## Andrew P. Ingersoll

Print publication date: 2013

Print ISBN-13: 9780691145044

Published to Princeton Scholarship Online: October 2017

DOI: 10.23943/princeton/9780691145044.001.0001

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# Jupiter Winds and Weather

Chapter:
(p.162) 8 Jupiter Winds and Weather
Source:
Planetary Climates
Publisher:
Princeton University Press
DOI:10.23943/princeton/9780691145044.003.0008

# Abstract and Keywords

This chapter examines the effect of winds on Jupiter's weather. The Great Red Spot is an atmospheric structure—a storm—that is free to move about under the laws of fluid dynamics. On Earth, these laws lead to turbulence, chaos, and limited predictability. By comparison, the Red Spot is well behaved. It stays in one latitude band, rolling like a ball bearing between two conveyor belts—a westward current to the north and an eastward current to the south. All the large-scale features are remarkably constant. Atmospheric scientists during the Voyager encounter were surprised by the areas outside the Red Spot and the three white ovals—formerly featureless areas that had become turbulent convective regions. The chapter first provides an overview of long-range weather forecasting on Jupiter before discussing the dynamics of rotating fluids, momentum transfer by eddies, stability of zonal jets, geostrophic balance, vorticity, and abyssal weather.

# 8.1 Long-Range Forecasting

A PERSONAL ANECDOTE ILLUSTRATES THE AMAZING properties of Jupiter’s weather. I was a member of the imaging team that had to prepare for the encounter of Voyager 1 with Jupiter on March 5, 1979. We had to decide where to point the camera during closest approach in order to photograph the most interesting features at the highest possible resolution. At closest approach, the field of view of the camera would be much too small to photograph the whole planet, so we had to choose the interesting features and predict where they would be. The engineers wanted our predictions four weeks in advance, in order to translate our requests into language that the spacecraft could understand and not disrupt the delicate maneuvers that would slingshot the spacecraft to Saturn. In other words, we had to make a four-week weather forecast of the storms on Jupiter.

A four-week forecast of the storms on Earth is not feasible now and may be theoretically impossible. The traveling storms don’t last that long, and they behave erratically during their short lifetimes. The stationary highs and lows last longer, but they are locked to the (p.163) continents and oceans. Jupiter doesn’t have continents and oceans—only a massive atmosphere down to its center. However, Earth-based observers had been watching the Great Red Spot ever since Robert Hooke discovered it in 1664. Telescopes had been improving when Hooke made his observations, and it is likely that the Red Spot had been in existence long before he discovered it.

Since there are no solid surfaces to organize the flow, the Red Spot is an atmospheric structure—a storm— that is free to move about under the laws of fluid dynamics. Those laws, as we know them on Earth, lead to turbulence, chaos, and limited predictability. By comparison, the Red Spot is well behaved. It stays in one latitude band, rolling like a ball bearing between two conveyor belts—a westward current to the north and an eastward current to the south. All the large-scale features are remarkably constant (fig. 8.1). Consistent with the rolling motion, small spots inside the Red Spot move around counterclockwise (fig. 7.5). The Red Spot itself usually moves westward relative to the magnetic field, which we assume is tied to the interior of the planet, but sometimes it slows down and moves eastward. These changes of velocity take place over periods of years, and do not prevent forecasts over a four-week period. The Voyager imaging team eventually used junior high school mathematics—a straight line on graph paper—to extrapolate the positions and make a beautiful mosaic of high-resolution images that covered the Red Spot from end to end and top to bottom.

The big surprise for atmospheric scientists during the Voyager encounter was not our success in predicting the (p.164)

Figure 8.1. Voyager image of Jupiter in 1979 compared to a Cassini image taken in 2000. The jet streams blow east-west and are strongest at the edges of the light and dark bands. The colors of the bands are remarkably constant from 1979 to 2000. Even when the colors do change, the latitudes and speeds of the jets remain constant.

(Sources: http://photojournal.jpl.nasa.gov/, PIA00343 and http://photojournal.jpl.nasa.gov/, PIA04866)

locations of the Red Spot and other large-scale features. We had been following them for years using Earth-based telescopes, and we knew how predictable they were. For instance, the counterclockwise band just to the south of the Red Spot’s band had split into three pieces over a two-year period in 1938–39. The pieces consolidated into three white ovals, each rotating counterclockwise, and the spaces between filled with featureless clouds—or so we thought. The ovals were still there in 1979, but what surprised us was the enormous activity within the featureless areas, the areas outside the Red Spot and the three white (p.165) ovals. The activity had been difficult to see because it involved small-scale features that were below the resolution of Earth-based telescopes. As Voyager closed in, its camera saw clouds popping up, churning around, and mixing on time scales of hours. In our eyes, the formerly featureless areas had become turbulent convective regions. The big surprise was how the large ovals could last for decades or centuries in the midst of all this chaos.

