# ATOC 4720 class34 1. The horizontal equations of

ATOC 4720 class34 1. The horizontal equations of motion: smaller-scale motion 2. The vertical equation of motion 3. The thermal wind Previous class:

GEOSTROPHY: Northern Hemisphere (NH): y L

H CF x PGF P1 P2 P3 P4 P5

Geostrophic wind value: In PBL, friction is important. V cross the isobars!

Frictional convergence toward the low pressure! Important! Cross-isobar flow due to friction The gradient wind

1. Smaller-scale convection: GEOSTROPHY BREAKS DOWN z y x 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 motion

In z direction: Newtons second law of motion for unit mass: negligible Large-scale motion, T: 1day; W:10m/s: Even for T=1000s,

Free atmosphere negligible Hydrostatic balance Hydrostatic 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 relation Geostrophic wind speed: Perform vertical derivation:

Between 2 layers: Substitude (Z2-Z1) from the hypsometric equation (2.29) (for dry air)

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