Angular Momentum in Planetary Atmospheres

Angular Momentum in Planetary Atmospheres

Buffalo Astronomical AssociationMay 8, 2009

Jude S. SabatoAssistant Professor of Earth Science

Buffalo State College

Outline

1. Overview of planetary atmospheres2. Angular momentum in rotating atmospheres3. Earth’s Hadley Circulation and Jet Streams4. Mars’ Hadley Circulation5. Super-rotation on Venus and Titan6. Jet formation on Jupiter

Outline


Planetary Atmospheres

Atmospheres we’ll talk about today…

• Earth• Mars• Venus• Titan (Saturn’s largest moon)• Jupiter

Planetary AtmospheresObject Composition

(“dry”)Condensibles Surface

PressureSurface Temperature

Atmospheric Dynamics

Venus 97% CO23% N2

SO2H2SO4

90,000 mbar 750 K Super-rotating

Earth 78% N221% O21% Ar

H2O 1000 mbar 288 K Hadley CellsJet StreamsMonsoons

Mars 96% CO22.5% N21.5% Ar

CO2H2O (trace)

10 mbar 220 K Hadley CellsJet StreamsDry Monsoons?

Jupiter 90% H210% He

NH3H5NSH2O?

No solid surface

165 K (at 1000 mbar)

Multiple jetsMacroturbulence

Titan 100% N2 CH4 1500 mbar 95 K Global Hadley CellSuper-rotationMethane cycle

Outline


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

Let’s break down the atmosphere into symmetric and wavy components…

Atmospheric Angular MomentumJet Streams and Storms

Flow variable (Wind, Temperature, Pressure, etc.)

Symmetric part Wavy part

= +Symmetric part

conserves its angular

momentum…

…if there are no waves

Take home points:• Atmospheric angular momentum is conserved

if 1. There are no torques on the atmosphere2. 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

Atmospheric Angular Momentum

Outline


EarthThere 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


MarsMars 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


Venus

Venus in the ultraviolet

VenusVenus’ 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 than your spoon!

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

George Hadley’s original idea to explain the trade winds (1735)

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

False color RADAR image

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?

So what about super-rotation…

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


Jupiter

Multiple Jets and macroturbulence

Jupiter

Jet Formation

Stirring

wavebreaking

wavebreaking

E-W Wind

Angular momentum divergence

Angular momentum divergence

Angular momentum convergence

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:

SummaryAngular 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



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



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



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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Angular Momentum in Planetary Atmospheres