PLANETARY ATMOSPHERES

(1)

PLANETARY ATMOSPHERES

Sébastien LEBONNOIS

CNRS Researcher

Laboratoire de Météorologie Dynamique, Paris

XXVIII Canary Islands Winter School of Astrophysics – Solar System Exploration 3. Atmospheric dynamics and circulation regimes

(2)

Equations of the atmospheric fluid

Circulation patterns in terrestrial atmospheres Instabilities and wave activitiy

Vortices

XXVIII Canary Islands Winter School of Astrophysics – Solar System Exploration Planetary Atmospheres – 3. Atmospheric dynamics and circulation regimes

PLANETARY ATMOSPHERES

Atmospheric dynamics and circulation regimes

(3)

Equations of the atmospheric fluid

Circulation patterns in terrestrial atmospheres Instabilities and wave activitiy

Vortices

Planetary Atmospheres – 3. Atmospheric dynamics and circulation regimes

PLANETARY ATMOSPHERES

Atmospheric dynamics and circulation regimes

XXVIII Canary Islands Winter School of Astrophysics – Solar System Exploration

(4)

Basic laws

Equation of state : ideal gas law

We consider the atmospheric gas as ideal :

p =  ^{R T} R = R /* 

R = 8.314 J mol*

^-1

K

^-1

pressure density temperature

mean molecular mass

(5)

Basic laws Hydrostatic equilibrium

p(z)

p(z+dz)

 g

Fluid elemental particle at rest

altitude

gravity

(6)

Basic laws

Scale height

Combining ideal gas law and hydrostatic equilibrium :

When T is taken as constant (isothermal atmosphere) :

(7)

Basic laws

Adiabatic lapse rate

For a parcel recieving the heat quantity  q, from first principle of thermodynamics we get :

When this parcel moves adiabatically :

=>

Specific heat capacity at constant pressure

(8)

Basic laws

Potential temperature

Moving adiabatically a parcel from (p,T) to a reference pressure p

₀

, its temperature will be  , defined as the potential temperature.

To get the expression for  , we integrate this expression

If c

_p

does not depend on T, we get

 ^{= R / c}

_p

(9)

Momentum equations Spherical coordinates, local frame

Lagrangian view vs

Eulerian view

(10)

Momentum equations

Momentum equations derived in the local frame

relative acceleration

pressure gradient

= + gravity + friction + +Coriolis force

centrifugal force

(11)

Momentum equations Approximations

Hydrostatic balance Geostrophic balance Cyclostrophic balance

Gradient wind balance

Quasi-geostrophic equations Primitive equations

thin atmosphere : z << a

(12)

Momentum equations Thermal wind equation

- __1

r y

__p = ________u² tan  a

 : latitude

a :planet radius

yields

( )

2 u² __ = - ____ __u



T



R tan 

 cst vertical zonal wind

gradient

temperature

meridional gradient

with  = - ln __p p_ref

Cyclostrophic balance

(13)

Equations of the atmospheric fluid

Circulation patterns in terrestrial atmospheres Instabilities and wave activitiy

Vortices

PLANETARY ATMOSPHERES

Atmospheric dynamics and circulation regimes

(14)

Energy redistribution

Thermal radiation Solar insolation

Solar energy absorbed

Annual average energy balance for Earth's atmosphere

(15)

Energy redistribution

Solar insolation Thermal radiation

At top of atmosphere, as a function of seasons

(16)

Energy redistribution

The case of Mars : role of surface thermal inertia

Equinox Solstice

(17)

Meridional circulation

Driving mechanism

(18)

Meridional circulation

Effect on the zonal wind

(19)

Meridional circulation

Mars Hadley cells

EARTH

MARS Mean meridional circulation

(from simulations, mass flux in 10⁹ kg s^-1)

Northern winter solstice

(20)

Meridional circulation Mars Hadley cells

Summer

Winter

Jet stream

Mean zonal wind (m/s) Northern winter solstice

(21)

Meridional circulation Venus and Titan : slow rotation

Extension of Hadley cells from equator to the poles

Highspeed jet

Earth Venus

(22)

Meridional circulation

Titan : impact of seasons

(23)

Superrotation Observations : Venus

Venus Express/VIRTIS cloud tracking

50 km 50 km 70 km

60 km 60 km

Venus Express/VeRa temperatures

=> thermal wind equation

(24)

Superrotation Observations : Titan

Cassini/CIRS thermal winds retrieval

(Ls ~ 300°, northern winter)

(25)

Superrotation

Highspeed jet planetaryscale waves

Equatorial superrotation

Mechanism : angular momentum transport

mean meridional circulation

(26)

