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Angular Momentum Cycle. Balance Equations Angular Momentum in the Climatic System Observations Closing the Cycle of Angular Momentum. Angular momentum of a parcel with unit mass. Balance Equations The total angular momentum of the Earth remains constant. is the moment of force (torque).

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Angular Momentum Cycle


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angular momentum cycle

Angular Momentum Cycle

Balance Equations

Angular Momentum in the Climatic System

Observations

Closing the Cycle of Angular Momentum

slide2

Angular momentum of a parcel with unit mass

Balance Equations

The total angular momentum of the Earth remains constant

is the moment of force (torque).

If the total torque vanishes

M

Mr

rR

Eq.:

slide3

1. Earth

Angular Momentum in the Climatic System

sphere

2a. Atmosphere (solid rotation)

spherical shell

me= ma~106

2b. Atmosphere (zonal wind, the relative angular momentum)

      • Mr Mr (DJF-JJA)
  • NH~5.31025kg m2 s-1NH~9.41025kg m2 s-1
  • SH ~7.61025kg m2 s-1SH ~-4.6 1025kg m2 s-1
slide4

NP

3. Ocean (very coarse estimate, no reliable measurements exist)

  • Zonal circulation

450

-0.51025kg m2 s-1

100Sv

00

slide5

b) Meridional shift of air and water masses

+ + +

300

z=2cm

0.81025kg m2 s-1

Patm=2mb

00

The observed changes of the angular momentum of atmosphere are 51025kg m2 s-1, Oceanic ones are< 11025kg m2 s-1



600

-600

Conclusion: Adjustment of the solid Earth‘s rotation to the

rotation of fluid

slide6

Because MrDJF > MrJJA , JJA > DJF

LOD[ms ]=0.168 Mr[1025kg m2 s-1]

If Mr=5x1025kg m2 s-1LOD=0.8ms

The relative angular momentum can be computed actronomically, as well as from the observed velocities:

Mr =5x1025kg m2 s-1 correponds to u=2m s-1.

Because the angular momentum is conserved

angular momentum in the atmosphere
Angular Momentum in the Atmosphere

Multiply the equation of momentum

with

Have in mind:

Pressure, Friction

Torques

}

Tropics-source

Mid-latitudes-sink

Meridional

Transportt

of angular momentum

observations
Observations

Ship reports

Sink

Source

closing the cycle of angular momentum
Closing the Cycle of Angular Momentum

Wind~10ms-1

Currents~ 10-2ms-1 -10-1ms-1

Small contribution of the oceanic transport