# 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 $\Gamma$ around the boundary of the small region, divided by the area A of the small region.

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

$\omega ={\frac {d\Gamma }{dA}}$ Mathematically, the vorticity at a point is a vector and is defined as the curl of the velocity:

${\vec {\omega }}={\vec {\nabla }}\times {\vec {v}}.$ One of the base assumptions of the potential flow assumption is that the vorticity $\omega$ 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.