where the chemical reactions are occurring, then the 28

depleted air was probably brought there by a downdraft. If 29

one knows the rate of the chemical reaction, one can often 30

estimate the speed of the updraft or downdraft. 31

Figure 11.6, from Fletcher et al. (2011), shows some of 32

the tracers of vertical motion. The data are from the Cassini 33

VIMS instrument and are from spectra in the 4.6–5.1µm 34

atmospheric window. A window is where the gases of the 35

atmosphere are especially transparent, and photons in this 36

spectral range are sampling the 1–3 bar pressure region. 37

Clouds are the main source of opacity, and the solid and 38

dotted curves are from two different models of the clouds. 39

Ammonia (upper right graph) is generally abundant at low 40

altitude and is depleted by precipitation at high altitude. 41

Abundant ammonia usually means it was brought there by 42

an updraft. Thus the updrafts have high ammonia and the 43

downdrafts have low ammonia. Thus the spike at |φ| < 8, 44

where φ is the latitude, is a sign of upwelling at the equator. 45

Similarly the troughs at 8 < |φ| < 20 are a sign of down- 46

2In principle, mass conservation requires that a meridional convergence bebalanced by a vertical divergence of the flow. Thus, one could theoreti-cally imagine that a meridional convergence could be balanced either byupward motion above the convergence level, or by downward motion be-low the convegence level (or a combination). Because of the strong stablestratification in the stratosphere, the magnitude of the upward flow abovethe convergence level should be limited, and thus we expect a significantdegree of downward motion below the convergence level. Analogous ar-guments lead to the conclusion that upward motion should occur belowlocations of meridional flow divergence.

7


Fig. 11.6.— Tracers of vertical motion. The graphs are derived from 5-µm spectra obtained by the Cassini VIMS instru-ment, which senses thermal emission from the 1–3 bar pressure range. The solid and dotted curves employ two differentassumptions about cloud opacity. Although the optical depth of the deep cloud is relatively constant, the cloud base pres-sure is lower (cloud height is greater), which is suggestive of equatorial upwelling. The higher NH3 mole fraction out tolatitudes of ±8 is suggestive of upwelling, and the troughs at ±(8− 20) are suggestive of downwelling. The AsH3 molefraction shows a distribution that is almost opposite to that of NH3, which is not fully understood. One possible explanationis that the pattern of upwelling and downwelling reverses at some level and the two gases are reflecting that reversal. FromFletcher et al. (2011).

welling. The broad downwelling in the cyclonic regions on1

either side of the equator is consistent with the expected2

convergence of meridional flow into a region with an east-3

ward jet on the equatorward side and a westward jet on the4

poleward side.5

Figure 11.7, from Janssen et al. (2013), tells a similar6

story. The data show thermal emission at 2.2-cm wave-7

length, in the microwave region, and were taken by the8

Cassini radar instrument acting as a radiometer. Ammonia9

vapor is the main source of opacity at this wavelength—10

clouds are unimportant—so the bright areas are places of11

reduced ammonia abundance, which allows radiation from12

the warmer, deeper levels to escape into space. The de-13

pleted bands within ±10 of the equator are evidence of14

downwelling. The black band on the equator is an image of15

Saturn’s rings, which are colder than the planet. The dotted16

line gives the time of ring plane crossing, and the dashed17

line gives the time of the closest approach of the spacecraft18

to the planet. As the spacecraft moved in and out of the ring19

plane, which it did on July 24, 2010, the rings covered a20

part of the opposite hemisphere, affording a brief look at the21

equator. The equator itself is not so bright, and is consistent22

with ammonia abundance near the saturation value, as it is23

over most of the planet outside the subtropical (±10) band.24

Within that band, the ammonia must be depleted down to 1

1.5 bars to fit the high brightness temperatures (Laraia et al. 2

2013). 3

The distribution of NH3 on Saturn resembles the distri- 4

bution of H2O on Earth. On both planets there is rising in 5

the tropics and sinking in the subtropics, although on Earth 6

the subtropics extend further out, to ±30. On Earth the 7

circulation is called the Hadley cell, and the band of ris- 8

ing motion at the equator is called the Intertropical Conver- 9

gence Zone (ITCZ), a feature of which are the high cumu- 10

lus clouds associated with deep convection. The clouds of 11

Saturn show a similar pattern (lower left of Figure 11.6) in 12

which the base pressure of the deep cloud is less, indicat- 13

ing displacement to higher altitude. However the Hadley 14

cell analogy may be misleading, because Earth has equato- 15

rial easterlies (westward winds) and Saturn has equatorial 16

westerlies (eastward winds). The eddy sources and the con- 17

figuration of zonal accelerations they induce may therefore 18

differ significantly between the two planets. 19

Gases other than ammonia tell a somewhat different 20

story, and the differences are not fully understood. Fig- 21

ure 11.6 shows that the latitude distribution of arsine, AsH3 22

is almost the opposite of the NH3 distribution. Arsine has 23

a dip at the equator and broad peaks on either side of the 24

8


Fig. 7 with a value ranging over about ±0.5%. Errors in the removalof gain as well as sidelobe signal variations using the quiescent-band averages will lead to errors as well, which we judge to be rel-atively small by examining the time dependence of these averagesin Fig. 8. Conservatively, we expect an absolute uncertainty better

than 2%, or a brightness temperature uncertainty less than 3 K.Large-scale systematic errors are smaller, perhaps as much as 1 Kfrom equator to pole as discussed above, and <1 K elsewhereSmall-scale errors are consistent with the white noise of the indi-vidual measurements, !0.1 K.

Fig. 9. Final cylindrical maps of Saturn from the five observation campaigns. The absolutely calibrated maps are shown in the five panels as residuals from a model thatassumes ammonia to be fully saturated in the cloud-forming region. The dashed and dotted lines indicate periapsis and ring plane crossings, respectively (there were noobservations made exactly at ring plane crossing for the 2005 and 2011 maps). Planetographic latitudes are indicated by black ticks on the vertical scales, planetocentric bywhite. The unobserved portions of the maps are shaded to the equivalent brightness for the fully saturated model, so that, except for the ring blockage around the equator, themaps indicate that the ammonia cloud region is everywhere unsaturated. Orbital characteristics and mapping details are given in Tables 2 and 3, and uncertainties andcaveats concerning the maps are given in the text.

M.A. Janssen et al. / Icarus 226 (2013) 522–535 531









Fig. 11.7.— Thermal emission at 2.2-cm wavelength obtained by the Cassini radar instrument operating as a radiometer.The black band at the equator is the rings, which are low emitters because they are cold. Gaseous NH3 blocks the radiationfrom warmer, deeper levels and emits at colder levels, so regions that are depleted in NH3 appear bright. Latitudes out to±10 appear to be depleted in NH3, which implies downwelling. Although difficult to see due to blockage by the rings,the equator itself is dark, implying upwelling. The great northern storm is visible in the March 20, 2011 map at 30-40

planetographic latitude and 0-180 west longitude. A smaller storm is visible at −45 latitude and 330 west longitude.Both storms show NH3 depletion. From Janssen et al. (2013).

equator out to ±20. One of the cloud models shows an1

extension of the peak to a latitude of −30, but the other2

model does not. The distribution of phosphine, PH3 (not3

shown), is a lot like that of arsine. Degeneracies between4

the retrievals of the cloud properties and the abundances of5

trace species like AsH3 can occur (e.g Giles et al. 2017),6

so the AsH3 results shown in Figure 11.6 should perhaps7

be viewed as tentative until more analysis has been per-8

formed; nevertheless, the different cloud models explored9

by Fletcher et al. (2011) all pointed toward an equatorial dip10

in AsH3 relative to the surrouding latitudes, suggesting that11

it should be taken seriously. Both arsine and phosphine are 1

in chemical equilibrium at much deeper levels than those 2

probed in the 4.6–5.1µm data, and they are destroyed by 3

photolysis at high altitudes. That they don’t show the same 4

patterns as NH3 has interesting implications. 5

Fletcher et al. (2011) discuss the possibility of stacked 6

meridional circulation cells, the top one with rising air at 7

the equator, as in Earth’s Hadley circulation, and the bot- 8

tom one—the reverse cell—with sinking at the equator. The 9

NH3 cloud base is around 1.5 bars, as shown in Figure 11.3, 10

so its mixing ratio should be large up to that level in an up- 11

9


draft. Above that level it loses ammonia by condensation.1

A downdraft could carry ammonia-depleted air down be-2

low the 1.5-bar level until it eventually mixes with air from3

the planet’s interior. Thus the NH3 distribution shown in4

Figure 11.6 is consistent with an Earth-like Hadley cell ex-5

tending down at least to the ∼2-bar level. The AsH3 dis-6

tribution is consistent with a reverse Hadley cell since its7

chemical transformations are taking place at much deeper8

levels. The base pressure of the deep cloud, shown in the9

lower left panel of Figure 11.6, is about 2.0 bars at the equa-10

tor and 2.8 bars on either side of the equator. This could be11

interpreted in two ways. If the cloud particles are NH4SH or12

H2O, and have been carried up from deeper levels, then the13

higher altitude (lower base pressure) at the equator would14

signify an updraft. However, if the cloud base pressure were15

entirely dependent on the abundance of a condensing gas,16

then the lower base pressure would signify a lower abun-17

dance of the condensing gas and hence a downdraft. The18

latter would be consistent with a reverse cell, with sinking19

motion at the equator. Note however that the upper cell is20

consistent with a meridional circulation that is driven by21

an eddy acceleration acting in the opposite direction as the22

zonal winds in the upper troposphere. The lower meridional23

cell would seem to require forces that accelerate the zonal24

winds, and such forces do exist, as we now describe.25

11.2.5. Eddies And The Momentum Budget26

The above analysis takes the zonal winds at cloud top27

(Figure 11.2) as given. The eddy-induced acceleration op-28

posing the jet direction was postulated to account for the29

wind’s decay with height above the cloud-top level. In con-30

trast, observations demonstrate that at the cloud level, ed-31

dies transport momentum that acts to drive the jets. Here32

we describe these observations and their interpretation.33

By themselves, the zonal-mean of the eddy winds aver-34

age out to zero, but the eddies can have a net effect when35

the northward and eastward components act together. Con-36

sider a latitude band with an eastward jet to the north and37

a westward jet to the south. The eddy winds, with compo-38

nents u′ and v′, induce motion of air parcels north and south39

in the space between the two jets. (Here, as before, u is the40

zonal wind, and v is the meridional wind; primes denote41

deviations from the zonal average.) But if the parcels going42

north have more eastward momentum than the parcels go-43

ing south, there will be a net transfer of momentum to the44

north. This would add to the eastward momentum of the45

eastward jet and it would subtract it from the westward jet,46

speeding up each jet in its respective direction.47

Such a hypothesis is testable if one has good measure-48

ments of the eddy velocities. Parcels moving north (v′ > 0)49

would also be moving east (u′ > 0), and parcels mov-50

ing south (v′ < 0) would also be moving west (u′ < 0).51

In both cases the parcel trajectories would be tilted along52

a northeast-southwest line, and the measured eddy winds53

would have u′v′ > 0, where the overbar denotes the zonal54

mean. The eddy-momentum flux is ρu′v′, where ρ is the55

density. The eddy-momentum flux is a stress, and it has 1

units of force per unit area. A positive tilt (u′v′ > 0) im- 2

plies a northward transport of eastward momentum by the 3

eddies. A tilt the other way (u′v′ < 0) would represent 4

a negative eddy-momentum flux—a northward transport of 5

westward momentum by the eddies. In either case, if u′v′ 6

and ∂u/∂y have the same sign, where u is the mean zonal 7

wind and y is the northward coordinate, then the eddies are 8

adding momentum to the zonal jets. 9

Figure 11.8, from Del Genio and Barbara (2012), shows 10

the sign of the correlation. At almost all latitudes, u′v′ and 11

∂u/∂y have the same sign. Both quantities are positive 12

at latitudes 50-57N, 33-42N, 10-25S, 28-35S, and 45-48S. 13

Both quantities are negative at latitudes 42-50N, 10-33N, 14

35-40S, and 48-52S. The data are noisy because the eddy 15

winds are weak—only a few m s−1, but the data clearly 16

indicate that Saturn’s eddies are acting as a force that ac- 17

celerates the zonal jets. Both Voyager and Cassini observed 18

similar behavior at Jupiter (Beebe et al. 1980; Ingersoll et al. 19

1981; Salyk et al. 2006). 20

This sounds like negative viscosity, and indeed that term 21

was used to describe such phenomena, which are observed 22

not only in Earth’s atmosphere but also the oceans, the Sun, 23

and laboratory experiments (Starr 1968). However, using 24

an eddy viscosity to relate a local stress like ρu′v′ to a lo- 25

cal rate of strain like ∂u/∂y is often a meaningless exer- 26

cise (Phillips 1969). Energy transfer from smaller to larger 27

scales does not violate any thermodynamic principle, and 28

an eddy-momentum transfer that generates a shear flow— 29

zonal jets—can arise naturally through the interaction of 30

turbulence with the planetary rotation. Since the eddies are 31

putting energy into the zonal flow, they must have their own 32

source of energy. That could come from below, as inter- 33

nal heat powers convection currents that rise into the cloud 34

layer. Or it could come from the sides, as lateral tempera- 35

ture gradients release their potential energy into a longitudi- 36

nally varying wave in a process called baroclinic instability 37

(e.g., Vallis 2006; Holton and Hakim 2013). 38

This eddy force at cloud level, which acts to acceler- 39

ate the zonal jets, is opposite in sign to that postulated in 40

the upper troposphere that tends to decelerate the jets, and 41

it has the opposite effect on the meridional overturning. 42

This reversal in sign of the eddy acceleration with height 43

could lead to stacked meridional circulation cells, the eddy- 44

momentum forces that oppose the jets driving the upper cell 45

and the eddy-momentum forces that accelerate the jets driv- 46

ing the lower cell. Neither of these meridional cells how- 47

ever, is like the Earth’s Hadley circulation (see Vallis 2006 48

or Schneider 2006 for reviews). On Earth, the eddy acceler- 49

ations in the subtropics are westward, whereas the eddy ac- 50

celerations occurring within Saturn’s equatorial jet are east- 51

ward, leading to eddies driving a reverse meridional cell on 52

Saturn. The direct circulation cell on Saturn, which seems 53

to start at ∼2 bars and extend into the stratosphere (Fig- 54

ure 11.5), is driven by an eddy acceleration opposing the 55

zonal jets, which is opposite to the eddy momentum force 56

at deeper levels. 57

10


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u0v0 uFigure 4: fig. 11.15

5

Fig. 11.8.— Eddy momentum transport and zonal winds. The left panel shows the mean zonal wind profile u obtained bytracking individual cloud features. The right panel shows the number of measured wind vectors in each 1 bin of latitude.The middle panel shows the covariance u′v′ between the eastward eddy wind u′ and the northward eddy wind v′, where aneddy is defined as the residual after the mean zonal wind has been subtracted off. Multiplied by the density, this covarianceis the eddy momentum transport—the northward transport of eastward momentum by the eddies. This transport tends tohave the same sign as ∂u/∂y, where y is the northward coordinate, which indicates that the eddies are putting energy intothe mean zonal wind and not the reverse. From Del Genio and Barbara (2012).

