Hostname: page-component-84b7d79bbc-dwq4g Total loading time: 0 Render date: 2024-07-29T19:21:21.095Z Has data issue: false hasContentIssue false

A note on integral representations in Stokes flow

Published online by Cambridge University Press:  17 February 2009

J. R. Blake
Affiliation:
CSIRO Division of Mathematics and Statistics, P.O. Box 1965, Canberra, A.C.T., 2601, Australia.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

An alternative method via generalised functions is used to obtain the surface integral representation for a finite body in an infinite fluid in Stokes flow. The problem is further generalised to a finite number of intersecting finite bodies in an infinite and semi-infinite fluid. Possible applications to line distributions for axi-symmetric bodies are discussed.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1975

References

[1]Blake, J. R., ‘A note on the image system for a stokeslet in a no-slip boundary’. Proc. Camb. Phil. Soc. 70, (1971), 303–10.CrossRefGoogle Scholar
[2]Blake, J. R., and Chwang, A. T., ‘Fundamental singularities of viscous flow. Part I. The image system in the vicinity of a stationary no-slip boundary’. J. Eng. Math. 8, (1974),2329.Google Scholar
[3]Chwang, A. T., and Wu, T. Y., ‘Hydro-mechanics of low Reynolds number flow. Part I. Rotation of axi symmetric prolate bodies’. J. Fluid Mech. 63, (1974),607–22.CrossRefGoogle Scholar
[4]Chwang, A. T., and Wu, T. Y., ‘Hydro-mechanics of low Reynolds number flow. Part II. Singularity method for Stokes flow’. J. Fluid Mech. 67 (1975),787815.Google Scholar
[5]Happel, J., and Brenner, H., Low Reynolds Number Hydro-dynamics (Prentice Hall, 1965).Google Scholar
[6]Jones, D. S., Generalised Functions (McGraw-Hill, 1966).Google Scholar
[7]Ladyzhenskaya, O. A., The Mathematical Theory of Viscous Incompressible Flow (Gordon and Breach, 1963).Google Scholar
[8]Oseen, C. W.. Neuere Methoden und Ergebnisse in der Hydrodynamik (Leipzig, 1927).Google Scholar