Fast and Slow: The
Dynamics of Superrotation
Phenomena in Planetary
Atmospheres:
IV. Fast rotators
Peter Read
University of Oxford, UKPlan• Local and global super-rotation in atmospheres around rapidly
rotating planets• Earth• Troposphere?
• Stratosphere & Mesosphere• Mars• Global middle atmosphere• Tidal jets

• Gas and ice giants• Equatorial jets

Where do we observe superrotation (and how strong)? T
Earth - Annual mean

[zonally averaged] circulationU[As observed - ERA40- Kallberg et al. 2004]

Y
3

Where do we observe super-rotation (andData credit: Randal et al [2004]
how strong)?
Zonal mean wind (Annual Mean)

10• Equatorial values of s < 0most of the time
• Mass-weighted(compressible) global valuesof S ~ 0.010-0.017• Magnitudes ~ 0.01

Pressure (hPa)• Earth’s troposphere

1000
-50

• Earth’s stratosphere &Mesosphere

0Latitude (deg)50

Local super-rotation (Annual Mean)
10

Pressure (hPa)• Annual mean equatorial 𝑢!
westward except around 0.1
and 10-3 hPa• NB Eddy driven!

100

100

1000
-50

0
Latitude (deg)50

Where do we observe super-rotation (andhow strong)?
Data credit: Randal et al [2004]• Earth’s troposphere• Equatorial values of s < 0most of the time
• Mass-weighted(compressible) global valuesof S ~ 0.010-0.017• Magnitudes ~ 0.01

• Earth’s stratosphere &Mesosphere• Annual mean equatorial 𝑢!
westward except around 0.1
and 10-3 hPa• NB Eddy driven!

Why doesn’t Earth’s troposphere super-rotate
20
Mitchell, Birner, Lapeyre, Nakamura, Read, Riviere, Sánchez(locally)?
Image credit: Mitchell et al. [2019]a) Baroclinic instability in
mid-latitudes• Forces waves in midlatitudes [Eastward forcing]• Waves dissipate in tropics[Westward forcing]

DEC−FEB 1979−2013
20

15

Pseudoheight (km)• Eddy-driven jets mostly
driven by (westwardpropagating) Rossby
waves• Origin of Rossby waves?

the t
torq
grav

In b
ward
is ne
ple,
ual
flank
posi
flux
sour

10

5

0

−50

0
Latitude

50

2

−2

40 m s2.4.4
edd

Why doesn’t Earth’s troposphere super-rotate(locally)?
• Eddy-driven jets mostly
driven by (westwardpropagating) Rossby waves• Origin of Rossby waves?
a) Baroclinic instability in
mid-latitudesb) Tropical divergence fromdeep convection• Waves launched in tropics[Eastward forcing]• Waves dissipate in midlatitudes [Westward forcing]!"•≈ 𝑆 = −𝜵. 𝒗𝝌 𝜁!#• [Sardashmukh & Hoskins
1988]

Image credit: Sardeshmukh & Hoskins [1988]

Why doesn’t Earth’s troposphere super-rotate
Image credit: Suarez & Duffy [1992](locally)?
• Origin of Rossby waves?
a) Baroclinic instability in midlatitudesb) Tropical divergence fromdeep convection• Transition to equatorial
super-rotation as tropicalheating is increased• Suarez & Duffy [1992]• 2-level PE numerical model• Additional tropical heatsource (~Q0 sin 2l)

Why doesn’t Earth’s troposphere super-rotate
Image credit: Suarez & Duffy [1992](locally)?
• Origin of Rossby waves?
a) Baroclinic instability in midlatitudesb) Tropical divergence fromdeep convection• Transition to equatorial
super-rotation as tropicalheating is increased• Suarez & Duffy [1992]• 2-level PE numerical model• Additional tropical heatsource (~Q0 sin 2l)

Barotropic

Baroclinic

Why doesn’t Earth’s troposphere super-rotate(locally)?
Image credit: Arnold et al. [2012]• Origin of Rossby waves?
a) Baroclinic instability in
mid-latitudesb) Tropical divergence fromdeep convection• Transition to superrotation as tropicalheating is increased• Non-zonal heating anomaly
in n-level PE model (CAM)• Strong bifurcation
associated with equatorial
Rossby wave resonance?

Where do we observe super-rotation (andhow strong)?
Zonal mean wind (Annual Mean)

10• Annual mean equatorial 𝑢!
westward except around 0.1
and 10-3 hPa• NB Eddy driven!

0

Local super-rotation (Annual Mean)

2

10
-50

-4

0
Latitude (deg)

50
10-2

Pressure (hPa)• Equatorial values of s < 0most of the time10
• Mass-weighted(compressible) global valuesof S ~ 0.010-0.017
10• Magnitudes ~ 0.01

• Earth’s stratosphere &Mesosphere

Data credit: Randal etal [2004]

10-2

Pressure (hPa)• Earth’s troposphere

-4

100

102

-50

0
Latitude (deg)50

Where do we observe super-rotation (andhow strong)?
• Earth’s troposphere• Equatorial values of s < 0most of the time
• Mass-weighted(compressible) global valuesof S ~ 0.010-0.017• Magnitudes ~ 0.01

• Earth’s stratosphere &Mesosphere• Annual mean equatorial 𝑢!
westward except around 0.1
and 10-3 hPa• NB Eddy driven!