After the Voyager encounters, many of us believed that there was some special property of Jupiter’s atmosphere that allowed large vortices to exist for decades or hundreds of years. Maybe it had to do with the winds below the clouds, which we couldn’t see. Or maybe large vortices required special initial conditions—unlikely events that created them. In my first attempts at modeling the Red Spot, I carefully chose its initial shape and winds to match the observations.85 But soon it became clear that we didn’t have to be so careful. Long-lived vortices were easy to make—they formed spontaneously. Different people with different assumptions were all getting long-lived vortices in their numerical models.86,87,88 One could start off with an unstable shear flow and a small perturbation. The perturbation amplitude would grow with time, and the shear flow would spin off numerous waves and eddies. The eddies would start merging and soon there was only one eddy left, a giant oval like the Great Red Spot that lasted indefinitely. Since the ovals existed in a computer, one could experiment with them. For instance, the ovals tended to be elliptical with the long axis east-west, just like the ovals on Jupiter, but one could (p.166) pick them up and turn them north-south—crosswise to the flow. The oval would shake violently and then regain its preferred east-west orientation. Or one could place two ovals at slightly different latitudes so they were moving at slightly different speeds, with the fast one catching up to the slow one. The collision usually led to a merger, although the resultant vortex had to shed some material before settling down. In other words, long-lived vortices form spontaneously in unstable shear flows, and they are stable once they have formed. The Jovian ovals may need a little energy to counteract friction, but they seem to acquire it by merging with smaller vortices.

These models were much simpler than the models used in numerical weather forecasting, which have sunlight and infrared radiation, continents and oceans, clouds, and precipitation. Maybe the Earth is too complicated to have long-lived storms—there are too many competing processes. In particular, the Earth is stormier than Jupiter. The large storms, like the winter storms at midlatitude, draw their energy from the equator-to-pole temperature gradient, which represents a source of potential energy. The winter storms are constantly forming and dying and eclipsing older storms, and the sunlight falling on the equator is constantly renewing the potential energy. This is different from the ovals in the Jupiter simulations, which have no competition once they have formed. In fact, there are analytic models from before the computer age that have stable ovals in shear flows.89 These pencil-and-paper solutions to horizontal flow without viscosity were once viewed as a curiosity. Now (p.167) they are used to describe nature on a grand scale. The message is that maybe Earth is special, and that long-lived vortices are the rule and not the exception.

# 8.2 Rotating Fluids

Earth’s rotation is what makes hurricanes spin counter-clockwise in the northern hemisphere and clockwise in the southern hemisphere. It is what makes the jet streams flow west to east and not from equator to pole or from day to night. Rotation makes the planet oblate, and it gives rise to the Coriolis force, which acts on objects that are moving relative to the rotating system. The giant planets are rapid rotators, so rotation is important in their atmospheric motions. Moreover, the colored clouds make it easy to track the motions. Because they are so photogenic, the giant planets are often regarded as laboratories for studying the dynamics of rotating fluids.90

Jupiter and Saturn are noticeably oblate (box 8.1). At Jupiter’s equator, the distance from the center of the planet to the 1-bar pressure level is 71,492 km, but at the pole the distance is 66,854 km. The oblateness, or flattening (difference between equatorial and polar radii divided by the equatorial radius) is 6.5% for Jupiter, 9.8% for Saturn, and 0.34% for Earth. Oblateness arises from the planet’s rotation and is proportional to the ratio of the centrifugal force to gravity. The centrifugal force is trying to throw things away from the axis of rotation, and gravity is trying to pull things back into a spherical shape. Since the centrifugal force (actually force per unit

mass) at the equator is RΩ‎2, where R is the equatorial radius and Ω‎ is the angular velocity, the oblateness is of order RΩ‎2/g.

The giant planets are more oblate than Earth because they are large and they rotate faster. The angular velocity of rotation is 2p divided by the length of the day, which for Jupiter is 9 h 55 m 29 s. Since Jupiter is a fluid planet with no solid surface, the period is determined from the daily wobble of the magnetic field. The field is fixed relative to the planet’s interior, but it is tilted by 10° with respect to the rotation axis, so it appears to wobble when viewed from a nonrotating reference frame. Saturn’s magnetic field has no measureable tilt, so the length of day is less certain. Atmospheric periods, which are based on the cloud motions at specific latitudes, range from 10 h 11 m to 10 h 41 m. Saturn’s rotation period is probably within this range. Saturn’s oblateness is larger than Jupiter’s mainly because its gravitational acceleration g is smaller, which follows from its smaller mass.

