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The stability of a trailing-line vortex in compressible flow

Published online by Cambridge University Press:  26 April 2006

Jillian A. K. Stott  and
Peter W. Duck
Jillian A. K. Stott
Affiliation:
Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK Present address: School of Mathematics, University of New South Wales, Australia.
Peter W. Duck
Affiliation:
Department of Mathematics, University of Manchester, Manchester, M13 9PL, UK
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Abstract

We consider the inviscid stability of the Batchelor (1964) vortex in a compressible flow. The problem is tackled numerically and also asymptotically, in the limit of large (azimuthal and streamwise) wavenumbers, together with large Mach numbers. The nature of the solution passes through different regimes as the Mach number increases, relative to the wavenumbers. At very high wavenumbers and Mach numbers, the mode which is present in the incompressible case ceases to be unstable, whilst a new ‘centre mode’ forms, whose stability characteristics are determined primarily by conditions close to the vortex axis. We find that generally the flow becomes less unstable as the Mach number increases, and that the regime of instability appears generally confined to disturbances in a direction counter to the direction of the rotation of the swirl of the vortex.

Throughout the paper comparison is made between our numerical results and results obtained from the various asymptotic theories.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 269 , 25 June 1994 , pp. 323 - 351
Copyright
© 1994 Cambridge University Press

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