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A note on the viscous diffusion of rolled vortex sheets

Published online by Cambridge University Press:  19 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, 92320 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, 92320 Chatillon, France
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Abstract

It is well known that vortex sheets are diffused by viscosity. For a plane sheet this diffusion is described by a linear diffusion equation. Here we consider a rolled vortex sheet, and show that the viscous diffusion of the vorticity concentrated at the turns of the sheet, when they are very closely spaced, can also be described by a linear equation, in appropriately transformed variables.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 90 , Issue 1 , 16 January 1979 , pp. 197 - 201
Copyright
© 1979 Cambridge University Press

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References

Guiraud, J. P. & Zeytounian, R. Kh. 1977 A double-scale investigation of the asymptotic structure of rolled-up vortex sheets. J. Fluid Mech. 79, 93.Google Scholar
Moore, D. W. 1975 The rolling up of a semi-infinite vortex sheet. Proc. Roy. Soc. A 345, 417.Google Scholar
Moore, D. W. & Saffman, P. G. 1973 Axial flow in laminar trailing vortices. Proc. Roy. Soc. A 333, 491.Google Scholar
Stewartson, K. & Hall, M. G. 1963 The inner viscous solution for the core of a leading-edge vortex. J. Fluid Mech. 15, 306.Google Scholar