The eddy-momentum flux driving the jets at cloud level1

has been observed directly on Jupiter and Saturn (Beebe2

et al. 1980; Ingersoll et al. 1981; Salyk et al. 2006; Del Ge-3

nio and Barbara 2012). In contrast, there is no direct ob-4

servational confirmation of the eddy acceleration above the5

clouds that is postulated to oppose the jets. The term eddy6

includes all motions that remain after the zonal mean has7

been subtracted off—waves, vortices, convective plumes8

and any other non-axisymmetric component of the motion.9

Evidence for the eddy force opposing the jets comes from10

the decay of the zonal winds with height as inferred from11

temperature gradients (Figure 11.5). Evidence for a reverse12

meridional circulation cell comes from the AsH3 and PH313

distributions, but further evidence comes from the distribu-14

tion of lightning, as we discuss below.15

11.2.6. Lightning And Moist Convection16

Lightning is evidence of moist convection. The violent17

updrafts in a thunderstorm are a crucial element for electri-18

cal charge separation, which occurs when large ice particles 1

fall through upwelling air that contains small liquid droplets 2

(Uman 2001; MacGorman and Rust 1998). The charg- 3

ing mechanism is not well understood, but three phases of 4

water—solid, liquid, and vapor—in the cloud at once seem 5

to be necessary. On giant planets, with their three-tiered 6

structure (Figure 11.3), it is not immediately clear which 7

cloud produces the lightning (Yair et al. 2008). For a solar 8

composition atmosphere, the mole fractions of H2O, NH3, 9

and H2S, in units of 10−4 are 9.7, 1.3, and 0.29, respectively 10

(these values depend on the abundance of helium, which is 11

poorly known; here we have used the latest He/H2 estimate 12

from Sromovsky et al. 2016). For Saturn, enrichment by 13

a factor of 10 is likely (Fletcher et al. 2009; Fletcher et al. 14

2012), and uniform enrichment would raise all these num- 15

bers by the same factor. Thus on the basis of abundance 16

alone, water is the condensable gas most likely to produce 17

lightning. Also, water is the only gas where the tempera- 18

tures and abundances allow three phases to exist at the same 19

11


level in the atmosphere. For Saturn the triple point of water1

occurs at a pressure of about 10 bars (Figure 11.3). This2

number depends on the temperature profile, but is relatively3

independent of the enrichment factor. Increasing the lat-4

ter mostly affects the depth of the liquid cloud, extending5

it down to p = 20 bars and T = 330 K for 10 times solar6

abundances.7

Figure 11.9, from Dyudina et al. (2013), shows the8

brightness distribution of a typical lightning flash as seen9

from the Cassini spacecraft. Every pixel in the vicinity of10

the flash is plotted as a function of its horizontal distance11

from the flash center. This removes the effects of foreshort-12

ening and shows that the flashes are roughly circular. The13

half width at half maximum (HWHM) of the brightness dis-14

tribution is about 100 km, and that is related to the depth of15

the lightning relative to the tops of the clouds—the level16

where the photons emerge. That depth is approximately17

equal to 1.5 times the HWHM. Cloud parameters—both18

their height and their scattering properties—create a large19

uncertainty. Dyudina et al. (2013) estimate that the tops20

are probably NH3 or NH4SH clouds at depths exceeding21

Fig. 11.9.— Spatial distribution of brightness of two light-ning flashes vs. distance from the flash center. The distri-butions would appear circular if viewed from directly over-head. The half width at half maximum, defined as the ra-dius where the brightness is half of the central brightness,is about 100 km. From these data, scattering models indi-cate that the vertical distance from the lightning source tothe top of the clouds where the photons are detected is inthe range 125–250 km. The data are consistent with a light-ning source in the water cloud (Figure 11.3). From Dyudinaet al. (2013).

1.2 bars, in which case the lighting is in the water cloud. 1

Nighttime imaging of Jupiter by the Galileo spacecraft 2

showed that lightning is concentrated in the belts (Little 3

et al. 1999; Gierasch et al. 2000), and that was a surprise. 4

The traditional view, which was based on Voyager observa- 5

tions of the upper troposphere (Gierasch et al. 1986), was 6

that the belts are regions of descent and the zones are re- 7

gions of ascent, for several reasons: The zones exhibit a 8

thick, bright, relatively uniform cloud deck, whereas the 9

belts exhibit patchier, generally thinner clouds. The ammo- 10

nia mixing ratios at and above the clouds are small in the 11

belts and large in the zones, signifying descent and ascent, 12

respectively. The belts are warm, signifying high-entropy 13

air brought down from above, and the zones are relatively 14

cold. Lighting therefore seemed unlikely in the belts, since 15

moist convection requires moist air brought in from below. 16

This led Ingersoll et al. (2000) to postulate that perhaps the 17

belts have upwelling at the base of the cloud and down- 18

welling at the tops. This amounted to a pair of meridional 19

circulation cells turning in opposite directions, one on top 20

of the other. Showman and de Pater (2005) showed that 21

this stacked-cell scenario also best explains the deep am- 22

monia abundances from 1–5 bars, which indicates that belts 23

and zones are both depleted in ammonia relative to the pre- 24

sumed deeper atmosphere. According to this new picture, 25

the traditional view was not wrong, but it was based only on 26

the properties of the upper circulation cell. Lightning and 27

ammonia had provided a view to deeper levels, at least on 28

Jupiter. The data for Saturn are less clear, partly because 29

lightning is such a rare event on that planet. 30

Figure 11.10, from Dyudina et al. (2007), shows light- 31

Fig. 11.10.— Lightning activity during the first two yearsof the Cassini orbital mission. The top panel shows signalsdetected by the RPWS instrument, which is on all the timeand is sensitive to lightning all over the planet. The lowerpanel shows when storm clouds were seen by the Cassiniimaging system. Both panels show that there was no light-ning for 445 days from the end of 2004 to the beginning of2006. For comparison, there are ∼2000 lightning storms atany given moment on Earth. From Dyudina et al. (2007).

12


ning intensity over a 2-year period from 2004 to 2006 as1

recorded by the Radio and Plasma Wave Science (RPWS)2

instrument on Cassini. The RPWS is a radio receiver and3

spectrometer, and it is “on” all the time. The figure shows4

that there was lighting activity on days 200–270 in 2004,5

then a 445-day gap with no lightning, followed by activ-6

ity on days 350–385 in 2005. Only one storm was active7

during each of the two periods, and it might have been the8

same storm, as indicated by the drift rate in longitude shown9

on the bottom part of the figure. The storm was located at10

−35 planetocentric latitude, at the center of the westward11

jet shown in Figure 11.2. This latitude band became known12

as “storm alley” during the first few years of the Cassini13

mission. The storm was a multi-armed complex, 2000 km14

in diameter, which spawned smaller spots at a rate of one15

every 1–2 days. These drifted off to the west relative to the16

central complex. The smaller spots began with high, thick17

clouds that dissipated in the first day, leaving a dark spot18

that consisted either of a hole in the clouds or else a deep19

cloud with a low reflectivity (Dyudina et al. 2007). The20

small bright spot in the lower left corner of Figure 11.7, the21

image taken on March 20, 2011, is also at−35 latitude. Its22

brightness at 2.2-cm wavelength indicates that it is a region23

of low abundance of ammonia vapor, which is consistent24

with a hole in the clouds. The latitude band at the center of25

the westward jet at−35 seems to have been active over the26

10+ years of the Cassini orbital mission.27

During the Cassini mission, the northern hemisphere did28

not have a lightning storm until December 5, 2010, when29

the RPWS suddenly started detecting lightning signals and30

the imaging system detected a new cloud at 35 latitude. As31

in the southern hemisphere, the latitude of the storm coin-32

cided with the center of a westward jet (Figure 11.2). How-33

ever the northern storm was a different beast from those in34

storm alley. Its head remained the most active part, but by35

late January its tail had spread around the planet to the east36

and was encountering the head from the west (Fischer et al.37

2011; Sanchez-Lavega et al. 2011). The tail was depleted in38

ammonia, as seen in the March 20, 2011 map at 2.2 cm (Fig-39

ure 11.7). The head spawned a series of large anticyclonic40

vortices, 10,000 km in north-south dimension, which also41

drifted to the east, but more slowly than the debris in the42

tail. When the first of these—also the largest—encountered43

the head in June 2011, the head broke up and essentially44

ceased to exist (Sanchez-Lavega et al. 2012; Sayanagi et al.45

2013). The chapter by Sanchez-Lavega et al. in this book is46

devoted to the giant storm, and we will only discuss a few47

features that are especially relevant to this dynamics chap-48

ter.49

Figure 11.11, from Achterberg et al. (2014), shows50

changes from 2009 to 2011, before and after the storm,51

using infrared data from the Cassini CIRS instrument. Fig-52

ures 11.11a and 11.11b show that the storm warmed the53

latitude band from 30–45. The warming also showed up54

as an increase in the emitted power at that latitude (Li et al.55

2015). Figures 11.11c and 11.11d show evidence of gas56

having been brought up from the level of the water cloud, as57

inferred from the relative abundance of the two states of the 1

H2 molecule. The observed warming made ∂T/∂y more 2

negative on the north side of the disturbed band and more 3

positive on the south side. The thermal-wind equation then 4

says there should have been an increase in ∂u/∂z on the 5

north side and a decrease on the south side. If we are seeing 6

the tops of the clouds, and if u is constant underneath, we 7

should see an increase in u to the north and a decrease to 8

the south, and that is what was observed (Sayanagi et al. 9

2013). 10

Lightning on Jupiter was seen mostly in the belts, which 11

are the regions of cyclonic shear (Little et al. 1999; Gierasch 12

et al. 2000). Lightning on Saturn was seen near the cen- 13

ters of the westward jets, which have cyclonic shear on the 14

equatorward side and anticyclonic shear on the poleward 15

side. Thus the two planets appear to be different. However, 16

Dyudina et al. (2013) noted that within the giant storm there 17

were small regions of cyclonic shear, and they were where 18

the lightning occurred. The giant storm consisted of an anti- 19

cyclonic head with a chain of large anticyclones stretching 20

off to the east, each one rolling in a clockwise direction. 21

The narrow regions where they came close together were 22

cyclonic. A cyclonic region has low pressure at the cen- 23

ter, with the inward pressure gradient force balancing the 24

outward Coriolis force. In a terrestrial hurricane, this leads 25

to convergent flow in the boundary layer, where friction at 26

the ocean surface slows the wind and weakens the Corio- 27

lis force, leading to an unbalanced pressure gradient force 28

acting inward. The inward flow picks up moisture from the 29

ocean surface, leading to intense moist convection around 30

the center. One might think that the same process is hap- 31

pening on the giant planets, since moist convection occurs 32

in the cyclonic regions. But how this might work without 33

an ocean, or a physical surface against which friction can 34

occur, is unclear. The deep atmosphere below the clouds 35

would have to provide a frictional force on the cloud layer 36

that leads to convergence. If the flow below the clouds were 37

sufficiently turbulent, with large vertical stresses, it might 38

do the job. But that theory needs to be worked out. 39

11.2.7. Stability Of the Zonal Jets 40

The cloud-top zonal jets on Jupiter and Saturn are re- 41

markably constant in time. Their positions and wind speeds 42

haven’t changed much over 100 years, although small dif- 43

ferences between Voyager and Cassini were observed, espe- 44

cially at the equator (Peek 1958; Porco et al. 2003; Vasavada 45

et al. 2006; Li et al. 2013; Garcıa-Melendo et al. 2011). This 46

remarkable constancy motivates a consideration of the ex- 47

tent to which the jets are dynamically stable. The definition 48

of a stable flow is one in which infinitesimal perturbations 49

cannot grow in amplitude. There exist a class of theorems 50

that provide information on jet stability for the idealized 51

case of zonally symmetric jets, with no forcing or damping, 52

and several of these have been evaluated for Saturn. 53

Most stability theorems are cast in terms of the poten- 54

tial vorticity (PV), which, for the case of a single-layer, 55

13

Showman et al.: The Global Atmospheric Circulation of Saturn 11.2 OBSERVATIONS OF THE TROPOSPHEREShowman et al.: The Global Atmospheric Circulation of Saturn 3 OBSERVATIONS OF THE TROPOSPHERE

Fig. 11.11.— Saturn in the infrared before (2009) and after (2011) the great northern storm of 2010-2011. The data werecollected by the Cassini CIRS instrument and are sensitive to the 300-mbar level. The top two panels show that the stormwarmed the latitude band from 30–45 by 3 K. The bottom two panels show that the warming was due to air rising fromthe water cloud (Figure 11.3), as inferred from a change between the two states, ortho and para, of the H2 molecule. FromAchterberg et al. (2014).

3.7. Stability of the zonal jets1095

The zonal jets on Jupiter and Saturn are remarkably1096

constant in time. Their positions and wind speeds haven’t1097

changed much over 100 years, although small differences1098

between Voyager and Cassini were observed, especially1099

at the equator (Peek 1958; Porco et al. 2003; Vasavada1100

et al. 2006; Li et al. 2013; Garcıa-Melendo et al. 2011).1101

The definition of a stable flow is one in which infinitesi-1102

mal perturbations cannot grow in amplitude. For zonal jets1103

on rotating planets, an important quantity is the potential1104

vorticity (PV). It is a conserved dynamical tracer of the1105

motion—“conserved” because its value does not change1106

under certain common conditions—no viscosity, no heat1107

exchange, and no mixing as the parcel moves around, and1108

“dynamical” because it is computed from dynamical vari-1109

ables like wind and temperature. An inert gas is an exam-1110

ple of a passive tracer. It is conserved but not dynamical.1111

There are many ways to compute PV, depending on1112

what approximations, if any, are used for the equations1113

of motion. The rigorous form is Ertel’s potential vorticity1114

(Vallis 2006)1115

PVErtel =1

(2 + r v) · rS (9)

Here S is specific entropy, another conserved tracer pro-1116

vided the fluid is moving adiabatically, i.e., without ex-1117

changing heat with its surroundings or dissipating ki-1118

netic energy. Conservation of PV requires both of these1119

conditions—no heat exchange and no dissipation. Notice1120

that PV is a scalar although it is constructed from vectors,1121

and it is a local quantity that is associated with individual1122

fluid elements. For approximate equations of motion like1123

the Boussinesq, anelastic, and quasi-geostrophic equations1124

there are approximate forms of PV, but it is still a con-1125

served tracer. The single-layer, shallow water version is1126

PV = + f

h(10)

where = k · (r v). Here is the vertical compo-1127

nent of vorticity—twice the angular velocity due to the1128

motion relative to the rotating planet, and f is the verti-1129

cal component due to the planet’s rotation. Thus is the1130

relative vorticity, f is the planetary vorticity, and + f is1131

the absolute vorticity. In this shallow-water form, h is the1132

depth of the fluid. The inverse dependence on h reflects1133

the fact that stretching along the rotation axis (increasing1134

h) causes a contraction toward the axis and a decrease in1135

the moment of inertia, causing the parcel to spin faster1136

and + f to increase. The PV of the parcel is conserved1137

because the numerator and denominator change together.1138

Note that, for a stratified, three-dimensional atmosphere,1139

the Ertel version (9) can be written in the form (10) if one1140

uses the component of vorticity that is perpendicular to1141

surfaces of constant specific entropy, and if one treats h as1142

a differential mass per unit area between surfaces of con-1143

stant specific entropy.1144

17

Showman et al.: The Global Atmospheric Circulation of Saturn 3 OBSERVATIONS OF THE TROPOSPHERE






















(Vallis 2006)1115

PVErtel =1

(2 + r v) · rS (9)












PV = + f

h(10)



















17

Showman et al.: The Global Atmospheric Circulation of Saturn 3 OBSERVATIONS OF THE TROPOSPHERE






















(Vallis 2006)1115

PVErtel =1

(2 + r v) · rS (9)












PV = + f

h(10)



















17

Fig. 11.11.— Saturn in the infrared before (2009) and after (2011) the great northern storm of 2010-2011. The data werecollected by the Cassini CIRS instrument and are sensitive to the ∼300-mbar level. The right panels show that the stormwarmed the latitude band from 30–45 by ∼3 K. The left panels show that the warming was due to air rising from depthsnear the water cloud (Figure 11.3). The equilibrium ratio of the two states of the H2 molecule, ortho and para, dependson temperature. At depth, the expected para fraction is smaller, whereas at the cloud tops, it is larger. The conversionbetween the two states occurs on relatively long timescales. Thus, the sudden emergence of a zonal band of air with lowpara fraction—as seen in panel (d)—suggests that this air was transported from depth, but that there has not yet beensufficient time for the para fraction of this air to relax into the larger para fraction associated with equilibrium at the coldtemperatures of the cloud tops. From Achterberg et al. (2014).

