Potential vorticity
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Potential vorticity (PV) is a quantity which is proportional to the product of vorticity and stratification that, following an air parcel, can only be changed by diabatic or frictional processes. It plays an important role in the generation of vorticity in cyclogenesis (the birth and development of a cyclone), especially along the polar front.
It is useful in tracing intrusions of stratospheric air deep into the troposphere in the vicinity of jet streaks, a concentrated region within a jet stream where the wind speeds are the strongest. It can also be used to explain how a range of mountains like the Andes can make the upper westerly winds swerve towards the equator and back.
Baroclinic instability requires the presence of a potential vorticity gradient along which waves amplify during cyclogenesis.
[edit] PV conservation
It can be shown through a combination of the first law of thermodynamics and momentum conservation that potential vorticity can only be changed by diabatic heating (such as latent heat release from condensation) or frictional processes. This conservation is the atmospheric equivalent to inertia. A spinning ice skater with their arms spread out laterally can accelerate their rate of spin by contracting their arms. Similarly, when a vortex of air is broad, it is in turn, slow. When the air converges, to maintain potential vorticity, the air speed increases, resulting in a stretched vortex. Divergence causes the vortex to spread, slowing down the rate of spin.