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Rotational compressible inviscid flow with rolled vortex sheets. An analytical algorithm for the computation of the core

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 C.N.R.S., Université de Paris VI, Tour 66, Place Jussieu, 75230 Paris Cedex 05, and O.N.E.R.A., 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 O.N.E.R.A., 92320 Chatillon, France
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Abstract

Previous work on irrotational incompressible inviscid flow (Guiraud & Zeytounian 1977) is extended to rotational and compressible flow. A formal proof is given that, within the core, one may avoid computing with the sheet by defining an equivalent continuous flow. One shows how the vorticity and the entropy gradient between the turns of the sheet are transported along trajectories of the equivalent continuous flow.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 101 , Issue 2 , 27 November 1980 , pp. 393 - 401
Copyright
© 1980 Cambridge University Press

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References

Brown, S. N. 1965 The compressible inviscid leading-edge vortex. J. Fluid Mech. 22, 17–32.Google Scholar
Brown, S. N. & Mangler, K. W. 1967 An asymptotic solution for the centre of a rolled-up conical vortex sheet in compressible flow. Aero. Quart. 18, 354–366.Google Scholar
Chorin, A. J. & Bernard, P. S. 1973 Discretization of a vortex sheet with an example of rollup. J. Comput. Phys. 13, 423–429.Google Scholar
Corcos, G. M. & Sherman, F. S. 1976 Vorticity concentration and the dynamics of unstable free shear layers. J. Fluid Mech. 73, 241–264.Google Scholar
Damms, S. M. & Küchemann, D. 1974 On a vortex sheet model for the mixing between two parallel streams. I. Description of the model and experimental evidence. Proc. Roy. Soc. A 339, 451–461.Google Scholar
Fink, P. T. & Soh, W. K. 1978 A new approach to roll-up calculations of vortex sheet. Proc. Roy. Soc. A 362, 195–209.Google Scholar
Germain, P. 1971 Progressive waves. L. Prandtl memorial lecture in Jahrbuch 1971 der D.G.L.R., pp. 11–30.
Germain, P. 1977 Méthodes asymptotiques en mécanique des fluides. In Dynamique des Fluides, Lee Houches, Juillet 1973 (ed. R. Balian & J. L. Peube). Gordon & Breach.
Guiraud, J. P. & Zeytounian, R. Kh 1977 A double-scale investigation of the asymptotic structure of rolled-up vortex sheets. J. Fluid Mech. 79, 93–102.Google Scholar
Guiraud, J. P. & Zeytounian, R. Kh. 1979a A note on the viscous diffusion of rolled vortex sheets. J. Fluid Mech. 90, 197–201.Google Scholar
Guiraud, J. P. & Zeytounian, R. Kh. 1979b Note sur un mécanisme d'instabilité pour le coeur d'une nappe tourbillonnaire enroulée. La Recherche Aérospatiale 2, 85–88.Google Scholar
Huberson, S. 1980 Calcul numérique d'écoulements avec nappes tourbillonnaires enroulées. La Recherche Aérospatiale no. 1980–3, 197–204.Google Scholar
Mangler, K. W. & Weber, J. 1967 The flow near the centre of a rolled up vortex sheet. J. Fluid Mech. 30, 177–196.Google Scholar
Moore, D. W. 1975 The rolling up of a semi infinite vortex sheet. Proc. Roy. Soc. A 345, 417–430.Google Scholar
Moore, D. W. 1976 The stability of an evolving two-dimensional vortex sheet. Mathematika 23, 35–44.Google Scholar
Moore, D. W. & Griffith-jones, R. 1974 The stability of an expanding circular vortex sheet. Mathematika 21, 128–133.Google Scholar
Patnaik, P. C., Sherman, F. S. & Corcos, G. M. 1976 A numerical simulation of Kelvin-Helm-holtz waves of finite amplitude. J. Fluid Mech. 73, 215–240.Google Scholar
Smith, J. H. B. 1968 Improved calculations of leading-edge separation from slender, thin, delta wings. Proc. Roy. Soc. A 306, 67–90.Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley-Interscience.
Widnall, S. 1975 The structure and dynamics of vortex filaments. Ann. Rev. Fluid Mech. 7, 141–165.Google Scholar