The dynamics of planetary atmospheres

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Presentation transcript:

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

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

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

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

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

Adjustments equation of horizontal motion geostrophic approximaton hydrostatic approximation

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

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

acoustic waves

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

Rossby waves Search for the solution in form

Eliminating P and use incompressibility,

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

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

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

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

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

Ls=93-97 Ls=113-115 Ls=127-136

Cyclonic vortices Anticyclonic vortex

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

VIRTIS image of the Southern Polar vortex @ 5.0 µm

Titan: another superrotating atmosphere Mingalev et al., 2008

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

Giant planets zones belts

Hot spot

Polar vortex

32 km/pix