1. Space Science: Atmospheres Part- 8
Read CH Chap. 2
dePL 4.5
GENERAL CIRCULATION
HADLEY CELL
ROTATING FRAME
CORIOLIS FORCE
TOTAL TIME DERIVATIVE
GEOSTROPHIC FLOW
GRADIENT WIND
CYCLOSTROPHIC FLOW
INERTIAL FLOW CYCLONIC

2. General Circulation DIFFERENTIAL HEATING => FLOW
Both longitudinal and latitudinal
Global
Percentage Heat Input Per Day
E V* M J
dT/Te 0.68% % 38% 1.5x10-3 %
*If one use the planet rotation rate then
the ratio becomes >100%

3. Horizontal Pressure Differences In troposphere T ~ [Ts -  z]
(p/po) = (T/To); x = /(-1); =cp/cv
High Lapse
Low Lapse pH pL pH pL
=> Z po po
Often called a thermal wind
General picture: Circulation Cells
Local Scale : Land / Sea Breezes
Planetary Scale : Hadley Cell
remember: d2z/dt2 ~ - (gz/T)[ w - ]

4. Sea Breeze
clouds
Land Breeze

5. z Buoyancy Equation LAND SEA Early am T Noon Evening Night cloud
Sea Breeze
Evening
Night
Land Breeze
Buoyancy Equation

6. are directly from surface
Mars Troposphere
heating and cooling
are directly from surface
and rates are high
1200
800 20 30
200
200
Rapid surface heating
2400
1600
200
200
Rapid convection T T
Like a land/ sea breeze but on a planetary scale          Te is essentially at the surface

7. VENUS TROPOSPHERE GIANT HADLEY CELL
Clouds
Pole IR
Equator
Hot air rises in equatorial regions
cooled air falls in polar regions
But Venus also has horizontal
day-night circulation!
Therefore, even in absence of rotation
the circulation can be complex

8. DAY – NIGHT VENUS ROTATION Day Night Tropospheric Winds
PERIOD ~ 243 days (retrograde)
Day
Night
Tropospheric Winds
~ 4 day rotation
Also thermospheric Winds
(Cyclostrophic )

9. Hadley Cells on Earth

10. Effect of Rotation H = High Pressure; L= low Pressure
ITCZ =Intertropical Convergence Zone

11. Black small circle is Io
Jupiter’s Atmosphere
Dominate by circulation cells and zonal winds marked by different colored cloud layers
Black small circle is Io

12. Planet Rotation
Write Newton’s Law in the rotating frame in which we measure positions, speeds and accelerations
Acceleration of a parcel of air
= - Pressure Gradient
+ Gravity
+ Coriolis
+ Centrifugal
+ Viscosity
Usually obtain approximate solutions
Hydrostatic Law = Gravity and Pressure
Compare forces (accelerations)
Ekman Number = Viscous / Inertial
Ekman = 1/Reynolds
Boundary Layer --> viscous
Rossby Number = Convection/Coriolis

13. Rotating Reference Frame: Simple Caseq

14. Rotating Reference Frame (Cont.)
Force or Momentum Equation
Applies in an Inertial Frame

15. Rotating Frame (cont.)

16. Substitute the Velocity

17. Acceleration in Inertial Frame has
3 components in a Rotating Frame

18. variations in air density
Continuity Equation
variations in air density
Rate of change = divergence of
of density the flow
If we follow a parcel of air, then it is useful to rewrite density changes on left

20. In Rotating Coordinate
follow an air mass

21. Write Eqs: in Scaled Variables typically non - dimensional
First: Meteorologists use reduced pressure (hydrostatic piece of Eq.)
“Surface” no longer // to planet’s surfaee
Momentum Eq:new variables(incompressible)

22. Size Scales

23. Geostrophic Flow

24. Simplify – Go back to Regular Units
Geostrophic Flow
Simplify – Go back to Regular Units k f

25. Geostrophic Flow Prob.H 7.1, 7.4, 7.5
(Steady flow) H
Non-rotating L j’ H
Rotating i’ L
j ’ L i’ H

26. Simple Picture
Coriolis ‘Force’
Start W
Observer v v¢ W v

27. Geostrophic Flow (cont.)
(approach to steady state)
t=0 L H L H L L
Southern Hemisphere
Flow is Opposite L

28. FORCES Steady flow Pressure Gradient = 2 r v x W
Coriolis H
OPPOSITE ABOUT A LOW
Pressure Gradient = 2 r v x W
counter clockwise: cyclonic
clockwise: anti cyclonic

29. Near surface pressures suggest flow pattern

30. 2 –D Flow: ‘Flat’ Surface
Gradient Wind Equation
Curved Motion r

31. Gradient Wind Equation discuss direction normal to the flow
Ignore Eq. 1:
discuss direction normal to the flow
Northern
Southern
centrifugal
centrifugal
coriolis
coriolis
Counterclock
cyclonic
Clockwise
anticyclonic
Period = ½ period of the focault
pendulum

32. centrifugal = - press. grad.
CYCLOSTOPHIC FLOW
Case 2
centrifugal = - press. grad.
cent. p. L
Venus : Polar Vorticity

33. Centripetal term is zero
GEOSTROPHIC FLOW
Centripetal term is zero
(e.g., large scale flow) L H L L L
( anticyclonic )
Nothern Hemisphere
Southern Hemisphere
(cyclonic) H L L L

34. Ü Þ GRADIENT WIND Ü Ü Anamolous Þ Þ L H L cor. p. cor. ® ® p. c. c. p.
North ( f > 0 )
Regular
cor. p. Þ
cor. Ü Ü Þ L H p. c. c.
Anamolous p. Ü Þ L Ü c.
cor.

35. Problems Geostrophic Flow Dp = 5 mb between
Washington and Charlottesville
Find v.
Cyclostrophic Flow
Dp = 5 mb over 10 km
Inertial Flow at Charlottesville
v = 20 m/s
r = ?
Pressure Force =0