= Stokes flow between touching counter-rotating cylinders
{c}
An inner cylinder of radius $a$ centered at $(0,a)$ and an outer cylinder of radius $2a$ centered at $(0,2a)$ have polar boundaries $r=2a\sin\theta$ and $r=4a\sin\theta$. If their angular velocities are $\Omega$ and $-\Omega/4$, respectively, the no-slip <Stokes flow> between them has streamfunction
$$
\psi=\frac{a\Omega\sin\theta}{r}
(r-2a\sin\theta)(r-4a\sin\theta).
$$
Its unique interior stagnation point is $(x,y)=(0,2\sqrt2a)$, and its nonzero streamlines are closed curves around that point.
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