shallow-water flow is1

PV =ζ + f

h(11.2)

where ζ = k · (∇×v) is the relative vorticity, v is the fluid2

velocity, and k is the vertical unit vector. In this shallow-3

water form, h is the depth of the fluid. Under friction-4

less, adiabiatic conditions, the PV is a materially conserved5

quantity (e.g. Vallis 2006). The inverse dependence on h6

reflects the fact that stretching along the rotation axis of the7

fluid parcel (thereby increasing h) causes a contraction to-8

ward the parcel’s rotation axis and a decrease in the mo-9

ment of inertia, causing the parcel to spin faster and ζ + f10

to increase. The PV of the parcel is conserved because the11

numerator and denominator change together. Note that, for12

a stratified, three-dimensional atmosphere, the PV can also13

be written in the form (11.2) if one uses the component of14

vorticity that is perpendicular to surfaces of constant spe-15

cific entropy, and if one treats h as a differential mass per16

unit area between surfaces of constant specific entropy.17

The simplest stability theorem, which dates back to18

Rayleigh, with modification for rotating planets, is the19

Charney-Stern criterion (Vallis 2006). It says that a zonal20

flow is stable—infinitesimal disturbances cannot grow—if21

PV varies monotonically in the cross-stream direction. If22

we ignore the stretching term by treating h as a constant, we23

obtain the barotropic stability criterion, which states that a24

steady zonal flow u(y) is stable provided25

d(ζ + f)

dy= β − uyy ≥ 0 (11.3)

where β = df/dy = 2Ω cosφ/a and dζ/dy = −uyy. Here26

β is the planetary vorticity gradient, φ is latitude and a is27

the radius of the planet. Note that β is always positive but 1

it goes to zero at the poles. The subscript y is a derivative, 2

and uyy is the curvature of the zonal velocity profile, which 3

is positive at the centers of the westward jets (Figure 11.2). 4

If this curvature is less than β at every latitude, the flow is 5

stable provided we can ignore the stretching term. Jupiter’s 6

zonal jets violate the barotropic stability criterion (Ingersoll 7

et al. 1981; Limaye 1986; Li et al. 2004). Here we describe 8

an application of stability criteria to Saturn, starting with 9

the barotropic stability criterion and moving on to the more 10

general Ertel and quasi-geostrophic versions. 11

Figure 11.12, from Read et al. (2009a), shows the zonal- 12

mean velocity u(y), the vorticity ζ = −uy , and the cur- 13

vature uyy = −ζy in the left, center, and right panels, re- 14

spectively. The smooth curve in the right panel is β, which 15

varies with latitude as cosφ. One can see that the curvature 16

exceeds β at the latitudes of the westward jets, indicating a 17

violation of the barotropic stability criterion. The violation 18

is more evident near the poles, i.e., the difference β − uyy 19

is more negative there, partly because the jets have more 20

curvature there, but also because β is approaching zero. 21

Read et al. (2009a) also use temperature profiles derived 22

from infrared observations by the Cassini CIRS instrument 23

to estimate the magnitude of the stretching term. They cal- 24

culate Ertel PV and quasi-geostrophic PV, including the 25

stretching term, as functions of latitude and show that the 26

stretching term has little effect, at least in the upper tropo- 27

sphere and lower stratosphere where the analysis was done. 28

At these altitudes the atmosphere is so stably stratified that 29

the stretching is small. Although Ertel PV is the right quan- 30

tity to use, the barotropic stability criterion gives the same 31

result, that the centers of the westward jets are where the 32

stability criterion is violated. One might get a different re- 33

sult if one could measure Ertel PV within and below the 34

14

Showman et al.: The Global Atmospheric Circulation of Saturn 11.3 OBSERVATIONS OF THE STRATOSPHERE

Mean zonal wind (m s−1) Relative vorticity (s−1) Curvature of zonal wind uyy (m−1 s−1)

Fig. 11.12.— Stability of Saturn’s zonal jets. The barotropic stability criterion states that a zonal flow is stable provided thecurvature uyy of the zonal velocity profile does not exceed the planetary vorticity gradient β. Stable means that disturbancesto the profile cannot grow, but violation of the criterion does not mean that they will grow. The left panel shows the zonalvelocity profile u. The middle panel shows the relative vorticity −uy associated with the zonal flow, where the subscriptmeans differentiation of u with respect to the northward coordinate y. The right panel shows the curvature uyy (jaggedcurve) and β (smooth curve, given by 2Ω cosφ/a), along with the zero-curvature line for reference (straight vertical line).At the latitudes where the curvature is positive, it clearly exceeds β, indicating that the barotropic stability criterion isviolated. The barotropic stability criterion belongs to a more general class of stability theorems that use potential vorticity(PV) as the diagnostic quantity. The rigorous form uses Ertel’s PV, but the results are the same, at least for the uppertroposphere where the velocity profile is measured. From Read et al. (2009a).

clouds, but that is not possible with the remote sensing data1

that we have.2

Violation of the barotropic stability criterion or any of3

the related stability criteria does not mean that the flow4

is unstable. Further, instability does not mean that the5

flow cannot exist. The hexagon that surrounds the pole at6

mean planetocentric latitude of 76 marks the path of a me-7

andering jet that violates the barotropic stability criterion8

(Antunano et al. 2015). The jet may be unstable, but the9

disturbance has grown into a steady finite-amplitude wave.10

Presumably the wave stopped growing due to non-linear11

effects that are not included in the linear stability analy-12

sis. Ingersoll and Pollard (1982) describe a stability crite-13

rion that invokes interior flow, in which the zonal winds are14

aligned on cylinders concentric with the planets axis of rota-15

tion. Dowling (1995a,b) has argued that Jupiter’s jets could16

be stable according to Arnol’d’s second stability criterion, 1

which states that the flow will be stable to nonlinear pertur- 2

bations if there is a reference frame in which the reversals 3

of the PV gradient coincide with reversals in the sign of ve- 4

locity. Read et al. (2009b) found that the upper tropospheric 5

and stratospheric winds appear to be close to neutral stabil- 6

ity according to this criterion; see Dowling (2014) for a de- 7

tailed discussion. The reference period they derived is ∼5 8

minutes shorter than the System III reference period, and 9

they propose that the period derived from Arnol’d second 10

stability criterion is the rotation period of Saturn’s interior. 11

11.3. Observations of the Stratosphere 12

In the absence of visible tracers, the primary source 13

of data constraining the winds and circulation in Saturn’s 14

15


stratosphere is from observations in the thermal infrared.1

Observations in the collision-induced hydrogen continuum2

longward of 16µm provide information on the temperatures3

in the upper troposphere between roughly 50 to 500 mbar.4

Observations in the ν4 band of methane near 7.7µm provide5

information on temperatures in the middle and upper strato-6

sphere, between 0.5 and 5 mbar for typical observations,7

extending to about 0.01 mbar for observations with very8

high spectral resolution, or limb viewing observations from9

Cassini. However, these thermal observations have verti-10

cal resolution of a pressure scale height, and are thus not11

sensitive to wave structure on small vertical scales.3 Tem-12

perature profiles with vertical resolution of a few kilometers13

can be obtained through radio occultation observations, in14

which the radio signal from a spacecraft is observed as the15

spacecraft passes behind a planet at seen from Earth, and16

from stellar occultations. Radio occultations are generally17

sensitive to the lower stratosphere and upper troposphere18

between about 0.1 mbar and 1 bar, while stellar occultations19

generally sense the upper stratosphere or higher.20

The first spatially resolved thermal observations of Sat-21

urn were made in the ν9 band of ethane at 12µm (Gillett22

and Orton 1975; Rieke 1975) during southern summer, and23

showed emission increasing from north to south, peaking at24

the south pole. Subsequent observations in the ν4 methane25

band at 8µm (Tokunaga et al. 1978; Sinton et al. 1980)26

showed similar variations. Since methane is expected to be27

meridionally mixed, these observations indicated that the28

emission variations are caused by a north-to-south temper-29

ature gradient, with stratospheric temperatures warmest at30

the south (summer) pole.31

The first spacecraft observation in the thermal infrared32

was made by the Pioneer 11 infrared radiometer (IRR) in33

1979, just prior to northern spring equinox. IRR observed34

in two bands at 20µm and 45µm, sensitive to the upper35

troposphere, between 10N and 30S (Ingersoll et al. 1980;36

Orton and Ingersoll 1980), finding the temperatures within37

10 of the equator ∼2.5 K colder than higher latitudes.38

Soon afterward, the Infrared Interferometer Spectrometer39

(IRIS) on Voyagers 1 (1980) and 2 (1981) mapped Sat-40

urn at 5 to 45µm. Retrievals of upper tropospheric tem-41

peratures (Hanel et al. 1981, 1982; Conrath and Pirraglia42

1983) showed no equator to pole temperature gradient in the43

southern hemisphere, and north polar temperatures roughly44

3Atmospheric waves generated in the troposphere can propagate into thestratosphere where they can exert a strong effect on the dynamics. Broadly,such waves fall into two classes (neglecting acoustic waves which tend tobe unimportant for the meteorology). Gravity (or buoyancy) waves ariseby virtue of buoyancy forces associated with vertical motion of air parcelsin a stably stratified medium; they are the internal atmosphere equivalentof the waves one observes on the surface of the ocean. Rossby waves arisefrom a restoring force associated with meridional motion of air parcels inthe presence of a latitudinal gradient of the planetary vorticity (i.e., theCoriolis parameter f ). Rossby waves tend to have larger scales and longerperiods than gravity waves. Mixed wave modes also exist, as well as wavetypes specific to the equatorial regions, such as Kelvin wave modes. All ofthese waves can influence the mean flow when they break or are absorbed.See Holton and Hakim (2013) for introductions to these waves.

5 K colder than the equator in the upper troposphere at pres- 1

sures less than about 300 mbar. In addition to the large- 2

scale gradient, the upper tropospheric temperatures showed 3

variations of around 2 K, with the gradient anticorrelated 4

with the zonal winds (Conrath and Pirraglia 1983). A lim- 5

ited set of temperature profiles, covering roughly between 1 6

bar and 1 mbar, were also obtained by the radio occultation 7

experiments on Pioneer 11 (Kliore et al. 1980) and Voy- 8

agers 1 and 2 (Lindal et al. 1985). These profiles showed 9

a broad tropopause with the temperature minimum at about 10

50 mbar, with mid-stratospheric temperatures of∼ 140K at 11

midlatitudes and ∼ 120K near the equator. The near equa- 12

torial profiles also showed small-scale vertical oscillations 13

that were interpreted as vertically propagating waves. 14

Subsequent ground-based observations taken during 15

northern summer showed enhanced emission at the north 16

pole in the stratospheric methane and ethane bands (Gezari 17

et al. 1989), but not at wavelengths sensitive to the tro- 18

posphere (Ollivier et al. 2000). These observations, when 19

compared to earlier observations, were interpreted as ev- 20

idence for seasonal evolution of the temperatures as pre- 21

dicted by radiative models (Cess and Caldwell 1979; 22

Bezard and Gautier 1985), with warm temperatures at the 23

summer pole and the strength of the radiative response 24

weaker at higher pressures where the radiative time con- 25

stants are longer. 26

Just prior to the arrival of Cassini at Saturn, Greathouse 27

et al. (2005) observed Saturn at high spectral resolution in 28

2002 near southern summer solstice, using the methane ν4 29

band to retrieve southern hemisphere temperatures between 30

0.01 and 10 mbar. They found a general equator to pole 31

temperature gradient, with the south pole 10 K warmer than 32

the equator. In early 2004, Orton and Yanamandra-Fisher 33

(2005) used the Keck telescope to image Saturn in the CH4 34

and H2 bands, allowing the retrieval of temperatures at 100 35

mbar and 3 mbar at 3000 km spatial resolution. They also 36

found a 10 K temperature increase between the equator and 37

the summer pole in the stratosphere, with a sharp ∼5 K 38

increase between 69S and 74S planetocentric latitude. 39

The arrival of Cassini at Saturn in mid-2004, near south- 40

ern mid-summer, began a period of quasi-continuous mon- 41

itoring of Saturn’s thermal emission by the Cassini Com- 42

posite Infrared Spectrometer (CIRS) which is planned to 43

continue until northern summer solstice in 2017. Flasar 44

et al. (2005) showed temperature retrievals of the south- 45

ern hemisphere from data taken during the approach of 46

Cassini to Saturn. They found a 15 K temperature gradi- 47

ent between the equator and south pole at 1 mbar, decreas- 48

ing with increasing pressure. This temperature gradient is 49

larger than the 5 K expected from radiative models for the 50

season, which Flasar et al. (2005) suggested may be caused 51

by adiabatic heating from subsidence at the pole. The first 52

global temperature cross-sections were made by Fletcher 53

et al. (2007, 2008), using CIRS data to retrieve zonal-mean 54

temperatures between 0.5 and 5 mbar in the stratosphere 55

and 50 to 800 mbar in the troposphere; an updated version 56

of their results is shown in Figure 11.5. At the 1-mbar level, 57

16


they found a 30 K temperature difference between the warm1

southern summer pole and the cold northern winter pole;2

the temperature gradient is nearly monotonic from pole to3

pole except for a local temperature maximum at the equa-4

tor, and a roughly 3 K warming between 80N and the north5

pole. At higher pressures, the global temperature gradient6

becomes weaker, and small-scale variations correlated with7

the zonal winds appear. CIRS limb viewing observations8

allowed Fouchet et al. (2008) and Guerlet et al. (2009) to9

extend temperature retrievals up to the 0.01 mbar pressure10

level. Surprisingly, they found that the large-scale pole-11

to-pole temperature gradient was weaker at 0.1 mbar and12

0.01 mbar than at 1 mbar, despite the thermal timescales13

becoming shorter at lower pressures. They also found that14

the temperature profile oscillates with altitude at equatorial15

and low latitudes, with equatorial temperature alternately16

warmer and colder than temperature at ±15. Long-term17

monitoring from ground-based observations by Orton et al.18

(2008) showed that the difference between equatorial and19

low-latitude temperatures also oscillates in time, with a pe-20

riod near 15 Earth years. This equatorial oscillation will be21

discussed in more detail in section 11.3.3.22

Cassini CIRS has continued to monitor Saturn’s thermal23

structure through equinox and into northern spring (Fletcher24

et al. 2010; Fletcher et al. 2015; Guerlet et al. 2011; Sin-25

clair et al. 2013; Sylvestre et al. 2015). Outside of the26

equatorial region, the seasonal temperature variations are27

broadly consistent with models (Fletcher et al. 2010; Fried-28

son and Moses 2012; Guerlet et al. 2014), with a warm-29

ing of the northern hemisphere and cooling of the southern30

hemisphere. The seasonal variations are discussed in detail31

in the chapter by Fletcher et al. in this volume.32

11.3.1. Zonal Mean Winds33

As described in Section 11.2, the meridional tempera-34

ture gradients observed in the upper troposphere are posi-35

tively correlated with the measured cloud-top zonal winds36

at many latitudes. Using the thermal-wind equation (11.1),37

this result implies that the zonal winds observed at cloud38

level decay with altitude into the stratosphere, over a verti-39

cal scale of about six pressure scale heights. Furthermore,40

because the eastward and westward wind gradients are of41

similar magnitude, while the cloud top winds are predomi-42

nantly eastward, the decay of the jets is to a finite eastward43

velocity and not zero, as measured in the System III refer-44

ence frame. Further evidence for net eastward stratospheric45

winds was provided by the analysis of the 1989 occultation46

of 28 Sgr by Nicholson et al. (1995), who found that winds47

of around 40 m s−1 were needed near the 2.5 mbar level48

between 25N and 70N to fit the observed timings of the49

central flash. As can be seen in Figure 11.5, many—though50

not all—of the off-equatorial jets decay in speed with de-51

creasing pressure. Figure 11.5 also makes plain that the52

middle stratosphere winds are generally eastward as mea-53

sured System III, except at high southern latitudes. As men-54

tioned previously, however, the System III reference frame55

may not represent the true interior rotation rate, and other 1

possible interior rotation rates would imply different val- 2

ues for the overall stratospheric winds (in particular, several 3

proposals for the interior rotation rate are faster than the 4

System III rotation rate, which would imply stratospheric 5

winds weaker—that is, more westward—than shown in Fig- 6

ure 11.5). That said, there is no dynamical reason to expect 7

that the mean zonal velocity in the troposphere or strato- 8

sphere is the same as in the deep interior. 9

Observations of seasonal changes in the zonal mean 10

stratospheric temperatures into early northern spring (Fletcher 11

et al. 2010; Sinclair et al. 2013; Fletcher et al. 2015) show 12

a weakening of the equator-to-pole temperature gradients, 13

with the hemispheric average stratospheric ∂T/∂y becom- 14

ing less negative. This implies corresponding changes in the 15

stratospheric zonal winds, with northern hemispheric winds 16

becoming more westward and southern hemispheric winds 17

more eastward, as can be seen in the results of Fletcher 18

et al. (2015), who used the thermal wind approximation to 19

estimate the winds at 100, 1 and 0.5 mbar poleward of 60 20

from 2005 to 2013. 21

11.3.2. Meridional Circulation 22

The zonal-mean circulation in the stratosphere can be in- 23

ferred from the observed temperature field using the ther- 24

modynamic energy equation 25

∂T

∂t+ v

∂T

∂y+ w

(∂T

∂z+

g

cp

)=

q

cp, (11.4)

