1. The dynamics of planetary atmospheres
Theoretical concept is formulated in the
Geophysical Fluid Dynamics –
the dynamics of stratified fluid on a rotating sphere

2. Hadley cell circulation Solar flux easterly (passat) flow tidal buldge
convective flow
westerly jet

3. “Primitive” equations: fluid on a rotating sphere
momentum
energy
continuity
eqn. of state
modifications
absolute vorticity
Boussinesq approximation:
everywhere but gravity

4. Spherical coordinate system:
z, w
y, v
x, u

5. Useful numbers
Coriolis parameter
-plane approximation
Rossby parameter
Rossby number

6. Adjustments
equation of horizontal motion
geostrophic approximaton
hydrostatic approximation

7. Ro << 1 thermal wind equation
Opposite case: Ro >> 1
cyclostrophic approximation

8. Wave motion in the atmosphere
Elasticity sound
Buoyancy gravity waves
Coriolis force inertial waves
Planetary-scale forced oscillations of any type are called tides

9. acoustic waves

10. gravity waves -potential temperature Brunt-Vajsala frequency
For non-vertically propagating waves,
Group velocity

11. Rossby waves
Search for the solution in form

12. Eliminating P and use incompressibility,

13. Solsticial circulation on Mars
Solar flux
thermal tide
westerly jet
Rossby waves

14. Ls = 92, North hemisphere [kg/m2]
Water vapor column:
Ls = 92, North hemisphere [kg/m2] 0
180

15. Ls = 113, North hemisphere [kg/m2]
Water vapor column:
Ls = 113, North hemisphere [kg/m2] 0
180

16. Ls = 143, North hemisphere [kg/m2]
Water vapor column:
Ls = 143, North hemisphere [kg/m2] 0
180

17. OMEGA observations of the residual seasonal frost around South pole
OMEGA observations of the residual seasonal frost around South pole. Ls = 236-243 1.5 m band depth

18. Ls=93-97
Ls=113-115
Ls=127-136

19. Cyclonic vortices Anticyclonic vortex

20. Venus case (symmetric mode)
multiple Hadley cells?
VIRTIS image of the Southern Polar 5.0 µm
convective flow
thermal tide
superrotation

21. VIRTIS image of the Southern Polar vortex @ 5.0 µm

22. Titan: another superrotating atmosphere
Mingalev et al., 2008

23. Vertical velocity on Titan: a signature of thermal tide
z=550 km

24. Giant planets
zones
belts

25. Hot spot

26. Polar vortex

30. 32 km/pix