Data credit: Randal etal [2004]

Where do we observe super-rotation (andhow strong)?
Equatorial Local Super-rotation• Equatorial values of s < 0• Mass-weighted(compressible) global valuesof S ~ 0.010-0.017• Magnitudes ~ 0.01

• Earth’s stratosphere• Equatorial values of s range
over ±0.14 due to QuasiBiennial Oscillation andSemi-Annual oscillations• NB Eddy driven!

10

100
1000
1960

1965

1970
Year

1975

1980

1

Pressure (hPa)• Earth’s troposphere

Pressure (hPa)

1

10

100
1000
1985

1990

1995

2000
Year

2005

Laboratory experiments: Internal wave
streaming with standing wave forcing• Analogue of the Earth’s QBO• Plumb & McEwan [1978]• Interaction of standing internal
gravity waves with mean flow
(forced from below – or above)• Super-position of clockwise andanticlockwise moving waves• Leads to oscillating mean
azimuthal flow as either
travelling wave accelerates zonal
flow

Laboratory experiments: Internal wave
streaming with standing wave forcing• Analogue of the Earth’s QBO• Plumb & McEwan [1978]• Interaction of standing internal
gravity waves with mean flow
(forced from below – or above)• Super-position of clockwise andanticlockwise moving waves• Leads to oscillating mean
azimuthal flow as either
travelling wave accelerates zonal
flow

Laboratory experiments: Internal wave
streaming with standing wave forcing• Analogue of the Earth’s QBO• Plumb & McEwan [1978]• Interaction of standing internal
gravity waves with mean flow
(forced from below – or above)• Super-position of clockwise andanticlockwise moving waves• Leads to oscillating mean azimuthal
flow as either travelling wave
accelerates zonal flow
• NB Needs a minimum forcing
amplitude

Laboratory experiments: Internal wave
streaming with standing wave forcing
a)

b)

z

−c

0

z

−c

+c

c)

d)

z

−c
e)

+c

0

0

z

+c

−c
f)

0

ward anomaly
ward, as illus
eastward anom
scending andimage of the fi
self and an os
being determi
rate of dissipa
celeration of t
so a shorter p
speeds symm
for example,
The mean flow
with the flow
ilar to the sym+c

2.8 Conclus

Laboratory experiments: Internal wave
streaming with standing wave forcing

No mean flow
[Credit Otobe et al. 2018]

Mean flow develops and feeds back onto waves

Laboratory experiments: Internal wave
streaming with standing wave forcing
a)

b)

z

@
@

(⇠)

•

=

exp

@
@
+⇤
@⇠
@⇠

⇤

Z ⇠

◆

✓

(

)

⇠

exp

Z ⇠

( +

)

⇠

◆

−c

0

−c

+c

c)

+c

0

d)

z

z

= !/

•
•

✓

=

z

=(
/( ( ))

)/(

⌫)

−c

0

+c

e)

−c

0

+c

f)

• ⇤ = ⌫ /( ( ) )• ⇤ =/( ( ))

2.8 Conclu

z

−c

0
u

z

+c

ward anomal
ward, as illu
eastward ano
scending andimage of theself and an obeing determ
rate of dissip
celeration of
so a shorter
speeds symm
for example,
The mean flo
with the flow
ilar to the sy

−c

0
u

+c

In this chap
comprehensi
Earth, Mars,among themtion, which arized the dev

Laboratory experiments: Internal wave
streaming with standing wave forcing• Onset of mean flow oscillation
as wave forcing amplitude isincreased depends onparameters (e.g. N2)

=

·

= .

·

= .

8

12
10
A2

2

A

Linear fit
4

A2 (mm/s)2A2 (mm/s)26

8Linear fit

6
4

2
2

0

=)

0

11

12
13
14
Forcing amplitude (mm)

15

11

11.5

12

12.5 13 13.5 14
Forcing amplitude (mm)

14.5

15

• Small N2 -> SUB-critical Hopf
• Larger N2 -> SUPER-critical Hopf
• [Semin et al. 2018]

Laboratory experiments: Internal wave
streaming with standing wave forcing
@
@

=

@
@
+⇤
@⇠
@⇠

• ⇤ = ⌫ /( ( ) )• ⇤ =/( ( ))

=

·

= .

0.35

·

= .

8

Subcritical
Tricritical
Supercritical

0.3
0.25

10

Linear fit
4

8

Linear fit

6
4
2
0

12
13
14
Forcing amplitude (mm)

15

0.2

Stable

0.15

Cl
Na

Unstable

0.1

2

11

Λ1

A

A2 (mm/s)2A2 (mm/s)2

A2

2

Mg
Cl

2

12

6

0

⇤

11

11.5

12

12.5 13 13.5 14
Forcing amplitude (mm)

14.5

=)

=)
=)

15

0.05
0

0

1

2

Λ2

3

4

Where do we observe superrotation (and how strong)?
• Mars atmosphere• Annual mean zonal wind
exhibits midlatitude
westerly jets and mostly
easterly flow in the tropics• Weak westerly flow on theequator below 20 km
altitude• Local super-rotation s
peaks at around 0.03
• Seasonal variations?