where v and w are the meridional and vertical velocities, 26

cp is the specific heat, and q is the specific radiative heat- 27

ing/cooling rate. Due to the strong stratification in Saturn’s 28

stratosphere, the vertical advection term is much larger than 29

the meridional advection term, and so the meridional advec- 30

tion is often ignored when estimating the vertical velocity.4 31

Observations of stratospheric temperature allow estimates 32

of the time derivative term and the factor in parentheses. 33

Given estimates of the radiative heating/cooling q/cp from 34

radiative-transfer models and observations, Equation (11.4) 35

can be used to estimate the vertical velocity. The veloci- 36

ties v, w in (11.4) are the so-called “residual mean veloci- 37

ties” (see e.g., Andrews et al. 1987, section 3.5) which in- 38

clude eddy fluxes as well as the advective transport. In the 39

Earth’s stratosphere, the residual mean circulation is a good 40

4The meridional advection term scales as v∆Tmerid/L, where ∆Tmerid

is the characteristic meridional temperature contrast, which occurs over ameridional scale L. Considering a vertically isothermal temperature pro-file for simplicity, the vertical advection term scales simply as w g/cp.The continuity equation implies that v/L ∼ w/D, where D is the char-acteristic vertical scale of the circulation. The ratio of the meridional tothe vertical advection term is therefore cp∆Tmerid/(gH). We insertnumbers for the global-scale seasonal meridional circulation, for which∆Tmerid ∼ 20 K (see Figure 11.5). Noting that the circulation is coher-ent over many scale heights vertically (Figure 11.13), and that the scaleheight is H ∼ 50 km at these temperatures, we adopt D ∼ 300 km. Us-ing cp ≈ 1.3 × 104 J kg−1 K−1 and g ≈ 10 m s−2 shows that the ratioof horizontal to vertical advection terms is ∼0.1.

17

Showman et al.: The Global Atmospheric Circulation of Saturn 11.3 OBSERVATIONS OF THE STRATOSPHEREShowman et al.: The Global Atmospheric Circulation of Saturn 4 OBSERVATIONS OF THE STRATOSPHERE

Fig. 11.13.— Zonal-mean vertical velocities (in mm s1) versus latitude and pressure obtained diagnostically from Equa-tion (12) using the observed temperature and its seasonal variation, combined with estimates of radiative heating andcooling. From Fletcher et al. (2015).

Fig. 11.14.— Low-latitude stratospheric temperatures on Saturn (in K) determined from Cassini/CIRS observations in2005/2006 (left) and 2010 (middle). The difference in shown in the right panel. Note the existence of a low-latitudeoscillatory structure whose phase shifted downward between 2005/2006 and 2010. From Guerlet et al. (2011).

was produced by Friedson and Moses (2012), using a fully1501

3D general circulation model adapted to Saturn. Their1502

model also uses a mechanical forcing at the lower bound-1503

ary to produce the observed tropospheric zonal winds,1504

along with random thermal perturbations in the tropo-1505

sphere to simulate generation of waves by convection,1506

and includes realistic radiative forcing. Their model pro-1507

duced global scale temperature gradients generally con-1508

sistent with observations, though temperatures were 5 K1509

too warm in the summer stratosphere. The modeled merid-1510

ional transport was dominated at low latitudes by a season-1511

ally reversing Hadley circulation, with broad upwelling at1512

low latitudes and strong subsidence near 25 in the winter1513

hemisphere, consistent with the circulation inferred from1514

the ethane and acetylene measurements of Guerlet et al.1515

(2009). At mid-latitudes they found 1-mbar eddy mixing1516

timescales of just over 100 years, slightly longer than the1517

photochemical timescale for acetylene and shorter than for1518

ethane, consistent with the observations.1519

22

Fig. 11.13.— Zonal-mean vertical velocities (in mm s−1) versus latitude and pressure obtained diagnostically from Equa-tion (11.4) using the observed temperature and its seasonal variation, combined with estimates of radiative heating andcooling. From Fletcher et al. (2015).

approximation to the net transport of conserved constituents1

(Dunkerton 1978).2

Flasar et al. (2005) estimated the vertical velocities3

needed to produce the observed warm temperatures at the4

south pole by balancing the vertical advection with the time5

derivative of the temperature, assuming temperature varia-6

tions on the order of the observed equator-to-pole gradient7

on a seasonal timescale, finding w ∼ 0.1 mm s−1. Fletcher8

et al. (2015) used the thermodynamic energy equation to9

estimate the vertical velocity at latitudes poleward of 6010

averaged over the first ten years of the Cassini mission11

(2004-2014), using temperatures from Cassini CIRS and12

net radiative heating from the model of Guerlet et al. (2014).13

They also found velocities of the order of 0.1 mm s−1 near14

1 mbar, becoming weaker at higher pressures, with rising15

motion in the southern hemisphere and subsidence in the16

north (Figure 11.13). At this speed, it would take an air par-17

cel 15 years to rise 50 km, which is about one scale height18

in Saturn’s stratosphere.19

Information on the stratospheric meridional circulation20

can also be obtained from the observed distribution of dis-21

equilibrium chemical species. The most useful species are22

ethane (C2H6) and acetylene (C2H2), which have photo-23

chemical timescales in excess of a Saturn year in the mid-24

dle and lower stratosphere, with ethane having a somewhat25

longer timescale. Photochemical models predict that in the26

absence of meridional transport, ethane and acetylene will27

have a meridional distribution that follows the yearly mean28

solar insolation at pressures of 1 mbar and greater, with the29

abundance a maximum at the equator and decreasing to-30

ward the poles; at lower pressures the chemical timescales31

become shorter and the expected profiles follow the sea-32

sonally varying insolation (Moses and Greathouse 2005;33

Fouchet et al. 2009, see also the chapter by Fletcher et al.34

in this volume). Observations of ethane and acetylene from35

ground-based (Greathouse et al. 2005) and Cassini CIRS36

data (Howett et al. 2007; Guerlet et al. 2009; Hesman et al. 1

2009; Sinclair et al. 2013; Sylvestre et al. 2015) found the 2

1–2-mbar acetylene abundance decreased from the equa- 3

tor towards the poles as predicted by photochemical mod- 4

els, while the ethane abundance was approximately constant 5

with latitude. These observations have been interpreted as 6

evidence that meridional mixing occurs on a timescale in- 7

termediate between the photochemical timescale of acety- 8

lene and ethane (Greathouse et al. 2005; Guerlet et al. 2009; 9

Hesman et al. 2009). However, Moses et al. (2007) have 10

pointed out that the ethane and acetylene photochemistry 11

are strongly coupled, such that the meridional profile of 12

acetylene should track that of ethane even in the presence 13

of transport. Furthermore, CIRS observations by Sinclair 14

et al. (2013) and Fletcher et al. (2015) show an increase in 15

the 2-mbar abundances of ethane and acetylene in the north- 16

ern hemisphere and decrease in the southern hemisphere, 17

which they interpret as evidence of hemispheric transport 18

on seasonal timescales. Thus, the global meridional distri- 19

bution of ethane and acetylene is poorly understood. 20

In addition to the large-scale variations, acetylene and 21

ethane both show a localized enhancement at the south pole 22

at millibar pressures (Hesman et al. 2009; Sinclair et al. 23

2013; Fletcher et al. 2015). As the acetylene and ethane 24

abundances increase with altitude, this is consistent with 25

downward transport at the south pole indicated by tempera- 26

ture data. Using CIRS limb data, Guerlet et al. (2009) found 27

a local maximum in the acetylene and ethane abundance at 28

25N at 0.1 and 0.01 mbar, which they attribute to subsi- 29

dence in the downward branch of a meridional circulation. 30

This interpretation is consistent with the general circula- 31

tion model of Friedson and Moses (2012) which produces a 32

seasonally varying low-latitude circulation with rising mo- 33

tion in the summer hemisphere and subsidence in the winter 34

hemisphere. The Equatorial Semi-Annual Oscillation (see 35

Section 11.3.3) may also contribute to the subsidence at this 36

18


Fig. 11.14.— Low-latitude stratospheric temperatures on Saturn (in K) determined from Cassini/CIRS observations in2005/2006 (left) and 2010 (middle). The difference is shown in the right panel. Note the existence of a low-latitudeoscillatory structure whose phase shifted downward between 2005/2006 and 2010. From Guerlet et al. (2011).

latitude (Fouchet et al. 2008).1

The earliest, pre-Cassini, models of the meridional cir-2

culation (Conrath and Pirraglia 1983; Conrath et al. 1990)3

assumed a circulation that is mechanically forced in the tro-4

posphere, modeled by imposing the observed zonal winds5

at the lower boundary, and assumed zonal momentum bal-6

ance between the Coriolis acceleration of the meridional7

wind and damping of the zonal wind by eddies. Parame-8

terizing the zonal acceleration due to the eddies as −u/τf ,9

where τf is the eddy-damping timescale, this balance can10

be written fv = u/τf . Conrath et al. (1990) also included11

radiative forcing from solar heating and radiative cooling.12

This model produces upward motion and cold temperatures13

on the equatorward side of eastward jets, and downward14

motion and warm temperatures on the poleward side, as15

well as the observed decay of the zonal jet with altitude.16

The resulting upper tropospheric temperature perturbations17

are consistent with the Voyager IRIS observations when the18

frictional and radiative timescales are comparable, τf ∼ τr.19

A more detailed model of the stratospheric circulation20

was produced by Friedson and Moses (2012), using a fully21

3D general circulation model adapted to Saturn. Their22

model also uses a mechanical forcing at the lower boundary23

to produce the observed tropospheric zonal winds, along24

with random thermal perturbations in the troposphere to25

simulate generation of waves by convection, and includes26

realistic radiative forcing. Their model produced global27

scale temperature gradients generally consistent with ob-28

servations, though temperatures were ∼5 K too warm in29

the summer stratosphere. The modeled meridional trans-30

port was dominated at low latitudes by a seasonally revers-31

ing Hadley circulation, with broad upwelling at low lati- 1

tudes and strong subsidence near 25 in the winter hemi- 2

sphere, consistent with the circulation inferred from the 3

ethane and acetylene measurements of Guerlet et al. (2009). 4

At mid-latitudes they found 1-mbar eddy mixing timescales 5

of just over 100 years, slightly longer than the photochem- 6

ical timescale for acetylene and shorter than for ethane, 7

consistent with the observations. Note, however, that the 8

model was unable to reproduce the Semi-Annual Oscilla- 9

tion (see next section), which compromised the model’s 10

ability to capture the observed variations in temperature and 11

constituents at low latitudes associated with the oscillation. 12

11.3.3. Equatorial Semi-Annual Oscillation 13

A common feature of equatorial stratospheres in rapidly 14

rotating atmospheres is the presence of quasi-periodic os- 15

cillations, in both time and altitude, of the zonally averaged 16

temperature and wind fields. The best studied of these are 17

the Quasi-Biennial Oscillation (QBO) in the Earth’s lower 18

stratosphere, in which alternating layers of eastward and 19

westward zonal mean winds, with associated warm and cold 20

temperatures, slowly descend with a variable periodicity av- 21

eraging approximately 28 months (Baldwin et al. 2001). A 22

similar oscillation, with a more regular semi-annual period, 23

is also seen in the upper stratosphere and mesosphere. An 24

approximately four year periodicity in Jupiter’s equatorial 25

temperatures was found in an analysis of groud-based data 26

by Orton et al. (1991). Leovy et al. (1991) proposed that 27

this Quasi-Quadrennial Oscillation (QQO) was analogous 28

to the terrestrial QBO, and calculation of the stratospheric 29

winds from CIRS temperature measurments by Flasar et al. 30

19


(2004) showed the presence of a vertical oscillation in the1

zonal winds.2

Using 24 years of ground-based data, Orton et al. (2008)3

found an oscillation of Saturn’s equatorial brightness tem-4

peratures, in both 7.8µm methane emission and 12.2µm5

ethane emission, with a period of roughly 15 Earth years,6

which has been labeled the Saturn Semi-Annual Oscilla-7

Fig. 11.15.— Low-latitude, stratospheric zonal winds onSaturn calculated based on the observed meridional tem-perature gradients using the thermal-wind equation (11.1).The equation is integrated from the 20-mbar level and so theplotted winds are differences relative to those at 20 mbar.The thermal-wind equation breaks down near the equator,and the winds equatorward of the dashed lines are interpo-lated on isobars from regions outside the dashed lines. Notethe existence of an oscillatory structure in the magnitude ofthe zonal wind with height, which has shifted downward in2010 relative to its phase in 2005/2006. The difference isplotted in the bottom row. From Guerlet et al. (2011).

