Planetary interiors:
Magnetic fields, Convection and Dynamo Theory
1. Observational background to planetary structure
Chris Jones, Department of Applied Mathematics
University of Leeds UK

FDEPS Lecture 1, Kyoto, 28th November 2017

Section 1.
Observational background to planetary structure
1.1 Interior of the Earth(1.1) Interior of the Earth2/65

Internal structure of the EarthInterior structure of Earth
Columnar flow and Tangent cylinder
Earth’s radius is 6371 km. Earth’s fluid outer core radius 3480 km,
solid inner core radius 1220 km.
Radius ratio of solid inner core to outer core is 0.35.
Mantle convects on a timescale of millions of years. Fluid velocity
in the core is ∼ 5 × 10−4 m s−1 , so turn-over time is ∼ 100 years.
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Internal structure deduced from seismology
No shear waves (S-waves) can travel
through liquid outer core: sound waves(P-waves) are refracted at core-mantle
boundary (CMB) because they travel
slower in the core. creating P-wave
shadow zone.
P-wave velocity also changes in the
inner core.
Seismology enables us to work out the inner core and outer coreradii. Also gives the density of the core as a function of radius r ,the Preliminary Reference Earth model (PREM).
Density of outer core just below that of liquid iron at highpressure, suggesting outer core is a mixture of liquid iron withlighter elements (Oxygen, Sulphur?)
Inner core is nearly pure liquid iron.
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Length of day long term

The length of the day back to 1000 B.C. can be worked out from
eclipse records.
The day is gradually getting longer, mainly due to the friction of
the ocean tides raised by the Moon. The day is now about about
70 ms longer than it was 4000 years ago.
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Decadal variations of the length of the day

There are also variations on a decadal timescale (Green and Red
curves). These are due to fluid motion in the Earth’s core.
The total angular momentum of the Earth is constant on thesetimescales, so if core fluid rotates faster, the mantle must rotate
slower to compensate. The length of the day measurses therotation rate of the mantle.
By looking at how the Earth’s magnetic field moves, we canestimate how fast the core is rotating, and work out how fast the
mantle rotates. Blue curves give predicted length-of-day signal.
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Precession and Nutation

The Earth is an oblate spheroid (shaped like an orange). The
gravitational pull of the Moon and the Sun makes the Earthprecess about the ecliptic pole once every 26,000 years.
There are also small wobbles about the precessing track with aperiod of about a year.
It is now possible to measure these wobbles very accurately, using
very long baseline interferometry (VLBI).
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Nutation signals

Nutation is measured as a small displacement of the latitude andlongitude of the rotation axis of the Earth. Figure is a 20 year
record of the longitude variation: latitude variation looks similar.
Nutation is roughly periodic, but different frequencies can beextracted by Fourier analysis.
Some of these frequencies depend on conditions in the liquid coreof the Earth, so it may be possible to use nutation to get
information about conditions inside the core.
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Thermal convection in the core
Outer core is believed to be convecting. This is the main reason
why the Earth’s core moves relative to the mantle.
Driven by thermal convection and compositional convection.
Thermal convection: the Earth was hot when it was formed.
Gravitational collisions occurred building the Earth up from smaller
pieces. These collisions released a lot of energy.
The Earth, including the core, has been cooling down for 4.5 billion
years. A significant fraction of the heat leaving the core is carriedby thermal conduction, but not all of it.
The rest is carried by convection, that is hot fluid rising and cooler
fluid sinking. This is stirring the core, and this stirring generates
the Earth’s magnetic field by dynamo action.
The flow is slow, about 5 × 10−4 metres/sec, about the speed of asnail.
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The adiabatic temperature gradient
The pressure rises as we go deeper into the coredp
= −g ρ,dr(1.1)

As core fluid rises, it expands because the pressure goes down,
and so it cools. The adiabatic temperature gradient is
 dT 
drad= −g αTad /cp ,(1.2)

