Planetary Sciences

CKSS 20

Hadley circulation=

At low inclinations,

a planet 's equator receives more heat ; not air

rises and flows towards regions of low pressure (poles) .

This circulation forms a cell,

known as Hadley cell.

For a slowrotator

,or no rotation

,there is only one Hadley cell .

For Earth,

Griolis forces deflect the flow and breaks it into 3 cells .

Interesting detail : rising hot air expands adiabatic -14,

ads and givesout its humidity .

This is why we have rain forests in the equator . andin the Pacific Northwest

.The air that is coming back at = 35 latitude

is dry ,and forms the deserts

.

show in map that the deserts are in a

line : California .

American Southwest, Sahara,

Arabia,

Iran,

Gobi.

In the

Southern Hemisphere : Atacama,

Namibia,

Australia .

storm-

Conservation of vorticity W =JXU

Take the momentum equation and curl it i

# ÷ - Wftu ) + ( w .

Hu+1g,tpxtp - VTZ:

for rotational fbwu× = - RyUy = rn

Tu = 0 by construction,

and the first term ( compression ) cancels.

The second term also cancels because w=Txu=zrE points in the

z - direction,

so w . t= w Ja, yet the flow does not depend on Z

.

6,

we are left with

13£ = ft, Fpx Jp + UTJ

If the flow is poly topic , p= KY ,so tp×tp=0 .

If the Reynolds number is high we can ignore the viscous term , andtheirfourth

t.

i.e. Vortiaty is conserved.

Because of this property ,storms in the

atmosphere of the giant planets ( such as the Great Red spot ) are

Stable over long periods of time.

subsurfaj.fi#monsConsider the heat conduction equation

of = - KJT

Where K is the thermal conductivity and g is the heat flux .

¥ = -

9€ in DX =- DT ¥

-

for DT÷ Ts - Tmeh ; DX =D = depth of ocean

|d=H3K-⇒.k⇒.

Ts : surface temperaturefs: surface heat flux .

For Europe,

Tt 100k ; K~~ 3 WhK

F ul 0 - 100mg.

;D → 5 - 50 km

Radiogenic=I@5The Earth is measured to produce

-Hr :(4.5+-0.5 ) . 10' ' 2N÷

from radioactive decay in its bulk.

To convert this to an energy flux we

do simple dimension analysis :

[F¥hf=÷s '

'

'÷e=¥gt4df⇒=EndedA ]

.

Soof,+

=

Hr.p4l3TR÷T ;Ft=lHrpR)

.

For Europa ,this is 5 mwlm ?

Notice that even without tidal heating ,thisradiogenic heating would still

produce an ocean . The difference is that in this case,

the ocean

would lie at greater depths and we would not see tectonics in Europa .

In fat ,all icy bodies should have oceans .