The centrifugal force is a static force in the rotating system and is indistinguishable from gravity for stationary (p.170) objects. The surface of a lake and a weight hanging from a string feel the resultant of two forces—the centrifugal force and the gravitational attraction of the planet’s mass. Mean sea level reflects this balance too. The reason we all don’t slide to the equator under the action of the centrifugal force is that we already did—the entire Earth has slid. We don’t worry about the centrifugal force because it is incorporated into gravity and into our definition of a level surface like mean sea level. The Coriolis force, which acts on mass that is moving relative to the rotating reference frame, upsets this balance and is therefore a major factor in the dynamics of rotating fluids (box 8.2).

Imagine a ball tossed back and forth on a merry-go-round that is turning counterclockwise like the Earth viewed from the North Pole. When the ball is in the air it travels in a straight line, but the merry-go-round rotates below it. As viewed from the rotating system, the trajectory appears to curve to the right, and we would say there was a force to the right of the velocity. This is the usual explanation for the Coriolis force, but it is not quite correct. The ball is actually feeling two forces when viewed in the rotating system. One is the Coriolis force, which acts to the right of the velocity, and the other is the centrifugal force, which acts radially outward from the axis of rotation (box 8.3).

To balance the Coriolis force, a horizontal air current blowing in a straight line in the northern hemisphere must have another force pushing to the left. In a planetary atmosphere, this other force is pressure. The high pressure is on the right of the current, and the

low pressure is on the left, so the net force—the pressure gradient force—is to the left. The balance is called geostrophic balance (box 8.4). Except at the equator, large-scale, slowly rotating jets and vortices are always in approximate geostrophic balance. Even if the current is

not exactly in a straight line, the high pressure is on the right. This is why the flow is counterclockwise around a low-pressure center in the northern hemisphere and is clockwise around a high-pressure center. The directions are reversed in the southern hemisphere.

Why are Coriolis forces so important for the weather of rotating planets and so unimportant in daily life? The answer has to do with the time scale of events in our daily lives. A batter hitting a 95-mile-per-hour fast-ball has 0.43 seconds from the time the ball leaves the pitcher’s hand to the time the ball crosses the plate. During that time, the Earth has rotated 0.0017 degrees. The line between the pitcher and the catcher has rotated by (p.176) the same amount—the catcher moving to the left as seen from the pitcher’s mound, assuming the game is being played at midlatitudes in the northern hemisphere. The ball travels in a straight line relative to a nonrotating reference frame, but it appears to curve to the right in the northern hemisphere. The result is that the ball will miss its target by 0.011 of an inch. Contrast this small effect with that on a storm system that rotates once in several days around its axis, or a current that flows for days on end in a straight line relative to the surface of a rotating planet. Without the pressure gradient force pushing to the left, the deflection of the wind by the Coriolis force would be huge.

The Rossby number U/(fLh) is an inverse measure of the importance of rotation. U/Lh is the rate at which a vortex moves its own diameter, or it is the velocity of the ball divided by the distance to the plate. If that rate is slow compared to the rate at which the planet turns, then the Rossby number is small and rotation is dominant. For the pitcher and catcher, the Rossby number is 104 and rotation is negligible. For a storm of diameter 2000 km and wind speeds of 10 m s−1, the Rossby number is 0.05. Thus large-scale, slow-moving flows are dominated by rotation. Since U and Lh are vague terms (“typical” velocities and length scales), there is no unique definition of the Rossby number. Nevertheless, it provides order-of-magnitude estimates of terms in the equations of motion.

Geostrophic balance implies that the high pressure is to the right of the flow in the northern hemisphere (p.177) and to the left of the flow in the southern hemisphere. Equivalently, one can say that the height of a constant pressure surface is greater to the right of the flow in the northern hemisphere and greater to the left of the flow in the southern hemisphere. This is because pressure increases with depth, so greater height means greater pressure underneath (box 8.5). Examples include the midlatitude jet streams on Earth, which blow generally from west to east. The height of the 500-mbar surface is 5800 m near the equator and 5100 m at the pole. The eastward winds in between are in approximate geostrophic balance.

