= Solution
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,
$$
\boxed{\nabla\times v=-\frac{\partial v_x}{\partial y}\,e_z
=2v_0y e^{-y^2}e_z.}
$$
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.
\Image[/past-exam-of-the-mathematical-methods-ii-course-of-the-university-of-oxford/2017-resit-shear-and-critical-contours.png]
{title=Gaussian shear vorticity and contours around a minimum and two saddles}
{description=Original analytic field and contour plots. The shear arrows are scaled uniformly; the marked contour at level two factors into a line and a parabola through the saddle points.}
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