EART 160: Planetary Science 20 February 2008. Last Time Elastic Flexure Paper Discussion – Titan...
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Transcript of EART 160: Planetary Science 20 February 2008. Last Time Elastic Flexure Paper Discussion – Titan...
EART 160: Planetary Science
20 February 2008
Last Time
• Elastic Flexure
• Paper Discussion – Titan Atmosphere– Tobie et al., 2005
• Planetary Atmospheres– General Description
Today
• Homework 4 due, 5 out– Oh, huzzah.
• Planetary Atmospheres– Atmospheric Structure– General Circulation– Thermal Balance– Origin / Geochemistry
Atmospheric Structure
Convection, Weather, Clouds
T increases with alt. Stable to convectionCools by radiation
Shooting stars burn up
Low density, heated by X-rays
Free electrons, ionsAffects radio wave propagation
Exobase – Height at which 1/e particles can escape
Heating due to UVabsorption by O3
Atmospheric Pressure
• Atmosphere is hydrostatic:
• Ideal Gas Law:
• Combining these two:
gdzzdP )(
NRTPV
zRT
gPP
RT
gP
dz
dP
exp0
P Pressure Densityg Gravityz HeightV VolumeN Number of MolesR Gas ConstantT Temperature Mass of one Mole
Assuming: Isothermal Atmosphere Constant Gravity
Scale Height
• Let H = RT/g:
• P = P0 e-z/H
• H is the scale height of the atmosphere– Distance over which P
drops by 1/e
• Mass of a column of atmosphere– Mc = P/g
Venus Earth Mars Jupiter Saturn Uranus Neptune
H (km) 16 8.5 18 18 35 20 19
Atmospheric Temperature• Of course, temperature actually does vary with height• If a packet of gas rises rapidly (adiabatic), then it will expand and,
as a result, cool• Work done in cooling = work done in expanding
pC dT
pC
g
dz
dT
• Combining these two equations with hydrostatic equilibrium, we get the dry adiabatic lapse rate:
Cp is the specific heat capacityof the gas at constant pressure
• On Earth, the lapse rate is about 10 K/km• What happens if the air is wet?
dPM
VdP
General Circulation
• Zonal Mean Circulation– Wind parallel to lines
of latitude
• Fastest Transport • What drives zonal
winds?– Angular Momentum
Conservation!– dv = -2 dR
R
R
Zonal Winds
• Westerlies– Near-surface winds that
blow from the west in mid-latitudes
• Trade Winds– Light winds that blow
from the east in the tropics
• Winds alternate between prograde (eastwards) and retrograde (westwards)
Hadley Circulation
• Parcels of atmosphere rise and fall due to buoyancy (equator is hotter than the poles)
• The result is that the atmosphere is broken up into several Hadley cells
• Each cell makes a band of zonal wind
Rotation Cells
• How many cells depends on the Rossby number (i.e. rotation rate)
v
RRo planet sin2
Venus
Ro = 0.02
1 Cell / hemisphere
Ro = 4
3 Cells / hemisphere
Earth Jupiter
Ro = 30
5 Cells / hemisphere
R: planet radius, : rotation rate, : latitude, v: wind speed
Zonal Winds on Giant Planets
• The reason Jupiter, Saturn, Uranus and Neptune have bands is because of rapid rotations (periods ~ 10 hrs)
• The winds in each band can be measured by following individual objects (e.g. clouds)
Atmospheric Dynamics
• Solve a set of coupled dynamical, radiative and possibly chemical equations. – General Circulation Models (GCM)
• Coriolis Force– Objects moving on a rotating planet get
deflected
• Geostrophic Wind– Balance Between Pressure Gradients and
Coriolis Force
Geostrophic balance• In some situations, the only significant forces acting are due
to the Coriolis effect and due to pressure gradients
• The acceleration due to pressure gradients is
• The Coriolis acceleration is 2 v sin
• In steady-state these balance, giving:
x
P
1
x
Pv
sin2
1
• The result is that winds flow along isobars and will form cyclones or anti-cyclones
• What are wind speeds on Earth?
L L
Hisobars
pressure
Coriolis
wind
Next Time
• Planetary Atmospheres– Thermal Balance– Climate Change– Origin and Loss