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Near-neutral centre-modes as inviscid perturbations to a trailing line vortex

Published online by Cambridge University Press:  20 April 2006

K. Stewartson  and
S. N. Brown
K. Stewartson
Affiliation:
Department of Mathematics. University College London, Gower Street. London WC1E 6BT
S. N. Brown
Affiliation:
Department of Mathematics. University College London, Gower Street. London WC1E 6BT
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Abstract

Inviscid linear perturbations to a columnar trailing line vortex are found in the form of centre-modes. These near-neutral modes, occurring at moderate values of the azimuthal wavenumber n, are the analogue of the ring modes for large n discussed by Stewartson & Capell (1985). The appearance and disappearance of these modes as the swirl parameter varies may partly explain the difficulties encountered by numerical analysts in the computation of such modes. In addition, instabilities are found at higher values of the swirl parameter than have previously been reported.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 156 , July 1985 , pp. 387 - 399
Copyright
© 1985 Cambridge University Press

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References

Bergman, K. H. 1969 On the dynamic instability of convective atmospheric vortices. Ph.D. thesis, Department of Atmospheric Sciences, University of Washington.
Duck, P. W. & Foster, M. R. 1980 The inviscid stability of a trailing line vortex. Z. angew. Math. Phys. 31, 523–530.Google Scholar
Howard, L. N. & Gupta, A. S. 1962 On the hydrodynamic and hydromagnetic stability of swirling flows. J. Fluid Mech. 14, 463–476.Google Scholar
Leibovich, S. & Stewartson, K. 1983 A sufficient condition for the instability of columnar vortices. J. Fluid Mech. 126, 335–356.Google Scholar
Lessen, M., Singh, P. J. & Paillet, F. 1974 The stablity of a trailing line vortex. J. Fluid Mech. 63, 753–763.Google Scholar
Pedley, T. J. 1968 On the instability of rapidly rotating shear flows to non-axisymmetric disturbances. J. Fluid Mech. 31, 603–614.Google Scholar
Stewartson, K. & Brown, S. N. 1984 Inviscid centre-modes and wall-modes in the stability of swirling Poiseuille flow. IMA J. Appl. Maths 32, 311–333.Google Scholar
Stewartson, K. & Capell, K. 1985 On the stability of ring modes in a trailing line vortex: the upper neutral points. J. Fluid Mech. 156, 369–386.Google Scholar
Stewartson, K. & Leibovich, S. 1985 On the stability of a columnar vortex to disturbances with large azimuthal wavenumber: the lower neutral points. (In preparation.)