 Stokes flow between touching counter-rotating cylinders

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 streamfunctionIts unique interior stagnation point is $(x,y)=(0,2\sqrt{2}a)$, and its nonzero streamlines are closed curves around that point.