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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
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.
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- Research Article
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- © 1980 Cambridge University Press
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.