Here α is the coefficient of thermal expansion and cp the specificheat. The heat flux carried down this gradient by conduction isFad = −κρcp

 dT 
dr

ad

= −K

 dT 
dr

ad

(1.3)

Here κ is the thermal diffusity, and K is the thermal conductivity.
Pozzo et al. (2012) found that the thermal conductivity is larger athigh pressure, doubling the previous value of K
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Condition for convection
Thermal convection only occurs if the heat flux produced bycooling (and possibly radioactivity) is greater than the amountthat can be carried by conduction.
That is the actual heat flux F > Fad for convection.
It is believed that the Earth is convecting, but other planets such
as Mars and Venus have F < Fad , so don’t convect and don’t havea dynamo.
When convection occurs, it can transport the heat outwards with
only a very small superadiabatic temperature gradient, so−dT  dT − −=  << 1
dr
dr ad

(1.4)

.
So in the Earth’s convecting core, the temperature gradient will beclose to adiabatic. Temperature of core: CMB about 4000K, innercore 5,500K.
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The geotherm

At bottom of mantle there is athermal boundary layer D 00 .
In the outer core, geotherm isclose to adiabatic.
Heat flux carried by conduction
only ∼ 0.5TW at the ICB, risingto ∼ 10TW at the CMB. Mostly
because of larger surface area.

If latent heat is dominant heat source, possible that core issuperadiabatic (convecting) near ICB and subadiabatic (stable)
near CMB.
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The liquidus and the Inner CoreWhy does the inner core freeze at the centre where it is hottest?
Melting temperature of outer core material depends on pressure aswell as temperature. High pressure in the interior causes the innercore to solidify.
The P-T curve along which the core material melts is called theliquidus. It intersects the temperature curve, which is close toadiabatic, at the inner core.
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Compositional convection
Compositional convection: iron in the liquid outer core is acombination of iron and lighter elements (Sulphur, Oxygen). As
almost pure iron solidifies onto the inner core, it releases buoyant
light material at the inner core boundary (ICB), which rises up andstirs the fluid.
How do we know this? Seismology indicates the outer core issignificantly less dense than liquid iron, so there must be a lightcomponent. The inner core is quite close to the density of puresolid iron.
The light material released at the may collect at the top below thecore-mantle boundary (CMB) (stably stratified ‘inverted ocean’) or
it may just mix.

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Thermal history of the Earth

When the Earth formed, it was hot, so the liquidus and thetemperature curve didn’t intersect, so there was no inner core.
If there is no radioactivity in the core, the rate of cooling is fastenough that the inner core formed less than 1Gyr ago. Much
younger than Earth.
Rocks aged 3.5Gyr old which have been magnetised are known, so
the geomagnetic field is much older than the inner core.
Dynamo not always driven by compositional convection, which
requires an inner core. Could have been driven then by thermal
convection alone.

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Differentiation of terrestrial planets
The gravitational energy of formation, GM 2 /R, must have turned
into heat, and this is enough heat to ensure that the Earth andother terrestrial planets started hot enough to melt the rock.
The heaviest element present in large quantities, iron, made its
way to the centre of the planet, releasing more gravitationalenergy. This process is known as differentiation, and can happen ina few Kyrs only.
This forms the structure of terrestrial planets, with iron cores androcky mantles.
The heat of formation is ultimately the most likely energy sourcefor planetary dynamos. Convection carries the heat flux outward,
but there was so much initial heat, the planets havn’t yet cooled
down.
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Radioactivity in the Core?
Radioactive elements are present in the mantle, and contribute alarge part of the heat coming out of the Earth’s surface (44TW).
Did the differentiating iron take any radioactive materials with it
down to the core, like Uranium or radioactive Potassium K40 ?
Potassium is depleted in the mantle, but did it evaporate into
space at formation or end up in planetary cores?
If it didn’t, then the core is gradually cooling down, at a current
rate of around 1K every 10Myr, which is possible.
With radioactivity, the core might be in thermal equilibrium, withthe heat flux out of the core balancing the radioactive input.
These different scenarios have implications for solid inner coreformation and for dynamo theory.
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Mantle Convection
Large density jump at the Core-Mantle Boundary (CMB). Earthappears to be the only planet that currently has plate tectonics(mantle convection).
Although the mantle is a solid on short timescales (seismology) it
can flow slowly on long-timescales. Shifts the plates around on
100Myr timescale.
Mantle convection transports the 46TW of heat generated in theinterior to the surface. Heat flux at the CMB probably around
10-15TW.
Plumes coming out of the Core-Mantle boundary, may go rightthrough the mantle and emerge at hotspots like Hawaii and
Iceland.

