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Equations of Motion in Small-Scale Convection

Learn about the horizontal and vertical equations of motion in smaller-scale convection, as well as the thermal wind relation and the breakdown of geostrophy. Discover the importance of friction and the effects of the Coriolis term. Explore the hydrostatic balance in different scales of convection.

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Equations of Motion in Small-Scale Convection

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

  2. Previous class: GEOSTROPHY: Northern Hemisphere (NH): y L H CF PGF P1 P2 P3 P4 P5 x

  3. Geostrophic wind value:

  4. In PBL, friction is important. V cross the isobars! Frictional convergence toward the low pressure! Important!

  5. Cross-isobar flow due to friction

  6. The gradient wind

  7. 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

  8. Acceleration term: Coriolis term: Therefore, the Coriolis term can be NEGLECTED! Geostrophy breaks down! 0

  9. 2. The vertical equation of motion In z direction: Newton’s second law of motion for unit mass: Free atmosphere negligible negligible Large-scale motion, T: 1day; W:10m/s: Even for T=1000s,

  10. 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.

  11. 3. Thermal wind relation Geostrophic wind speed: Perform vertical derivation: Between 2 layers:

  12. Substitude (Z2-Z1) from the hypsometric equation (2.29) (for dry air)

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