The Effect of Rotation Period on Atmospheric Circulations

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The Effect of Rotation Period on Atmospheric
Circulations
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Why does rotation rate matter?

• Affects geostrophic assumption

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The Range of Rotation Rates in the Solar System
Rotation Period 243 days O 3.00x10-7 rad s-1
Rotation Period 9h 50m 30.0s O 1.77x10-4 rad s-1
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4 types of planetary rotation

• Geostrophic Planets
• Cyclostrophic Planets
• Tidally locked Geostrophic Planets
• Tidally locked Cyclostrophic Planets
• The difference comes in the effectiveness of the
  Coriolis Force and the zonal average

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Why the switch?

• The switch occurs because the Rossby Radius of
  Deformation increases with decreasing Rotation
  Rate
• Rossby Radius of Deformation Length scale at
  which rotational effects become as important as
  buoyancy effects. LRNH/f
• N Brunt-Vaisala frequency ((g/?)(??/?z))0.5
• g force of gravity
• ? potential temperature
• H scale height
• f Coriolis parameter

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Geostrophic Planets

• Most of the planets in the solar system
• Jupiter
• Earth
• Saturn
• Planets have rotation periods less than 4 days
• Pressure Gradient balanced by the Coriolis Effect

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Zonally Averaged zonal wind speed
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Cyclostrophic Planets

• Slowly Rotating Planets
• Venus
• Uranus
• Planets have rotation period greater than 4 days
• Pressure Gradient not balanced by Coriolis
  Effect, need to take into account curvature
  effects

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So, what happens as the rotation period decreases?

• The Hadley cell spreads poleward
• Decreases the meridional temperature gradient
• Subtropical jet moves poleward
• Easterlies spread across the surface
• The upper atmosphere disconnects from the surface
  (due to Rossby Penetration Depth)

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Rossby Penetration Depth

• Distance through the atmosphere that a
  disturbance can penetrate.
• HRILR/N
• I((f2VT/r)(f?))0.5
• VT tangential velocity
• r radius
• ? vertical component of relative vorticity

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Habitability

• So, which is potentially more habitable?
• Earth
• Earth rotating at 10 hours
• Earth rotating at 243 days

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Tidal locking

• Planets orbiting low mass stars (stars with mass
  less than 60 solar mass) have habitable zones
  inside their tidal locking radii

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So what do tidally locked planets look like?
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So, what happens with tidal locking?

• The planets are forced through a stationary eddy
  (Rossby wave)
• Ordinarily geostrophic planets still retain
  geostrophic character
• Ordinarily cyclostrophic planets still retain
  cyclostrophic character