Where do we observe super-rotation(and how strong)?
Zonal/annual mean u MY28-9• Mars atmosphere

-60

10.0

0
20

40

-2

0

20

-40

60

40

20

60

Pressure (Pa)

1.0
20

100.0
0

0

-50

0

0
Latitude (deg)50

Zonal mean s MY28-9
-0.6
0
-0.
50

-0.80
-0.70

1.0

-0.90

0.1
40

.
-0

-0.3

0

100.0
-50

0
Latitude (deg)

-0.20
-0.3
0
-0.
40
-0.
-0.6 50
0
-0.7
0
-0.80
-0.90

10.0
-0.10

Pressure (Pa)• Annual mean zonal wind
exhibits midlatitude
westerly jets and mostly
easterly flow in the tropics• Weak westerly flow on theequator below 20 km
altitude• Local super-rotation s
peaks at around 0.03
• Seasonal variations?

0.1

50

Where do we observe super-rotation(and how strong)?
• Mars atmosphere• Annual mean zonal wind
exhibits midlatitude
westerly jets and mostly
easterly flow in the tropics• Weak westerly flow on theequator below 20 km
altitude• Local super-rotation s
peaks at around 0.03
• Seasonal variations?

Sm

0.2

Where do we observe super-rotation(and how strong)?
0.1
0.0

3000

3200

3400
Time (sol)

3600

3800

Local super-rotation• Mars atmosphere

S0

Sm0

0.06
0.2
0.04
0.1
0.02
0.0
200
0.00

300

MY28
3200

3000

400
LS (deg)
3400
Time (sol)

500

600

3600

MY29 3800

700

Global super-rotation
0.06
S0• Annual mean zonal wind
exhibits midlatitude
westerly jets and mostly
easterly flow in the tropics• Weak westerly flow on theequator below 20 km
altitude• Local super-rotation s
peaks at around 0.3• Seasonal variations?
• Global super-rotation
varies from ~0 to 0.07

Global super-rotation

0.3

0.04
0.02
0.00
200

300

400
LS (deg)

500

600

700

Super-rotation in the Martian
atmosphere

LEWIS AND READ: MARTIAN ATMOSPHERIC SUPERROTATION• Local super-rotation s
peaks at around theequinoxes [LS ~ 0o and180o]• [Lewis & Read 2003]

15 - 3𝑢! at p = 136 Pa[z ~ 10 km]

Super-rotation in the Martian
atmosphere15 - 4• Local super-rotation s
peaks at around theequinoxes [LS ~ 0o and180o]• [Lewis & Read 2003]• Enhanced by increased
dust loading [x5]LEWIS AND READ: MARTIAN ATMOSPHERIC SUPERROTATION

𝑢! at p = 136 Pa[z ~ 10 km]

Super-rotation in the Martian
atmosphere• Local super-rotation s
peaks at around theequinoxes [LS ~ 0o and180o]• [Lewis & Read 2003]• Enhanced by increased
dust loading [x5]Terrestr

but intense but northern summer islived.
This impression that the main zona
pally the result of angular momentum
ional overturning circulation is furthe
𝑢!sideration
with of the eddy fluxes of moclinic instabilities developing in assoc
ional temperature gradients in the vici
streams in the Earth’s atmosphere ten
momentum into sharpened secondaryat mid-latitudes. On Mars, however,instabilities of the westerly zonal jets t
andwithout
baroclinic-barotropic
character (Barntends to flatten
Diurnalcycleand weaken the jets
tude. This may be a consequence ofradius on Mars being of around the s
therefore larger relative to the underlyof the zonal jet). Theoretical studies
1983) suggest that the sense of mom
under such circumstances, eliminating
nent of the jets.
The tropics are much less prone toDifference
ment of large scale flow instabilities.
of large quantities of suspended mine
mal tides may be amplified, even at r
the point where nonlinear interaction
tion of significant eddy-driven jet flo
an example from a model simulation
the LMD Mars GCM (Forget et al.,2003) with a large concentration ofSuper-rotation in the Martian
atmosphere

LEWIS AND READ: MARTIAN ATMOSPHERIC SUPERROTATION

maximum solar heating is higher in the atmosphere, thecells appear to form a quadrupole pattern with horizontal
convergence and vertical divergence at around 10 km
altitude over the equator. The pattern of four cells in themeridional circulation appears to be induced by the presence of atmospheric tidal components, forced most strongly,
symmetrically about the equator at equinox. In experiments
without tidal forcing, shown in the following
section, theSomeridional circulation tends to be dominated by a single cellat most times of year.
[18] The equinoctial regime is transitional, as the atmosphere switches from a northern summer to winter solsticial
circulation, with the larger, northern hemisphere (clockwise)cell growing to dominate the cross equatorial circulation astime progresses. The relative strengths of the northern andsouthern hemisphere cells in Figure 5 are sensitive to theaveraging period chosen. As observed by Haberle et al.
[1993], the intensity of the Hadley circulation in the model
is very sensitive to the subsolar latitude, where heating is a
maximum [Schneider, 1983; Lindzen and Hou, 1988].
Figure 6 shows the meridional circulation from the northernhemisphere summer period, dominated by a single, anticlockwise cell which grows in intensity with dust loading
and circulates around the region of the equatorial jet. A
single, dominant Hadley cell is more typical of the Martiancirculation at most times other than close to equinox [e.g.,
Haberle et al., 1993; Forget et al., 1999].

