Editing Conservative vector field (section)

=== Vorticity ===
{{main article|Vorticity}}

The [[vorticity]] <math>\boldsymbol{\omega}</math> of a vector field can be defined by:
<math display="block">\boldsymbol{\omega} ~ \stackrel{\text{def}}{=} ~ \nabla \times \mathbf{v}.</math>

The vorticity of an irrotational field is zero everywhere.<ref>{{citation|title = Elements of Gas Dynamics|first1 = H.W.|last1 = Liepmann|author-link1 = Hans W. Liepmann|first2 = A.|last2 = Roshko|author-link2 = Anatol Roshko|publisher = Courier Dover Publications|year = 1993|orig-year = 1957|isbn = 0-486-41963-0}}, pp. 194–196.</ref> [[Kelvin's circulation theorem]] states that a fluid that is irrotational in an [[inviscid flow]] will remain irrotational. This result can be derived from the [[vorticity transport equation]], obtained by taking the curl of the [[Navier–Stokes equations]].

For a two-dimensional field, the vorticity acts as a measure of the ''local'' rotation of fluid elements. The vorticity does ''not'' imply anything about the global behavior of a fluid. It is possible for a fluid that travels in a straight line to have vorticity, and it is possible for a fluid that moves in a circle to be irrotational.