potential vorticity. barotropic instability water vapor loop

Potential Vorticity

Barotropic Instability

• Water Vapor Loop

President’s Day

• http://www.atmos.washington.edu/academic/videos/PresidentsDayStorm.html

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

Positive PV Anomaly Near Trop

Negative PV Anomaly Near Trop

Surface +PV Anomaly

Piecewise PV Inversion

Stoelinga 1996: Overheads

Lee Troughing and PV

• Conservation of potential vorticity

– conserved for adiabatic frictionless motion• Ratio of absolute vorticity and depth of vortex

(Holton 2004, p. 96)

p

gfP Ertel Potential Vorticity

• Conservation of potential vorticity

– for a homogeneous incompressible fluid• evaluated at constant height

(Holton 2004, p. 96)

Const/ hfP z Potential Vorticity

• 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)

• Conservation of potential vorticity– For westerly flow impinging on

an infinitely long mountain range…

• (a) upstream, zonal flow is uniform (u/y = 0, v=0), = 0

• (b) deflection of upper surface upstream of barrier increases h absolute vorticity must increase air column turns cyclonically

(Holton 2004, p. 98)

(a) (b) (c) (d) (e)

• 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 becomes negative air column drifts equatorward

ATMS 316- Background

(Holton 2004, p. 98)

(a) (b) (c) (d) (e)

• 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 becomes positive air column drifts poleward

(a) (b) (c) (d) (e)

• 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)

ATMS 316- Background(a) (b) (c) (d) (e)

(Ahrens 2005, p. 222)

• 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

Alps and Smaller Ranges More Complicated With All Kinds of

Baroclinic Effects

Tropopause +PV anomalies often apparent in water vapor imagery

Trop Pressure

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.

The End