Hostname: page-component-8448b6f56d-mp689 Total loading time: 0 Render date: 2024-04-20T10:13:10.095Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on the image system for a stokeslet in a no-slip boundary

Published online by Cambridge University Press:  24 October 2008

J. R. Blake
J. R. Blake
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge
Get access Rights & Permissions [Opens in a new window]

Abstract

The velocity and pressure fields for Stokes's flow due to a point force (‘stokeslet’) in the vicinity of a stationary plane boundary are analysed, using Fourier transforms, to obtain the image system required to satisfy the no-slip condition on the boundary. The image system, which is illustrated by diagrams, is found to consist of a stokeslet equal in magnitude but opposite in sign to the initial stokeslet, a stokes-doublet and a source-doublet, the displacement axes for the doublets being in the original direction of the force. The influence of the wall on the near and far fields is discussed. In the far field it is found that a stokeslet aligned parallel to the wall produces a stokes-doublet far-field, whereas a stokeslet normal to the wall produces a combination of a source-doublet and a stokes-quadrupole far-field. Although results can be alternatively derived by the method of Lorentz (7) using a reciprocal theorem, the present method yields much more clearly the form of the image system.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 70 , Issue 2 , September 1971 , pp. 303 - 310
Copyright
Copyright © Cambridge Philosophical Society 1971

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Batchelor, G. K.J.Fluid Mech. 41 (1970), 545.CrossRefGoogle Scholar
(2)Cox, R. G. J.Fluid Mech. 44 (1970), 791.CrossRefGoogle Scholar
(3)Happel, J. and Brenner, H.Low Reynolds Number Hydrodynamics (Prentice-Hall; Englewood Cliffs N.J. 1965).Google Scholar
(4)Ejike, V. B. C. O.Internat. J. Engng. Sci. 8 (1970), 891.CrossRefGoogle Scholar
(5)Erdelyi, A.Table of Integral Transforms (McGraw-Hill; New York, 1954).Google Scholar
(6)Ladyzhenskaya, O. A.The mathematical theory of viscous incompressible flow (Gordon and Breach; London 1963).Google Scholar
(7)Lorentz, H. A.Zittingsverlag Akad. v. Wet. 5 (1896), 168.Google Scholar
(8)Sneddon, I. N.Fourier Transforms (McGraw-Hill; New York, 1951).Google Scholar
(9)Stokes, G. G.Trans. Cambridge Philos. Soc. 9 (1851), 8.Google Scholar