Angular Momentum in Planetary Atmospheres

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```							Angular Momentum in Planetary
Atmospheres
Buffalo Astronomical Association
May 8, 2009

Jude S. Sabato
Assistant Professor of Earth Science
Buffalo State College
Outline
1.   Overview of planetary atmospheres
2.   Angular momentum in rotating atmospheres
3.   Earth’s Hadley Circulation and Jet Streams
5.   Super-rotation on Venus and Titan
6.   Jet formation on Jupiter
Outline
1.   Overview of planetary atmospheres
2.   Angular momentum in rotating atmospheres
3.   Earth’s Hadley Circulation and Jet Streams
5.   Super-rotation on Venus and Titan
6.   Jet formation on Jupiter
Planetary Atmospheres
•   Earth
•   Mars
•   Venus
•   Titan (Saturn’s largest moon)
•   Jupiter
Planetary Atmospheres
Object Composition Condensibles   Surface       Surface       Atmospheric
(“dry”)                    Pressure      Temperature   Dynamics
Venus   97% CO2    SO2            90,000 mbar   750 K         Super-rotating
3% N2      H2SO4
Earth   78% N2     H2O            1000 mbar     288 K         Hadley Cells
21% O2                                                Jet Streams
1% Ar                                                 Monsoons
Mars    96% CO2    CO2            10 mbar       220 K         Hadley Cells
2.5% N2    H2O (trace)                                Jet Streams
1.5% Ar                                               Dry Monsoons?
Jupiter 90% H2     NH3            No solid      165 K (at 1000 Multiple jets
10% He     H5NS           surface       mbar)          Macroturbulence
H2O?
Titan   100% N2    CH4            1500 mbar     95 K          Global Hadley Cell
Super-rotation
Methane cycle
Outline
1.   Overview of planetary atmospheres
2.   Angular momentum in rotating atmospheres
3.   Earth’s Hadley Circulation and Jet Streams
5.   Super-rotation on Venus and Titan
6.   Jet formation on Jupiter
Momentum

Momentum measures motion and mass:

momentum = mass x velocity
Momentum

Newton’s First Law: “An object at rest will
remain at rest and an object in motion will
move in a straight line at constant speed,
unless acted on by a force.”

force = change in momentum
Momentum
Angular Momentum

Angular Momentum measures spinning
motion:

Angular Momentum = radius x mass x velocity
Angular Momentum

Newton’s First Law (revisited): “An object that is
not spinning will remain so and a spinning object
will continue spinning at constant speed and in
the same orientation, unless acted on by a
twisting force (torque).”

torque = change in angular
momentum
Angular Momentum
Atmospheric Angular Momentum
Jet Streams and Storms
Let’s break down the atmosphere into symmetric and wavy
components…

Symmetric part
conserves its
=        angular
momentum…
+   …if there are no
waves

Flow variable (Wind,
Temperature, Pressure,   Symmetric part       Wavy part
etc.)
Atmospheric Angular Momentum
Take home points:
• Atmospheric angular momentum is conserved
if
1. There are no torques on the atmosphere
2. There are no atmospheric waves
• Atmospheric waves open the door to super-
rotation
• angular momentum transfer associated with
atmospheric waves can generate E-W jets
Outline
1.   Overview of planetary atmospheres
2.   Angular momentum in rotating atmospheres
3.   Earth’s Hadley Circulation and Jet Streams
5.   Super-rotation on Venus and Titan
6.   Jet formation on Jupiter
Earth
There are so many interesting dynamical
phenomena in Earth’s atmosphere!
We’ll focus on the Hadley Circulation and Jet
Streams…
• Hadley Cells Driven by low latitude convection
• Hadley Cells approximately conserve angular
momentum
• Angular momentum conservation means fluid
moves in rings around the planet – not at all true!
Earth
Earth
Earth
Earth
• Angular momentum conservation in the
Hadley Cell generates a subtropical Jet Stream
– Subtropical jet is unstable and becomes wavy
– These atmospheric waves (midlatitude storms)
can sometimes generate a second jet stream
Earth
Monsoons by angular momentum too!

