Hostname: page-component-8448b6f56d-jr42d Total loading time: 0 Render date: 2024-04-23T11:54:45.575Z Has data issue: false hasContentIssue false
  • English
  • Français

On Stokes flow about a torus

Published online by Cambridge University Press:  26 February 2010

W. H. Pell  and
L. E. Payne
W. H. Pell
Affiliation:
National Bureau of Standards, Washington, D.C., U.S.A.
L. E. Payne
Affiliation:
The Institute for Fluid Dynamics and Applied Mathematics, The University of Maryland, U.S.A.
Get access

Extract

In previous papers [1, 2], the authors have solved the Stokes flow problem for certain axially symmetric bodies, with the velocity at infinity uniform and parallel to the axis of symmetry. Each of the bodies considered possessed the property that the meridional section intercepted a segment of the axis of symmetry. In the present paper this assumption is removed; in addition, we shall consider the particular case of the Stokes flow about a torus.

Type
Research Article
Information
Mathematika , Volume 7 , Issue 1 , June 1960 , pp. 78 - 92
Copyright
Copyright © University College London 1960

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

1.Payne, L. E. and Pell, W. H., “The Stokes flow problem for a class of axially symmetric bodies”, Journal of Fluid Mechanics, 7 (1960), 529–549.CrossRefGoogle Scholar
2.Payne, L. E. and Pell, W. H., “The Stokes flow problem for a class of axially symmetric bodies, II: The flow about a spindle”, Quart. Appl. Math. (to appear).Google Scholar
3.Dyson, F. W., “On the potential of an anchor ring”, Phil. Trans. Roy. Soc., 184 (1892), 43–95.Google Scholar
4.Sternberg, E. and Sadowsky, M. A., “Axisymmetric flow of an ideal incompressible fluid about a solid torus”, J. of Applied Mechs., 20 (1953), 393–400.CrossRefGoogle Scholar
5.Sokolnikoff, I. S., Mathematical theory of elasticity, 2nd ed. (New York, 1956), pp. 28–29.Google Scholar
6.Weiss, G. and Payne, L. E., “Torsion of a shaft with a toroidal cavity”, J. of Applied Physics., 25 (1954), 1321–1328.CrossRefGoogle Scholar
7.Milne-Thomson, L. M., “Theoretical hydrodynamics”, 2nd ed. (New York, 1950).Google Scholar
8.Hobson, E. W., Spherical and ellipsoidal harmonics (Cambridge 1931).Google Scholar
9.Payne, L. E., “Representation formulas for solutions of a class of partial differential equations”, Tech. Note BN-122, Institute for Fluid Dynamics and Applied Mathematics, Univ. of Md., February 1958.Google Scholar
10.Weinstein, A., “Generalized axially symmetric potential theory”, Bull. Amer. Math. Soc., 59 (1953), 20–38.CrossRefGoogle Scholar
11.Ghosh, S., “On the steady motion of a viscous liquid due to the translation of a tore parallel to its axis”, Bull. of the Calcutta Math. Soc., 18 (1927), 185–194.Google Scholar