Milne-Thomson circle theorem


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.[1][2] 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)

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