tion (SSAO). Using CIRS limb observations from 2005 to 1

2006, Fouchet et al. (2008) retrieved temperatures between 2

20 and 0.003 mbar and found equatorial temperature oscil- 3

lations similar to those seen in the QBO and QQO (Fig- 4

ure 11.14), confined within ∼10 of the equator and oscil- 5

lating in height with a wavelength of several scale heights. 6

These equatorial perturbations are flanked by temperature 7

perturbations of opposite sign from ∼10–20 latitude. Cal- 8

culation of the zonal winds from the thermal wind equa- 9

tion reveals vertically alternating eastward and westward 10

jets (Figure 11.15); the presence of a stratospheric jet was 11

also inferred from CIRS nadir viewing data (Li et al. 2008). 12

CIRS limb observations from 2010 (Guerlet et al. 2011) 13

showed that the pattern of winds and temperatures had de- 14

scended in altitude over the intervening five years, as is seen 15

in the QBO. The descent of the temperature field was also 16

observed in equatorial temperature profiles from Cassini ra- 17

dio occultations (Schinder et al. 2011), and cloud tracking 18

measurments from Cassini imaging have shown variations 19

in the velocity of the equatorial jet at the tropopause (Li 20

et al. 2011). Comparisons of Cassini CIRS temperatures 21

from 2009 with a reanalysis of Voyager IRIS thermal data 22

from one Saturn year earlier (Sinclair et al. 2013) found that 23

temperatures at 1–2 mbar were ∼7 K warmer in 2010 than 24

1980 at the equator, and ∼4 K cooler at ±10 latitude, in- 25

dicating the that period of the SSAO is not exactly one-half 26

of a Saturnian year. 27

The terrestrial QBO is driven by the interaction of a spec- 28

trum of vertically propagating waves—of both eastward and 29

westward phase velocities—with the zonal wind. Absorp- 30

tion of the waves by the zonal flow, through radiative or 31

frictional damping, produces a momentum transfer between 32

the wave and zonal flow that accelerates the flow toward 33

the zonal phase velocity of the wave (Lindzen and Holton 34

1968). The momentum transfer is most effective as the 35

wave approaches a critical level where the zonal phase ve- 36

locity of the wave matches the zonal wind velocity and the 37

vertical wavelength and vertical velocity go to zero. In the 38

presence of a jet with vertical wind shear, this results in 39

the waves being absorbed at altitudes slightly below where 40

the wind speed matches the wave phase velocity—and be- 41

low the altitude where the jet speed peaks. This causes the 42

pattern of zonal winds to slowly migrate downward over 43

time (note that, as contours of zonal wind are not mate- 44

rial surfaces, this does not imply downward transport of air 45

parcels themselves). As the jet descends, its lower bound- 46

ary becomes sharper and as the jet descends to the tropo- 47

sphere it dissipates, allowing the waves to now propagate to 48

higher altitudes, where they accelerate a new jet. Equato- 49

rial confinement of the oscillation can be explained by two 50

possible mechanisms. First, the waves driving the oscilla- 51

tion may be equatorially confined. Secondly, at latitudes 52

away from the equator, Coriolis forces become important, 53

and the wave induced momentum convergences may be par- 54

tially balanced by Coriolis forces on the meridional circu- 55

lation induced by the waves, instead of by the momentum 56

changes to the winds. Full details on the terrestrial QBO 57

20

Showman et al.: The Global Atmospheric Circulation of Saturn 11.4 DYNAMICS OF THE ZONAL JETS

can be found in the review by Baldwin et al. (2001). The1

wave modes responsible for the observed oscillations are2

poorly constrained, even on the Earth, although Kelvin and3

eastward-propagating gravity waves are most likely for con-4

tributing the eastward jet accelerations, and mixed Rossby-5

gravity waves and westward-propagating gravity waves are6

most likely for contributing the westward jet accelerations.7

In case of Saturn’s SAO, the amplitude and period of8

the oscillation likely contain information about the types,9

spectra, and amplitudes of the wave modes that drive it, and10

detailed dynamical modeling may thus provide information11

about the wave properties in Saturn’s stratosphere. Anal-12

ogy with the Earth would suggest that such waves might13

arise from convective forcing in the troposphere, so in prin-14

ciple the properties of the SSAO might lead to improved un-15

derstanding of the extent to which tropospheric convection16

on Saturn couples to the overlying stratified atmosphere.17

Moreover, although primarily an equatorial phenomenon,18

Earth’s QBO exerts a global influence, and this is also likely19

to be the case on Saturn, though detailed observations and20

modeling will be necessary to quantify this possibility.21

11.3.4. Stratospheric Response To the 2010 Storm22

One of the most surprising consequences of the large23

convective storm, known as a Great White Spot (GWS) that24

began in December 2010 (see chapter by Sanchez-Lavega25

et al.), was the observation of large changes in the ther-26

mal structure of the stratosphere at northern midlatitudes.27

Observations taken in January 2011 by Cassini CIRS and28

ground-based telescopes (Fletcher et al. 2011) showed a29

cool region in the stratosphere above the anticyclonic vortex30

associated with the storm, flanked by two warmer regions31

nicknamed the “beacons,” 16 K warmer than the cold region32

at roughly 0.5 mbar, much larger than any zonal contrasts33

previously seen in thermal observations of Saturn’s strato-34

sphere. Subsequent observations from CIRS and ground35

based telescopes (Fletcher et al. 2012) showed the beacons36

moving westward at differing rates, with one of the bea-37

cons remaining located above the convective plume asso-38

ciated with the storm, while increasing in temperature. At39

the end of April 2011, the two beacons merged, resulting40

in a single warm oval, with a longitudinal extent of 70, a41

latitudinal extent of 30 and a peak temperature of 220 K42

at 2 mbar, 80 K warmer than the background atmosphere43

and the warmest stratospheric temperatures ever observed44

on Saturn. This new warm oval moved westward at a veloc-45

ity intermediate between the two original beacons, and was46

centered about 1.5 scale heights lower in the atmosphere.47

The temperature of the beacon dropped by 20 K over the48

next two months, after which the temperature slowly de-49

clined by 0.11 ± 0.01 K day−1 and the width of the warm50

spot shrank by 0.16±0.01 deg day−1. Fletcher et al. (2012)51

used the thermal-wind equation to calculate the wind fields52

for the initial beacons in March 2011, and for the merged53

beacon in August 2011. The winds reveal that the hot spots54

are coherent anticyclonic vortices, with tangential winds of55

70–140 m s−1 for the pre-merger vortices, and ∼200 m s−1 1

for the final merged vortex. 2

The beacons were associated with perturbations of 3

chemistry as well as temperature, providing additional 4

insight into the dynamics. The abundances of ethylene 5

(C2H4) and acetylene increased significantly in the hot bea- 6

con core (e.g., at pressures of order ∼1 mbar) relative to 7

pre-storm conditions, and ethane apparently also increased 8

in abundance, though more modestly (Fletcher et al. 2012; 9

Hesman et al. 2012; Moses et al. 2015). One-dimensional 10

photochemical models show that the temperature increase 11

alone, while modifying the chemisty, is insufficient to ex- 12

plain the observed increases (Cavalie et al. 2015; Moses 13

et al. 2015). Therefore, dynamics likely played a role. In 14

particular, all three species increase with altitude at pres- 15

sures of ∼1–10 mbar, so a likely explanation is that sub- 16

sidence occurred inside the beacon, advecting the greater 17

high-altitude abundances of these species downward into 18

the beacon core region. The compressive temperature in- 19

crease associated with such descent would also naturally 20

explain the high beacon temperatures. Nevertheless, the 21

descent velocity required to explain the chemical abun- 22

dances in photochemical models is surprisingly large— 23

Moses et al. (2015) suggest that ∼10 cm s−1 is required. 24

It is not clear whether this is consisent with the magnitude 25

of descent needed to explain the temperature increase, nor 26

how it would be generated. 27

Models of moist convection on Saturn indicate that the 28

convective plumes will not penetrate above the upper tro- 29

poshere, 150 mbar or so (Hueso and Sanchez-Lavega 2004), 30

and modeling of Cassini imaging data of the plume indi- 31

cated that the cloud tops were at 400 mbar or deeper. It is 32

thus unlikely that the stratospheric perturbations were pro- 33

duced directly by the convective plumes associated with the 34

GWS (Garcia-Melendo et al. 2013). Sayanagi and Show- 35

man (2007) showed that tropospheric storms can cause sig- 36

nificant wave generation, and that such waves can propagate 37

into the stratosphere where they exert a significant dynam- 38

ical effect when they break or become absorbed. Fletcher 39

et al. (2012) noted that the storm was located at a latitude 40

where the zonal winds have been suggested to be barotrop- 41

ically unstable (Achterberg and Flasar 1996; Read et al. 42

2009a), and where quasi- stationary Rossby waves may po- 43

tentially propagate upward from the troposphere to the strat- 44

sophere. They therefore suggested that the strong pertur- 45

bations in the stratosphere were the result of waves, either 46

gravity or Rossby waves, generated by the convection im- 47

pinging on the statically stable tropopause, propagating into 48

the stratosphere. This conjecture still needs to be tested with 49

additional numerical modeling. 50

11.4. Dynamics of the Zonal Jets 51

11.4.1. Jet Structure 52

As described in Section 11.2, Saturn rotates rapidly, and 53

the large-scale dynamics is in approximate geostrophic bal- 54

ance. Although we lack detailed observations of the deep 55

21


interior, dynamical balance arguments can be used to con-1

strain the structure of the jets there. In particular, for a zonal2

flow at low Rossby number, it can be shown that, to good3

approximation (Showman et al. 2010)4

2Ω∂u

∂z∗≈ g

ρ

(∂ρ

∂y

)p

, (11.5)

where z∗ is the coordinate parallel to the rotation axis, g is5

gravity, and ρ is density. This is a generalized thermal-wind6

equation that is valid in the deep molecular interior even7

in the presence of non-hydrostatic motions. If the density8

is constant on isobars—that is, if the fluid is barotropic—9

then Eq. (11.5) implies that the zonal wind is constant on10

surfaces parallel to the rotation axis, i.e.,11

∂u

∂z∗≈ 0. (11.6)

