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:[3]

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

See also

References

  1. ↑ Batchelor, George Keith (1967). An Introduction to Fluid Dynamics. Cambridge University Press. p. 422. ISBN 0-521-66396-2.
  2. ↑ Raisinghania, M.D. Fluid Dynamics.
  3. ↑ Tulu, Serdar (2011). Vortex dynamics in domains with boundaries (Thesis).