Lecture 4: Jupiter

A. P. Ingersoll

api@gps.caltech.edu

1. Jupiter is a big topic. We will talk about the composition of the atmosphere,lightning, the zonal jets, and the long‐lived vortices. The Great Red Spot was visible
in the first telescopes more than 300 years ago.
2. The cloud bands change very little from Voyager time to Cassini time. Thechemicals that cause the different colors have not been identified. The most likely
chemicals are organic compounds and sulfur compounds. The bands follow lines ofconstant latitude, which shows that the rotation of the planet is controlling theorientation of the bands.
3. The first topic is the composition of the gases in Jupiter’s atmosphere. The column
labeled “sun” is what you would get if you cooled a piece of the sun down to Jupiter’s
temperature. The elements would combine with hydrogen to form water, methane,ammonia, and hydrogen sulfide. The noble gases would not combine. The column
labeled “Jupiter” shows the measured values, which are about 3 x solar, or threetimes what you would get by cooling a piece of the sun.
4. Most of the measurements come from the Galileo entry probe, which had a mass
spectrometer that took data from 1 bar to 20 bar. Most elements are 3 x solar.
Helium and neon probably separated into the core. Most people think that oxygen
was removed as water from the place where the probe went in, but it is possible thatoxygen is less abundant than 3 x solar. In order to get all these elements to have thesame enrichment factors relative to solar, Jupiter must have received its volatiles asicy planetesimals that formed at temperatures below 40 K.
5. One puzzle is that the measured abundances of ammonia, H2S, and water (left) do
not follow a model based on their saturation vapor pressures (right). The model
assumes that the deep atmosphere is well mixed and is representative of the planet
as a whole. The water abundance of the deep atmosphere is uncertain. The
spacecraft died while the abundance was still rising.
6. The problem may be that the Galileo probe went into a “hot spot,” which is a giant
hole in the clouds. It looks hot because infrared radiation escapes from deeper
levels. This is a 5 micron image (wavelength = 5 x 10‐6 m), where the gases in theatmosphere are transparent. There is a hot spot in the bright band just north of theequator.
7. Here is a hot spot in visible light. It looks dark because there are no clouds toreflect the sunlight. The clouds are made of NH3, H2S, and H2O. No clouds means low
abundances of these gases. The hot spot might be a place where dry air from thestratosphere has been pushed downward.
8. Showman etal demonstrated that a wave with vertical excursions of 2‐4 times theinitial pressure (left) is more stable than one with smaller excursions (right).

[Showman et al, Science 289, 1737 (2000)]. These large vertical excursions could
explain the depressed values of these compounds much deeper than thecondensation levels.
9. Nakajima etal [Geophys. Res. Lett. 27, 3129‐3132 (2000)] have a model of moist
convection on Jupiter. They argue that the water condensation level (WCL), which
occurs at 5‐6 bars, should be very stable, since the molecular mass of water isgreater than that of hydrogen. Dry air above = lower density = stable.
10. Here is the stability parameter N2. Because N2 is so large, it requires a large
amount of energy to push low‐density dry air down to 20 bars through the dense
lower atmosphere with its large amount of water vapor. Showman etal did not takethis effect into account. The alternative is that O/H on Jupiter is less than that on thesun, but that upsets theories of solar system formation.
11. Here are measurements of temperature based on the radio occultation method.
The radio waves do not penetrate below 1 bar for Jupiter. The lower portion fits adry adiabat, which is consistent with a convective troposphere.
12. Here is a model of the stratosphere and troposphere based on adiabatic lower
atmosphere and solar abundances of N, S and O. The gases condense to form cloudsof NH3, NH4SH, and H2O. The water cloud is ~100 km below the top of the ammonia
cloud. It is the thickest cloud, since water is the most abundant condensable vapor
in a solar composition atmosphere.
13. This is a night side image of Jupiter showing moonlit clouds (light from Io makes
the clouds visible in a long exposure of the camera). The bright spots are lightning.
The image covers an area from the equator to a latitude of 50°. Repeated images
over a day show the lightning is always coming from the same place, so these must
be individual storms.
14. Here are 3 storms over a 2 minute period. The lightning flashes are different, but
the storms are the same.
15. The lightning flashes are wide – about 150 km in diameter. We modeled this as apoint source at an unknown depth below the tops of the cloud. The photons diffuse
up through the cloud. You infer the depth from the width of the flashes, and thedepth is at least 100 km. This means the lightning is in the water cloud or deeper.
16. Some facts about Jovian lightning. Some of the flashes are 3 times brighter thanthe brightest flashes on Earth, but the storms are farther apart, so the total opticalpower per unit area is ¾ the value for Earth. [Little etal Icarus 142, 306‐323 (1999)]
17. Galileo was able to image the planet on the day side, and then image the sameclouds several hours later when they were on the night side. The night side image