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Mantle Convection Plumes

Yuan and Romanowicz, 2017.
ULVZ’s are Ultra low velocity zones, where the seismic speed issurprisingly small. Hot buoyant mantle rises up in a plume,
eventually emerging as a volcano.
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Heat flux at the CMB

The heat flux passing through the CMB is controlled by the
mantle.
Because mantle convection is inhomogeneous, with a low heat flux
under the Atlantic and Pacific, the core heat flux is similarly
inhomogeneous.
Possible that the convection pattern and hence the dynamo in thecore could reflect this inhomogeneity.
(1.1) Interior of the Earth

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1.2 Interiors of other planets(1.2) Interiors of other planets

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Plate tectonics on other planets? Venus

Venus might be expected to have plate tectonics, but the surface
suggests not.
Venus surface does look quite recent, around 500Myr old however,with a lack of cratering compare to the Moon.
Possibly Venus undergoes periodic resurfacing: heat fromradioactivity builds up in the interior because it can’t escape bymantle convection.
No mantle convection means low heat flux through the iron core,so heat flux small enough to be conducted down the adiabat. So
no core convection.

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Plate tectonics on other planets?
Mars also doesn’t seem to have mantle convection at present. But
there was a dynamo in the past, which magnetized the surface
layers.
Mars has two very different hemispheres

Left Topographic map with Tharsis region prominent: Right
Magnetic field of Mars, indicating the hemispheric structure is
deep-seated. (Note longitude plotted differently! Hellas basin(blue) is nonmagnetic.)(1.2) Interiors of other planets

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What happened on Mars?

It has been suggested that a dipolar m = 1 (spherical harmonics
Plm ) mantle convection may have occurred in the past, giving riseto this structure.
Alternatively, could be due to a giant impact.
Crustal magnetization is strong and global, so Mars must have had
a strong magnetic field when the Southern Uplands formed. The
Hellas basin formed about 500Myr after Mars formation, and isnonmagnetic.
Mars used to have a dynamo, but it switched off about 350Myr
after formation. What caused it to fail?

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Mercury structure from Messenger

Mercury is a small planet, but is has a large iron core, so Mercury’smagnetic field is probably due to a dynamo.
It is the high overall density of Mercury that indicates the large
core.
Nutation observations suggest the core is at least partially liquid.
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Moons of JupiterThe internal structure of Jupiter’s 4 largest moons has been
worked out from their gravity fields.
The largest, Ganymede, has an internally generated magnetic field,
so it probably has a liquid iron core and a convection driven
dynamo.
The other moons apparently do not have internal fields, though Io
is difficult as any internal field would be swamped by Jupiter’s field.
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Structure of the giant planets

The rocky core is actually entirely conjectural. It can’t be seen in
the gravity field, and consistent models can be produced with nocore. Its drawn in because its hard to understand how Jupiter orSaturn formed without a core.

