= Solution
A simple closed loop that does not surround the cylinder bounds a surface wholly in the fluid. At time zero, <Stokes theorem> gives zero <circulation> because its <vorticity> is zero. The smooth impermeable exterior flow transports this loop without changing its winding about the obstacle. Pulling a loop at time $t$ back to time zero and using <Kelvin's circulation theorem> therefore gives
$$
\boxed{\Gamma=0\quad\text{on nonenclosing loops}}.
$$
This is the contractible-loop case of <irrotational circulation in an exterior domain>. Equivalently, the initially vanishing <vorticity> remains zero under the inviscid barotropic <vorticity> equation.
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