Editing Vortex (section)

===Vorticity===
[[Image:Crow instability contrail.JPG|thumb|The [[Crow instability]] of a jet aeroplane's [[contrail]] visually demonstrates the vortex created in the atmosphere (gas fluid medium) by the passage of the aircraft.]]
A key concept in the dynamics of vortices is the [[vorticity]], a [[vector (geometry)|vector]] that describes the ''local'' rotary motion at a point in the fluid, as would be perceived by an observer that moves along with it. Conceptually, the vorticity could be observed by placing a tiny rough ball at the point in question, free to move with the fluid, and observing how it rotates about its center. The direction of the vorticity vector is defined to be the direction of the axis of rotation of this imaginary ball (according to the [[right-hand rule]]) while its length is twice the ball's [[angular velocity]]. Mathematically, the vorticity is defined as the curl (or rotational) of the [[velocity field]] of the fluid, usually denoted by <math>\vec \omega</math> and expressed by the [[vector analysis]] formula <math>\nabla \times \vec{\mathit{u}}</math>, where <math>\nabla</math> is the [[nabla operator]] and <math>\vec{\mathit{u}}</math> is the local flow velocity.<ref>{{cite book|url=http://www.princeton.edu/~gkv/geoturb/turbch.pdf|page=1|access-date=2012-09-26|year=1999|first=Geoffrey|last=Vallis|title=Geostrophic Turbulence: The Macroturbulence of the Atmosphere and Ocean Lecture Notes|publisher=[[Princeton University]]|url-status=dead|archive-url=https://web.archive.org/web/20131228115711/http://www.princeton.edu/~gkv/geoturb/turbch.pdf|archive-date=2013-12-28}}</ref>

The local rotation measured by the vorticity <math>\vec \omega</math> must not be confused with the angular velocity vector of that portion of the fluid with respect to the external environment or to any fixed axis. In a vortex, in particular, <math>\vec \omega</math> may be opposite to the mean angular velocity vector of the fluid relative to the vortex's axis.