= Milne-Thomson circle theorem
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{title2=$W(z)=f(z)+\overline{f(a^2/\bar z)}$}
= Milne-Thomson's circle theorem
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The <Milne-Thomson circle theorem> constructs a circular impermeable boundary in a two-dimensional <potential flow>. Suppose an incident <complex potential of a two-dimensional potential flow> $f$ is analytic on and inside $|z|=a$, with its physical singularities outside that disk. Then the displayed $W$ has constant <stream function> on $|z|=a$. The proof is the identity $a^2/\bar z=z$ on the circle: there $W=f(z)+\overline{f(z)}$ is real. Hence the circle is a <streamline> and satisfies the <no-penetration boundary condition>. The reflected term has its image singularities inside the obstacle. Additional imposed <circulation> must be specified separately. The theorem is named after <Louis Melville Milne-Thomson>.
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