1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3....
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![Page 1: 1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3. The thermal wind ATOC 4720 class34.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d485503460f94a23dd0/html5/thumbnails/1.jpg)
1. The horizontal equations of motion: smaller-scale motion
2. The vertical equation of motion
3. The thermal wind
ATOC 4720 class34
![Page 2: 1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3. The thermal wind ATOC 4720 class34.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d485503460f94a23dd0/html5/thumbnails/2.jpg)
H L
Northern Hemisphere (NH):
P1 P2 P3 P4 P5x
y
PGFCF
Previous class:GEOSTROPHY:
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Geostrophic wind value:
![Page 4: 1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3. The thermal wind ATOC 4720 class34.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d485503460f94a23dd0/html5/thumbnails/4.jpg)
In PBL, friction is important.
Frictional convergence toward the low pressure! Important!
V cross the isobars!
![Page 5: 1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3. The thermal wind ATOC 4720 class34.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d485503460f94a23dd0/html5/thumbnails/5.jpg)
Cross-isobar flow due to friction
![Page 6: 1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3. The thermal wind ATOC 4720 class34.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d485503460f94a23dd0/html5/thumbnails/6.jpg)
The gradient wind
![Page 7: 1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3. The thermal wind ATOC 4720 class34.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d485503460f94a23dd0/html5/thumbnails/7.jpg)
x
y
z
1. Smaller-scale convection: GEOSTROPHY BREAKS DOWN
Observations for small-scale convection:
Velocity U-V: 20 m/s;Time T (100-1000s)= S
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Acceleration term:
Coriolis term:
Therefore, the Coriolis term can be NEGLECTED! Geostrophy breaks down!
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![Page 9: 1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3. The thermal wind ATOC 4720 class34.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d485503460f94a23dd0/html5/thumbnails/9.jpg)
2. The vertical equation of motionIn z direction: Newton’s second law of motion for unit mass:
negligible Free atmospherenegligible
Large-scale motion, T: 1day; W:10m/s:
Even for T=1000s,
![Page 10: 1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3. The thermal wind ATOC 4720 class34.](https://reader030.fdocuments.in/reader030/viewer/2022032800/56649d485503460f94a23dd0/html5/thumbnails/10.jpg)
Hydrostatic balanceHydrostatic balance is well satisfied even by mesoscale convection.
Exercise: find out for what scale convection (vertical velocity and timescale), hydrostatic balance can break down.
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3. Thermal wind relationGeostrophic wind speed:
Perform vertical derivation:
Between 2 layers:
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Substitude (Z2-Z1) from the hypsometric equation (2.29)
(for dry air)
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