Editing Vorticity (section)

==Specific sciences==

===Aeronautics===
In [[aerodynamics]], the [[lift (force)|lift]] distribution over a [[finite wing]] may be approximated by assuming that each spanwise segment of the wing has a semi-infinite trailing vortex behind it. It is then possible to solve for the strength of the vortices using the criterion that there be no flow induced through the surface of the wing. This procedure is called the vortex panel method of [[computational fluid dynamics]]. The strengths of the vortices are then summed to find the total approximate [[circulation (fluid dynamics)|circulation]] about the wing. According to the [[Kutta–Joukowski theorem]], lift per unit of span is the product of circulation, airspeed, and air density.

===Atmospheric sciences===
The '''relative vorticity''' is the vorticity relative to the Earth induced by the air velocity field. This air velocity field is often modeled as a two-dimensional flow parallel to the ground, so that the relative vorticity vector is generally scalar rotation quantity perpendicular to the ground. Vorticity is positive when – looking down onto the Earth's surface – the wind turns counterclockwise. In the northern hemisphere, positive vorticity is called [[cyclonic rotation]], and negative vorticity is [[anticyclone|anticyclonic rotation]]; the nomenclature is reversed in the Southern Hemisphere.

The '''absolute vorticity''' is computed from the air velocity relative to an inertial frame, and therefore includes a term due to the Earth's rotation, the [[Coriolis parameter]].

The '''[[potential vorticity]]''' is absolute vorticity divided by the vertical spacing between levels of constant [[potential temperature|(potential) temperature]] (or [[entropy]]). The absolute vorticity of an air mass will change if the air mass is stretched (or compressed) in the vertical direction, but the potential vorticity is [[Conservation law (physics)|conserved]] in an [[adiabatic]] flow. As [[adiabatic]] flow predominates in the atmosphere, the potential vorticity is useful as an approximate [[Flow tracer|tracer]] of air masses in the atmosphere over the timescale of a few days, particularly when viewed on levels of constant entropy.

The [[barotropic vorticity equation]] is the simplest way for forecasting the movement of [[Rossby wave]]s (that is, the [[trough (meteorology)|troughs]] and [[ridge]]s of 500&nbsp;[[pascal (unit)|hPa]] [[geopotential height]]) over a limited amount of time (a few days). In the 1950s, the first successful programs for [[numerical weather forecasting]] utilized that equation.

In modern numerical weather forecasting models and [[general circulation model]]s (GCMs), vorticity may be one of the predicted variables, in which case the corresponding time-dependent equation is a [[prognostic equation]].

Related to the concept of vorticity is the [[Hydrodynamical helicity|helicity]] <math>H(t)</math>, defined as

:<math>H(t) = \int_V \mathbf v \cdot \boldsymbol{\omega} \, dV</math>
where the integral is over a given volume <math>V</math>. In atmospheric science, helicity of the air motion is important in forecasting [[supercell]]s and the potential for [[tornado|tornadic]] activity.<ref name="Scheeler2017">{{cite journal|last1=Scheeler|first1=Martin W.|last2=van Rees|first2=Wim M.|last3=Kedia|first3=Hridesh|last4=Kleckner|first4=Dustin|last5=Irvine|first5=William T. M.|title=Complete measurement of helicity and its dynamics in vortex tubes|journal=Science|volume=357|issue=6350|year=2017|pages=487–491|issn=0036-8075|doi=10.1126/science.aam6897|pmid=28774926|bibcode=2017Sci...357..487S|s2cid=23287311|doi-access=free}}</ref>