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On the stability of a columnar vortex to disturbances with large azimuthal wavenumber: the lower neutral points

Published online by Cambridge University Press:  21 April 2006

K. Stewartson  and
S. Leibovich
K. Stewartson
Affiliation:
Department of Mathematics, University College, London, UK
S. Leibovich
Affiliation:
Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY 14853, USA
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Abstract

The inviscid instability of a columnar trailing-line vortex at large values of the azimuthal wavenumber n near neutral conditions is considered. This extends an earlier analysis (Leibovich & Stewartson 1983), which is not accurate near the limiting values of the axial wavenumber for which instabilities exist. Here an asymptotic expansion is derived for the solution in the neighbourhood of the lower neutral point and the results compared with existing computations a t moderate values of n. For these weak instabilities disturbances are centred near the axis of the vortex and the relevant equation is solved in the complex plane by a generalized saddle-point method. In addition, the marginal stability of the vortex is examined, and an estimate obtained of the value of the swirl parameter above which the vortex is stable at large values of n.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 178 , May 1987 , pp. 549 - 566
Copyright
© 1987 Cambridge University Press

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