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| '''Potential vorticity''' (PV) is a quantity which is proportional to the dot product of [[vorticity]] and [[Stratification (mathematics)|stratification]] that, following a [[air parcel|parcel]] of air or water, can only be changed by [[diabatic]] 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]], and in analyzing flow in the ocean.
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| In [[meteorology]], the '''potential vorticity unit''' (PVU) is defined as <math>{10^{-6} \cdot K \cdot m^2 \over kg \cdot s} \equiv 1 PVU</math>.
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| It is also 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 acts as a [[flow tracer]] in the ocean as well. 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.
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| [[Baroclinic instability]] requires the presence of a potential vorticity gradient along which waves amplify during cyclogenesis.
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| ==PV conservation==
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| [[Image:Potential vorticity conservation.GIF|thumb|200px|''Convergence and divergence of an air parcel'']]
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| [[Carl-Gustav Rossby|Carl-Gustaf Rossby]] first introduced potential vorticity in his 1936 paper "Dynamics of steady ocean currents in the light of experimental fluid mechanics". This work was based on an analysis of a shallow water model of the Gulf Stream. The concept was developed further, within a few years of Rossby's seminal paper, by [[Hans Ertel]]. Mathematically, Ertel's form of potential vorticity is given by the equation:
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| <CENTER>
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| <math>{\rm PV} = \frac{1}{\rho}\,\zeta\,^a\cdot\,\nabla\theta</math>
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| </CENTER>
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| where <math>\rho</math> is the fluid [[density]], <math>\zeta^a</math> is the absolute [[vorticity]] and <math>\nabla \theta</math> 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. | |
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| ==See also==
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| * [[Vorticity]]
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| * [[Circulation (fluid dynamics)]]
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| ==Further reading==
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| {{Refbegin}}
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| * Hoskins, B.J., McIntyre, M.E. and Robertson, A.W. "On the use and significance of isentropic potential vorticity maps". Quarterly Journal of the Royal Meteorological Society, volume 111 (1985): 877-946.
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| * Rossby, C-G. "Dynamics of steady ocean currents in the light of experimental fluid mechanics". Papers in Physical Oceanography and Meteorology, volume 5 (1936): 2-43.
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| *{{cite book |author=Roulstone, Ian; Norbury, John |title=Invisible in the Storm: the role of mathematics in understanding weather |location=Princeton |publisher=Princeton University Press |year=2013 |isbn=978-0-691-15272-1 }}
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| * Thorpe, A.J., Volkert, H. and Ziemiański, M.J. "The Bjerknes' circulation theorem: a historical perspective." Bulletin of the American Meteorological Society, volume 84 (2003): 471-480.
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| {{Refend}}
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| ==External links==
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| * [http://amsglossary.allenpress.com/glossary/search?id=potential-vorticity1 AMS Glossary entry]
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| * [http://www.atm.damtp.cam.ac.uk/mcintyre/papers/ENCYC/epv-times.pdf Potential vorticity] by Michael E. McIntyre
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| {{DEFAULTSORT:Potential Vorticity}}
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| [[Category:Oceanography]]
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