• Local super-rotation s peaks
at around the equinoxes [L~ 0o and 180 ]• [Lewis & Read 2003]

15 - 9𝑇! spectra at p = 25 Pa[z ~ 25 km]
Realistic topography• Enhanced by increased dust
loading [x5]• Role of thermal tides andtopography?

• Easterly tides• Interaction with m=2
topography generates
westerly Kelvin wave “nonmigrating” tide
• Topography
4. Tidalactually
Forcing
REDUCESsuper-rotation–[ ] Wilson and Hamilton [1996] describe an experiment
WHY? in which removing the diurnal cycle from their model
19

resulted in no westerly flow over the equator. In this section,
results from a series of similar experiments are described in

Flat topography

A super-rotating SAO in the Martian atmosphere• A semi-annual oscillation in 𝑢! isseen in reanalyses ofobservations of the Martian
middle and lower atmosphere[Ruan et al. 2019 Icarus]• Seen between ±40o latitude• Wind doesn’t always reverse• Diagnose forcing using TEM
equation for zonal momentum

10o-40oN

10oN-10oS

10o-40oS[Ruan et al. 2015]𝑢! (m s-1)

A super-rotating SAO in the Martian atmosphere• Diagnose forcing using TEM equation forzonal momentum
1.

2

3

1

4
3

3 (transient)• Forcing similar to Earth SAO[Ruan et al. 2015]2• Westward phase dominated by horiz. adv. [1]• Eastward phase dominated by Kelvin modes• Plus important role for thermal tides &stationary waves

3 (Kelvin)

3 (stationary)

3 (Thermal tides)

4Super-rotation in Gas/Ice Giant planet[Credit, Sanchez-Lavega et al. 2019]
atmospheres82
Sánchez-Lavega, Sromovsky, Showman, Del Genio, Young, Hueso, Garcı́a-Melendo, Kaspi, Orton et al.
Jupiter 𝑢!

Figure 4.12 Jupiter zonal wind profiles. Red is from Voyager data
(Limaye, 1986), black (Garcı́a-Melendo et al., 2011a) and blue (Porco
et al., 2003) are from Cassini data, and green is from HST data
(Garcıa-Melendo and Sánchez-Lavega, 2001).

Saturn 𝑢!
4.7 Jupiter and Saturn: Mean wind at cloud level
4.7.1 Upper cloud level

Figure 4.12 Jupiter zonal wind profiles. Red is from Voyager data
(Limaye, 1986), black (Garcı́a-Melendo et al., 2011a) and blue (Porco
et al., 2003) are from Cassini data, and green is from HST data
(Garcıa-Melendo and Sánchez-Lavega, 2001).

Jupiter has between 7 and 8 jets per hemisphere at the nominal
ammonia cloud level (⇠ 700 mbar) as shown in Figure 4.12.
Its distribution is not symmetrical and is dominated by a strong
equatorial jet with maximum velocities of 140 m s 1 . A particular feature of Jupiter’s zonal wind system is the presenceof a strong eastward jet at 24 N with measured maximum velocities between 120 ms 1 and 180 ms 1 (Maxworthy, 1984;
Limaye, 1986; Simon, 1999; Garcıa-Melendo and SánchezLavega, 2001; Asay-Davis et al., 2011; Barrado-Izagirre et al.,2013; Sánchez-Lavega et al., 2017; Tollefson et al., 2017).
There 4.13
is notSaturna southern
therepresents
24 N jet,Voyager
only a ⇠60
Figurezonal counterpart
wind profile. for
Green
data
1
(Sánchez-Lavega
2000);
black
is Cassini
imagingin the sits
ms jet at -27 etS,al.,
very
close
to thelocationwheredata
the GRS
continuum(350–500
red is Cassini
imaging
the profile(-23 ). Perhaps
thembar);
GRS presenceaccounts
fordatatheinwindstrongly
absorbingband at 890-nm(60–250mbar)Before theasymmetryat ⇠ methane±24 latitudes,
but it is
unknown.
(Garcı́a-Melendo et al., 2011b).
Cassini encounter with Jupiter in 2000, the equatorial jet always

Where do we observe super-rotation(and how strong)?
Zonal velocity (m s-1)

• Giant planet (a ~ 11.aEarth)rotates rapidly (trot = 9.926
hours)• Multiple eastward andwestward zonal jets in eachhemisphere at cloud tops
• Strong (>100 m s-1) eastward
equatorial jet• Local super-rotation at cloud
tops peaks at around smax =+0.006 at the equator

140
120
100
80
60
40
20
0
15

10

5
0
-5
Planetographic Latitude (degs)

-10

-15

-10

-15

(b) Local super-rotation index
Local Super-rotation s• Jupiter’s atmosphere(a) Zonal velocity

0.02
0.00
-0.02
-0.04
-0.06
-0.08
15

10

5
0
-5
Planetographic Latitude (degs)

Super-rotation in Gas/Ice Giant planet[Credit, Sanchez-Lavega et al. 2019]
atmospheres
90

92
Sánchez-Lavega, Sromovsky, Showman, Del Genio, Young, Hueso
Sánchez-Lavega, Sromovsky, Showman, Del Genio, Young, Hueso, Garcı́a-Melendo, Kaspi, Orton et al.

