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Part-6c
Circulation (Cont)
Means of Transferring Heat
Global Circulation
Easterlies /Westerlies
Polar Front
Planetary Waves
Gravity Waves
Mars Circulation
Giant Planet Atmospheres
Zones and Belts
Global Circulation on Earth
Coriolis parameter f ~ 0
but rotates fast enough so day/ night
differences small (unlike Venus)
Warm air rises to the tropopause
Equator to pole Hadley Cell
Equatorial low + polar high
Winds and Temperatures
solid: T(C)
dashed: v(m/s)
heavy line: tropopause
Earth with Rotation f≠0
Rising Tropical air returns
at higher latitudes
roughly three cells
f>0
x
• •
x
f=0
f=0
•
f<0
Form mid-latitude highs with transport
southward (weak easterlies, f small)
and northward (stronger westerlies, larger f)
Also a polar high
Note: upper troposphere global flow
‘Thermal Wind’
Horizontal gradient in T and/ or Γ
Geostrophic flow can intensify with z
Geostrophic wind : Fa = -"p
v
** v = -
1 )
k $ [%" p] h
#f
)
k local vertical , " h local horiz. (used // earlier)
p & poexp(-z/H) ; H = kT/mg
Therefore small surface pressure difference, but different
T can give large pressure difference at high altitudes
Using * * slope of v vs. altitude proportional
to the horizontal temperature gradient
'v
( "T h
'z
Horizontal temperature differences
causes increasing pressure
differences with altitude, intensifying
geostrophic flow
Earth Global Circulation
(Cont.)
Note: When a cold air mass and a
warm air mass interact, the differences
in pressure increases with altitude: H
~kT/mg --> Stronger winds at higher
altitudes, westerlies become jets
between 30o and 70o
Geostrophic circulation around
highs and lows
can be organized as easterlies and
westerlies
Pressure/Flow Maps
Polar high also
Red: ITCZ
Upper Troposphere
Geostrophic but disconnected from
land and sea masses
Rossby Waves
bring warm air north and cool air south
As seen from earlier slide, westerly motion
about the polar low. Waves break off-->
highs + lows. Wave crests move slowly west
Upper Troposphere Wave
Winter
geopotential height [= ∫g dz] of isobar
Rossby Waves and Vorticity
Include convection term
v
v v 1
"v v
v
+ ( v # $) v = % 2& ' v % $p
"t
(
2%D
"u
"
"
1"p
+ (u
+ v ) u=f v%
"t
"x
"y
("x
"v
"
"
1"p
2.
+ (u
+ v ) v = %f u %
"t
"x
"y
("y
v
continuity ) $ # v = 0 ; incompressible
"u "v
3.
+
=0
"x "y
Differentiate 1. with respect to y and 2. with respect
1.
to x + subtract and then use 3.
"v "u ˆ
v
Define vorticity of the flow : * =
%
=k # $'v
"x "y
Find
d
d
" r
[+ + f ] = 0 ; as usual = + v • $
dt
dt
"t
Therefore, Conserve Total Vorticity [+ + f ]
If f decreases (air moves south), then + must increase
PLANETARY WAVES
< ~ 0.5 bar Earth
Ω
L
H
Upper Troposphere Rossby Waves
Westerlies
(Incompressible Flow)
Total Vorticity Conserved
d[ζ+f]/dt = 0
ζ = k•∇xv vorticity
Northern Hemisphere
ζ > 0 counterclockwise; ζ < clockwise
Southern Hemisphere
South Pole
ζ< 0 counterclockwise; ζ >0 clockwise
f < 0 increasing northward
Wave Period
rotation rate + temperature difference
Outer cylinder hot inner cool
A type of baroclinic wave
Angular momentum from boundary
transferred to fluid,
Usual turbulence: large to small scale
Here small scale goes to organized flow
Rossby Waves and Jet Streams
~50-400km/hr (earth equator 3000km/hr
break off to form weather
Polar Jet
Geopotential Heights of 300mbar Level
Earth’s Thermospheric
flow near exobase
Note: Day / Night effects
Unlike troposphere
Gravity Waves
g
#
(%d & ' )z
T
Stable conditions : %d > ' : ˙z˙ $ & ( B2 z ; waves
with the Brunt - Vaisala frequency
" a ˙z˙ = - ( " a - ")g
˙z˙ $ -
!
