Past exam of the mathematical methods II course of the University of Oxford / 2017 resit / 3 / a

The arrows point in the positive $x$ direction, with largest speed $v_0$ on $y=0$ and rapidly decreasing length away from that line. Since only $v_x$ is nonzero,The vorticity points towards positive $z$ above the centre line and negative $z$ below it. A small fluid element therefore has local angular velocity $(\nabla \times v)/2$: anticlockwise above and clockwise below when viewed from positive $z$. At $y=0$, its speed is maximal but its local vorticity is zero. Translation speed and local rotation are different properties.