Uranus 𝑢!

Neptune 𝑢!

70

70

−30

−30

−40

−40

Planetographic Latitude, oshown
as the solid curve in Fig.60 4.21, is available in tabular
60
A
B
form50at 1 intervals (Sromovsky 50
et al., 2015). The dotted curveis the40 reflection of the solid curve
40 about the equator, revealing
small
asymmetries between
30 mid-latitude and large high-latitude
30
20
hemispheres.
The open circles in 20
the figure are the results of av10
eraging
the 2012-2014 results in 210 latitude bins. The dispersion
0of the0 binned results near the equatorare a result of differences−10−10
between the motions of waves and the motions of small discrete−20−20
features.
4.11.3−50 Symmetry properties−50

Lindal et al. 1990
−60
−60
Sromovsky
et al. (2012b) provided
individual
fits1991to the 2009
Limaye & Sromovsky
Sromovsky et al. 2001
−70
−70
2011 2009, and 2011
and 2011 data sets combined and forKarkoschka
the 2007,
Fry & Sromovsky 2004
−80
−80
data−90sets combined. They showedthat these data sets alone−90−10 distinguish−5
0 between
510−600 −400
0200 mod400
cannotsymmetric
and−200
asymmetric
Eastward drift rate, /hEastward wind speed, m/s
els. They also combined the data from 1997 through 2005 (seeFigure 4.24 Neptune wind results from Voyager radio measurements
Figure 4.21 Adopted zonal wind profile (solid curve) from
Sromovsky
et jetsal., 2009, and references therein), selecting only
NB SUB-rotating
equatorial(Lindal et al., 1990), cloud tracking in Voyager 2 images (Limaye and
Sromovsky et al. (2015), which combines Keck results fromthose with wind errors < 10 m/s and latitude errors  0.5 , andoat one edthat regio
were also
convectio
and curre
The V
drift rate
zonal wito be dis
all meas
period of
betweenbar radii
1990). T
group reshown w
sharp chacurves ar
fit the oSuper-rotation in Gas/Ice Giant planet
atmospheres• Origin of equatorial jets?
• How are they driven?
• Why are some eastward and others westward?
• Deep or shallow?
• Role of eddies vs axisymmetric circulations?
• Detailed shape (local minima/off-equatorial maxima)….?

• Three basic mechanisms
1. Vertically propagating/dissipating equatorial planetary waves?
2. Meridional momentum transport – tropics vs midlatitudes?
3. Deep convective/thermal Rossby waves….?

Super-rotation in Gas/Ice Giant planet
atmospheres• Origin of equatorial jets?
• How are they driven?
• Why are some eastward and others westward?
• Deep or shallow?
• Role of eddies vs axisymmetric circulations?
• Detailed shape (local minima/off-equatorial maxima)….?

• Three basic mechanisms
1. Vertically propagating/dissipating equatorial planetary waves?
2. Meridional momentum transport – tropics vs midlatitudes?
3. Deep convective/thermal Rossby waves….?

Super-rotation in Gas/Ice Giant planet
atmospheres

T. MAXWORTHY

1224• Origin of equatorial jets: 1.
Vertically propagating/dissipating equatorial planetary
waves?

DISSIPATIONyHEPMAL0• Cf Gravity wave streaming
mechanism [Maxworthy 1975]

TROPOPAUSE
t---------+WAVE SOURCES

FIG. 1. DIAGRAMhiATIC
ATMOSPHERICDRAWINGTEMPERATURE

OF THE

DISTRIBUTIONPHYSICALAND

PROPAGATINGTHE

SITUATION

AT

THE

CHARACTEROF

THJ3 INTERNALTO THEEQUATOR,SHOWINGKELVINTHE
WAVE“EAST.”The motion producing

the waves is assumed to be in the troposphere while the visible clouds which
are observed to convect at -100 m/set extend a small distance into the stratosphere. C,, and C,
are the wave phase and group velocities, respectively, and 3. its horizontal wavelength.