Geostrophic balance also explains why the speed of the jet stream increases with altitude from Earth’s surface up to 10 km altitude. It is because the equator is warmer than the poles, and the air columns at the equator are taller than those at the poles. As a result, the height difference between the equator and poles is more pronounced at high altitudes than at low altitudes. The east-ward wind is proportional to the height difference, so the eastward wind increases with height. This increase of eastward zonal wind with altitude when temperature decreases toward the pole is called a thermal wind (box 8.6). A warm-core vortex like a hurricane is another example. Standing at the center of a northern-hemisphere hurricane looking outward is like standing at the equator looking toward the pole. In both cases the warm air is at your back. The warm-core vortex becomes more clock-wise with altitude, which is like the eastward zonal wind increasing with altitude.

In the southern hemisphere the eastward wind also increases with altitude and the temperature decreases toward the pole, but here the temperature is increasing with latitude and the Coriolis force is to the left of the wind. The net result is the same: There is an eastward jet stream in each hemisphere whose speed increases with altitude, and both are in approximate geostrophic balance (box 8.6) with temperature greater at the equator and less at the pole. Similarly, hurricanes in the southern hemisphere become more counterclockwise with altitude.

(p.181) Vorticity is a measure of spin, which is ubiquitous in rotating fluids (box 8.7). The sign of vorticity follows a right-hand rule, in which counterclockwise rotation is defined as positive and clockwise rotation as negative. For a patch of fluid rotating counterclockwise as if it were a solid body, vorticity is twice the angular velocity. For an eastward zonal flow u that depends on the northward coordinate y, the vorticity is −du/dy. Cyclonic vorticity is defined to be in the same direction as the vertical component of the planet’s rotation. On Earth a large-scale cyclone is counterclockwise in the northern hemisphere and clockwise in the southern hemisphere. An anticyclone is the opposite. For all planets, the north pole is defined by the orbital motion around the Sun and not by the spin. So we say that Venus spins backward. Nevertheless, on all planets, a cyclonic vortex is in the same direction as the vertical component of the planet’s rotation and is always a low-pressure center. Cyclonic and anticyclonic shear zones are bands of low and high pressure, respectively, that wrap around the planet at constant latitude.

The vorticity of the solid planet is 2Ω‎, and the vertical component is 2Ω‎ sin ϕ‎, where ϕ‎ is latitude. The quantity 2Ω‎ sin ϕ‎ is known either as the planetary vorticity (box 8.8) or as the Coriolis parameter (box 8.2), depending on the context, and is represented by the symbol f. Planetary vorticity is an important term in the expression for potential vorticity (box 8.8), which is conserved on fluid parcels as they move and evolve. The derivative of f with respect to the northward coordinate y is called β‎ and is equal to (2Ω‎/R) cos ϕ‎, where R is the planetary radius. β‎

is known as the planetary vorticity gradient, and it figures prominently in the theory of planetary waves and in the stability of zonal jets (box 8.9).

# 8.3 Order from Chaos

Perhaps we shouldn’t have been surprised when Voyager revealed the chaotic small-scale motions near the Red Spot and other long-lived ovals. Dynamical models of Jupiter’s atmosphere, based on the same principles that were used to build weather-forecast models for Earth, had not yet produced Red Spots in 1979, but they had demonstrated that ordered flow could evolve from chaotic motions. The process involves an inverse cascade of energy from small scales to large scales. The models considered a thin layer of fluid supported on the surface of a rotating planet.91,92 The Coriolis force and the pressure force defined the laws of motion for this simple system. The flow was forced by continuously adding small vortices—spinning parcels of fluid, which were chosen

at random to be clockwise or counterclockwise. The kinetic energy put in by the forcing was removed by friction, and the flow was allowed to evolve.

In these numerical experiments, one finds that the like-signed vortices merge with one another to make larger vortices. This merging continues until the vortices reach a characteristic size (U/b)1/2. Here U is the average speed of the flow, and β‎ is the planetary vorticity gradient (box 8.9). When the vortices get close to this size, they stop growing in the north-south direction. They continue to grow in the east-west direction, stretching out until they become bands that wrap around the planet on constant latitude circles. The remnants of the vortices are the shear zones pictured in figure 7.6. The currents around their peripheries have become the zonal jets. The shear zones with an eastward current on the south (p.187) side and a westward current on the north side, like the band that holds the Great Red Spot, have counterclockwise shear. These alternate in latitude with the clockwise shear zones, and their widths are of order (U/b)1/2. If one regards the random input of small vortices as chaos and the final pattern of wide bands as order, then order has evolved from chaos. Certainly the scale of the flow has increased, and the direction of the flow has acquired an east-west orientation.

