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Potential Vorticity and Barotropic Instability in Atmospheric Dynamics

Explore how potential vorticity and barotropic instability impact weather dynamics, conservation laws, and cyclogenesis. Learn more about tropopause anomalies and lee cyclogenesis theory.

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Potential Vorticity and Barotropic Instability in Atmospheric Dynamics

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  1. Potential Vorticity

  2. Barotropic Instability • Water Vapor Loop

  3. President’s Day • http://www.atmos.washington.edu/academic/videos/PresidentsDayStorm.html

  4. http://www.atmos.albany.edu/daes/atmclasses/atm305/climomaps.htmlhttp://www.atmos.albany.edu/daes/atmclasses/atm305/climomaps.html

  5. Positive PV Anomaly Near Trop

  6. Negative PV Anomaly Near Trop

  7. Surface +PV Anomaly

  8. Piecewise PV Inversion

  9. Stoelinga 1996: Overheads

  10. Lee Troughing and PV

  11. Conservation of potential vorticity • conserved for adiabatic frictionless motion • Ratio of absolute vorticity and depth of vortex Ertel Potential Vorticity (Holton 2004, p. 96)

  12. Conservation of potential vorticity • for a homogeneous incompressible fluid • z evaluated at constant height Potential Vorticity (Holton 2004, p. 96)

  13. Conservation of potential vorticity • When the depth of the vortex changes following motion, its absolute vorticity must change to maintain conservation of potential vorticity (Holton 2004, p. 98)

  14. (b) (c) (d) (e) (a) • Conservation of potential vorticity • For westerly flow impinging on an infinitely long mountain range… • (a) upstream, zonal flow is uniform (du/dy = 0, v=0), z = 0 • (b) deflection of upper q surface upstream of barrier  increases h  absolute vorticity must increase  air column turns cyclonically (Holton 2004, p. 98)

  15. ATMS 316- Background (b) (c) (d) (e) (a) • Conservation of potential vorticity • For westerly flow impinging on an infinitely long mountain range… • poleward drift in (b) also causes increase in f • (c) as column crosses mountain, h decreases  absolute vorticity must decrease  z becomes negative  air column drifts equatorward (Holton 2004, p. 98)

  16. (b) (c) (d) (e) (a) • Conservation of potential vorticity • For westerly flow impinging on an infinitely long mountain range… • equatorward drift in (c) also causes decrease in f • (d) as column crosses mountain, h increases  absolute vorticity must increase  z becomes positive  air column drifts poleward

  17. ATMS 316- Background (b) (c) (d) (e) (a) • Conservation of potential vorticity • For westerly flow impinging on an infinitely long mountain range… • (e) alternating series of ridges and troughs downstream of mountain range • cyclonic flow pattern immediately to the east of the mountains (lee side trough)

  18. (Ahrens 2005, p. 222)

  19. Alps and Smaller Ranges More Complicated With All Kinds of Baroclinic Effects • Lee cyclogenesis • Preferred regions of cyclogenesis • Alps • Narrow mountain range • Theory that applies to Alps lee cyclogenesis is modifed from that used to describe lee cyclogenesis of the Rockies • Ageostrophic effects dominate and the modification of baroclinic instability by the Alps is more difficult to analyze

  20. Tropopause +PV anomalies often apparent in water vapor imagery

  21. Trop Pressure

  22. Terminology: PV Streamer • A PV-streamer is an elongated band of potential vorticity, generally in the upper troposphere. It is mesoscale in width and synoptic scale in length. • In the upper troposphere, they are associated with stratospheric–tropospheric mass exchange, particularly in the area where the tropopause folds.

  23. The End

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