that in thii region the temperatureis almost con-can be shown that the waves do not affect the metwo waves have neither the same wavelength nor themixed Rossby-gravity
wave momentum can begin
same magnitude of phase speed and best agreement
and eventuallywith observations is found when a is a function of to produceanegativevelocitygradienta retrograde flow at high altitudes.
height. Obviously it is premature to try to quantify
all of these effects at the present time. As more
information becomes available, the range of the
I
1
2.0 1
I
study can be narrowed to take them into account.
1.8
Our present purpose is only to present a reasonable
1.6
first model and show what consequences arise fromit. Only the future can tell what the final values of
1.4
Y
the disposable parameters are likely to be.
2 1.2
It is also possible to argue crudely about limits
j 1.0
on the values for U, and Ld based on a stability
criterion. We assume that the shear layers created; 0.8
by the waves will adjust themselves so that anys!J 0.6that isformedstreaming
will create disturbances or• instability
Cf Gravity
wave
0.4
turbulence
that willthen limit the magnitude
mechanism[Maxworthy1975] of themean shear. That is, in some sense we create a self0.2
system.
The most likely
criterion is that the• limiting
Upwardpropagating
equatorial
0
-100
0
KUJ
300
4m
5aJ
Richardson
number(gs)/(XJ/a~)~will
alwaysbe
Kelvinwaves
accelerate
𝑢
!
where
J!a VELCCITY,
m, ml4s
greater than a. A representative value for XJ/az istheyin dissipate
𝑢! should≈ 𝑐 (for
UJL,
our system, toward
although we
in a more Fro. 2. VRLoCnY pR0Fr~R.sFORTHE C A S E A = -1 AND
retiedmodel
compute local values and adjust the A JET muwrmri
OF 12,000 km, i.e. C,’ = 460 m/see,strongforcing)c,’ = -260 m/s=.
parameters at every stage. For this first model theIn this case there is no stress at the tropopause so that
simplest approach is called for, so thatthe underlying fluid need have no net velocity. For sevenvalues of Ka*: (1) 5 X 10-lB; (2) 5 x 10-r’; (3)5 x 10-l*; (4) 5 x 10-l’; (5) 5 x lo-“; (6) 5 x lo-“;(7) 5 x 10-e.

Super-rotation in Gas/Ice Giant planet
atmospheres• Origin of equatorial jets: 1.
Vertically propagating/dissipating equatorial planetary
waves?

300 K; the model predicts 440 m s peak winds at just
3:8! latitude. We must remember, however, that thepeak wind is always off the equator as far as thegeneralised model holds and that the model simply fails

Super-rotation in Gas/Ice Giant planet
atmospheres
250• Demonstrate in idealised
numerical models [Yamazaki et al.
2005]• Double-peaked profile in 𝜑?
• Combine with meridional
overturning circulation (cf HH80)?

200

Wind Speed [m s-1]

• Origin of equatorial jets: 1.
Vertically propagating/dissipating equatorial planetary
waves?

CassiniVoyager
Held-Hou model
modified model

150

100

50

0

-50

15

10

5

0

-5

-10

-15

Latitude (planetographic)
Fig. 2. Jupiter’s equatorial winds: observed winds and prediction of
simple models of a Hadley-type circulation which assume conservationof angular momentum. Cassini data is the same as that used in Fig. 1;
Voyager data cortesy of Dr. A.A. Simon-Miller (see Simon, 1999).

Super-rotation in Gas/Ice Giant planet
atmospheres

ARTICLE IN PRESS
515

Y.H. Yamazaki et al. / Planetary and Space Science 53 (2005) 508–525

0

20

40

Pressure (bars)

40

120

20

0

60
20

20

1.00

40

40

60

60
0

Pressure (bars)

80

40

-10

-5

(a)

0

5

10

15

0

10.00
-15

0

0

-10

0

5

10

15

Latitude (degs)

Meridional streamfunction for Run 613

Meridional streamfunction for Run 650
0.01

0.0

0.01

0.01

-5

(a)

Latitude (degs)

20

60

600
4
20

10.00
-15

Equilibrium T field

0.0

Pressure (bars)

0.0

Pressure (bars)

0.0

1.00

0.10

0.0

0
0.

-5.0

5.0

1.00

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10000.00
-15

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-12
-8

-10

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0
Latitude (degs)

-4

5

(b)

-8 -12

10

15

-10

-5

5

10

10.00
-15

15

Fig. 6. Latitude–height maps of zonal velocity (a) and meridional
streamfunction (b) from a simulation of a flow using the mechanistic
model of Li et al. (1997) and Li and Read (2000), for the pure Kelvinwave forcing scenario.

(b)

-10

10.0

5.
0
-1

0
Latitude (degs)

15.0

0.0

1000.00-4.0-5.0-10 0.0

0.0

5.0

(22)

10.00
-15

0.0

0

1620
8 12
4

10.0

10.00

5.0

Pressure (hPa)

1.00

0.10

0.0

0.10

100.00e residual
nents are

0.10

80

0.0

(21)

100

1.00

0.0

diffusion
fusion is
can also
ak smallfield F isux and its

0.10

0

overturning circulation (cf HH80)?
513

20

40

40

ARTICLE IN• PRESS
Combine with meridional/ Planetary and Space Science 53 (2005) 508–525

Zonal Velocity for Run 650

0.01

20

• Origin of equatorial jets: 1.
Vertically propagating/dissipating equatorial planetary
waves?

Zonal Velocity for Run 613

0.01

-15.0
-10.0
-5.0

-5

0

5

10

15

Latitude (degs)

Fig. 7. Latitude–height maps of zonal velocity (a) and meridional
streamfunction (b) from a simulation of a flow using the mechanistic
model of Li et al. (1997) and Li and Read (2000), for the combined
Hadley–Kelvin forcing scenario.

Super-rotation in Gas/Ice Giant planet
atmospheres• Origin of equatorial jets: 1.
Vertically propagating/dissipating equatorial planetary
waves?

