1. The horizontal equations of motion: smaller-scale motion

2. The vertical equation of motion

3. The thermal wind

ATOC 4720 class34

H L

Northern Hemisphere (NH):

P1 P2 P3 P4 P5x

y

PGFCF

Previous class:GEOSTROPHY:

Geostrophic wind value:

In PBL, friction is important.

Frictional convergence toward the low pressure! Important!

V cross the isobars!

Cross-isobar flow due to friction

The gradient wind

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

Acceleration term:

Coriolis term:

Therefore, the Coriolis term can be NEGLECTED! Geostrophy breaks down!

0

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,

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.

3. Thermal wind relationGeostrophic wind speed:

Perform vertical derivation:

Between 2 layers:

Substitude (Z2-Z1) from the hypsometric equation (2.29)

(for dry air)