The small-scale eddies constantly putting energy into the zonal jets is another example of a negative viscosity phenomenon, which we discussed in connection with the superrotation of the Venus atmosphere (box 3.14). It seems to occur on Jupiter as well. A fluid parcel moving from southwest to northeast (SW-NE) on a diagonal trajectory is carrying eastward momentum northward. If it returns on the same SW-NE diagonal trajectory, it is carrying westward momentum southward. To do so, it must have deposited eastward momentum during its northmost excursion and deposited westward momentum during its southmost excursion. In both cases, the product of the northward eddy wind v' and the east-ward eddy wind u' is positive. The average with respect to longitude is $u′ v′ ¯ ,$ and it is the northward transport of eastward momentum per unit mass (box 3.14). If $u′ v′ ¯$ is positive, and if there is an eastward jet to the north and a westward jet to the south, then the eddies are accelerating the jets. More generally, if $u′ v′ ¯$ and /dy have the same sign, then the eddies are putting energy into the jets. Here ū is the average eastward wind speed and (p.188)

Figure 8.2. Eddy momentum transport vs. latitude on Jupiter. The continuous curve (left scale) shows the shear in the zonal wind. Where the shear is positive, the speed of the eastward wind is increasing with latitude. The points (right scale) show the northward transport of eastward momentum by the eddies. The positive correlation between the points and the curve means that the eddies are tending to increase the energy of the zonal wind.

(Adapted from fig. 5 of Salyk et al. [2005])93

y is the northward coordinate. If the signs are opposite, then the eddies are taking energy out of the jets. One can examine the eddies and jets on Jupiter to see which way they are arranged.93 The result is shown in figure 8.2. The shear changes sign as one moves from one latitude to another, but when $u′ v′ ¯$ is positive, /dy is positive as well. This means that the eddies are putting energy into the jets and not the other way around.

The multiple jet streams demonstrate a striking difference between the weather patterns on Jupiter and (p.189) those on the Earth. On Earth there is one eastward jet in each hemisphere. On Jupiter there are five or six (fig. 7.6). What’s more, the jet streams are remarkably steady. They don’t meander north and south, as jet streams on Earth do. The Jovian jets stay at their chosen latitudes unless they are interrupted by a large oval like the Great Red Spot. Even these interruptions are very stable and predictable, since both the jets and the ovals are constant in time. Changes in the speeds and latitudes from the Voyager encounter in 1979 and the Cassini encounter in 2000 are almost undetectable (fig. 8.1).

The numerical models of jets forced by eddies lead to jets whose characteristic width is of order (U/b)1/2. Another way to look at this is through the stability of the jets—why don’t they break up into waves and eddies (box 8.9)? A zonal flow may be steady, but it is not necessarily stable. Steady means that the flow doesn’t vary with time. Stable means that the flow doesn’t vary even if you perturb it slightly. An example is a zonal flow with a small-amplitude, wavelike perturbation. Waves come in a variety of shapes and sizes (wavelengths). If none of the physically possible waves can grow, then the flow is stable. If any of the waves can grow, then the flow is unstable. Usually stability depends on the gradients of the flow and not on the flow itself. For an atmosphere on a rotating planet, the simplest criterion is that the flow is stable if β‎ − ūyy ≥ 0, where β‎ is the planetary vorticity gradient (box 8.9) and ūyy is the curvature of the velocity profile—the second derivative with respect to the (p.190) northward coordinate y. This is the so-called Rayleigh-Kuo stability criterion or sometimes the barotropic stability criterion (box 8.9). Since β‎ is positive at all latitudes, the stability criterion is most likely to be violated at the centers of the westward jets, where ūyy is large and positive. Comparison with observation is difficult because taking the second derivative of noisy data is fraught with uncertainty. But one can draw parabolas of the form u = u0 + ½ β‎y2 and plot them alongside the measured velocity profile u(y). The result is shown in figure 8.3.94 Many of the westward jets have curvature equal to that of the parabola, which means that their width in latitude is of order (U/β‎).1/2 This generally agrees with the numerical models, but some of the westward jets have more curvature than the parabola, indicating that the flow violates the barotropic stability criterion.

