Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-21T04:48:25.278Z Has data issue: false hasContentIssue false
  • English
  • Français

The drag on a sphere moving axially in a long rotating container

Published online by Cambridge University Press:  19 April 2006

L. M. Hocking ,
D. W. Moore  and
I. C. Walton
L. M. Hocking
Affiliation:
Department of Mathematics, University College, London
D. W. Moore
Affiliation:
Department of Mathematics, Imperial College, London
I. C. Walton
Affiliation:
Department of Mathematics, Imperial College, London
Get access Rights & Permissions [Opens in a new window]

Abstract

A container of viscous incompressible liquid is bounded by rigid parallel planes and rotates steadily about an axis normal to these planes. A rigid sphere moves steadily parallel to the rotation axis and the Rossby and Ekman numbers characterizing the motion are both small. The drag on the sphere is calculated in the case when the length of the Taylor column is comparable to the axial dimension of the container. Viscous effects are allowed for in the boundary of the Taylor column, but the Ekman layers on the sphere and on the bounding planes are shown not to affect the drag to leading order. The determination of the drag involves solving dual integral equations. This is done numerically and, for the limiting cases of long and short containers, analytically. The interaction of the Taylor column and the ends of the container leads to an increase in the drag over its value in an unbounded fluid, but the increase is smaller than that measured by Maxworthy (1970).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 90 , Issue 4 , 27 February 1979 , pp. 781 - 793
Copyright
© 1979 Cambridge University Press

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

Abramowitz, M. & Stegun, I. A. 1964 Handbook of Mathematical Functions. Washington: Nat. Bur. Stand.
Barnard, B. J. S. & Pritchard, W. G. 1975 J. Fluid Mech. 71, 43.
Bretherton, F. P. 1967 J. Fluid Mech. 28, 545.
Grace, S. F. 1926 Proc. Roy. Soc. A 113, 46.
Magnus, W. & Oberhettinger, F. 1954 Functions of Mathematical Physics. New York: Chelsea.
Maxworthy, T. 1970 J. Fluid Mech. 40, 435.
Moore, D. W. & Saffman, P. G. 1968 J. Fluid Mech. 31, 635.
Moore, D. W. & Saffman, P. G. 1969 Phil. Trans. Roy. Soc. A 264, 597.
Morrison, J. A. & Morgan, G. W. 1956 Tech. Rep. Div. Appl. Math., Brown Univ. no. 8.
Stewartson, K. 1952 Proc. Camb. Phil. Soc. 48, 168.
Stewartson, K. 1966 J. Fluid Mech. 26, 131.
Taylor, G. I. 1917 Proc. Roy. Soc. A 93, 99.
Taylor, G. I. 1921 Proc. Roy. Soc. A 100, 114.
Taylor, G. I. 1922 Proc. Roy. Soc. A 102, 180.
Titchmarsh, E. C. 1937 Theory of Fcurier Integrals. Oxford: Clarendon Press.
Tranter, C. J. 1971 Integral Transforms in Mathematical Physics. Methuen.
Watson, G. N. 1958 Theory of Bessel Functions. Cambridge University Press.