# Vorticity

pseudovector field in continuum mechanics

Vorticity is a mathematical concept used in fluid dynamics. It 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 in a small region of fluid flow is equal to the circulation ${\displaystyle \Gamma }$ around the boundary of the small region, divided by the area A of the small region.

${\displaystyle \omega _{av}={\frac {\Gamma }{A}}}$

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:

${\displaystyle \omega ={\frac {d\Gamma }{dA}}}$

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

${\displaystyle {\vec {\omega }}={\vec {\nabla }}\times {\vec {v}}.}$

One of the base assumptions of the potential flow assumption is that the vorticity ${\displaystyle \omega }$ is zero almost everywhere, except in a boundary layer or a stream-surface immediately bounding a boundary layer.

Because a vortex is a region of concentrated vorticity, the non-zero vorticity in these specific regions can be modelled with vortices.