Violation of the stability criterion does not necessarily mean that the flow is unstable, but for many types of flow it does. The numerical models,90, 91, 92 in which small-scale eddies are constantly putting energy into the zonal jets, never violate the stability criterion, although they come close. The fact that the width of the jets is of order (U/β‎)1/2 means that β‎ is controlling the curvature of the jets, and this is consistent with the numerical models. But the fact that the curvature of the westward jets sometimes exceeds β‎ is inconsistent with the numerical models, and this is a mystery. This relation between the width of the jets and their speed generally agrees with observation, but it does not establish the value of either width or (p.191)

Figure 8.3. Application of the barotropic stability criterion to Jupiter’s zonal jets. The theorem says that the flow is stable if the curvature of the zonal velocity profile (second derivative with respect to the north-ward coordinate) is less than the planetary constant β‎. The points are measurements of the zonal velocity profile, and the parabolas have curvature equal to β‎. The jets generally follow the parabolas, indicating that the beta effect is relevant. But the fact that some of the points fit within the parabolas means that those jets violate the criterion and could be unstable.

(Adapted from fig. 8 of Li et al., 2004)94

(p.192) speed. Obviously, these are important quantities that a successful theory must explain.

# 8.4 Abyssal Weather

Although the thin-layer models are successful in producing jets from eddies, they tend to produce a westward jet at the equator. The winds in the models are opposite to the observed zonal winds on Jupiter and Saturn. A different class of models simulates motions in the planetary interior.95 These models had been developed for studying fluid motions in the interior of the Sun and in the core of the Earth. In these cases, the internal heat provides energy for the motions. Radiative heat loss in the planet’s atmosphere makes the warm temperatures of the planetary interior more buoyant, and this sets up convection currents that bring heat up to the surface. The rotation of the planet provides a strong constraint on the organization and direction of the motion. The interior winds organize themselves as cylinders concentric with the planet’s axis of rotation. Each cylinder has its own angular velocity. These models suggest that the zonal velocities we see in the atmosphere (fig. 7.6) are the surface manifestation of the rotation on cylinders in the interior.

Interestingly, in these models the outermost cylinders, which intersect the surface at low latitudes, rotate faster than the average. In other words, the deep models give eastward jets at the equator, as observed. The (p.193) Galileo probe entered the atmosphere at 7° north latitude. It was tracked down to the 20 bar level, which is only 0.2% down to the center of the planet starting at the tops of the clouds. But in that layer, about 150 km thick, the winds increased with depth from 100 m s−1 at cloud top to 180 m s−1 at 20 bars.96 This does not prove that the winds extend through the planet on cylinders, but it provides support for the theory that the winds are deep. At that one place on the planet, the winds below the clouds were greater than the winds within the clouds.

These successes of the interior models do not mean the issue is settled. First, on Uranus and Neptune, cloud features at the equator move in the retrograde direction, or slower than the planet as a whole. Any valid theory has to explain the winds on all four giant planets. Second, the parameters of the models affect the winds. Several modeling groups are trying to treat the eddies realistically, letting them draw energy from sunlight heating the equator and from internal heat rising from the interior. Other groups have been experimenting with the viscosity, letting it be a function of latitude to reflect the greater penetration depth of the cylinders at high latitude into the planetary interior.97 Changing these parameters affects the direction of the jets, and some thin-layer models give eastward jets at the equator.

The variation of the flow with depth is a major unknown, and it adds uncertainty to the models. A thinlayer model is a good approximation in a region of strong, stable stratification, where the lapse rate is much (p.194) less than the adiabatic lapse rate (box 3.2). The stable stratification inhibits vertical motion, and the flow is approximately horizontal. Stable stratification is likely within and above the clouds, but it becomes less likely below cloud base. With weak stratification, the vertical component of the flow can be as large as the horizontal component, and that invalidates the thin-layer models.

Currently there is a disconnect between the two kinds of models. One problem is lack of information, and the other is lack of resources. Although we have exquisite information about the flow at the tops of the clouds, we have very little information about the flow structure below. One can build models of the deep flow, but it is hard to test them. The resource problem is that no computer can handle thin-layer models and 3-D models simultaneously. The thin-layer models require high spatial resolution and small time steps, and the 3-D models require long numerical integrations. The compromise is that thin-layer models are run with simplified assumptions about the flow underneath, and 3-D models are run with unrealistically coarse resolution.

