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On singularity formation in three-dimensional vortex sheet evolution

Brady, M. and Pullin, D. I. (1999) On singularity formation in three-dimensional vortex sheet evolution. Physics of Fluids, 11 (11). pp. 3198-3200. ISSN 1070-6631. doi:10.1063/1.870216.

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It is shown that if a doubly-infinite vortex sheet has cylindrical shape and strength distributions at some initial time, then this property is retained in its subsequent evolution. It is also shown that in planes normal to the generator of the cylindrical sheet geometry, the nonlinear evolution of the sheet is the same as that of an equivalent strictly two-dimensional sheet motion. These properties are used to show that when an initially flat vortex sheet is subject to a finite-amplitude, three-dimensional normal mode perturbation, weak singularities develop along lines which are oblique to the undisturbed velocity jump vector at a time that can be inferred from an extension of Moore's [Proc. R. Soc. A 365, 105 (1979)] result for two-dimensional motion.

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Additional Information:Copyright © 1999 American Institute of Physics. Received 6 April 1999; accepted 10 June 1999. This work was partially supported by NSF Grant No. CTS 9634222. The authors are grateful for useful discussions with S. J. Cowley.
Subject Keywords:vortices; flow instability; motion
Issue or Number:11
Record Number:CaltechAUTHORS:BRApof99
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:1878
Deposited By: Tony Diaz
Deposited On:22 Feb 2006
Last Modified:08 Nov 2021 19:43

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