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Analyzing Geostrophic Winds and Their Effects Using Scale Analysis

Scale analysis of geostrophic winds, friction effects, and gradient wind. Identify important processes and obtain geostrophy for each velocity component. Northern Hemisphere geostrophic winds and frictional effects in the planetary boundary layer.

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Analyzing Geostrophic Winds and Their Effects Using Scale Analysis

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  1. ATOC 4720 class33 1. The geostrophic wind: scale analysis 2. Effects of friction 3. The gradient wind

  2. 1. The geostrophic winds: scale analysis For unit mass, HORIZONTAL equation of motion: Scale analysis: estimate the order of magnitude for each term, using the observed values. Very useful tool to identify the most important processes

  3. Observed scales: Velocity V: 10-30 m/s; Time t (1 day): S; /S (Mid Latitude) Above from atmospheric Planetary boundary layer (PBL), friction is small (a=0).

  4. Acceleration term: Coriolis term: The Coriolis term is one order of magnitude larger Than the acceleration term. In free atmosphere, friction is negligible. Therefore, to the lowest order: 0 0

  5. Geostrophic balance: PGF is balanced by CF:

  6. Horizontal equations of motion in component form In the above, we discussed the Vector form: In real situation, we often use component form:

  7. z y x (for simplicity, we look at local Cartesian coordinate:) Horizontal equation of motion in “x” direction, with a Unit vector “i”: Similarly, In “y”:

  8. Exercise: Perform scale analysis for each equation, to obtain geostrophy for each velocity component, using the observed scales provided earlier. Geostrophic winds: (P-vertical coordinate) (Z-vertical coordinate) Gestrophic winds:

  9. Northern Hemisphere (NH): y L H CF PGF P1 P2 P3 P4 P5 x

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

  11. 3. The gradient wind

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