(1.2) Interiors of other planets

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Metallic hydrogen
Metallic hydrogen layer is caused by the high pressure. The matteris squashed into a small space, and so the particle velocity goes up(exclusion principle).
Hydrogen ionizes, and so becomes electrically conducting. This
allows currents to flow and hence a dynamo.
Increase in particle velocity due to the exclusion principle increases
the pressure, see e.g. Kippenhahn, Weigert and Weiss, 2012.
High pressure physicists have developed sophisticated equations ofstate, giving pressure in terms of density and temperature, using
quantum mechanics methods.
These techniques also give the electrical and thermal conductivities
at very high pressure, e.g. French et al. 2012.
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Saturn and the ice giants
Saturn’s lower mass leads to lower pressures and hence a smaller
metallic hydrogen region.
Helium rain: the upper parts of gas giants have lower helium
content than solar ratio. Suggestion is that there is aninhomogenous region where a helium/hydrogen phase transition
occurs leading to helium droplets forming and helium ‘rain’.
Ice Giants, Uranus and Neptune. These planets have a mantle
believed to be a water-ammonia ocean, which has an ionicelectrical conductivity. This is where the dynamo is believed to be.
However, ionic conductivity is much lower than from metallic
hydrogen or liquid iron. Further complication is that Uranus hasvery little heat flux coming from interior.

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Dilute core model for Jupiter?

The standard French et al. model used for dynamo simulations fits
the new Juno gravity data results rather well.
However, different density functional theories give different
equations of state. Using one of these would allow a different
equilibrium structure model that still satisfied Juno constraints.
Helium rain-out might have led to a dilute core model: also might
have given rise to the stable layer suggested by Saturn’s
axisymmetric field.
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1.3 Earth’s magnetic field(1.3) Earth’s magnetic field

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Br at Earth’s surface
Earth: mainly dipolar magnetic field. Inclination of dipole axis torotation axis currently 11.5◦ .

-0.1mT

0.1mT

Field at the CMB in year 2000, units 10−3 T. Note the non-dipolar
behaviour in the South hemisphere: the weak field associated with
the South Atlantic anomaly.
(1.3) Earth’s magnetic field

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Earth’s field evaluated at the CMB
Field at Core-Mantle boundary, CMB, can be reconstructed fromsatellite and observatory data. Strength ∼ 8 × 10−4 Tesla = ∼ 8
Gauss.

Field at the CMB in year 2000, units 10−3 T. Note the intense flux
patches near Canada and Siberia. Patches under Africa are moving
westward. Field at poles surprisingly low.
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Geomagnetic field and Secular Variation
Geomagnetic field is described in terms of the Gauss coefficients ofthe spherical harmonic expansion outside the core B = −∇Ψ,
∇ · B = 0, so ∇2 Ψ = 0, Laplace equation.
∞ m=n
X
X  rs n+1
Pnm (cos θ)(gnm cos mφ + hnm sin mφ). (1.5)Ψ = rsr
n=1 m=0

Magnetic field Br measured at thesurface, but mantle insulating, so
can extrapolate field Br to
Core-Mantle boundary (CMB).
Radial geomagnetic field at CMB in
1980 and 2000.
Small changes occur in 20 years.
Secular variation is firsttime-derivative of geomagnetic field.
Some Westward drift is visible.
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South Atlantic anomaly and dipole decline• Dipole moment, proportional to g10 , isdeclining steadily since 1850.
IGRF=International Geomagnetic Reference
Field. GUFM is a field model constructedby synthesizing available data since 1590.
• Plot of field intensity |B| shows the weak
patch in the South Atlantic. Corresponds
to reversed field when extrapolated down
to the core.
• This patch is growing, which is why
dipole is declining. Reversal ahead?
Note that extrapolation down to the CMB only works for n and mless than about 15. We cannot see very small scale features at theCMB.
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Dynamo theory for planetary magnetism
No permanent magnetism above the Curie point, 800◦ C for iron.
Earth’s outer core between 4000K and 5500K.
Fluid motion in the core produces dynamo action (Larmor, 1919)
the magnetic field obeys the induction equation which is∂B= ∇ × (u × B) + η∇2 B,
∂t