After Bordoni and
Schneider 2008,
Nature Geoscience
Outline
1.   Overview of planetary atmospheres
2.   Angular momentum in rotating atmospheres
3.   Earth’s Hadley Circulation and Jet Streams
5.   Super-rotation on Venus and Titan
6.   Jet formation on Jupiter
Mars
Mars has a Hadley Circulation too…
• Driven by convection
• Much greater degree of angular momentum
conservation, however…
• Angular momentum conservation means fluid moves in
rings around the planet – probably not true for Mars
either
– Jet stream is unstable and becomes wavy (still true for
Mars)
– Atmospheric waves (midlatitude storms) do not generate a
second jet because the planet is too small
– Topography/surface heating can force waves that move the
atmospheric angular momentum from place to place
Mars
Mars

• Mars topography/surface thermal inertia may
have an “elevated heat island” effect
• Elevated heat island drives Indian Monsoon
(maybe, or better partially)
• Is there a “dry monsoon” on Mars?
• One way or another the atmosphere is not
“moving in rings” (transport properties are not
axisymmetric)
Outline
1.   Overview of planetary atmospheres
2.   Angular momentum in rotating atmospheres
3.   Earth’s Hadley Circulation and Jet Streams
5.   Super-rotation on Venus and Titan
6.   Jet formation on Jupiter
Venus

Venus in the ultraviolet
Venus
Venus’ atmosphere appears to be super-
rotating…

Super-rotation: winds aloft at the equator are
faster than the planet’s rotation

This is akin to stirring a cup of coffee and
observing that the coffee is circulating faster
Titan

Titan in the infrared
Titan

• Titan has a global Hadley Cell

• Titan’s upper atmosphere is in a state of
super-rotation, like Venus
Titan

Titan

• CH4 on Titan behaves very much like water on
Earth (“methanological” cycle)

• Links between seasonal and methanological
cycle could drive angular momentum changes
in the atmosphere and the solid surface
Titan
Recent observations show a
slight change in Titan’s spin
rate…

This could be evidence of a
liquid water ocean between
the solid interior and icy
surface.

What’s the culprit? It could be
angular momentum
transfer between the
surface and the
atmosphere.

The fly-wheel crust of Titan?
Any East-West asymmetries could be responsible
• On Titan: ???
• On Venus:
– “moving candle” = Venus is rotating very slowly; the Sun
heats one side for quite a while; radiative cooling on the
other side
– Atmospheric waves, from wind over mountains, propagate
upward and deposit momentum in the upper atmosphere
• They’re both slow-rotators ---- easy to get super-
rotation in a model with slow rotation
• Bottom line: we know what kinds of mechanisms can
generate super-rotation but we don’t know which of
these, if any, are operating in which atmosphere
Outline
1.   Overview of planetary atmospheres
2.   Angular momentum in rotating atmospheres
3.   Earth’s Hadley Circulation and Jet Streams
5.   Super-rotation on Venus and Titan
6.   Jet formation on Jupiter
Jupiter

Multiple Jets and macroturbulence
Jupiter
Jet Formation
wave
breaking
Angular momentum
divergence

Stirring              Angular momentum convergence

Angular momentum
divergence
wave
breaking
E-W Wind
Jet Formation
Jupiter
Jets form by stirring at small scales, exciting waves and
transporting angular momentum across latitude circles.

• Stirring is thought to be by “thunderstorms”
• Equatorial super-rotation requires atmospheric waves to travel across
the equator
• Why so many jets? That is, what determines the jet width?
 size of the planet
 speed of the wind
 rotation rate of the planet

Rhines Length:
Summary
Angular momentum is a unifying concept in
atmospheric dynamics.

Earth
• Earth’s Hadley Cell is approximately angular
momentum conserving (sometimes, sort of)
• Angular momentum conserving theories accurately
predict width of the cells and the existence of a jet
stream
• Monsoons may be a result of dynamical regime shifts
between nearly (symmetric) angular momentum
conserving flow to wave driven flow
Summary
Angular momentum is a unifying concept in
atmospheric dynamics.

Mars
• Mars’ Hadley Cell is much more angular momentum
conserving than Earth’s but is still not “rings of fluid”
• Angular momentum conserving theories accurately
predict width of the cells on Mars as well
• A type of dry Monsoons may be driving non-
axisymmetric transport of H2O, CO2 and dust
Summary
Angular momentum is a unifying concept in
atmospheric dynamics.

Venus and Titan
• Super-rotation in both atmospheres
• Several mechanisms are possible causes but none are
certain (and may be different for each atmosphere)
• Titan’s atmosphere may be exchanging significant
angular momentum with the surface, causing spin
rate changes
Summary
Angular momentum is a unifying concept in
atmospheric dynamics.

Jupiter
• Multiple jets and macroturbulence
• Equatorial super-rotation as well
• Angular momentum transport can form jets, while
a planet’s size, rotation rate and atmospheric wind
speeds determine their width/number
THANK YOU!

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