This result is analogous to the standard Taylor-Proudman12

theorem (Pedlosky 1987), except that it does not make13

any assumption of constant density. It implies that, for a14

barotropic flow, the zonal wind is constant along lines par-15

allel to the rotation axis, and is valid even if the mean den-16

sity varies by orders of magnitude from the atmosphere to17

the deep interior, as it does on Saturn. On the other hand, if18

density varies on isobars—that is, if the fluid is baroclinic—19

then (11.5) implies that the zonal wind varies along surfaces20

parallel to the rotation axis.21

These results have been used to argue for several end-22

point scenarios regarding the interior wind structure. Con-23

vective mixing is normally thought to homogenize the in-24

terior entropy, which would suggest a nearly barotropic in-25

terior in which variations of density on isobars are small.26

Convective plumes of course involve thermal perturbations,27

but simple mixing-length estimates suggest that at Saturn’s28

heat flux these convective density variations induce only29

slight deviations from a barotropic state (Showman et al.30

2010). Based on arguments of this type, Busse (1976) sug-31

gested that the observed zonal winds on Jupiter and Sat-32

urn extend downward into the interior on surfaces paral-33

lel to the rotation axis following Equation (11.6); the ob-34

served zonal winds would then be the surface manifesta-35

tion of concentric, differentially rotating cylinders of fluid36

centered about—and parallel to—the rotation axis. On the37

other hand, other authors have suggested that perhaps the38

jets on Jupiter and Saturn extend only a few scale heights39

into the interior (e.g. Ingersoll and Cuzzi 1969; Stone 1973;40

Ingersoll 1976). In this case, Eq. (11.5) demands the ex-41

istence of latitudinal thermal variations, and would imply42

that, just below the cloud deck, the cyclonic bands are43

cooler (denser) than the anticyclonic bands. The required44

temperature differences, ∼5–10 K, are modest, and could45

plausibly be supplied by variations in latent or radiative46

heating between latitude bands. Intermediate scenarios are47

also possible, with horizontal temperature gradients and48

vertical variation of the jets in the cloud layer superposed49

on deep, nearly barotropic jets in the interior (Vasavada and50

Showman 2005). Liu et al. (2013, 2014) suggested yet an- 1

other scenario based on the assumption that the interior en- 2

tropy is only homogenized in the direction of z∗, while al- 3

lowing for entropy variations in the direction toward/away 4

from the rotation axis. Via Equation (11.5), this scenario 5

also implies significant thermal wind shear and a gradual 6

decay of the jets with depth. 7

It has long been recognized that the above arguments 8

may break down in the metallic hydrogen interior at pres- 9

sures ≥ 106 bars. There, the high electrical conductivity 10

allows sufficiently strong Lorentz forces to alter the forces 11

balances, causing a breakdown of geostrophy. It has been 12

suggested that the Lorentz forces will act to brake the zonal 13

flows, leading to weak winds in the metallic region (e.g. 14

Busse 1976, 2002). The transition from molecular to metal- 15

lic hydrogen is gradual (Nellis 2000), and several authors 16

have pointed out that significant magnetic effects on the 17

flow can occur even in the extended semiconducting re- 18

gion between the metallic interior and the overlying molec- 19

ular (electrically insulating) envelope (Kirk and Stevenson 20

1987; Liu et al. 2008). In particular, Liu et al. (2008) ar- 21

gued that the observed zonal winds cannot penetrate deeper 22

than 96% and 86% of the radius on Jupiter and Saturn, re- 23

spectively, because otherwise the Ohmic dissipation would 24

exceed the planets’ observed luminosities. If such Lorentz- 25

force braking occurs at the base of the molecular region 26

and leads to weak winds there, and if the overlying jets are 27

nearly barotropic, then Equation (11.6) would suggest that 28

the winds may be weak throughout much of the molecular 29

interior—and not just in the metallic and semiconducting 30

regions (Liu et al. 2008). Nevertheless, the models to date 31

have been largely kinematic, and more work is needed to 32

determine self-consistent solutions to the full magnetohy- 33

drodynamic problem (Glatzmaier 2008). The main region 34

that can escape such coupling is at low latitudes—there, it is 35

possible for Taylor columns to extend throughout the planet 36

without ever encountering electrically conducting layers. 37

Interestingly, the width of this region is similar to the ob- 38

served width of the equatorial jets on Jupiter and Saturn. 39

An attractive scenario is therefore that the equatorial jets 40

penetrate throughout the planet along surfaces parallel to 41

the rotation axis (approximately following Equation 11.6 in 42

the deep atmosphere), while the higher-latitude jets truncate 43

at some as-yet poorly determined depth. Juno and Cassini 44

will provide observational constraints on this question in the 45

next year. 46

11.4.2. Models Of Jet Formation 47

Thorough reviews of models for jet formation on Jupiter 48

and Saturn were provided by Vasavada and Showman 49

(2005) and Del Genio et al. (2009); here, we summarize 50

only the highlights, emphasizing developments within the 51

last ten years. Two classes of model have been introduced 52

to explore the zonal jets on Jupiter and Saturn. In one ap- 53

proach, which we dub the “shallow forcing” scenario, it 54

is assumed that baroclinic instabilities, moist convection, 55

22


and other processes within the cloud layer are responsible1

for driving the jets. This scenario has mostly been explored2

with thin-shell, one-layer and multi-layer atmospheric mod-3

els from the terrestrial atmospheric dynamics community.4

In another approach, which we dub the “deep forcing” sce-5

nario, it is assumed that convection throughout the interior6

leads to differential rotation in the molecular envelope that7

manifests as the zonal jets at the surface. This scenario8

has primarily been explored with Boussinesq and anelastic9

models of convection in spherical shells that are derived10

from the geodynamo and stellar convection communities.11

The distinction between the approaches is artificial, but12

because of the different communities involved, and the dif-13

ficulty of constructing a truly coupled atmosphere-interior14

circulation model, the distinction has persisted over the15

∼40-year history of the field. Nevertheless, new attempts16

are being made to bridge this gap, an area that will see17

major progress in the next decade.18

It is important to emphasize that the issue of whether19

the jets exhibit deep or shallow structure is distinct from20

whether the jet driving occurs primarily in the atmosphere21

versus the interior (Vasavada and Showman 2005; Show-22

man et al. 2006). Because of the nonlocal nature of the at-23

mospheric response to eddy driving, zonal jets that extend24

deeply into the interior can result from eddy accelerations25

that are primarily confined to the atmosphere (Showman26

et al. 2006; Lian and Showman 2008; for theory, see Haynes27

et al. 1991). Likewise, under some conditions, convection28

throughout the interior can produce jets that may exhibit29

confinement near the outer margin of the planet (Kaspi et al.30

2009).31

Models for the atmospheric jet formation generally as-32

sume that the zonal jets result from the interaction of tur-33

bulence with the β effect that is associated with latitudinal34

variations in the Coriolis parameter. Early work empha-35

sized two-dimensional, horizontally non-divergent models36

and one-layer shallow-water models. More recently, sev-37

eral three-dimensional models have been performed.38

One-layer models are intended to represent an appropri-39

ate vertical mean of the atmospheric flow. They are mo-40

tivated by the observation that the atmospheric winds on41

Jupiter and Saturn are approximately horizontal—with gen-42

erally small horizontal divergence—and were originally in-43

tended to capture the flow in a presumed shallow weather44

layer below the clouds. More broadly, however, they serve45

as an ideal process model to explore the dynamics of zonal46

jets and vortices in the simplest possible context, thereby47

shedding insights into dynamical mechanisms that may also48

occur (but be harder to identify) in more realistic systems.49

In one-layer models, the effect of convection must be pa-50

rameterized, typically by introducing small-scale vorticity51

sources and sinks that flucuate in time. Damping is com-52

monly represented using a frictional drag.53

Most work to date has been performed with the two-54

dimensional, horizontally non-divergent model. This sys-55

tem captures the interaction of turbulence with the β ef-56

fect, but neglects buoyancy, gravity waves, and any effects57

associated with a finite Rossby deformation radius (an as- 1

sumption that is not strictly valid on Jupiter and Saturn, 2

where the deformation radius is comparable to or smaller 3

than the meridional jet width). When forced with small- 4

scale turbulence under conditions of fast rotation and rel- 5

atively weak frictional drag, these models generally pro- 6

duce multiple zonal jets whose meridional widths scale 7

with the Rhines scale (U/β)1/2, where U is a charac- 8

teristic wind speed5(e.g. Williams 1978; Nozawa and Yo- 9

den 1997; Huang and Robinson 1998; Sukoriansky et al. 10

2007, and many others). Interestingly, these models lack 11

an unusually strong equatorial jet as occurs on Jupiter and 12

Saturn—intead, the equatorial jet tends to resemble the 13

higher-latitude jets in speed and structure, and it often is 14

not centered precisely around the equator. These models 15

also tend not to produce large, long-lived coherent vortices 16

that coexist with the jets, such as Jupiter’s Great Red Spot 17

or smaller but analogous vortices on Saturn. Both of these 18

discrepancies likely result from the lack of a finite deforma- 19

tion radius in the 2D non-divergent model. Despite these 20

failures, the ease of analyzing this model has led to cru- 21

cial insights into the workings of inverse energy cascades 22

(Sukoriansky et al. 2007) and the physical mechanisms for 23

jet formation (e.g. Dritschel and McIntyre 2008). 24

The one-layer shallow-water model represents a more 25

realistic system because it includes the effect of buoyancy 26

(via a horizontally variable vertical layer thickness), gravity 27

waves, and a finite deformation radius, albeit still in a con- 28

text that does not capture detailed vertical structure. In the 29

context of giant planets, the model captures the behavior of 30

an active atmospheric weather layer that overlies an abyssal 31

layer (representing the deep planetary interior) whose winds 32

are specified, usually to be zero. The related, one-layer 33

quasi-geostrophic (QG) model provides a simplification by 34

restricting the flow to be nearly geostrophic, which filters 35

gravity waves while retaining the effect of a finite deforma- 36

tion radius. Showman (2007) and Scott and Polvani (2007) 37

presented the first forced turbulence calculations of jet for- 38

mation in the shallow water system, and Li et al. (2006) 39

performed a similar study in the QG system. These authors 40

showed that multiple zonal jets can result from small-scale 41

forcing, and that in many cases, the jet widths are compara- 42

ble to the Rhines scale (U/β)1/2. Interestingly, the defor- 43

mation radius influences jet formation, and when it is suf- 44

ficiently small, can suppress the formation of jets entirely, 45

leading to a flow dominated by vortices—an effect first de- 46

scribed in the QG system (Okuno and Masuda 2003; Smith 47

2004) before being extended to the shallow-water system 48

(Showman 2007; Scott and Polvani 2007). Thomson and 49

McIntyre (2016) showed in a QG model that the presence 50

of specified, zonally symmetric jets in the abyssal layer 51

can help to increase the straightness of the weather-layer 52

5In Rhines’ original theory, this corresponds to an eddy velocity associatedwith the turbulence, but in other contexts other velocity scales such asthe zonal-mean zonal wind can also be appropriate (see, e.g., Scott andDritschel 2012).

23


jets, causing the flow to more closely follow latitude cir-1

cles. Using a simple parameterization of convective forcing,2

their model also naturally produces a preference for con-3

vection in belts rather than zones, as observed on Jupiter. In4

some cases, especially when jets in the abyssal layer exist,5

the weather-layer jets in one-layer shallow-water and QG6

models can violate the Charney-Stern stability theorem, in7

agreement with Jupiter and Saturn (Showman 2007; Scott8

and Polvani 2007; Thomson and McIntyre 2016).9

Under conditions appropriate to Jupiter and Saturn—10

namely, small Rossby number and a deformation radius a11

few percent of the planetary radius—shallow-water mod-12

els typically produce a broad, fast westward equatorial jet13

(Cho and Polvani 1996; Iacono et al. 1999; Showman 2007;14

Scott and Polvani 2007). This equatorial flow intensifica-15

tion could be considered a step forward from the 2D non-16

divergent model, since the equatorial jets of Jupiter and Sat-17

urn are faster and wider than the jets at higher latitudes.18

However, although Uranus and Neptune exhibit westward19

equatorial flow, this result represents a major failing for20

Jupiter and Saturn, where the equatorial flow is eastward.21

Nevertheless, Scott and Polvani (2008) showed that under22

certain conditions, shallow-water models can generate east-23

ward equatorial jets resembling those on Jupiter and Sat-24

urn. They speculate that the key property allowing emer-25

gence of eastward (rather than westward) equatorial flow26

is the usage of radiative rather than frictional damping.27

However, this is inconsistent with the findings of Show-28

man (2007), who adopted radiative damping and yet al-29

ways obtained westward equatorial jets. Most likely, spe-30

cific types of both forcing and damping are necessary. A31

similar “thermal shallow water” model presented by Warne-32

ford and Dellar (2014) exhibits equatorial superrotation at33

short radiative time constant but subrotation at long radia-34

tive time constant, although the value of the radiative time35

constant at the transition between these regimes is too short36

to explain the transition from the Jupiter/Saturn regime to37

the Uranus/Neptune regime. The dynamical mechanisms38

controlling the equatorial jet properties in all these shallow-39

water-type models remain poorly understood and deserve40

further study.41

Over the past 15 years, several three-dimensional mod-42

els have been published showing how zonal jets can develop43

in the atmosphere. Following on earlier work by Williams44

(2003), Lian and Showman (2008) showed that baroclinic45

instabilities in the weather layer (induced by meridional46

temperature differences associated with the latitudinal gra-47

dients in radiative heating) can generate multiple zonal jets.48

These jets do not remain confined to the cloud layer where49

they are driven, but rather can extend deep into the in-50

terior as long as friction there is weak. The model pro-51

duces statistical distributions of eddy momentum fluxes that52

match observations on Jupiter and Saturn, as well as jets53

that remain stable while violating the Charney-Stern stabil-54

ity criterion. Both Williams (2003) and Lian and Show-55

man (2008) showed that sharp latitudinal temperature gra-56

dients near the equator can lead to equatorial superrotation.57

Schneider and Liu (2009) presented a shallow 3D model 1

(truncated at 3 bars), which, as in Williams (2003) and Lian 2

and Showman (2008), produces multiple mid-to-high lat- 3

itude jets in response to baroclinic instabilities associated 4

with latitudinal temperature gradients. Moreover, they in- 5

troduced a simple convective parameterization which al- 6

lows the emergence of Jupiter-like equatorial superrotation 7

in response to equatorial convection in the model. 8

Several 3D models now exist that explain the overall fea- 9

tures of the circulation on all four giant planets, including 10

the transition from equatorial superrotation on Jupiter and 11

Saturn to equatorial subrotation on Uranus and Neptune. 12

Lian and Showman (2010) incorporated a hydrological cy- 13

cle that captures the advection, condensation, rain out, and 14

latent heating associated with water vapor, providing the 15

first test of the long-standing hypothesis that such latent 16

Showman et al.: The Global Atmospheric Circulation of Saturn 6 DYNAMICS OF ZONAL JETS

Fig. 11.37.— 3D atmosphere simulations demonstrating that latent-heat release associated with condensation of water canlead to zonal jet patterns qualitatively resembling all four giant planets. Top, middle, and bottom rows are three modelsrepresenting Jupiter, Saturn, and Uranus/Neptune, which are assumed to have water abundances of 3, 5, and 30 times solar,respectively. Colorscale represents zonal wind in m s1. Left column shows oblique view and right column shows viewlooking down over the north pole. The Jupiter and Saturn cases develop equatorial superrotation and many off-equatorialjets at higher latitudes, while the Uranus/Neptune model exhibits a three-jet pattern comprising broad equatorial subrotationand high-latitude eastward jets. From Lian and Showman (2010).

using a simple Newtonian relaxation scheme. Simulations3805

were performed for Jupiter, Saturn, and Uranus/Neptune3806

conditions. Although the water abundance on the gi-3807

ant planets is unknown, the abundance of methane is 33808

times solar on Jupiter, 5–10 times solar on Saturn, and3809

20–50 times solar on Uranus and Neptune, and so Lian3810

and Showman (2010) adopted water abundances similar to3811

these values. The Jupiter and Saturn simulations exhibited3812

numerous mid-to-high latitude zonal jets and equatorial3813

superrotation, whereas the Uranus/Neptune models ex-3814

hibited a three-jet pattern with high-latitude eastward jets3815

and broad westward flow at low latitudes (Figure 11.37).3816

These are the first models that explain the overall circula-3817

tion pattern of all four giant planets—including the tran-3818

sition from equatorial superrotation for Jupiter/Saturn to3819

subrotation for Uranus/Neptune—within the context of a3820

single mechanism. They also produce storms qualitatively3821

resembling those on Jupiter and Saturn, in some cases in-3822

cluding storms that expand to cover a significant range of3823

longitudes, perhaps analogous to Saturn’s GWS.3824

Schneider and Liu (2009) and Liu and Schneider3825

(2010) presented dry primitive-equation models that build3826

on the work of Williams (2003a) and Lian and Showman3827

(2008) by testing the hypothesis that the high-latitude3828

jets could result from baroclinic instability and explor-3829

ing the conditions that can lead to equatorial superro-3830

tation. Their model is much shallower than those of3831

Lian & Showman—they placed their bottom boundary at3832

only 3 bars. In simulations of Jupiter, Schneider and Liu3833

(2009) found that multiple mid-to-high latitude zonal jets3834

emerged due to baroclinic instabilities resulting from the3835

meridional insolation gradient, and they moreover found3836

that equatorial superrotation emerged in response to low-3837

latitude convection (represented in their model with a sim-3838

ple dry convective adjustment scheme). Specifically, they3839

suggest that convection leads to significant horizontal di-3840

vergence which causes a net Rossby wave source near3841

the equator, and that radiation of these Rossby waves to3842

surrounding latitudes causes a horizontal convergence of3843

eddy momentum onto the equator, driving the superro-3844

tation. Following Lian and Showman (2010), Liu and3845

Schneider (2010) extended the model of Schneider and3846

Liu (2009) to Saturn, Uranus, and Neptune, and likewise3847

showed that a transition can occur from equatorial super-3848

52

Fig. 11.16.— 3D atmosphere simulations demonstratingthat latent-heat release associated with condensation of wa-ter can lead to zonal jet patterns qualitatively resembling allfour giant planets. Top, middle, and bottom rows are threemodels representing Jupiter, Saturn, and Uranus/Neptune,which are assumed to have water abundances of 3, 5, and 30times solar, respectively. Colorscale represents zonal windin m s−1. Left column shows oblique view and right col-umn shows view looking down over the north pole. TheJupiter and Saturn cases develop equatorial superrotationand many off-equatorial jets at higher latitudes, while theUranus/Neptune model exhibits a three-jet pattern compris-ing broad equatorial subrotation and high-latitude eastwardjets. From Lian and Showman (2010).

24


heating is crucial in driving the circulation (e.g. Barcilon1

and Gierasch 1970; Ingersoll et al. 2000). Their results are2

shown in Figure 11.16. In addition to explaining the ob-3

served transition from superrotation to subrotation, as well4

as mid-to-high latitude jets qualitatively similar to those ob-5

served on the giant planets, their model also produces lo-6

cal “storm”-like features that crudely resemble convective7

thunderstorm events observed on Jupiter and Saturn. In8

some cases, their model exhibits large storm events, which9

bear resemblence to Saturn’s recent Great White Spot of10

2010-2011. Liu and Schneider (2010) extended the work of11

Schneider and Liu (2009) to all four planets, likewise show-12

ing a transition from equatorial superrotation on Jupiter and13

Saturn to equatorial subrotation on Uranus and Neptune, as14

well as other jet properties similar to those on the giant plan-15

ets. All of these models represent a major step forward.16

Nevertheless, the equatorial jet under Saturn conditions is17

insufficiently fast and broad, and more work is warranted to18

determine whether equatorial jets better resembling Saturn19

can be produced in this class of model.20

We now turn to discuss models of jet formation via con-21

vection in the interior. Busse (1976) first envisioned that22

the convection in the interior could organize into the form23

of Taylor columns aligned with the rotation axis, and that24

the Reynolds stresses associated with this convection would25

drive jets that would manifest as concentric, differentially26

rotating cylinders centered on the rotation axis. The ob-27

served zonal jets would then represent the outcropping of28

this differential rotation at the cloud level. Early investi-29

gations of this hypothesis involved analytical calculations,30

laboratory studies, and numerical simulations in the lin-31

ear and weakly nonlinear regime. These studies generally32

confirmed the columnar nature of the convection at low33

amplitude, and showed how the spherical planetary shape34

would promote the emergence of equatorial superrotation35

(see Busse 1994 and Busse 2002 for reviews). Only in re-36

cent years, however, have computational resources become37

sufficient to investigate the dynamics in the more strongly38

nonlinear regime relevant to the giant planets.39

The first such models adopted the Boussinesq approx-40

imation wherein the background density is assumed con-41

stant (i.e., the continuity equation is ∇ · v = 0). This as-42

sumption is not valid for the giant planets, but the dynam-43

ics are nevertheless rich and provide significant insights.44

Generally, these models explore convection in a spherical45

shell with boundaries that are free-slip in horizontal veloc-46

ity, and that are maintained at constant temperature (with47

the interior boundary being hotter than the outer bound-48

ary, allowing convection to occur). The earliest models ex-49

plored relatively thick shells, with an inner-to-outer radius50

ratio less than 0.7. These simulations showed that when51

the convection is sufficiently vigorous and friction suffi-52

ciently weak (i.e. the Rayleigh number sufficiently high53

and Ekman number sufficiently low), the convection can54

produce zonal jets whose speeds are signifantly faster than55

the convective velocities (Aurnou and Olson 2001; Chris-56

tensen 2001, 2002). The jets take the form of a broad equa-57

torial superrotating jet and, in some cases, a small number 1

of weaker jets at high latitudes. Despite the existence of 2

the superrotation, the zonal jet patterns in these models do 3

not resemble that on Jupiter and Saturn. Subsequent studies 4

considered thinner shells, with an inner-to-outer radius ra- 5

tio of∼0.9, and when appropriately tuned, these models are 6

able to produce superrotation comparable to that of Jupiter 7

and Saturn, along with multiple high-latitude jets (Heimpel 8

et al. 2005; Heimpel and Aurnou 2007; Aurnou et al. 2008, 9

see Figure 11.17). An issue is that, in all of these models, 10

the meridional width of the superrotation is controlled by 11

the depth of the inner boundary, and yet such a boundary 12

is artificial in the context of a giant planet (which lack any 13

such impermeable boundary in their molecular/metallic en- 14

velopes). 15

In Jupiter and Saturn, the density varies by a factor of 16

∼104 from the cloud deck to the deep interior, and re- 17

cently several models have started to include such radial 18

density variations via the anelastic approximation, which 19

allows the background density to vary radially, while (like 20

the Boussinesq system) filtering sound waves, which is a 21

reasonable approximation for the giant planet interiors. The 22

first such models were two-dimensional, considering con- 23

vection in the equatorial plane and investigating the emer- 24

gence of differential rotation (Evonuk and Glatzmaier 2004, 25

2006, 2007; Glatzmaier et al. 2009). These models demon- 26

© 2005 Nature Publishing Group

Previous analytical models of planetary zonal flow in a sphericalshell have assumed a relatively deep bottom boundary, such thathigh-latitude zonal jets develop from flows outside the tangentcylinder18. More recent numerical models of deep and stronglyturbulent three-dimensional quasigeostrophic convection10,11 haveproduced jets of realistic amplitudes. However, these moderatelythick fluid shells (with radius ratios x ¼ r i/ro ¼ 0.6–0.75) produceonly a pair of high-latitude jets in each hemisphere inside the tangentcylinder10,14, which cannot account for the observed pattern of jovianjets. Laboratory experiments of rotating convection in deep sphericalshells19 with x ¼ 0.35 and 0.70 have obtained zonal flow patterns thatare broadly comparable to the results of spherical numericalmodels9,10. However, multiple jets have been produced by idealizednumerical20 and experimental21 models with a cylindrical geometry, afree top surface, and a sloping bottom surface. In those local models,as well as our present global model, the jets are produced by thetopographic b-effect and follow Rhines scaling.There are various possible reasons why previous spherical shell

