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A note on the stability of a cylindrical vortex sheet

Published online by Cambridge University Press:  12 April 2006

Richard Rotunno
Richard Rotunno
Affiliation:
National Center for Atmospheric Research, Boulder, Colorado 80307
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Abstract

An inconsistency in a previous stability analysis of a cylindrical vortex sheet is resolved. It is found that disturbances with azimuthal wavenumbers m = 1 and 2 are stable, whereas previously the stability of these modes was uncertain. It has been hypothesized that the multiple-vortex phenomenon is initiated by such an instability (Ward 1972). Since double vortices (m = 2) arise, we are led to consider a central downdraft surrounded by a uniform updraft; for a non-zero vertical wavenumber γ, the modes m = 1 and 2 are destabilized. Our theory is supported by the observation that double vortices tend to form as intertwining spirals (i.e. they have vertical structure).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 87 , Issue 4 , 29 August 1978 , pp. 761 - 771
Copyright
© 1978 Cambridge University Press

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