angular momentum cycle
DESCRIPTION
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). - PowerPoint PPT PresentationTRANSCRIPT
Angular Momentum Cycle
1. Balance Equations
2. Angular Momentum in the Climatic System
3. Observations
4. Closing the Cycle of Angular Momentum
Balance EquationsThe total angular momentum of the Earth remains constant
M Angular momentum of a parcel with unit mass
acrM Frdt
Md
If the total torque vanishes 0dt
Md
n
ncrrM .)(
coscos22 urrM icu .M Mr
rMMM
Fr is the moment of force (torque).
rR
smR /464Eq.:
Angular Momentum in the Climatic System
1. Earth
s
mkgRmI ee
2332 .
1086.55
2
2a. Atmosphere (solid rotation)
s
mkgXIRmI eaa
22862 .
1001.1103
2
sphere
spherical shell
2b. Atmosphere (zonal wind, the relative angular momentum)
MM
dmuRdmM
r
r
01.0
cos Mr Mr (DJF-JJA)NH~5.31025kg m2 s-1 NH~9.41025kg m2 s-1
SH ~7.61025kg m2 s-1 SH ~-4.6 1025kg m2 s-1
me= ma~106
3. Ocean (very coarse estimate, no reliable measurements exist)
a) Zonal circulation
450
00
100Sv
NP
-0.51025kg m2 s-1
The observed changes of the angular momentum of atmosphere are 51025kg m2 s-1, Oceanic ones are< 11025kg m2 s-1
-600
600
12254
2
6
36
6
34
108.0
cos2cos2
skgmzR
ddzRM
b) Meridional shift of air and water masses
300
00
+ + +
z=2cm
Patm=2mb0.81025kg m2 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
Because the angular momentum is conserved
atmV
e constdvurI cos
Because MrDJF > Mr
JJA , 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.
dmuRdmM r cos
Angular Momentum in the Atmosphere
Multiply the equation of momentum
...cos
Fp
dt
dca
with r
cos
1
1
Rx
RyHave in mind:
...cos
RF
p
t
M
Pressure, Friction Torques
Tropics-sourceMid-latitudes-sink of angular momentum} Meridional
Transportt
Observations
uvCD 0
Ship reports
Source
Sink
Closing the Cycle of Angular Momentum
2
2
10 ~] [s
mvu
Wind~10ms-1
Currents~ 10-2ms-1 -10-1ms-1
2
2310~][s
mvu
410~][
][
ocean
atm
vu
vu 210~atm
ocean
m
m
Small contribution of the oceanic transport