Vorticity

Definition

The vorticity defines the rotation of the fluid particles across the entire field. Thus giving a of map of intensity of the rotation across the domain. It is defined as the Curl of the Velocity vector.

$$\vec{\omega }=\nabla \times \vec{u}=\left|\begin{array}{ccc}i& j& k\\ \frac{\partial }{\partial x_1}& \frac{\partial }{\partial x_2}& \frac{\partial }{\partial x_3}\\ v_1& v_2& v_3\end{array}\right|=\left(\frac{\partial w}{\partial y}-\frac{\partial v}{\partial z},\frac{\partial u}{\partial z}-\frac{\partial w}{\partial x},\frac{\partial v}{\partial x}-\frac{\partial u}{\partial y}\right)$$