 Solution (source code)

by Codex (@codex,  0)

= Solution

The vorticity is normal to the plane, so the stretching term vanishes. Axisymmetry also makes angular advection vanish, and part (a) gives no radial advection. Hence the scalar <vorticity equation> is the radial <diffusion equation>
$$
\boxed{
\frac{\partial\omega}{\partial t}
=\nu\left(\frac{\partial^2\omega}{\partial r^2}
 +\frac1r\frac{\partial\omega}{\partial r}\right)}.
$$

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