(1.6)

if the electrical conductivity is assumed constant. Full derivation in
lecture 3.
The induction term must overcome the diffusion term. The
magnetic diffusivity η = 1/µ0 σ, where σ is the electricalconductivity and µ0 = 4π × 10−7 is the permeability.
The ratio of induction to diffusion is approximately the Magnetic
Reynolds number Rm = U∗ `/η. Here U∗ is the typical fluid
velocity, ` the typical length scale, either outer core radius or gap
between inner/outer core.
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Magnetic Reynolds number

It can be proved that for induction to overcome diffusion in
spherical geometry, Rm must be greater than π 2 , and in practice inthe numerical dynamo simulations Rm of around 50 is needed for
dynamo action.
Earth’s core velocity U∗ ∼ 4 × 10−4 ms−1 , and Earth’s core size
` ∼ 3.5 × 106 m, giving Rm ∼ 700
U∗ from secular variation studies ‘Westward Drift’
Ohmic decay time `2 /π 2 η ∼ 20, 000 years
How is the velocity at the CMB found from observing thegeomagnetic field?

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Core-flow inversion
Ignore diffusion, (large Rm ) and take radial component of
induction equation,∂B= −(u · ∇)B + (B · ∇)u,
∂t

(1.7)

and since ur = 0 at CMB, get∂Br= −(u · ∇)Br .
(1.8)∂t
Since Br and ∂Br /∂t can be observed, we might hope to use thisequation to determine u. Unfortunately, there are two unknown
components of u and only one equation. Velocities along contoursof constant Br give no signal.
Assume tangential geostrophy, that is near CMB
2ρΩr̂ cos θ × u = −∇p,
(1.9)
Reasonable, as buoyancy and Lorentz forces small close to CMB.
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Core flow inversion (2)Taking the radial component of the curl of this force balance gives∇ · cos θu = 0,(1.10)and (1.8) and (1.10) are enough to reconstruct u.

20.0km/yr

20 km per year is 6 × 10−4 metres/sec. Slower than a snail! Notewestward drift in S. Atlantic, Indian Ocean. Pacific has low secularvariation. Waves or flow?
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Energy Sources for Planetary Dynamos• Dynamo energy source: Precession, Tidal interactions, Thermal
Convection, Compositional Convection
Tides and precession derive their energy from the Earth’s rotation.
Tides distort the CMB, precession is caused by the torques on the
Earth’s equatorial bulge. Earth’s axis of rotation precesses once
every 26,000 years.
Precessing systems lead to a core flow which is unstable, and these
instabilities can drive motion, just as buoyancy instabilities can.
Successful simulations have been done, but only with
Precession/rotation ratios of 10−3 . Stabilised even by very small
viscosity, so not clear it works in Earth’s core.

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Dipole moment
The dipole moment is M =4πrs3
g1 , whereµ0

g1 = (g10 )2 + (g11 )2 + (h11 )2

2.

The Earth’s dipole moment iscurrently decreasing faster thanfree decay rate, i.e. if there wereno dynamo! About half its valuein Roman times.
Growing reversed flux patches
under S. Africa?

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Reversals
Geomagnetic reversal record: last 5 million years

The Earth’s field reverses
randomly about once every 0.3
million years. There have been
periods as long as 60 million
years with no reversals(superchrons). Reversals occur
relatively quickly ∼ 10, 000 years.
During a reversal, the dipole axis
traces out a path at the Earth’s
surface: are there preferredlongitudes?

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Excursions
Dipole component varies significantly between reversals, theso-called excursions.

Current decline may be an excursion rather than a reversal.
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Other terrestrial planets

Three ideas for Mercury’s weak field:(i) No dynamo, but solar wind field amplified.
(ii) As Mercury cooled, inner core grew. Remaining liquid outer
core has progressively higher impurity content, so thin shell of
liquid iron. Thin shell dynamos have high harmonic content, lowdipole content.
(iii) Most of Mercury’s core is liquid, but mostly stably stratified asheat produced mostly carried by conduction. Dynamo only near
ICB, only small fraction of field penetrates stably stratified uppercore.

