PV Conservation
Mathematically, Ertel's form of potential vorticity is given by the equation:
where is the fluid density, is the absolute vorticity and is the gradient of the potential temperature. 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 released from condensation) or frictional processes. This conservation is the atmospheric equivalent to inertia. 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.
Read more about this topic: Potential Vorticity
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