# Potential vorticity

**Potential vorticity**(PV) is a quantity which is proportional to the dot product ofvorticity andstratification that, following a parcel of air or water, can only be changed bydiabatic or frictional processes. It is a useful concept for understanding the generation of vorticity incyclogenesis (the birth and development of a cyclone), especially along thepolar front , and in analyzing flow in the ocean.It is also useful in tracing intrusions of stratospheric air deep into the

troposphere in the vicinity of jet streaks, a concentrated region within ajet stream where the wind speeds are the strongest. It acts as aflow tracer in the ocean as well. It can also be used to explain how a range of mountains like theAndes can make the upper westerly winds swerve towards theequator and back.Baroclinic instability requires the presence of a potential vorticity gradient along which waves amplify during cyclogenesis.**PV conservation**Mathematically, one form of potential vorticity is given by the equation:

$\{\; m\; PV\}\; =\; frac\{1\}\{\; ho\},zeta,.\; abla\; heta$ where $ho$ is the fluiddensity , $zeta$ is the absolutevorticity and $abla\; heta$ is thegradient of thepotential temperature . It can be shown through a combination of thefirst law of thermodynamics 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 toinertia . 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 rince vortex. Divergence causes the vortex to spread, slowing down the rate of spin.**ee also***

Vorticity

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