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Published byMaximillian Jefferson Modified over 8 years ago
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Angular Momentum Cycle 1.Balance Equations 2.Angular Momentum in the Climatic System 3.Observations 4.Closing the Cycle of Angular Momentum
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Balance Equations The total angular momentum of the Earth remains constant Angular momentum of a parcel with unit mass If the total torque vanishes MM MrMr is the moment of force (torque). rRrR Eq.:
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Angular Momentum in the Climatic System 1. Earth 2a. Atmosphere (solid rotation) sphere spherical shell 2b. Atmosphere (zonal wind, the relative angular momentum) M r M r (DJF-JJA) NH~5.3 10 25 kg m 2 s -1 NH~9.4 10 25 kg m 2 s -1 SH ~7.6 10 25 kg m 2 s -1 SH ~-4.6 10 25 kg m 2 s -1 m e = m a ~10 6
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3. Ocean (very coarse estimate, no reliable measurements exist) a)Zonal circulation 45 0 0 100Sv NP -0. 5 10 25 kg m 2 s -1
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The observed changes of the angular momentum of atmosphere are 5 10 25 kg m 2 s -1, Oceanic ones are< 1 10 25 kg m 2 s -1 -60 0 60 0 b) Meridional shift of air and water masses 30 0 0 + + + z=2cm P atm =2mb 0. 8 10 25 kg m 2 s -1 Conclusion: Adjustment of the solid Earth‘s rotation to the rotation of fluid Conclusion: Adjustment of the solid Earth‘s rotation to the rotation of fluid
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Because the angular momentum is conserved Because M r DJF > M r JJA, JJA > DJF LOD[ms ]=0.168 M r [10 25 kg m 2 s -1 ] If M r =5x10 25 kg m 2 s -1 LOD=0.8ms The relative angular momentum can be computed actronomically, as well as from the observed velocities: M r =5x10 25 kg m 2 s -1 correponds to u=2m s -1.
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Angular Momentum in the Atmosphere Multiply the equation of momentum with Have in mind: Pressure, Friction Torques Tropics-source Mid-latitudes-sink of angular momentum } Meridional Transportt
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Observations Ship reports Source Sink
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Closing the Cycle of Angular Momentum Wind~10ms -1 Currents~ 10 -2 ms -1 -10 -1 ms -1 Small contribution of the oceanic transport
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