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The lee-wave régime for a slender body in a rotating flow. Part 2

Published online by Cambridge University Press:  29 March 2006

John W. Miles
John W. Miles
Affiliation:
Institute of Geophysics and Planetary Physics and Department of Aerospace and Mechanical Engineering Sciences, University of California, La Jolla
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Abstract

The axisymmetric motion of an inviscid, rotating liquid over a prescribed stream surface, say S, is constructed from assumed values of the velocity and azimuthal vorticity on S. The hypothesis of unseparated flow, which implies continuity of the vorticity on S, is shown to imply that: (a) the azimuthal vorticity and azimuthal circulation (relative to the basic flow) must be simply proportional to the perturbation stream function in the exterior of S; (b) the exterior field exhibits a dipole behaviour far upstream of the body, thereby satisfying Long's hypothesis of no upstream disturbance.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 42 , Issue 1 , 4 June 1970 , pp. 201 - 206
Copyright
© 1970 Cambridge University Press

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References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Greenspan, H. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Long, R. R. 1953 Steady motion around a symmetrical obstacle moving along the axis of a rotating fluid. J. Meteor. 10, 197–203.Google Scholar
Miles, J. W. 1969a The lee-wave régime for a slender body in a rotating flow. J. Fluid Mech. 36, 265–288.Google Scholar
Miles, J. W. 1969b Transient motion of a dipole in a rotating flow. J. Fluid Mech. 39, 433–442.Google Scholar