Vorticity is a concept used in fluid dynamics. In the simplest sense, vorticity is the tendency for elements of the fluid to "spin."

More formally, vorticity can be related to the amount of "circulation" or "rotation" (or more strictly, the local angular rate of rotation) in a fluid. The average vorticity Failed to parse (Missing texvc executable; please see math/README to configure.): \omega_{av}

Notionally, the vorticity at a point in a fluid is the limit as the area of the small region of fluid approaches zero at the point:

Mathematically, vorticity is a vector field and is defined as the curl of the velocity field:

In fluid dynamics, vorticity is the curl of the fluid velocity. It can also be considered as the circulation per unit area at a point in a fluid flow field. It is a vector quantity, whose direction is along the axis of the fluid's rotation. For a two-dimensional flow, the vorticity vector is perpendicular to the plane.

For a fluid having locally a "rigid rotation" around an axis (i.e., moving like a rotating cylinder), vorticity is twice the angular velocity of a fluid element. An irrotational fluid has no vorticity. Somewhat counter-intuitively, an irrotational fluid can have a non-zero angular velocity (e.g. a fluid rotating around an axis with its tangential velocity inversely proportional to the distance to the axis has a zero vorticity); see also forced and free vortex.