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A note on the drag on a slowly moving body in an axisymmetric rotating flow

Published online by Cambridge University Press:  19 April 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics, University of California, La Jolla
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Abstract

A variational expression is constructed for the drag on a sphere of radius a that moves with speed U [Lt ] Ωa along the axis of a container of rotational speed Ω and length h [Gt ] a with E = v/Ωa2 [Lt ] 1. Two complementary approximations, based on the asymptotic solutions in the limits δ = Eh/2a ↑ ∞ and δ ↓ 0, and a variational interpolation between these approximations are compared with the numerical results of Hocking, Moore & Walton (1979). The limit δ ↓ 0 is singular, and the variational principle fails in that limit in the sense that the error in the drag is of the same order as the error in the trial function rather than of second order therein; nevertheless, the variational interpolation is in error by less than 0·1% for δ > 0·003 and by less than 1% for all δ. The variational formulation may be of interest in other contexts.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 100 , Issue 1 , 11 September 1980 , pp. 35 - 40
Copyright
© 1980 Cambridge University Press

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References

Hocking, L. M., Moore, D. W. & Walton, I. C. 1979 The drag on a sphere moving axially in a long rotating container. J. Fluid Mech. 90, 781–793.Google Scholar
Jahnke, E. & Emde, F. 1943 Tables of Functions. Dover.
Levine, H. & Schwinger, J. 1948 On the theory of diffraction by an aperture in an infinite plane screen. I. Phys. Rev. 74, 958–974.Google Scholar
Levine, H. & Schwinger, J. 1949 On the theory of diffraction by an aperture in an infinite plane screen. II. Phys. Rev. 75, 1423–1432.Google Scholar
Saxon, D. S. & Schwinger, J. 1968 Discontinuities in Waveguides. Notes on Lectures by Julian Schwinger. Gordon and Breach.