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1.4 Magnetic fields of other planets(1.4) Magnetic fields of other planets

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Magnetic fields of other terrestrial planets
Mercury: internal field of dipolar structure. Strength at CMB∼ 1.4 × 10−6 T, which is surprisingly small. Rotates only once
every 57 days. Liquid iron core, radius 1900 km.
Venus: no magnetic field.
Ganymede: approx dipolar, inclination ∼ 10◦ . Strength at CMB∼ 2.5 × 10−4 T. Rotates once every 7 days. Core radius 480 km
Io: too close to Jupiter’s magnetic field to tell whether it has its
own magnetic field. Other large moons don’t have internal fields atpresent.
Extinct Martian field is deduced from strong crustal magnetism,
which suggests Mars had a dipole field in the past. Lunar rocks
also have remanent magnetism(1.4) Magnetic fields of other planets

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Mercury’s magnetic field

Mercury’s magnetic field from the Messenger mission.
The field is weak, but fairly axisymmetric. However, the field ismuch stronger in the northern hemisphere, so there is a quadrupole
and a dipole component.
Sometimes called a hemispherical dynamo.
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Other terrestrial planets 2
Venus rotates only once every 243 days. But Rossby numberU∗ /`Ω with Earth-like U∗ would still be small.
Venus appears to have no plate tectonics. This could reduce F andhence make Venus’s core subadiabatic.
Venus seems to have been resurfaced 300 million years ago.
Possibly there was mantle convection then, and possibly a dynamo.
High surface temperature unfavourable for remanent magnetism.
Ganymede has a weak surface field, but a small core, so at CMB
field is ∼ 2 Gauss, giving an Elsasser number of order unity.
Surprising that there is sufficient heating in the core to make it
convect.
Collapse of Martian dynamo possibly due to core becoming stably
stratified.
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Planetary magnetic fields: Giant planets
Giant planets are all rotating rapidly.
Jupiter: strong magnetic field, basically dipolar (more higher
harmonics than Earth), inclined 10◦ to rotation axis, about 17
gauss at surface.
Saturn: very axisymmetric field,
about 2.5 gauss at surface.

Dipole field of Saturn
Aurora of Saturn, produced byparticles moving along field lines(vi). Magnetic fields of Giant Planets

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Jupiter’s magnetic field-1.2mT

1.2mT

Radial magnetic field at the surface of Jupiter.
Tilted dipolar field, broadly similar to the geomagnetic field.
(vi). Magnetic fields of Giant Planets

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Saturn’s magnetic field-0.06mT

0.06mT

Radial magnetic field at the surface of Saturn.
Field is very axisymmetric. Possibly due to a stably stratified layer
in Saturn, with a zonal flow wiping out non-axisymmetriccomponents above the dynamo.
(vi). Magnetic fields of Giant Planets

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Ice Giant magnetic fields-0.12mT

Magnetic field of Uranus

0.12mT-0.1mT

0.1mT

Magnetic field of Neptune.

The fields were constructed from Voyager data.
The ice giants have non-dipolar magnetic fields, the quadrupoleand dipole components being of similar strength.

(vi). Magnetic fields of Giant Planets

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Dynamos in the Giant Planets
Electrical conductivity is due to very high pressure ionising
electrons (quantum effect).
Earth-like conductivity in the deep interior, gradually falling to low
values near the surface.
Giant planets are convecting, so thermal convection most naturalenergy source.
Some secular variation occurs on Jupiter, suggesting core flow
∼ 10−2 metres/sec. Rm large.
Why is Saturn’s field so axisymmetric? Stably stratified region
with strong differential rotation outside the dynamo region? This
could axisymmetrise the observed field
Uranus and Neptune have very unusual fields. Thin shell dynamos
suggested. Not much known about internal structure and heat
flux. Ionic conductivity is low, so Rm cannot be very large.