Equations of the atmospheric fluid

Circulation patterns in terrestrial atmospheres Instabilities and wave activitiy

Vortices

PLANETARY ATMOSPHERES

Atmospheric dynamics and circulation regimes

(27)

Convection Buoyancy

d / dz < 0 : unstable

=> convection

(28)

Convection Static stability

Brunt-Väisälä

(29)

Gravity waves

Mars Venus

(30)

Gravity waves

Mars

Pathfinder entry profile

Venus

VenusExpress/VeRa

Titan

Huygens/HASI

(31)

Planetary-scale waves Baroclinic waves

Anticyclone

Anticyclone Low pressure

Low pressure

Martian days Terrestrial days

Atmospheric pressure in Armagh (Irland, 50°N)) in 2002 (diurnal mean)

Atmospheric pressure at Lander Viking 2 site on Mars (48°N) (daily mean)

(32)

Planetary-scale waves

Barotropic waves

Barotropic instability criterion (colors)

and angular momentum transport by waves (black line) in a climate model of Titan's stratosphere

0.

(33)

Equations of the atmospheric fluid

Circulation patterns in terrestrial atmospheres Instabilities and wave activitiy

Vortices

PLANETARY ATMOSPHERES

Atmospheric dynamics and circulation regimes

(34)

Small-scale vortices Dust devils

EARTH

MARS

(35)

Small-scale vortices

Tornadoes

(36)

Synoptic vortices Earth hurricanes

Earth extra-tropical cyclones

(37)

Giant planet vortices

Jupiter (Voyager 1)

(38)

Giant planet vortices

Saturn (Cassini/ISS)

(39)

Polar vortices

EARTH (observation) MARS (model)

(40)

Polar vortices

VENUS

(41)

Polar vortices

TITAN

(42)

PLANETARY ATMOSPHERES

PLANETARY ATMOSPHERES

Sébastien LEBONNOIS

CNRS Researcher

Laboratoire de Météorologie Dynamique, Paris

Equations of the atmospheric fluid

Circulation patterns in terrestrial atmospheres Instabilities and wave activitiy

Vortices

PLANETARY ATMOSPHERES

Atmospheric dynamics and circulation regimes

Equations of the atmospheric fluid

Circulation patterns in terrestrial atmospheres Instabilities and wave activitiy

Vortices

PLANETARY ATMOSPHERES

Atmospheric dynamics and circulation regimes

Basic laws

Equation of state : ideal gas law

We consider the atmospheric gas as ideal :

p =  R T R = R* / 

R* = 8.314 J mol

K

Basic laws Hydrostatic equilibrium

Basic laws

Scale height

Combining ideal gas law and hydrostatic equilibrium :

When T is taken as constant (isothermal atmosphere) :

Basic laws

Adiabatic lapse rate

For a parcel recieving the heat quantity  q, from first principle of thermodynamics we get :

When this parcel moves adiabatically :

=>

Basic laws

Potential temperature

Moving adiabatically a parcel from (p,T) to a reference pressure p

, its temperature will be  , defined as the potential temperature.

To get the expression for  , we integrate this expression

If c

does not depend on T, we get

 = R / c

Momentum equations Spherical coordinates, local frame

Lagrangian view vs

Eulerian view

Momentum equations

Momentum equations derived in the local frame

Momentum equations Approximations

thin atmosphere : z << a

Momentum equations Thermal wind equation

( )

Cyclostrophic balance

Equations of the atmospheric fluid

Circulation patterns in terrestrial atmospheres Instabilities and wave activitiy

Vortices

PLANETARY ATMOSPHERES

Atmospheric dynamics and circulation regimes

Energy redistribution

Thermal radiation Solar insolation

Solar energy absorbed

Annual average energy balance for Earth's atmosphere

Energy redistribution

Solar insolation Thermal radiation

At top of atmosphere, as a function of seasons

Energy redistribution

The case of Mars : role of surface thermal inertia

Meridional circulation

Driving mechanism

Meridional circulation

Effect on the zonal wind

Meridional circulation

Mars Hadley cells

Meridional circulation Mars Hadley cells

Meridional circulation Venus and Titan : slow rotation

Extension of Hadley cells from equator to the poles

Meridional circulation

Titan : impact of seasons

Superrotation Observations : Venus

Venus Express/VIRTIS cloud tracking

Venus Express/VeRa temperatures

=> thermal wind equation

Superrotation Observations : Titan

Cassini/CIRS thermal winds retrieval

p =  ^{R T} R = R /* 

R = 8.314 J mol*

 ^{= R / c}