Milne-Thomson circle theorem

In fluid dynamics the Milne-Thomson circle theorem or the circle theorem is a statement giving a new stream function for a fluid flow when a cylinder is placed into that flow. It was named after the English mathematician L. M. Milne-Thomson.

Let \(w = f(z)\) be the complex stream function for a fluid flow with no rigid boundaries and no singularities within \(|z| = a\). If a circular cylinder \(|z| = a\) is placed into that flow, the complex potential for the new flow is given by:

\[w = f(z) + \bar{f}\left( \frac{a^2}{\bar{z}} \right)\]

See also

• Potential flow
• Conformal mapping
• Velocity potential