Potential vorticity is a quantity which is proportional to the dot product of vorticity and stratification

Stratification (mathematics)

-In mathematical logic:In mathematical logic, stratification is any consistent assignment of numbers to predicate symbols guaranteeing that a unique formal interpretation of a logical theory exists...

 that, following a parcel

Air parcel

In fluid dynamics, within the framework of continuum mechanics, a fluid parcel is a very small amount of fluid, identifiable throughout its dynamic history while moving with the fluid flow. As it moves, the mass of a fluid parcel remains constant, while—in a compressible flow—its volume may...

 of air or water, can only be changed by diabatic

Diabatic

A diabatic process is one in which heat transfer takes place, which is the opposite of an adiabatic process. In quantum chemistry, the potential energy surfaces are obtained within the adiabatic or Born-Oppenheimer approximation...

 or frictional processes. It is a useful concept for understanding the generation of vorticity in cyclogenesis (the birth and development of a cyclone), especially along the polar front

Polar front

In meteorology, the polar front is the boundary between the polar cell and the Ferrel cell in each hemisphere. At this boundary a sharp gradient in temperature occurs between these two air masses, each at very different temperatures....

, and in analyzing flow in the ocean.

In meteorology

Meteorology

Meteorology is the interdisciplinary scientific study of the atmosphere. Studies in the field stretch back millennia, though significant progress in meteorology did not occur until the 18th century. The 19th century saw breakthroughs occur after observing networks developed across several countries...

, the potential vorticity unit (PVU) is defined as .

It is also useful in tracing intrusions of stratospheric air deep into the troposphere

Troposphere

The troposphere is the lowest portion of Earth's atmosphere. It contains approximately 80% of the atmosphere's mass and 99% of its water vapor and aerosols....

 in the vicinity of jet streaks, a concentrated region within a jet stream

Jet stream

Jet streams are fast flowing, narrow air currents found in the atmospheres of some planets, including Earth. The main jet streams are located near the tropopause, the transition between the troposphere and the stratosphere . The major jet streams on Earth are westerly winds...

 where the wind speeds are the strongest. It acts as a flow tracer

Flow tracer

thumb|right|300px|On May 2, [[2001]], the Moderate-resolution Imaging Spectroradiometer obtained this spectacular image of the [[Atlantic Ocean]]'s [[Gulf Stream]]. The [[false color]]s in the image represent "[[brightness temperature]]" observed at the top of the [[atmosphere]]...

 in the ocean as well. It can also be used to explain how a range of mountains like the Andes

Andes

The Andes is the world's longest continental mountain range. It is a continual range of highlands along the western coast of South America. This range is about long, about to wide , and of an average height of about .Along its length, the Andes is split into several ranges, which are separated...

 can make the upper westerly winds swerve towards the equator

Equator

An equator is the intersection of a sphere's surface with the plane perpendicular to the sphere's axis of rotation and containing the sphere's center of mass....

 and back.

Baroclinic instability requires the presence of a potential vorticity gradient along which waves amplify during cyclogenesis.

PV conservation

Mathematically, Ertel

Hans Ertel

Hans Ertel was a German natural scientist and a pioneer in geophysics, meteorology and hydrodynamics.-Life and work:...

's form of potential vorticity is given by the equation:



where is the fluid density

Density

The mass density or density of a material is defined as its mass per unit volume. The symbol most often used for density is ρ . In some cases , density is also defined as its weight per unit volume; although, this quantity is more properly called specific weight...

, is the absolute vorticity and is the gradient

Gradient

In vector calculus, the gradient of a scalar field is a vector field that points in the direction of the greatest rate of increase of the scalar field, and whose magnitude is the greatest rate of change....

 of the potential temperature. It can be shown through a combination of the first law of thermodynamics

First law of thermodynamics

The first law of thermodynamics is an expression of the principle of conservation of work.The law states that energy can be transformed, i.e. changed from one form to another, but cannot be created nor destroyed...

 and momentum conservation that potential vorticity can only be changed by diabatic heating (such as latent heat released from condensation) or frictional processes. This conservation is the atmospheric equivalent to inertia

Inertia

Inertia is the resistance of any physical object to a change in its state of motion or rest, or the tendency of an object to resist any change in its motion. It is proportional to an object's mass. The principle of inertia is one of the fundamental principles of classical physics which are used to...

. A spinning ice skater with her arms spread out laterally can accelerate her rate of spin by contracting her 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 ring vortex. Divergence causes the vortex to spread, slowing down the rate of spin.

External links

• AMS Glossary entry
• Potential vorticity by Michael E. McIntyre