models have not produced multiple higher-latitude jets. Instead ofanalysing particular cases we list the following conditions that favourthe development of multiple high-latitude jets. Turbulent flow (thatis, high Reynolds number) constrained by rapid rotation (that is, lowRossby number) is necessary for the development of jets that followRhines scaling. A relatively thin fluid layer allows multiple jets toform at higher latitudes by decreasing the Rhines length andincreasing the latitudinal range inside the tangent cylinder.We use numerical modelling to study turbulent thermal convec-

tion in a rapidly rotating three-dimensional spherical shell, withsimulation parameters chosen to reflect our present understandingof Jupiter’s interior. The spherical shell geometry is defined by theradius ratio x ¼ r i/ro. We have chosen x ¼ 0.9, which represents asubstantially thinner shell than in previous models of rotatingconvection10,14. This value of the radius ratio corresponds to adepth in Jupiter of approximately 7,000 km, which is shallowerthan the phase boundary that separates the outer molecular fluid

from the liquid metal H–He core, estimated at 0.8–0.85 R J, whereR J < 70,000 km is the radius of Jupiter13. Measurements of increas-ing flow velocity with depth suggest that the surface winds are seatedin the deep molecular H2–He atmosphere22. However, increasingdensity and electrical conductivity with pressure result in inertial andLorentz forces that are expected to damp the zonal flow between 0.85and 0.95R J (refs 13 and 23). Thus we have chosen a simulation radiusratio that lies near the middle of current estimates. A description ofSaturn’s interior is similar to that of Jupiter except that lowersaturnian gravity roughly doubles the estimated layer depth.Selection of other simulation parameters (see Methods) is based

on recent numerical and experimental scaling analyses for convec-tion-driven zonal flows in thicker spherical shells11,24. An essentialingredient in this numerical simulation is that convective turbulenceis quasigeostrophic and close to the asymptotic state of rapid rotationin which viscosity and thermal diffusivity play a negligible role inthe dynamics. Thus, large discrepancies between the simulationparameters and those estimated for Jupiter should not stronglyaffect the character of the solution. We do not model the joviantroposphere, nor the effects of latitudinally varying insolation7,8.Furthermore, we model convection only within the region wherelarge-scale zonal flows are predicted to occur and we neglect deeperregions where convection may be vigorous but zonal flows areexpected to be weak. Although fluid compressibility effects areimportant to the dynamics of convection in the gas giants25, thefluid in our numerical model is assumed to be incompressible exceptfor thermal buoyancy effects (that is, the Boussinesq approximation).The omission of compressibility effects is possibly this model’sgreatest limitation. However, considering that we use a relativelythin convection layer, a Boussinesq treatment may be adequate tosimulate the large-scale dynamics12,13.Figure 2 shows the results of our numerical simulation and the

jovian zonal wind pattern. Figure 2a is a plot of Jupiter’s averagedsurface azimuthal (east–west) velocity profile relative to the deep-seated magnetic-field reference frame1. Although we focus here on

Figure 2 | Zonal flow for Jupiter and the numerical simulation. a, Thezonal wind of Jupiter. The Cassini space mission data was kindly providedby A. Vasavada. Wind speed may be converted to Rossby number usingRo ¼ v/Qro). b, Snapshot in time of the simulation’s outer-surfaceazimuthally averaged azimuthal (east–west) velocity. Dashed lines indicate

the latitude where the tangent cylinder intersects the outer surface, for thesimulation’s radius ratio (x ¼ r i/ro ¼ 0.9). c, Snapshot of the simulation’sazimuthal velocity field on the outer and inner spherical surface, and on ameridional slice. Red and blue colours represent prograde (eastward) andretrograde (westward) flow, respectively.

LETTERS NATURE|Vol 438|10 November 2005

194

Fig. 11.17.— The zonal flow on the outer and inner surfaceof a 3D convection simulation with an aspect ratio of 0.9,showing the eastward (red) and westward (blue) zonal ve-locities. The Boussinesq equations were solved, in whichthe background (reference) density is independent of ra-dius. Free-slip boundary conditions are used on both theinner and outer boundaries. Equatorial superrotation, andnumerous higher-latitude eastward and westward jets, de-velop. Adapted from Heimpel et al. (2005).

25


strated a new mechanism for generating equatorial superro-1

tation that does not exist in the Boussinesq system; as con-2

vective plumes rise and sink, the compressibility alters their3

vorticity in such a way as to promote Reynolds stresses that4

cause superrotation (Glatzmaier et al. 2009).5

More recently, several 3D anelastic convection mod-6

els have been developed (Kaspi 2008; Kaspi et al. 2009;7

Jones and Kuzanyan 2009; Jones et al. 2011; Gastine and8

Wicht 2012, and others). Like the Boussinesq models, these9

anelastic simulations generally exhibit equatorial superrota-10

tion and (in some cases) several higher-latitude zonal jets.11

If the spherical shell is thin, then the shell thickness con-12

trols the meridional width of the equatorial jet—just as in13

Boussinesq simulations. However, if the shell thickness be-14

comes sufficiently deep, then the equatorial jet width tends15

to become invariant to the location of the bottom boundary,16

which is an improvement over the situation in Boussinesq17

models. Nevertheless, in this situation, the superrotation in18

the simulations tends to be too broad and the higher lati-19

tude jets fewer in number compared to Jupiter and Saturn.20

In the models of Kaspi (2008) and Kaspi et al. (2009), the21

jets exhibit significant shear, becoming weaker with depth;22

in contrast, some other models exhibit weaker shear, with a23

more barotropic structure (Jones and Kuzanyan 2009; Gas-24

tine and Wicht 2012; Cai and Chan 2012; Gastine et al.25

2013; Chan and Mayr 2013). The difference likely result26

from the different treatment of the fluid’s thermodynamic27

properties, including the radial variation of density and es-28

pecially the entropy expansion coeffient, in these different29

models.30

A concern with these models is that the simulated pa-31

rameter regime is far from that of the giant planets; the32

simulated heat fluxes and viscosities are both too large33

by many orders of magnitude. Even within the simulated34

range, the jet speeds vary strongly with Rayleigh number35

and Ekman number. Therefore, even though it is possible to36

choose values of the Rayleigh number and Ekman number37

that yield realistic jet speeds, it is unknown whether such38

models would produce realistic jet speeds at the values of39

Rayleigh and Ekman number relevant to Jupiter and Sat-40

urn. Unforunately, computational resources will be insuf-41

ficient for directly simulating the planetary regime for the42

foreseeable future. Therefore, answering this question re-43

quires the development of scaling laws that can be extrap-44

olated from the simulated regime to the planetary regime.45

Christensen (2002) made a first attempt at this, suggesting46

a scaling law that could bridge the gap based based on an47

empirical assessment of his Boussinesq simulations. Show-48

man et al. (2011) used anelastic simulations to show that,49

within the simulated range of Rayleigh and Ekman num-50

bers, two distinct regimes exist, leading to distinct depen-51

dences of jet speeds on convective heat flux and viscosity.52

Christensen (2002) and Showman et al. (2011) both sug-53

gested an additional regime may exist wherein jet speeds54

become independent of viscosity when the viscosity is suf-55

ficiently small. More recent work, however, challenges the56

existence of a regime independent of viscosity and thermal57

diffusivity (Gastine et al. 2013, 2014). Additional work is 1

warranted. 2

All of the above models neglect any coupling to the 3

magnetic field. Recently, however, several models have in- 4

cluded the effect of an electrically conducting interior and 5

its coupling to the dynamics, allowing a joint investigation 6

of zonal-jet formation and dynamo generation of a magnetic 7

field. This is a challenging problem because the electrical 8

conductivity varies by many orders of magnitude with ra- 9

dius, a situation different from that encountered in the geo- 10

dynamo problem. This situation was first investigated in 11

Boussinesq models (Heimpel and Gomez Perez 2011) and 12

more recently in anelastic models (Duarte et al. 2013; Yadav 13

et al. 2013; Jones 2014) that allow both density and electri- 14

cal conductivity to vary strongly with radius. These models 15

show that the equatorial jet penetrates to a depth where the 16

Lorentz force becomes comparable to the Reynolds stress 17

associated with the convection (which effectively means 18

the jet is confined to the electrically insulating outer enve- 19

lope). Jets poleward of the equatorial superrotation tend 20

to be suppressed, because their bottoms penetrate into the 21

electrically conducting region where Lorentz forces can act 22

to brake the flows—an effect that extends throughout the 23

molecular envelope due to the nearly barotropic nature of 24

these jets (cf Equation 11.6). This suggests the possibil- 25

ity that the equatorial jet results from interior convection, 26

but the higher latitude jets result from atmospheric pro- 27

cesses including baroclinic instability and moist convection 28

(Vasavada and Showman 2005). 29

11.4.3. Detection Of Deep Dynamics By Gravity Mea- 30

surements 31

Information to date on Saturn’s deep winds has been in- 32

direct. This is likely to change in 2017, as towards the cul- 33

mination of its 13-year-long survey of the Saturnian system, 34

the Cassini spacecraft will shift into a highly inclined orbit 35

with a periapse between the planet and its rings—an orbit 36

ideally suited to measuring the small-scale structure of Sat- 37

urn’s gravitational field. During this phase, known as the 38

Cassini Grand Finale, the spacecraft will complete 22 or- 39

bits, six of which will be dedicated to gravity science. This 40

will be the final maneuver of Cassini before it descends into 41

the planet, terminating the mission. These gravity measure- 42

ments will allow the determination of Saturn’s gravity field 43

to much higher accuracy than exists today (Jacobson et al. 44

2006). The gravitational field is commonly represented us- 45

ing a spherical harmonic expansion (Hubbard 1984), and 46

so far only the lowest zonal harmonics J2, J4, and J6 have 47

been measured. These reflect the long-wavelength gravita- 48

tional perturbations associated primarily with the planet’s 49

rotational bulge, and provide essentially no information on 50

interior flows. Cassini’s proximal orbits will allow the mea- 51

surement of the gravity field at least up to J10, including the 52

possibility of measuring the odd gravity harmonics for the 53

first time (Kaspi 2013). 54

If the strong cloud-level winds extend sufficiently deep 55

26


The role of Lorentz forces in defeating zonal winds and therebyenabling dipole-dominated magnetic fields also offers an explana-tion why larger magnetic Prandtl numbers help. The reason likelyis that larger Pm values lead to stronger magnetic fields and thusstronger Lorentz forces. We can also now interpret the highly

time-dependent solutions with intermediate mean dipolarities.Here, the balance seems to be undecided (Fig. 4). Stronger Lorentzforces successfully suppress the zonal winds at times but never en-ough to establish the solution on the highly dipolar more stablebranch. At other times, Reynolds stresses succeed in driving stron-ger zonal flows that mostly create a weaker multipolar magneticfield.

To further test the theory that the zonal flows are decisive forthe field geometry we ran a few E = 10!4 cases with a no-slip outerboundary condition that largely prevents zonal flows from devel-oping. The results are mixed and not entirely conclusive, whichmay have to do with the fact that other flow components are alsoaffected by this change in boundary conditions. At vm = 95%, Nq = 0and Ra/Racr = 23.0, the no-slip boundary conditions indeed pro-mote a dipole-dominated solution with weak zonal flows wherewe only find multipolar solutions with strong zonal flows for afree-slip outer boundary condition (compare cases 3 and 4). Thesame positive effect was found for vm = 90%, Nq = 0 and Ra/Racr = 11.5 (cases 7 and 8). At vm = 90%, Nq = 1 and Ra/Racr = 5.2,however, we find bistable cases for both type of boundary condi-tions (cases 22d/m and 23d/m). In the no-slip case, both the di-pole-dominated and the multipolar solution have weak zonalflows. Free-slip outer boundary condition promotes dipolarity,but it is not a necessary condition to find this feature. Note thatsuch a bistable case for no-slip conditions has already been re-ported by Christensen and Aubert (2006).

Nρ=0 Nρ=1 Nρ=3 Nρ=4 Nρ=5

–0.031

–0.021

–0.010

0

+0.010

+0.021

+0.031

Fig. 7. Azimuthal averages of the zonal component of the flow. Each column of three plots has a different Nq, namely 0, 1, 3, 4 and 5 from left to right. In the bottom andmiddle rows, the poloidal field lines are plotted on top of the zonal velocity contours in units of Rossby number Ro = u/(Xro). The dotted line in the middle and bottom rowscorresponds to rm = 95% and rm = 80%, respectively. The top row shows the corresponding hydrodynamical solutions.

Fig. 8. Radial profile of magnetic energy flux (r2 Emag) averaged over time. Thedashed black line is the location of vm = 80%. These results correspond to the redtriangles and red dashed line from Fig. 5. The poloidal (dashed lines) and toroidal(dot-dashed lines) components are also shown for Nq = 5 and Nq = 0, with thecorresponding colours. The magnetic energy fluxes are normalized by theirmaximum values.

30 L.D.V. Duarte et al. / Physics of the Earth and Planetary Interiors 222 (2013) 22–34

Fig. 11.18.— Anelastic 3D simulations of convection in a giant planet interior including coupling to the magnetic field,from Duarte et al. (2013). Each image shows the zonal-mean structure of a distinct simulation; the color scale shows thezonal-mean zonal wind (expressed as a Rossby number) and the contours show poloidal magnetic field. Nρ denotes thenumber of density scale heights spanned from the outer to the inner boundary; the left column (Nρ = 0) denotes Boussinesqsimulations, while the right column (Nρ = 5) presents simulations with five density scale heights (inner density 148 timesthe outer density). The top row represent hydrodynamic models (no MHD effects). The middle and bottom rows representMHD simulations, with electrically insulating outer regions and electrically conducting inner regions. The transitionoccurs at a fractional radius of 0.95 and 0.8 for simulations in the middle and bottom rows, respectively. Robust equatorialsuperrotation can be seen in all models, which is confined to the electrically insulating region when MHD is used. Theinclusion of compressibility and magnetic effects suppress the formation of zonal jets at mid-to-high latitudes.

into the planet’s interior, then the density perturbations as-1

sociated with the jets will induce gravitational perturba-2

tions that are measurable. Because the equatorial bulge is3

an extremely broad-scale (long-wavelength) feature, it af-4

fects primarily the lowest harmonics, and contributes only5

a much smaller signal at the higher harmonics. In con-6

trast, the meridional scale associated with the zonal jets7

is smaller, and thus—if the jets extend sufficiently deep—8

they will induce substantial gravity signal at small merid-9

ional scales, corresponding to higher harmonics. This was10

first noted by Hubbard (1999), who used potential theory11

to show that if differential rotation on Jupiter penetrates the12

depth of the planet, then the high-order gravity moments13

will be dominated by the dynamical contribution rather than14

the contribution from rotational flattening. This study in-15

spired the Juno mission gravity experiment of Jupiter, and16

in turn motivated the Cassini Grand Finale gravity exper- 1

iment on Saturn. This potential-theory approach has re- 2

cently been further developed using more accurate concen- 3

tric Maclaurin-based interior models (Hubbard 2012; Kong 4

et al. 2012; Hubbard 2013; Hubbard et al. 2014; Kaspi et al. 5

2016). 6

A difficulty with these potential-theory approaches, 7

however, is that they are limited to fully barotropic systems 8

satisfying the Taylor-Proudman theorem (Equation 11.6), 9

where the flows are constant along cylinders. Therefore, 10

this approach cannot explore the possible consequences for 11

the gravity field if the flows penetrate only partway into the 12

interior and die off below some critical depth. 13

A second approach that allows an evaluation of winds 14

varying on cylinders is to use thermal-wind balance models 15

(Kaspi et al. 2010; Kaspi 2013; Kaspi et al. 2013; Liu et al. 16

27


2013). Given some assumed structure of the zonal winds,1

the thermal-wind relation (Equation 11.5) can be used to2

calculate the dynamically induced density gradients in the3

interior. These density perturbations in turn cause pertur-4

bations to the gravity field. The dynamical contributions to5

the gravity harmonics are defined as (Kaspi et al. 2010)6

∆Jdynn = − (Man)