shows the lightning (red), and it is correlated with small bright clouds on the dayside. [Dyudina et al 172, 24‐36 (2004)]
18. These small bright clouds have lifetimes of a few days. Time increases from top
to bottom. Each image is 20 hours later than the one above.
19. The lightning storms mostly occur in the dark bands, which are called “belts.”
The bright bands are called “zones.” There are jet streams on the edges between thebelts and the zones. The zones are anticyclonic (in the northern hemisphere, thezones have a eastward jet on the northern edge and a westward jet on the southernedge).
20. Here are the places where lightning was observed. Lightning occurs in thecyclonic belts. This is a puzzle because the dark belts are relatively cloud‐free andthe bright zones are relatively cloudy. Notice the multiple jet streams.
21. This is the traditional view, and it may be wrong. Updrafts in the zones produce
clouds. Downdrafts in the belts produce clear areas. I added the arrows to showwhat might be happening at the base of the clouds. Updrafts in the belts produces
lightning storms and moist convection. Why the circulation should reverse is amystery.
22. Here is a 60‐day movie of the northern hemisphere taken by Cassini. You can’t
see the pole because the spacecraft was only a few degrees above the equatorial
plane. To make this movie, Ashwin Vasavada had to put ~1000 images together intoa polar mosaic. The pole is in the center and the equator is in the corners. You cansee at least 6 jet streams in the northern hemisphere.
23. Here is the same movie with better resolution. You see more detail at the end
because the spacecraft was closer to Jupiter.
24. Here are the jet streams for Jupiter and Saturn. The winds are measured relative
to the interior of the planet, based on the wobble of the magnetic field. Jupiter’s field
is tilted by 10°, which gives a nice wobble. The problem is that Saturn’s field is nottilted, so we don’t know the interior rotation. For Saturn, these winds are based onradio emissions detected by Voyager, and they may give the wrong rotation. The
Galileo probe went in at 6.5° north latitude, where the wind at the top of the clouds(0.5 – 1.0 bar) is ~100 m/s. Notice that the winds are prograde (westerly) at theequator.
25. The winds increased with depth, which was a surprise, and then stayed constantuntil the probe died at 20 bars. These winds were determined by tracking the radio
signal from the probe and measuring its Doppler shift.

