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 4.Mars’ Hadley Circulation 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 4.Mars’ Hadley Circulation 5.Super-rotation on Venus and Titan 6.Jet formation on Jupiter

Planetary Atmospheres Atmospheres we’ll talk about today… Earth Mars Venus Titan (Saturn’s largest moon) Jupiter

Planetary Atmospheres ObjectComposition (“dry”) CondensiblesSurface Pressure Surface Temperature Atmospheric Dynamics Venus97% CO 2 3% N 2 SO 2 H 2 SO 4 90,000 mbar750 KSuper-rotating Earth78% N 2 21% O 2 1% Ar H2OH2O1000 mbar288 KHadley Cells Jet Streams Monsoons Mars96% CO 2 2.5% N 2 1.5% Ar CO 2 H 2 O (trace) 10 mbar220 KHadley Cells Jet Streams Dry Monsoons? Jupiter90% H 2 10% He NH 3 H 5 NS H 2 O? No solid surface 165 K (at 1000 mbar) Multiple jets Macroturbulence Titan100% N 2 CH mbar95 KGlobal 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 4.Mars’ Hadley Circulation 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

Let’s break down the atmosphere into symmetric and wavy components… Atmospheric Angular Momentum Jet Streams and Storms Flow variable (Wind, Temperature, Pressure, etc.) Symmetric partWavy 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 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 Atmospheric Angular Momentum

Outline 1.Overview of planetary atmospheres 2.Angular momentum in rotating atmospheres 3.Earth’s Hadley Circulation and Jet Streams 4.Mars’ Hadley Circulation 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

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 4.Mars’ Hadley Circulation 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 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 4.Mars’ Hadley Circulation 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 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 CH 4 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 1.Overview of planetary atmospheres 2.Angular momentum in rotating atmospheres 3.Earth’s Hadley Circulation and Jet Streams 4.Mars’ Hadley Circulation 5.Super-rotation on Venus and Titan 6.Jet formation on Jupiter

Jupiter Multiple Jets and macroturbulence

Jupiter

Jet Formation Stirring wave breaking wave breaking 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:

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 H 2 O, CO 2 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

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