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EVAT 554 OCEAN-ATMOSPHERE DYNAMICS

EVAT 554 OCEAN-ATMOSPHERE DYNAMICS. FILTERING OF EQUATIONS FOR ATMOSPHERE (CONT). LECTURE 6. (Reference: Peixoto & Oort, Chapter 3). Meridional Momentum Balance:. Length scale: L 10 6 m, l10 2 m Depth scale: H10 4 m, h 10 2 m Horizontal velocity scale: u,v 10 ms -1

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EVAT 554 OCEAN-ATMOSPHERE DYNAMICS

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  1. EVAT 554OCEAN-ATMOSPHERE DYNAMICS FILTERING OF EQUATIONS FOR ATMOSPHERE (CONT) LECTURE 6 (Reference: Peixoto & Oort, Chapter 3)

  2. Meridional Momentum Balance: Length scale: L106m, l102m Depth scale: H104m, h 102m Horizontal velocity scale: u,v 10 ms-1 Vertical velocity scale: w 10-2 ms-1 Horizontal pressure scale: p 10 mb = 1000 Pa Time Scale: L/u 105s or H/w 106s Radius of Earth: a=6.37x 106m Coriolis parameter: f,f' 10-4 s-1 Density of Air: r 1 kg m-3 Horizontal Eddy Viscosity: nH 10-1 m2s-1 Vertical Eddy Viscosity: nV 10-1 m2s-1 10-4 ms-2 10-3 ms-2 10-3 ms-2 10-4 ms-2 10-4 ms-2

  3. Horizontal Momentum Balance (zonal) (meridional) Geostrophic Balance Length scale: L106m, l102m Depth scale: H104m, h 102m Horizontal velocity scale: u,v 10 ms-1 Vertical velocity scale: w 10-2 ms-1 Horizontal pressure scale: p 10 mb = 1000 Pa Time Scale: L/u 105s or H/w 106s Radius of Earth: a=6.37x 106m Coriolis parameter: f,f' 10-4 s-1 Density of Air: r 1 kg m-3 Horizontal Eddy Viscosity: nH 10-1 m2s-1 Vertical Eddy Viscosity: nV 10-1 m2s-1 10-4 ms-2 10-3 ms-2 10-3 ms-2 10-4 ms-2 10-4 ms-2

  4. Horizontal Momentum Balance (zonal) (meridional) Geostrophic Balance Length scale: L106m, l102m Depth scale: H104m, h 102m Horizontal velocity scale: u,v 10 ms-1 Vertical velocity scale: w 10-2 ms-1 Horizontal pressure scale: p 10 mb = 1000 Pa Time Scale: L/u 105s or H/w 106s Radius of Earth: a=6.37x 106m Coriolis parameter: f,f' 10-4 s-1 Density of Air: r 1 kg m-3 Horizontal Eddy Viscosity: nH 10-1 m2s-1 Vertical Eddy Viscosity: nV 10-1 m2s-1 10-4 ms-2 10-3 ms-2 10-3 ms-2 10-4 ms-2 10-4 ms-2 “Rossby Number” Geostrophic Balance Holds when Ro << 1

  5. Horizontal Momentum Balance CF PGF d V (zonal) (meridional) Geostrophic Balance “Geostrophic Wind”

  6. Horizontal Momentum Balance CF PGF d V f =43o d=600 km W=7.27x10-5 s-1 f=2Wsin f Example: =5.6 m/s “Geostrophic Wind”

  7. Let us Revisit e.g. the Meridional Momentum Balance: Length scale: L106m, l102m Depth scale: H104m, h 102m Horizontal velocity scale: u,v 10 ms-1 Vertical velocity scale: w 10-2 ms-1 Horizontal pressure scale: p 10 mb = 1000 Pa Time Scale: L/u 105s or H/w 106s Radius of Earth: a=6.37x 106m Coriolis parameter: f,f' 10-4 s-1 Density of Air: r 1 kg m-3 Horizontal Eddy Viscosity: nH 10-1 m2s-1 Vertical Eddy Viscosity: nV 10-1 m2s-1 10-4 ms-2 10-3 ms-2 10-3 ms-2 10-4 ms-2 10-4 ms-2 What if the acceleration/non-linear term cannot be neglected? i.e., Ro 1

  8. Let us Revisit e.g. the Meridional Momentum Balance: Length scale: L106m, l102m Depth scale: H104m, h 102m Horizontal velocity scale: u,v 10 ms-1 Vertical velocity scale: w 10-2 ms-1 Horizontal pressure scale: p 10 mb = 1000 Pa Time Scale: L/u 105s or H/w 106s Radius of Earth: a=6.37x 106m Coriolis parameter: f,f' 10-4 s-1 Density of Air: r 1 kg m-3 Horizontal Eddy Viscosity: nH 10-1 m2s-1 Vertical Eddy Viscosity: nV 10-1 m2s-1 10-4 ms-2 10-3 ms-2 10-3 ms-2 10-4 ms-2 10-4 ms-2 What if the acceleration/non-linear term cannot be neglected? This applies to flows with strong curvature i.e., Ro 1

  9. Horizontal Momentum Balance: R Centripetal acceleration ac=V2/R V=(u2+v2)1/2 V=Rw “Gradient Wind Balance” (zonal) This applies to flows with strong curvature (meridional)

  10. Horizontal Momentum Balance: R Centripetal acceleration ac=V2/R V=(u2+v2)1/2 V=Rw “Gradient Wind Balance” (zonal) This applies to flows with strong curvature (meridional)

  11. Horizontal Momentum Balance: R Centripetal acceleration ac=V2/R V=(u2+v2)1/2 V=Rw “Gradient Wind Balance” (zonal) What about flow near the equator? (meridional)

  12. Horizontal Momentum Balance: R Centripetal acceleration ac=V2/R Near equator (e.g. Hurricane), Coriolis Force is negligible, and balance is between PGF and Centripetal acceleration V=(u2+v2)1/2 V=Rw “Cyclostrophic Balance” (zonal) What about flow near the equator? (meridional)

  13. Horizontal Momentum Balance (zonal) (meridional) Geostrophic Balance Generally an excellent approximation for ‘upper level winds’ Any evidence of breakdown of Geostrophy?

  14. Horizontal Momentum Balance (zonal) (meridional) Geostrophic Balance Relationship Between Temperature and Winds? Advection

  15. Horizontal Momentum Balance (zonal) (meridional) Geostrophic Balance Relationship Between Temperature and Winds? Advection

  16. Horizontal Momentum Balance (zonal) (meridional) Geostrophic Balance What can we say about this term?

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