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Axisymmetric rotating flow past a prolate spheroid

Published online by Cambridge University Press:  29 March 2006

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

The steady, inviscid, axisymmetric, rotating flow past a prolate spheroid in an unbounded liquid is determined on the hypothesis that all streamlines originate in a uniform flow far upstream of the body. The similarity parameters for the flow are κ = 2Ωa/U and δ = a/b, where 2a and 2b are the minor and major axes and Ω and U are the angular and axial velocities of the basic flow. Solutions are obtained both by separation of variables in prolate spheroidal co-ordinates and through the slender-body limit δ ↓ 0 with κ = O(1). Forward separation is found to occur for κ > κ*, where κ* lies between 2·2 and 2·3 for 0 < δ [les ] 1. The velocity on the body, the upstream axial velocity and the wave drag are calculated for κ < κ*.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 72 , Issue 2 , 25 November 1975 , pp. 363 - 371
Copyright
© 1975 Cambridge University Press

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References

Batchelor, G. K. 1970 An Introduction to Fluid Dynamics. Cambridge University Press.
Flammer, C. 1957 Spheroidal Wave Functions. Stanford University Press.
Hanish, S. et al. 1970 Tables of Radial Spheroidal Wave Functions, vol. 2. Washington: Naval Res. Lab., Rep. no. 7089.
Mcintyre, M. E. 1972 On Long's hypothesis of no upstream influence in uniformly stratified or rotating flow. J. Fluid Mech. 52, 209–243.Google Scholar
Maxworthy, T. 1970 The flow created by a sphere moving along the axis of a rotating, slightly viscous fluid. J. Fluid Mech. 40, 453–480.Google Scholar
Miles, J. W. 1969 The lee-wave régime for a slender body in a rotating flow. J. Fluid Mech. 36, 265–288.Google Scholar
Miles, J. W. 1970 The lee-wave régime for a slender body in a rotating flow. Part 2. J. Fluid Mech. 42, 201–206.Google Scholar
Miles, J. W. 1971 Boundary-layer separation in a rotating flow. J. Fluid Mech. 45, 513–526.Google Scholar
Miles, J. W. 1972 Axisymmetric rotating flow past a circular disk. J. Fluid Mech. 53, 689–700.Google Scholar
Orloff, K. & Bossel, H. 1971 Laser-Doppler velocity measurements of swirling flows with upstream influence. Bull. Am. Phys. Soc. 16, 1331 (abstract only).Google Scholar
Stuckey, M. M. & Layton, L. L. 1964 Numerical Determination of Spheroidal Wave Function Eigenvalues and Expansion Coefficients. Washington, D.C.: David Taylor Model Basin, AML Rep. no. 164.