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Some methods for flows past blunt slender bodies

Published online by Cambridge University Press:  28 March 2006

E. O. Tuck
E. O. Tuck
Affiliation:
Department of Mathematics, University of Manchester
Present address: David Taylor Model Basin, Washington, D.C. 20007.
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Abstract

It is suggested that the use of prolate spheroidal co-ordinates in certain problems involving slender bodies may lead to results which not only are more likely to be uniformly valid for blunt bodies, but in many cases require less complicated analysis than results obtained by standard methods which use cylindrical co-ordinates. The method is developed for a simple problem in potential theory and is then applied also to a problem in Stokes flow, yielding a procedure for obtaining the Stokes drag on a slender body of arbitrary shape. For comparison purposes, consideration is also given to the use of both cylindrical and di-polar co-ordinates, and as a by-product of the comparison of results on cylindrical and spheroidal systems some new simple formulae involving Legendre polynomials are obtained heuristically, and then rigorously proved.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 18 , Issue 4 , April 1964 , pp. 619 - 635
Copyright
© 1964 Cambridge University Press

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