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)

• Combine with meridional
ARTICLE IN PRESS
overturning circulation (cf HH80)?

azaki et al. / Planetary and Space Science 53 (2005) 508–525

lation observed in
e Baldwin et al.,t deep levels may
d profile observed
ent, however, thepproximately theare expected. But

150

Zonal wind [m/s]nds appear which
the 2D model
re not unexpected, since progradey stationary mean
ropagating Kelvinappear in the 2D
rced at the lower
ondition was non-

Jovian Zonal Wind at Cloud-Top
200

100
50
0
Observed (Cassini)
2D model (Kelvin+Hadley) at 400mb
3D model (Kelvin+Hadley) at 400mb
3D model (Kelvin only) at 400mb
3D model (Hadley only) at 400mb

-50
-100
20

15

10

5

0

-5

-10

-15

-20

Latitude [deg]Fig. 11. Comparison of observed and simulated cloud-top winds ofJupiter’s equatorial region.

appear just above the tropopause as seen in Fig. 10j.

Fig. 10. Evolution of mean zonal winds in GCM experiments: Top, middle and bottom panels show the evolution in the case of Kelvin-only, Hadley-only and combined forcings at 12, 24, 60, and
102 months after the thermal forcing was imporsed.

Super-rotation in Gas/Ice Giant planet
atmospheres• Origin of equatorial jets: 2.
Meridional momentum
transport – tropics vsmidlatitudes?

• Cf Earth’s tropics vs super-rotatingstate?
• Midlatitude baroclinic forcing vstropical convection?
• E.g. Young et al. [2019] Jupiter
GCM? – EASTWARD equatorial jetat p > 1 bar….

Super-rotation in Gas/Ice Giant planet
atmospheres• Origin of equatorial jets: 2.
Meridional momentum transport –tropics vs midlatitudes?
• Cf Earth’s tropics vs super-rotatingstate?
• Midlatitude baroclinic forcing vstropical convection?
• E.g. Young et al. [2019] Jupiter GCM?
– EASTWARD equatorial jet at p > 1
bar….
• Driven mainly by horizontal AM eddy
flux convergenceSuper-rotation in Gas/Ice Giant planet
atmospheres
98

Sánchez-Lavega, Sromovsky, Showman, Del Genio, Young, Hueso• Origin of equatorial jets: 2.
Meridional momentum
transport – tropics vsmidlatitudes?

• Cf Earth’s tropics vs super-rotatingstate?
• Midlatitude baroclinic forcing vstropical convection?
• E.g. Lian & Showman [2010] GCM?
• Driven mainly by horizontal AM
eddy flux convergence• Could account for eastward jets on
Jupiter & Saturn, but westward
jets on ice giants…..?
Figure 4.29 Atmospheric flow on the giant planets inThe smains inzonal-jeably conlatitudes
servatioequatori
tween thand Satchangestimescalclose tocertain lsign onthe barovorticity
thermaldata ana
gradienteral lati
stability
since theinstabili
the fluid
providesof atmogenerallria, whivelocity components is obvious. The right simulation is strongly
supercritical; the correlation between the outward and eastward
velocity components is weaker because of the complex, turbulent
convective structure. In both cases the momentum flux convergenceleads to equatorial superrotation.

Super-rotation in Gas/Ice Giant planet
atmospheres• Origin of equatorial jets: 3. Deep
convective/thermal Rossby
waves….?
• Deep convection organizedparallel to rotation axis
• Propagates like Rossby waves inDEEP spherical shell – i.e.
EASTWARD• E.g. Heimpel et al. [2005] GCM?
• Driven mainly by horizontal AM
eddy flux convergence

Figure 4.30 Zonal winds in a three-dimensional model of convection
in a thin spherical shell from Heimpel et al. (2005). The ratio of theinner and outer radii in the model is 0.9. The model is Boussinesq andthus ignores the increase of mean density with depth that occurs on thegiant planets. Equatorial superrotation and multiple off-equatorial jets
emerge, qualitatively similar to those on Jupiter.

boundaclosestcalledMot
Aurno
to-outecompaof thesimilar
Saturnflow bea bounsome qcarry onaturallatitud(solar(AurnoOn Jfour orrior, antant effhave band exmodelsplane,
helps cGlatzmSuper-rotation in Gas/Ice
Giantplanet100
Sánchez-Lavega, Sromovsky, Showman, Del Genio, Yo
atmospheres• Origin of equatorial jets: 3. Deep
convective/thermal Rossby
waves….?
• Deep convection organizedparallel to rotation axis
• Propagates like Rossby waves inDEEP spherical shell – i.e.
EASTWARD• E.g. Showman et al. [2011] GCM?
• Driven mainly by horizontal AM
eddy flux convergence in laterally
tilted vortices• Eastward u where dissipated.

Figure 4.31 Snapshots in the equatorial plane of two anelastic, 3D
simulations illustrating how the correlation between the convective
velocity components depends on the supercriticality (from Showman

Jupiter’s Quasi-Quadrennial Oscillation (QQO)• IRTF observations over
11years of T at ~20 hPa• See Orton et al. (1991)
Science & Leovy et al.
(1991) Nature• Discovery in 1991 by Glenn
Orton & colleagues oftemperature 𝑇! oscillations
in Jupiter’s stratosphere• Period ~ 4 Earth years• Analogue of QBO in
Earth’s stratosphere?
• Oscillations driven by upward
propagating equatoriallytrapped waves?

