Hostname: page-component-848d4c4894-x5gtn Total loading time: 0 Render date: 2024-06-03T23:53:11.374Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Brown, C. C. & Michael, W. H. 1954 Effect of leading edge separation on the lift of a delta wing. J. Aero. Sci. 21, 690.Google Scholar
Chorin, A. J. & Bernard, J. P. 1973 Discretization of a vortex sheet with an example of roll up. J. Comp. Phys. 13, 423.Google Scholar
Hall, M. G. 1961 A theory of the core of a leading-edge vortex. J. Fluid Mech. 11, 209.Google Scholar
Kaden, H. 1931 Aufwicklung einer unstabilen Unstetigkeirsfläche. Ing. Arch. 2, 140.Google Scholar
Mangler, K. W. & Weber, J. 1967 The flow near the centre of a rolled-up vortex sheet. J. Fluid Mech. 30, 177.Google Scholar
Moore, D. W. 1974 A numerical study of the roll-up of a finite vortex sheet. J. Fluid Mech. 63, 225.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. 1972 The motion of a vortex filament with axial flow. Phil. Trans. A 272, 403.Google Scholar
Moore, D. W. & Saffman, P. G. 1973 Axial flow in laminar trailing vortices. Proc. Roy. Soc. A 333, 491.Google Scholar
Rehbach, C. 1976 Numerical investigation of leading-edge vortex sheet for low aspect ratio thin wings. A.I.A.A. J. 14, 253.Google Scholar
Roy, M. 1957 Sur al théorie de l'aile en delta. Tourbillon d'apex et nappes en cornets. La Recherche Aéronautique, no. 56, p. 3.
Smith, J. H. B. 1968 Improved calculations of leading-edge separation from slender, thin, delta wings. Proc. Roy. Soc. A 306, 67.Google Scholar
Ting, L. 1971 Studys in the motion and decay of vortices. In Aircraft Wake Turbulence and its Protection (ed. J. H. Olsen et al.), p. 11. Plenum.
Widnall, S., Bliss, D. & Zalay, A. 1971 Theoretical and experimental study of the stability of a vortex pair. In Aircraft Wake Turbulence and its Protection (ed. J. H. Olsen et al.), p. 305. Plenum.