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The stability of a trailing line vortex. Part 1. Inviscid theory

Published online by Cambridge University Press:  29 March 2006

Martin Lessen ,
Pawan Jit Singh  and
Frederick Paillet
Martin Lessen
Affiliation:
Department of Mechanical and Aerospace Sciences, University of Rochester, New York 14627
Pawan Jit Singh
Affiliation:
Institute for Fundamental Studies, Department of Physics, University of Eochester, New York 14627
Frederick Paillet
Affiliation:
Department of Mechanical and Aerospace Sciences, University of Rochester, New York 14627
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Abstract

The inviscid stability of swirling flows with mean velocity profiles similar to that obtained by Batchelor (1964) for a trailing vortex from an aircraft is studied with respect to infinitesimal non-axisymmetric disturbances. The flow is characterized by a swirl parameter q involving the ratio of the magnitude of the maximum swirl velocity to that of the maximum axial velocity. It is found that, as the swirl is continuously increased from zero, the disturbances die out quickly for a small value of q if n = 1 (n is the azimuthal wavenumber of the Fourier disturbance of type exp{i(αx + nϕ − αct)}); but for negative values of n, the amplification rate increases and then decreases, falling to negative values at q slightly greater than 1·5 for n = −1. The maximum amplification rate increases for increasingly negative n up to n = −6 (the highest mode investigated), and corresponds to q ≃ 0·85. The applicability of these results to attempts at destabilizing vortices is briefly discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 63 , Issue 4 , 15 May 1974 , pp. 753 - 763
Copyright
© 1974 Cambridge University Press

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References

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