Jupiter’s Quasi-Quadrennial Oscillation (QQO)TEXES IRTF temperature measurements[Credit: Giles et al. 2020]• IRTF observations over
11years of T at ~20 hPa• See Orton et al. (1991)
Science & Leovy et al.
(1991) Nature

Models of QBO and QQO

Kelvin(m=2)• Quasi-linear wave models• (a) analytical and• (b) numerical mechanistic models ofequatorial waves and QBO-likeoscillations• Based on TEM formalism• Solve for structure of equatorial
waves with 𝑢! (𝑦, 𝑧)• Evolve 𝑢! (𝑦, 𝑧) with time in responseto ∇.(EP flux) due to each wave mode

MRG
(m=-11)
Oscillation period 𝜏 ≈ 𝐴!".$F’(y,z)∇. 𝑭T’(y,z)Simulated QQO [Li & Read (2000) PSS]

-200

-10o

0o

10o

20o

Simulated QQO [Li & Read (2000) PSS]TEXES IRTF temperature measurements[Credit: Giles et al. 2020]
-200

-10o

0o

10o

20o

Saturn’s Equatorial Oscillation (SEO)• Discovered in 2008 by Orton et al.
(2008 Nature) in IRTF measurementsof stratospheric temperatures• Period ~15 Earth years [~ 0.5 Saturnyears]• a semi-annual oscillation cf SAO?

• Confirmed in detailed Cassini
observations [Guerlet et al.
(2020) JGR]
• Driven by equatorial waves?
• Only n=1 equatorial Rossby mode
identified in observations…..

QQO in GCM simulations?

QQO in GCM simulations?

• Wave modes in the stratosphere (p<1 bar) include (Young & Read 2023 Icarus submitted)

Newly discovered Jovian stratospheric jet
nature astronomy
Articlehttps://doi.org/10.1038/s41550-023-02099-2

An intense narrow equatorial jet in Jupiter’s
lower stratosphere observed by JWST
Received: 25 April 2023
Accepted: 11 September 2023
Published online: xx xx xxxx
Check for updates

Ricardo Hueso 1 , Agustín Sánchez-Lavega 1, Thierry Fouchet 2,
Imke de Pater 3,4, Arrate Antuñano 1, Leigh N. Fletcher5,Michael H. Wong 6,7, Pablo Rodríguez-Ovalle 2, Lawrence A. Sromovsky 8,
Patrick M. Fry8, Glenn S. Orton9, Sandrine Guerlet2,10, Patrick G. J. Irwin 11,
Emmanuel Lellouch 2, Jake Harkett 5, Katherine de Kleer12, Henrik Melin 5,
Vincent Hue13, Amy A. Simon 14, Statia Luszcz-Cook 15,16 & Kunio M. Sayanagi17

The atmosphere of Jupiter has east–west zonal jets that alternate as afunction of latitude as tracked by cloud motions at tropospheric levels.
Above and below the cold tropopause at ~100 mbar, the equatorial
atmosphere is covered by hazes at levels where thermal infraredobservations used to characterize the dynamics of the stratosphere losepart of their sensitivity. James Webb Space Telescope observations of Jupiterin July 2022 show these hazes in higher detail than ever before and reveal thepresence of an intense (140 m s−1) equatorial jet at 100–200 mbar (70 m s−1
faster than the zonal winds at the cloud level) that is confined to ±3° of theequator and is located below stratospheric thermal oscillations that extend
at least from 0.1 to 40 mbar and repeat in multiyear cycles. This suggests thatthe new jet is a deep part of Jupiter’s Equatorial Stratospheric Oscillation andmay therefore vary in strength over time.
Jupiter and Saturn atmospheres have zonal jets with broad prograde
winds in their equatorial regions1,2. The winds are best observed atcloud-top levels but extend 3,000 km deeper in Jupiter3,4 and 8,000 km
in Saturn5,6. Above the cloud level, wind speeds decay with increasing altitude to nearly zero values at 20 mbar in most of Jupiter’s mid-latitudes7–9.
However, this pattern of vertical decay is spectacularly broken in Saturn’sequator, where an intense (400 m s−1) and narrow (5° width) jet is observed
10,11

relationship12,13, reveal the presence of intense stratospheric eastward
and westward winds alternating in direction as a function of altitudein the 0.1–40.0 mbar region8,14,15. The perturbations to the equatorial
stratospheric temperatures and inferred thermal winds vary periodically on multiyear timescales15–18, sharing characteristics with similar
phenomena on Earth, such as the quasi-biennial oscillation (QBO) andsemi-annual oscillation (SAO)12,19. Like their terrestrial counterparts,

Summary• Super-rotation on Earth troposphere is weak, mainly because eddy
forcing dominated by midlatitude baroclinic instability• Could be accelerated by enhanced divergent generation of Rrossby
waves in tropics• Role of thermal tides affect super-rotation of Mars lower atmosphere• Quasi-biennial/QQ oscillations in stratospheres due to upward
propagating waves• Equatorial jets opn gas giants?
• Several different possible mechanisms…