One hope is that spacecraft will be able to measure the signature of winds in the interiors of Jupiter and Saturn. The Coriolis forces associated with the winds are balanced by pressure forces, which require rearrangements of mass in the planetary interior. If the winds are deep enough and the mass involved is large enough, the effects will show up as slight irregularities in the gravity field. The Juno spacecraft will measure the gravity field of Jupiter, and the Cassini spacecraft will measure the gravity field of Saturn, (p.195) both in 2017. The spacecraft will be in polar orbits that bring the spacecraft close to the planet. The perturbations on the orbits of the spacecraft will reveal the deep winds if they are present. Also, Juno with its radio eyes can peer through the clouds down to pressures of 50 bars or more, and can see whether there are variations of water and ammonia at those levels. This will tell us if there is weather down there, or whether it is a chemically uniform, hot, dark, infinite abyss with no weather whatsoever.

# 8.5 Zones and Belts

Until the mid-twentieth century, amateur astronomers were the authorities on the spots and bands in Jupiter’s atmosphere. Most of the professional astronomers were busy studying stars and galaxies, and most of the professional meteorologists were studying Earth. The amateurs called the light and dark bands zones and belts, respectively. Although the zones and belts changed contrast and sometimes appeared to merge with their neighbors, they always reappeared at the same latitudes (fig. 8.1). They never disappeared forever. Consequently, they acquired names. Here is the sequence in the northern hemisphere: Equatorial Zone, North Equatorial Belt, North Tropical Zone, North Temperate Belt, North Temperate Zone, North North (sic) Temperate Belt, and so on. Spots circle the planet on lines of constant latitude, and the amateurs timed the spots’ recurrence periods at each latitude. Since the internal rotation period was unknown, the amateurs defined a uniformly rotating reference frame (p.196) for measuring spot positions. The observations revealed that the jets are on the boundaries between the belts and the zones, with the westward jets on the poleward sides of the belts and the eastward jets on the poleward sides of the zones. Thus the belts are cyclonic shear zones and the zones are anticyclonic shear zones. The jets are the most permanent feature of the belts and zones. The colors and contrast change more than the jets. The Great Red Spot sits in the South Tropical Zone, although it protrudes into the South Equatorial Belt to the north. In general, the long-lived oval spots are anticyclones and they sit in the zones, which are also anticyclonic.

We do not fully understand the connection between the colors of the belts and zones and their dynamics. We don’t know why the Red Spot is red, for instance. Color is like paint, and it depends on chemistry. If it were a strictly passive tracer, then it would mix to a uniformly bland color. Obviously color is not just a passive tracer—the chemistry must be responding to the dynamics because the dynamical structures like the belts and zones and long-lived ovals each has its own characteristic color. Understanding the chemistry would help us understand the dynamics and vice versa, but we are not at that point yet. The atmospheric gases are transparent, so the colors must originate on the cloud particles. The coloring agents could be sulfur, phosphorous, or organics (carbon compounds). Identifying the coloring agents is difficult because solid materials have broad spectral features that cannot be uniquely identified. Gases are the (p.197) opposite. Their spectra have narrow lines that give each gas a unique fingerprint (box 3.11).

The amateur astronomers, with their moderate-sized telescopes, have an important role to play. With high-speed digital cameras and the ability to rapidly process thousands of images, the amateurs now can take images of exceptional clarity. Moreover, they can respond to interesting weather phenomena on the giant planets in less than a day. In contrast, the large telescopes on Earth and the instruments on planetary spacecraft are scheduled weeks or months in advance and are difficult to reschedule. Thus the professional astronomers and the amateur astronomers complement each other.

The professional astronomers have access to high-resolution spectrometers and sensitive infrared detectors. Before the first spacecraft, they had measured the abundances of various gases—principally methane, ammonia, and hydrogen (box 3.11). They discovered that Jupiter has an internal energy source. And they determined the heights of the clouds in relation to the belts and zones. Figure 7.1 shows that 5-micron radiation is greatest in the belts and least in the zones. Recall that the gases in the atmosphere are transparent to 5-micron radiation but the clouds are not. The 5-micron hot spots are holes in the clouds where thermal emission from deeper, warmer levels can escape. Thus the zones are regions of uniform high clouds, and the belts are regions of patchy clouds with views to deeper levels. This led to the notion that the zones are sites of upwelling and the belts are sites of downwelling. The zones were supposed to be like the (p.198) Earth’s intertropical convergence zone (ITCZ), a region of frequent thunderstorms where precipitation exceeds evaporation (P − E > 0). The belts were supposed to be like the subtropical zones on either side of the equator, regions of fewer clouds and low relative humidity where P − E < 0. The circulation in the meridional plane (a vertical plane aligned north-south) was supposed to resemble the Hadley circulation on Earth (box 3.12), with low-level convergence in the zones and upper-level convergence in the belts. Whereas Earth had one ITCZ, Jupiter had several in each hemisphere, according to this view.