−1∫Pnρ

′rnd3r, (11.7)

where ρ′ is the deviation of the density caused by dynam-7

ics (i.e., the deviation from some static density distribution,8

ρstatic, that would exist in the absence of dynamics), Pn9

is the n-th Legendre polynomial, M is the planetary mass10

and a is the mean planetary radius. Kaspi et al. (2016)11

showed that in the barotropic limit the thermal-wind and12

potential-theory approaches give very similar results. How-13

ever, the thermal-wind models have typically been limited14

to spherical symmetry, resulting in inability to calculate the15

static (solid-body) gravity spectrum and neglecting the ef-16

fect of the oblateness of the planet on the dynamic grav-17

ity moments. Zhang et al. (2015) suggested that such ef-18

fects, namely the self gravity due to the dynamical varia-19

tion itself g(r, θ), can be important, and Cao and Steven-20

son (2015) suggested that the effect of the oblateness on the21

background mean state can be important for the gravity mo-22

ments. However, solving self-consistently for the full oblate23

system, Galanti et al. (2017) have shown that these oblate-24

ness effects give a very small contribution to the gravity25

moments, meaning that the spherical thermal wind captures26

well the leading order balance, and therefore can be used27

for calculating the gravity moments.28

Figure 11.19 shows the gravity field resulting from a29

model using the thermal-wind approach, where the grav-30

ity harmonics are shown as a function of the depth that the31

cloud-level winds extend beneath the cloud-level. It shows32

that beyond n = 10 the gravity signal induced by the wind33

structure becomes larger than the solid-body (static) gravity34

harmonics.35

Because Jupiter and Saturn are gaseous, aside from the36

cloud-level winds there is no apparent asymmetry between37

the northern and southern hemispheres. Therefore, the38

gravitational moments resulting from the shape and verti-39

cal structure of the planets have identically zero odd mo-40

ments (Hubbard 1984, 1999). Unlike the even gravity mo-41

ments that have a contribution both from the static den-42

sity distribution and the dynamics, the odd moments are43

caused purely by dynamics. Thus, any odd signal de-44

tected (J3, J5, J7, ...) will be a sign of a dynamical con-45

tribution to the gravity. Indeed, the cloud-level winds are46

not precisely symmetrical around the equator, and if these47

hemispheric differences extend into the interior, they could48

produce measurable odd harmonics (Figure 11.19)(Kaspi49

2013). Using also the thermal-wind approach, Liu et al.50

(2013) calculated the penetration depth of the winds on51

Jupiter with the additional assumption that the entropy gra-52

dient in the direction of the spin axis must be zero. This53

requirement sets the penetration depth of the winds, and54

they have also found that such a wind structure (which ex- 1

tends deep throughout the molecular envelope) should be 2

detectable by Juno and Cassini (Liu et al. 2013, 2014). 3

The main challenge of interpreting the gravity data will 4

be to invert the gravity measurements into meaningful wind 5

fields. Until recently all studies have been only in the direc- 6

tion of forward modeling; thus, given a hypothetical wind 7

structure (based on the observed surface winds and some 8

assumption regarding the penetration depth) the gravity mo- 9

ments are calculated via the effect of the winds on the den- 10

sity structure (e.g., Hubbard 1999; Kaspi et al. 2010; Liu 11

et al. 2013; Kong et al. 2012). However, in order to analyze 12

the gravity field that will be detected by Juno and Cassini 13

the inverse problem needs to be solved—calculating the 14

zonal wind profile given the gravity field. This causes a dif- 15

ficulty since a gravity field is not necessarily invertible and 16

a given gravity field might not have a unique corresponding 17

wind structure. Galanti and Kaspi (2016, 2017) propose to 18

address this using an adjoint based inverse method that will 19

allow the investigation of the giant planet dynamics using 20

the observed measured gravity field. This method has been 21

used extensively in the study of oceanic and atmospheric 22

fluid dynamics (e.g., Tziperman and Thacker 1989; Moore 23

et al. 2011). This method can be applied to any forward 24

relation between the gravity and the wind structure (e.g., 25

thermal-wind, potential-theory, etc.), and to 3D wind struc- 26

0 5 10 15 20

−10

−8

−6

−4

−2

Zonal harmonic degree n

log(|∆

Jn|)

Solid BodyH=10000H = 3000H = 1000H = 300

Fig. 11.19.— The gravity harmonics of Saturn correspond-ing to the static, rotationally flattened contribution (squares)and the contribution from dynamics (circles) calculated us-ing the thermal-wind model of Kaspi (2013). The dy-namical contributions to the gravity harmonics (∆Jn) areshown for four different assumptions about the character-istic length scale, H , over which the jets decay with depthinto the interior: H = 300 km (purple), H = 1000 km (or-ange), H = 3000 km (blue) and H = 10000 km (maroon).Filled (open) symbols indicate positive (negative) zonal har-monics. Black plus signs show the observed values of Jn,and the dashed line is the expected detectability limit of theCassini proximal orbits. The static values (Hubbard 1999)have only even components (odd harmonics are identicallyzero). From Kaspi (2013).

28

Showman et al.: The Global Atmospheric Circulation of Saturn 11.5 CONCLUSIONS

ture which give the full 3D gravity fields including contri-1

butions from longitudinal variations in the wind structure2

and meridional winds (Parisi et al. 2016).3

The coincidental timing of the Cassini proximal orbits4

with the Juno gravity experiment will provide an oppor-5

tunity to simultaneously probe the deep dynamics of both6

Saturn and Jupiter. Comparing the atmospheric dynamics7

on the two planets shows that the equatorial jet is much8

stronger and wider on Saturn, extending to latitude 30,9

with fewer high-latitude jets—but the jets are much stronger10

on Saturn reaching about 400 m s−1 depending on the ref-11

erence frame chosen (see section 11.2). The fact that the12

jets are stronger on Saturn means that the induced gravity13

anomalies will be generally larger as well. However, as Sat-14

urn is more oblate than Jupiter (Jupiter has an oblateness of15

6.5%), the static gravity harmonics due to the non-dynamic16

density distribution will likewise be larger than on Jupiter.17

These two factors imply that the ratio between the static and18

the dynamic gravity harmonics are roughly similar on both19

planets (Kaspi 2013).20

Despite the fact that no spacecraft will be visiting Uranus21

and Neptune in the near future, the strong and broad wind22

structure and smaller mass on these planets allows the use23

of these same techniques to infer the depth of the winds us-24

ing gravity moments that have already been measured. In25

particular, the speed and meridional breadth of the jets on26

Uranus and Neptune allow the possibility that—unlike the27

case of Jupiter and Saturn—even the low harmonics such28

as J4 can be significantly affected by dynamics. Using29

the gravity data then available, Hubbard et al. (1991) first30

showed that the fast winds must be confined to the out-31

ermost few % of these planets’ masses. Exploiting recent32

updates on the gravity harmonic J4 and its uncertainty (Ja-33

cobson 2007, 2009), Kaspi et al. (2013) were able to re-34

fine this constraint considerably, showing that the observed35

flows must be constrained to the outermost 1000 km of36

the planetary radius—corresponding to no more than 0.15%37

and 0.2% of the mass of Uranus and Neptune, respectively.38

Thus, the fast jets on Uranus and Neptune are relatively39

shallow.40

In summary, within the next few years, using the fact41

that if deep flows exist on giant planets they will induce a42

measurable gravity signal, we will finally address one of the43

longest-standing debates in planetary science regarding the44

depth of the observed zonal flows on all four giant planets45

(Vasavada and Showman 2005). Understanding if the flows46

are deep or shallow will allow tests between the theories of47

jet formation and energetics as discussed in Section 11.4.1–48

11.4.2. The upcoming few years therefore provide an excit-49

ing opportunity in the study of the atmospheric dynamics of50

Saturn and the other giant planets.51

11.5. CONCLUSIONS52

Saturn’s atmosphere exhibits a wealth of interacting dy-53

namical processes that present an interesting contrast with54

Jupiter. The dynamics are dominated by fast zonal jets55

whose meridional width, latitudinal positions, and speeds 1

have remained relatively constant over many decades. Sat- 2

urn’s clouds are organized into zonal bands that are modu- 3

lated by (and perhaps affect) the zonal jets, but the relation- 4

ship of the cloud bands to the jets themselves differs from 5

that on Jupiter and remains poorly understood. Observa- 6

tions indicate that eddies transport momentum up-gradient 7

into the cores of the zonal jets at cloud level, thereby main- 8

taining the jets. This points toward the importance of cloud 9

level processes in jet dynamics, but the exact processes 10

that power these jet-pumping eddies—baroclinic instability, 11

moist convection, or interaction of dry convection with the 12

stratified atmosphere—remain poorly understood. Light- 13

ning and storm activity—including small storms as well as 14

the Great White Spot of 2010-2011—provide constraints on 15

the thermal structure and vertical motion below the clouds. 16

There also exist a variety of vortices, waves, and other local 17

features at cloud level, with lifetimes of months to decades, 18

whose relationship to the jet dynamics remains enigmatic. 19

Notable features include the string of pearls (Sayanagi et al. 20

2014), the Ribbon, the polar hexagon (Baines et al. 2009), 21

and a significant population of small vortices that tend to 22

cluster predominantly at the latitudes of the westward jets 23

(e.g., Vasavada et al. 2006; Choi et al. 2009). Interestingly, 24

at and above the cloud level, the jets exhibit reversals in the 25

meridional gradient of potential vorticity, and the relative 26

stability of the jets despite these reversals has important im- 27

plications for the flow below the clouds. 28

A variety of observations place constraints on the cir- 29

culation in the upper troposphere and stratosphere, which 30

has important analogies to the stratospheric circulation on 31

the other giant planets as well as Earth. Saturn’s obliquity 32

of 27 causes seasonal temperature changes in the strato- 33

sphere, but there also exist a wealth of temperature vari- 34

ations at a variety of length and timescales that are likely 35

dynamical in origin. The temperature patterns above the 36

clouds suggest, through thermal-wind balance, that most 37

of the zonal jets decay with altitude in the upper tropo- 38

sphere. These temperature patterns, along with the am- 39

monia abundance near the clouds, are best explained by 40

a meridional circulation comprising ascent in the anticy- 41

clonic regions, producing the cold temperatures and high 42

ammonia abundances, and descent in the cyclonic regions, 43

producing the warm temperatures and low ammonia abun- 44

dances. Interestingly, such a circulation is thermally indi- 45

rect and is likely driven by absorption of waves propagating 46

from below. This is directly analogous to the wave-driven 47

circulations that exist in Earth’s stratosphere and that have 48

been inferred in the stratospheres of Jupiter, Uranus, and 49

Neptune. The source of the waves and the specific details 50

of this circulation in the Saturn context remain poorly un- 51

derstood. Additionally, stratospheric thermal perturbations 52

have been observed at low latitudes that suggest an oscil- 53

lation of equatorial winds and temperatures with a period 54

close to 15 years, which seems to be analogous to the terres- 55

trial Quasi-Biennial Oscillation, which is driven by a pop- 56

ulation of upward propagating waves generated by convec- 57

29


tion and other processes in the troposphere.1

Dynamical models do not yet come close to explain-2

ing this wealth of phenomena; nevertheless, significant3

progress in understanding the dynamics of zonal jets and4

local features has been made over the past ∼15 years. Over5

the past decade, highly idealized models have greatly im-6

proved our understanding of the processes that cause the7

flow to self-organize into zonal jets. More realistic three-8

dimensional models of the weather-layer flow are now ca-9

pable of explaining the equatorial superrotation and mul-10

tiple high-latitude jets on Jupiter and Saturn, although the11

superrotation in these models tends to be narrower and12

slower than that on Saturn. Models of convection through-13

out the planetary interior now include the multi-order-of-14

magnitude variation of density with radius and are like-15

wise starting to incorporate the coupling to magnetic fields,16

including the transition from electrically insulating in the17

molecular envelope to electrically conducting in the deeper18

interior. These models are now elucidating how the com-19

pressibility and coupling to magnetic fields influences the20

zonal jets and other aspects of the dynamics. These models21

show that convection in the interior can naturally produce a22

Saturn-like equatorial jet, but the coupling to magnetic ef-23

fects tends to suppress any higher latitude jets. An attractive24

hybrid scenario, which combines the strengths of the shal-25

low and deep models, might suggest that convection in the26

molecular envelope outside some tangent cylinder causes27

the broad equatorial jet, but that the mid-to-high-latitude28

jets result from atmospheric processes such as baroclinic in-29

stabilities or moist convection in the cloud layer (Vasavada30

and Showman 2005).31

Future progress in modeling and theory will occur on32

several fronts. Investigations of atmospheric, weather-layer33

processes and of deep, convective dynamics are usually34

conducted separately, using distinct classes of dynamical35

model that solve distinct equation sets and use distinct36

numerical codes. The distinction between “shallow” and37

“deep” processes is artificial, however, and in reality atmo-38

spheric and interior processes may interact in a variety of39

ways not included in current models. A new generation of40

GCMs that spans both atmosphere and interior processes is41

needed to explore this coupling, and this will be a major42

area of progress over the next decade. Global atmospheric43

models of jet formation do not yet include clouds, and yet44

clouds represent a significant fraction of the observational45

database for both Jupiter and Saturn, as well as influencing46

the dynamics through their mass loading, interaction with47

radiation, and latent heating and cooling due to their forma-48

tion and sublimation. Thus, significant progress is possible49

by including clouds in models, both in widening the range50

of observations against which the models can be tested, and51

by illuminating the extent to which clouds influence the at-52

mospheric circulation. Inclusion of realistic radiative trans-53

fer and chemistry into stratospheric GCMs will be a growth54

area, and will help shed light on the implications of tracers55

such as ethane and acetylene for the dynamics. The nature56

of the eddies or waves that apparently cause a deceleration57

of the upper tropospheric and lower stratospheric zonal jets, 1

and that cause the SSAO, are poorly understood. These and 2

many related topics concerning the zonal jets are amenable 3

to continued idealized theory and modeling. 4

Future progress will also depend crucially on improved 5

observations. Due to the Cassini mission, Saturn is perhaps 6

now the best-observed giant planet—outpacing Jupiter— 7

but many of the Cassini observations have yet to be ana- 8

lyzed, and significant progress is possible with the existing 9

data. For all four giant planets, improvements over the past 10

decade in groundbased astronomical facilities have led to a 11

renaissance in observations of cloud features and upper tro- 12

pospheric temperature structure from the ground—by pro- 13

fessional and amateur astronomers alike. These ground- 14

based observations will continue to play a crucial role in 15

filling in the temporal gaps between higher-quality, but 16

episodic, coverage from spacecraft missions. Moreover, 17

over the next several years, the Juno mission to Jupiter and 18

the Cassini Grand Finale at Saturn will provide gravity mea- 19

surements that promise to constrain the depth to which the 20

zonal jets extend below the visible cloud decks. Close-in 21

microwave and IR sounding of Jupiter by Juno, as well 22

as close-in sensing of Saturn with Cassini’s suite of in- 23

struments during the proximal orbits, may produce qual- 24

itatively new constraints on the cloud-level dynamics of 25

both planets. The Juno microwave radiometer will mea- 26

sure the global water abundance and the latitudinal variation 27

of water and ammonia below cloud base. Future missions 28

to the giant planets include the NASA Europa Multiple 29

Flyby Mission and the European Jupiter Icy Moon Explorer 30

(JUICE) mission, which will obtain observations of Jupiter 31

in addition to their prime targets of icy satellites starting 32

around 2030. Prospects for giant-planet missions beyond 33

the 2030s are currently nebulous, but there is strong sci- 34

entific merit—and interest—in missions to Uranus and/or 35

Neptune, as well as an entry probe mission to Saturn. This 36

activity will not only revolutionize our understanding of the 37

grandest planets in our solar system, but will also provide 38

a foundation for understanding the many brown dwarfs and 39

extrasolar giant planets that are being discovered and char- 40

acterized light years away. 41

Acknowledgments. We thank M. Flasar and an anony- 42

mous reviewer for helpful comments. APS acknowledges 43

support from the NASA Planetary Atmosphere program. 44

YK acknowledges support from the Israeli Ministry of Sci- 45

ence and the Minerva Foundation. 46

47

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