26. Major differences between Jupiter and the Earth. (1) There is only one eastward
jet stream in each hemisphere on Earth. The speed (upper panel on right) is ~30
m/s. (2) The emitted longwave radiation (upper panel on left) is low at the poles
because it is colder at the poles than at the equator.
27. On the giant planets the poles are just about as warm as the equator. The small
oscillations are associated with the jet streams. On small scales the temperature
gradient ∂T/∂y changes sign with latitude, which means the wind shear ∂u/∂zchanges sign, according to the thermal wind equation.
28. When you compare the wind shear computed from ∂T/∂y with the winds
observed by tracking clouds, you find they are anti‐correlated. The winds decay withheight. This is in the upper troposphere (~300 mbar), where the temperatures aremeasured.
29. Models of jet formation. Rhines [J. Fluid Mech. 69, 417‐443 (1975)] showed that
turbulence on a rotating sphere, which he approximated by a beta‐plane, willorganize itself into jets. He argued that the turbulent eddies grow by merging until
they reach a certain size, where Rossby wave radiation produces the jet. The
wavenumber (inverse of the size) is or order kβ = (β /U)1/ 2 , which is now called theRhines scale. Here β = df/dy is the planetary vorticity gradient, and U is the typicalvelocity of the flow. Williams [J. Atmos. Sci. 35, 1399‐1426 (1978)] applied theseideas to Jupiter. This is a time series of forced barotropic turbulence on a sphere.
€30. Freely evolving turbulence on a sphere [Yoden et al, Il Nuovo Cimento 22, 803‐812 (1999)] ]. There is no forcing or dissipation. When the sphere is not rotating(left), the flow organizes itself into large vortices. When the rotation is large (right),
the flow organizes itself into bands at constant latitude. Further integration leads toa single large vortex at the pole.
31. Cho and Polvani [Phys. Fluids 8, 1531‐1552 (1996)] followed freely‐evolving
turbulence to its final end state. This figure is for non‐divergent flow (infinite radiusof deformation); there are no mid‐latitude jets, just one anticyclonic polar vortex ineach hemisphere. Absolute vorticity is constant within each polar vortex. For finite
radius of deformation (not shown), there are bands and jets.
32. Li et al [Icarus 180, 113‐123 (2006)] changed the small‐scale forcing from arandom isotropic pattern to one resembling the small‐scale convection andlightning on Jupiter. Their forcing is only in the cyclonic regions – the belts, and it
covers only a small fraction of the area at any one time. The results are the same.
This is a quasi‐geostrophic (QG) model, so it does not include the equator.
33. Notice the tilted clouds, especially in the dark bands – the belts. The tilt is in thesame direction as the shear – counterclockwise in the belts in the northernhemisphere and clockwise in the belts in the southern hemisphere. If there is eddy

motion, northward and southward, along these tilted lines, it would imply aReynolds stress ρ u'v' that increases the shear. The divergence of the Reynoldsstress ∂( ρ u'v' )/∂y would increase the speed of the zonal jets.
34. Here are the measurements. The black is the shear ∂u/∂y and the red is u'v' . The€
fact that they are correlated means that the eddies are putting energy into the jets. If€
the two curves were anti‐correlated, it would mean that the eddies are taking
energy out of the jets. The power per unit mass is about 2 x the rate€ on Earth. This
energy conversion is large when you compare the power/area in sunlight at Earthand Jupiter (Earth’s is 25 times greater).
35. Until recently, these experiments with forced turbulence on thin spherical shells(shallow water turbulence) have failed to match the observations in one important
respect: The winds at the equator are retrograde (easterly), as they are on Earth,whereas Jupiter and Saturn have prograde winds (westerly) at the equator.
[Showman J. Atmos. Sci. 64, 3132‐ (2007)]
36. Experiments with deep spheres give prograde winds at the equator (red in theright image). The prograde region is outside the cylinder that is tangent to the innerboundary. This tangent cylinder is at the equator in the thin shell models, so theprograde flow does not exist in the thin shell models. [Christensen Geophys. Res.
Lett. 28, 2553‐2556 (2001)]
37. Another example of prograde flow in a deep sphere model [Heimpel and Aurnou
Icarus 187, 540‐557 (2007)]. The dashed lines are where the tangent cylinderintersects the surface.
38. Recently two groups have obtained prograde flow in thin shell models bychanging the dissipation. This model is by Scott and Polvani (2008, submitted toGeophys Res. Lett.). This is a shallow water model (one layer of fluid) withprescribed random small‐scale turbulence. They get prograde equatorial flow bydamping the height field (1/τrad > 0) but not damping the divergence or vorticity
fields (1/τfr = 0).
39. Here is divergence of the eddy momentum flux, showing it is into the jets, inagreement with the observations of u'v' and ∂u/∂y. [Scott and Polvani]
40. This is from a 3D model of Schneider and Liu [J. Atmos. Sci, 2008, in press].
Convection of internal heat€generates Rossby waves at the equator, which propagate
to higher latitudes, where they are damped. This damping is zero outside(equatorward) of the tangent cylinder, and it is large on the poleward side of thetangent cylinder. Except for this change in the damping, the model is a thin shellmodel.

