= Surface stagnation points of a circulating cylinder flow
{title2=$z_\pm=\pm a\sqrt{1-\gamma^2}+ia\gamma,\quad\gamma=\Gamma/(4\pi Ua)$}
For <complex potential of a two-dimensional potential flow> $w=U(z+a^2/z)-i\Gamma\log z/(2\pi)$, zeros of the <complex velocity> solve a quadratic. If $0<\gamma<1$, the displayed two roots are distinct and both have modulus $a$; positive <circulation> places them above the centreline. Their polar angles satisfy $\sin\theta=\gamma$. At the threshold $\gamma=1$ they merge at the top of the cylinder. This follows also from the surface tangential velocity $-2U\sin\theta+\Gamma/(2\pi a)$. The shifted <stream function> $U(r-a^2/r)\sin\theta-\Gamma\log(r/a)/(2\pi)$ is constant on the cylinder.
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