Lenticular
Clouds
Lee
Waves
Rising air at Lows and falling at Highs
also drive planet scale gravity
waves mixing the troposphere with upper
atmosphere
Gravity Waves at Mars
Mars Circulation
fluid density is low
coriolis effect can be significant
Axial Tilt : Warm Summer Pole
Strong Gradients
Strong Irregular Westerlies
L
Latitude
L
H
Winter
H
H
summer
Weak Easterlies
T
Dust storms at Mars
Giant Planets
Temperature and Cloud
Structure
Gas Giants
Jupiter (71,300km) and Saturn (60,300km)
Ice Giants
Uranus and Neptune (~25,000km)
Clouds ~0.3-2bars
indicative of winds
What are winds
relative to on a
gas ball?
Galileo
Gas Giants
Sun + Internal Heat (~1.7 x solar)
(J =1/25 , S = 1/100 Earth)
Fast rotors (~10hr)->High Wind Speeds
Small Scale Eddies Feed Zonal Flow
Jupiter:
Zonal Winds : Westerlies (bright)
Eq. ~150m/s J; 400m/s S
Belts
: Easterlies (dark)
Red Spot : High (counter clockwise)
Saturn : Yearly (30 year) Storms
X=1-D/Rp where D is thickness of H2 layer
FAST ROTOR
Horizontal
L
L
H
H
L
H
L
H
Vertical View
L
H
H
L
Giant Planet Atmospheres
Zones: westerlies (eastern flow; prograde)
Bright clouds (condensed from NH3
act to cool air, higher)
8(4) per hemisphere jupiter (Saturn)
Belts: easterlies (retrograde)
Dark clouds (warmer, drier descending air)
Jupiter’s Atmosphere
Dominate by circulation cells and
zonal winds marked by different
colored cloud layers which are
higher in belts than in zones
Black small circle is Io
Zonal Wind Speeds vs.
Latitude at cloud level
Positve u(m/s): Westerlies
Simulation of Eddys
converting to flow
Cassini image of Jupiter
showing small scale eddies
and larger scale zonal flow
Galileo probe: high speed
winds extend 1000’s km
deep
Jupiter Model
Shells of Rotating Gas
Seen as Surface Winds
Simulations of Equatorial and High Latitude
Jets on Jupiter in a Deep Convection Model
M. Heimpel et al. Nature 438, 2005
Jupiter and Saturn: Westerly Equatorial Flow
Uranus and Neptune: Easterly (like earth)
determined by depth of molecular fluid layer
Simulation Results
a Cassini data
b flow speed
+ to the east
(westerlies)
c model
red to east; blue to
west
Model
Turbulent (high Re)
Low Rossby
Uranus and Neptune
Atmospheres ~83%H2, 15%He and
2% CH4
Cores liquid primarily ‘icy’ materials
(water, ammonia and methane)
and rocky materials (Si etc.)
Internal T ~5000K (vs 20000K
Jupiter)
Equatorial winds are easterlies, as
at earth implying shallow layer
Magnetic fields not well aligned with
the rotation axis
Uranus is tipped on its side likely
due to impact
Tipped
Uranus
and its
rings
Good pictures of
Vertical structure
Some Definitions
BAROTROPIC- density a function of pressure [ρ(p,T)];
regions of nearly uniform temperature; buoyancy
forces small; lack of fronts: e.g. southeast U.S. in the
summer or the tropics (hence, barotropic).
BAROCLINIC-density is a function of p and T [ρ(p,T)];
surfaces of constant pressure can intersect:
bouyancy forces are important; ‘thermal winds’ result.
Distinct air mass regions exist; fronts separate
warmer from colder air. In a synoptic scale baroclinic
environment you will find the polar jet, troughs of low
pressure (mid-latitude cyclones) and fronts. There are
clear density gradients caused by the fronts.
SYNOPTIC Scale- (large scale) weather systems with
horizontal dimensions of hundreds of km; momentum
equations can be scaled (horiz: coriolis + pressure
gradient; vert: hydrostatic). Mesoscale: intermediate.
MERIDIONAL: north/ south
ZONAL: east / west
MONSOON- (from seasonal) wind pattern that reverses
direction on a seasonal basis (e.g., monsoonal winds
in the Indian ocean). Synoptic scale sea breeze: hot
air over land replaced by moist air from over ocean;
upward diversion by mountains produces heavy rain.