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The Iterated Equation of Generalized Axially Symmetric Potential Theory

IV. Circle Theorems

Published online by Cambridge University Press:  09 April 2009

J. C. Burns
J. C. Burns
Affiliation:
The Australian National UniversityCanberra, A.C.T.
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Milne-Thomson's well-known circle theorem [1] gives the stream function for steady two-dimensional irrotational flow of a perfect fluid past a circular cylinder when the flow in the absense of the cylinder is known. Butler's sphere theorem [2] gives the corresponding result for axially symmetric irrotational flow of a perfect fluid past a sphere. Collins [3] has obtained a sphere theorem for axially symmetric Stokes flow of a viscous liquid which gives a stream function satisfying the appropriate viscous boundary conditions on the surface of a sphere when the stream function for irrotational flow in the absence of the sphere is known.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 9 , Issue 1-2 , February 1969 , pp. 153 - 160
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Milne-Thomson, L. M., ‘Hydrodynamical Images’, Proc. Cambridge Philos. Soc. 36 (1940), 246–247;CrossRefGoogle Scholar
or Theoretical Hydrodynamics (MacMillan, 4th ed. 1960), 154.Google Scholar
[2]Butler, S. J. F., ‘A note on Stokes's stream function for motion with a spherical boundary’, Proc. Cambridge Philos. Soc. 49 (1953), 169–174;CrossRefGoogle Scholar
or Milne-Thomson, L. M., Theoretical Hydrodynamics (MacMillan, 4th. ed. 1960), 463.Google Scholar
[3]Collins, W. D., ‘A note on Stokes's stream function for the slow steady motion of a viscous fluid before plane and spherical boundaries’, Mathematika 1 (1954), 125–130.CrossRefGoogle Scholar
[4]Collins, W. D., ‘Note on a sphere theorem for the axisymmetric Stokes flow of a viscous liquid’, Mathematika 5 (1958), 118–121.CrossRefGoogle Scholar
[5]Burns, J. C., ‘The iterated equation of generalized axially symmetric potential theory. I Particular solutions’, Journ. Austr. Math. Soc., 7 (1967), 263–276.CrossRefGoogle Scholar