(vii). Dynamos in Giant Planets

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Major Problems in Planetary Dynamo theory(i) Why is Mercury’s field so weak?
(ii) Why does Venus not have a magnetic field?
(iii) Why are most planets dipole dominated? Why dogeomagnetic reversals occur?
(iv) What powered the geodynamo before inner core formation?
(v) What killed off the Martian dynamo?
(vi) How does Ganymede maintain a dynamo when its core is sosmall?
(vii) Why is Saturn’s field so axisymmetric?
(viii) Why are the fields of Uranus and Neptune non-dipolar?
(vii). Dynamos in Giant Planets

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1.5 Zonal flows on giant planets(1.5) Zonal flows on giant planets

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Zonal winds on the giant planets• Jupiter and Saturn have belts and zones associated with
east-west zonal flows: east-west flows independent of longitude• Also, long-lived storms such as the Great Red Spot on Jupiter• What drives these winds? Why are they so different from winds
on Earth?
Are the winds just on the surface, or do they reach deep into theplanet?

(viii). Zonal flows and storms in Giant Planets

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Jupiter from the Cassini Mission

Giant planets have banded structure. Also huge vortices such as
the Great Red Spot, and smaller white ovals.
(viii). Zonal flows and storms in Giant Planets

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South pole of Jupiter from the Juno Mission

Zonal flow bands don’t reach up to the poles.
Instead there are very large scale vortices.
(viii). Zonal flows and storms in Giant Planets

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Storms on Outer Planets

As well as the persistent zonal flows, also get giant storms on all
the outer planets.
Great Red Spot of Jupiter is only one we know has lasted hundredsof years. Noted by Hooke end of 17th century.
Great White spots on Saturn last typically a few years. There arealso vortices at Saturn’s poles.
Dark spot of Neptune lasted twenty years, but then disappeared.

(viii). Zonal flows and storms in Giant Planets

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The Great Red Spot

Giant storm, larger thanentire Earth. Anticyclonicvortex that has lasted over
300 years
Maintained by absorbing
small vortices.
Why doesn’t it break up?

(viii). Zonal flows and storms in Giant Planets

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Winds in the Giant Planets

Jupiter zonal flow

Saturn zonal flowMore variability in Saturn’s winds than Jupiter’s. Eastward(prograde) jets at equatorward side of dark belts, westward(retrograde) jets at poleward side of dark belts.
(viii). Zonal flows and storms in Giant Planets

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Galileo Probe

Probe entered 7◦ N, ineastward equatorial jet.
Found velocity increases
inward, supporting deep
convection model.

(viii). Zonal flows and storms in Giant Planets

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Winds on the Ice Giants

Note that the equatorial belt goes westward on the ice giants,
eastward on Jupiter and Saturn
Quite different from the Solar differential rotation, which has arapidly rotating equator and slowly rotating poles(viii). Zonal flows and storms in Giant Planets

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Zonal flows in Jupiter and Saturn

Jupiter: Large radius ratio,
narrowly confined bands

Saturn: Smaller radius ratio, lessconfined bands
Are zonal flows deep, 15,000 km, driven by convection in molecular
H/He layer, or shallow, confined to stably stratified surface layers?
Broader equatorial belt on Saturn suggests that the surface zonal
flow is affected by the deep structure(viii). Zonal flows and storms in Giant Planets

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Gravity field

The gravity field around giant planets can be expanded in sphericalharmonics
m=n

X  a n X
GM
V =
(1 +
Pnm (cos θ)(Cnm cos mφ + Snm sin mφ)
r
r
n=2

m=0

The gravity field is measured by satellites and gives information
about the distribution of mass inside the planet.
Juno (arrived July 2016) is measuring the gravity field accurately.
Centrifugal force affects mass distribution, so internal rotation rate
can in principle be determined.

(viii). Zonal flows and storms in Giant Planets

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