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A double-scale investigation of the asymptotic structure of rolled-up vortex sheets

Published online by Cambridge University Press:  11 April 2006

J. P. Guiraud  and
R. Kh. Zeytounian
J. P. Guiraud
Affiliation:
Laboratoire de Mécanique Théorique associé au CNRS, Université de Paris VI, Tour 66, Place Jussieu, 75230 Paris Cedex, 05 and ONERA, 32320 Chatillon, France
R. Kh. Zeytounian
Affiliation:
U.E.R. de Mathématiques Pures et Appliquées, Université de Lille I, B.P. 36, 59650 Villeneuve D'Ascq and ONERA, 32320 Chatillon, France
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Abstract

A double scale technique is used to determine the asymptotic behaviour of a rolled-up vortex sheet. The technique relies on a process of averaging out the saw-tooth-like behaviour of the flow variables, which generates a continuous solution having the structure of a vortex filament. The fine-scale behaviour of the flow is described and includes concentrated vorticity on the sheet. Application to the conical vortex sheet allows the solution of Mangler & Weber (1967) to be rederived. A further application, to Kaden's problem, is worked out and the results are in complete agreement with Moore's asymptotic formulae for the shape of the spiral.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 79 , Issue 1 , 20 January 1977 , pp. 93 - 112
Copyright
© 1977 Cambridge University Press

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