41. Another difference between the models and the observations. The northward
gradient of absolute vorticity β ‐ uyy is always positive in the models but it changes
sign in the data. This figure shows parabolas β = uyy at each of the westward jets. In
many cases the curvature of the u profile is greater than the curvature of theparabolas. In a barotropic fluid, β ‐ uyy changing sign is a necessary condition for
instability. In shallow water models the observed profiles are unstable. Perhaps 3D
effects are making them stable, but even the 3D models do not have β ‐ uyy changing
sign.
42. Now let’s talk about vortices. This is the Great Red Spot in red, blue and methane
filters. It is a southern hemisphere anticyclone and was discovered in the 1600’ssoon after the telescope was invented. Small spots go around the periphery in ~10days. The wind speeds are greater than 100 m/s. The size is 10,000 x 20,000 km, but
it has been shrinking for the past few decades. We measure the winds by tracking
clouds over 10 hours.
43. Here is a 60‐day movie taken by Voyager showing spots merging with the RedSpot. The direction of circulation is counterclockwise, since it is a southernhemisphere anticyclone. Some spots go around and other spots escape. The movie
also shows merging of small anticyclones (clockwise rotation) in the northernhemisphere.
44. This is a movie by Dowling and Ingersoll [J. Atmos. Sci 46, 3256 (1989)] of an
unstable flow evolving into a series of vortices that merge until there is only one
vortex in each latitude band. This unstable flow is taken from observation, so it has
β ‐ uyy < 0 at the centers of the westward jets. The final flow is weaker than theobservations, but it is stable.
45. Here is a figure from Dowling and Ingersoll. The final flow does not agree withthe observations – it is too weak. This is a problem. The experiments with forced
turbulence do not give β ‐ uyy < 0, and they do not give large ovals. The experimentswith large ovals either require creating the ovals with an initial condition or elsethey require β ‐ uyy < 0 as the initial condition.
46. The observations show many examples of merging. That raises the question ofwhere do the spots come from?
47. Sometimes they look like convective spots that arise in the belts, which tend to
be more turbulent than the zones. [Li etal. Icarus 172, 9‐23 (2004)]
48. In 1979 there were three white ovals in an anticyclonic band south of the RedSpot. The ovals are anticyclones, like the Red Spot, and they formed in 1938‐1939.
You can see two of them in this image. Each oval has a turbulent region to the west
and slightly to the north. The turbulent regions are cyclonic, like the turbulent
region to the north and west of the Red Spot. They also have the lightning storms.

49. Here is the view in 1998. Two of the large white ovals are close together. Thesmaller white oval to the south is in a different band. The cyclonic region between
the two large ovals is much smaller than it was, and soon it disappeared. The twoovals merged soon after that. The remaining two ovals merged a year later, and now
there is only one oval in that latitude band. It recently turned red.
50. Here is a south polar mosaic from Cassini. The remaining white oval is in the 4o’clock position. Notice the string of ~7 anticyclonic white ovals further to the south.
Notice the turbulent cyclonic regions to the north of each of the ovals.
51. Yousef and Marcus [Icarus 162, 74‐93 (2003)] have modeled the anticyclonicwhite ovals and the cyclonic turbulent regions to the north and west of each oval asa Karman vortex street. In this simulation, two ovals of the same sign of vorticity(dark) are orbiting with an opposite vorticity spot (white) that keeps them frominteracting. Another white spot approches the triplet and knocks the white spot
away. The remaining black spots quickly merge, implying that the cyclonic spot waskeeping the two white ovals apart.