Vorticity

Definition of Vorticity: Describes the locally spinning motion of a fluid. This is the common definition for Vorticity, other definitions can be discussed in the article

Notes

In three dimensions, the vorticity [math]\vec{\Omega}[/math] is a vector [math]\vec{\Omega} = \vec{\nabla} \times \vec{v}[/math], where [math]\vec{v}[/math] is the velocity vector with components [math](u, v, w)[/math] along the [math](x, y, z)[/math] directions.

In two dimensions [math](x, y)[/math], the vorticity is a scalar, [math]\Omega=\Large\frac{\partial v}{\partial x}\normalsize - \Large\frac{\partial u}{\partial y}\normalsize[/math].