The idea of upwelling in the zones and downwelling in the belts got support from the ammonia and vorticity distributions.98 The ammonia abundance is greatest in the zones and least in the belts, suggesting that the zones are moist updrafts and the belts are dry downdrafts. According to this hypothesis, the air loses its ammonia in the updrafts through precipitation and descends in the belts to pick up more ammonia deeper in the atmosphere. Further, the vorticity is anticyclonic in the zones and cyclonic in the belts. If one assumes that the vorticity is zero at cloud base—that the deep atmosphere is not moving except for small-scale turbulence—then the anticyclonic circulation of the zones would be like a warm-core vortex on Earth, where the winds become anticyclonic at high altitude. The cyclonic circulation of the belts would be like a cold-core vortex on Earth. So one would have hot air rising in the zones and cold air sinking in the belts, which is consistent with a thermally direct circulation like the Hadley circulation on Earth (box 3.12).

(p.199) The Hadley cell has heating by latent heat release in the rising air and cooling by outgoing infrared radiation in the sinking air. That was the assumption for the beltzone circulation on Jupiter. However, observations of lightning by the Galileo orbiter upset this assumption.83 The orbiter observed lightning flashes on the night side and correlated their locations with clouds on the day side (fig. 7.4). Lightning is an indicator of moist convection, in which the air is heated by condensation of water vapor. The lightning clouds look like thunderstorm clusters on Earth with cloudless areas in between. The problem is that the lightning occurs in the belts,99 which were supposed to be the sites of downwelling. The Hadley cell interpretation requires lightning and moist convection at the sites of upwelling, and those were supposed to be the zones. Also, the thunderstorm clusters probably require updrafts below the clouds to maintain the moisture supply. This led to speculations about two Hadley cells, one on top of the other, going in opposite directions.100 In this view, the belts would have upwelling at low altitudes and downwelling at high altitudes. The zones would be the opposite. This hypothesis has not been verified in the numerical models. Part of the problem is that we do not have a good understanding of moist convection in giant planet atmospheres.

The vorticity of the belts is cyclonic, meaning that they are bands of low pressure. On Earth, areas of low pressure are areas of convergence, since friction with the surface causes winds in the atmospheric boundary layer to converge there. Over the ocean this low-level convergence (p.200) brings in moisture, which leads to moist convection. A hurricane is the best example. Moist convection in the belts is consistent with lightning in the belts, but there is no atmospheric boundary layer to bring in the moisture. Perhaps convergence occurs below the base of the clouds anyway. The giant planets force us to think about what role land and ocean surfaces play in the dynamics of the atmosphere. Without such surfaces, the dynamics could be different from what they are on Earth.

Perhaps the whole picture of rising in the zones and sinking in the belts is wrong. The picture uses the thermally forced Hadley cell analogy, but on Earth the Hadley cell is confined to the tropics. The tropics are special because the Coriolis force is small there. On Venus and Titan the Hadley cell extends to higher latitudes because those planets are slow rotators and the Coriolis force is small everywhere. In contrast, Jupiter is a rapid rotator, and we should probably expect the Hadley cell to be confined closer to the equator than on Earth. In that case, the Hadley cell analogy should not apply to the multiple belts and zones at higher latitudes.

A better picture might be zonal jets forced by eddies (boxes 3.13 and 3.15), as discussed in section 8.3, “order from chaos.” An eddy-driven circulation12 might resemble the Earth’s Ferrel cell. It is a thermally indirect circulation, in which hot air is forced down and cold air is forced up. It exists at midlatitudes as a residual; it is not the dominant weather feature at those latitudes. Instead, the midlatitude weather is dominated by the eddy heat flux (box 3.13), which overshoots and drives (p.201) the Ferrel cell. Jupiter is different in this respect. On Jupiter the zonal winds are much larger than the eddy winds, and the belt-zone structure is the defining feature of the weather. What forces the Jovian eddies is still an open question. They could be like thunderstorms and hurricanes—forced by an energy source below the clouds, or they could be like midlatitude storms—forced by horizontal temperature gradients that arise from the uneven distribution of sunlight. If the zones and belts are like the Ferrel cell on Earth, one would have to explain all the other features—the uniform high clouds in the zones, the 5-micron hot spots in the belts, the lightning in the belts, and the abundant ammonia in the zones, which would have to follow from the processes that maintain the jets. These are some of the constraints that the correct theory must satisfy, and we are not there yet.

## Notes:

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