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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. easterly (passat) flow. Solar flux. tidal buldge. convective flow. westerly jet.
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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 easterly (passat) flow Solar flux 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 << 1thermal 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
gravity waves -potential temperature Brunt-Vajsala frequency For non-vertically propagating waves, Group velocity
Rossby waves Search for the solution in form
Solsticial circulation on Mars Solar flux thermal tide westerly jet Rossby waves
Water vapor column: Ls = 92, North hemisphere[kg/m2] 180 0
Water vapor column: Ls = 113, North hemisphere[kg/m2] 180 0
Water vapor column: Ls = 143, North hemisphere[kg/m2] 180 0
OMEGA observations of the residual seasonal frost around South pole. Ls = 236-2431.5 m band depth
Ls=127-136 Ls=113-115 Ls=93-97
VIRTIS image of the Southern Polar vortex @ 5.0 µm Venus case (symmetric mode) multiple Hadley cells? convective flow thermal tide superrotation
Titan: another superrotating atmosphere Mingalev et al., 2008
Vertical velocity on Titan: a signature of thermal tide z=550 km
Giant planets zones belts