If $u:\mathbb{R}^3\to \mathbb{R}^3$ is a velocity field one defines the vorticity as the curl \begin{align} \omega= \text{curl}(u). \end{align} I just read that vorticity measures the rotation of the motion. I can't imagine what the vorticity is. I computed examples as $u_1=(-y,x,0)$ and $u_2=(-y,x,z)$. For both the vorticity is $\omega=(0,0,2)$. I plotted both
For $u_1$ you can see that $(0,0,2)$ is perpendicular but how does it measure rotation? In the case of $u_2$ it is not perpendicular but also here I don't know what the vorticity has to do with rotation.