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The structure of organized vortices in a free shear layer

Published online by Cambridge University Press:  20 April 2006

R. T. Pierrehumbert  and
S. E. Widnall
R. T. Pierrehumbert
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139 Present address: Department of Meteorology, Massachusetts Institute of Technology.
S. E. Widnall
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
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Abstract

A new family of solutions to the steady Euler equations corresponding to spatially periodic states of a free shear layer is reported. This family bifurcates from a parallel shear layer of finite thickness and uniform vorticity, and extends continuously to a shear layer consisting of a row of concentrated pointlike vortices. The energetic properties of the family are considered, and it is concluded that a vortex in a row of uniform vortices produced by periodic roll-up of a vortex sheet must have a major axis of length approximately 50% or more of the distance between vortex centres; it is also concluded that vortex amalgamation events tend to reduce vortex size relative to spacing. The geometric and energetic properties of the solutions confirm the mathematical basis of the tearing mechanism of shear-layer growth first proposed in an approximate theory of Moore & Saffman (1975).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 102 , January 1981 , pp. 301 - 313
Copyright
© 1981 Cambridge University Press

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References

Browand, F. K. & Weidman, P. D. 1976 Large scales in the developing mixing layer. J. Fluid Mech. 76, 127–144.Google Scholar
Brown, G. L. & Roshko, A. 1974 On density effects and large structures in turbulent mixing layers. J. Fluid Mech. 64, 775–816.Google Scholar
Deem, G. S. & Zabusky, N. 1978 Stationary ‘V-states’, interactions, recurrence, and breaking. In Solitons in Action (ed. K. Longren & A. Scott), pp. 277–293. Academic.
Koochesfahani, M. M., Catherasoo, C. J., Dimotakis, P. E., Gharib, M. & Lang, D. B. 1979 Two point LDV measurements in a plane mixing layer. A.I.A.A. J. 17, 1347–1351.Google Scholar
Lamb, O. O. 1932 Hydrodynamics, 6th edn, pp. 224–229. Cambridge University Press.
Moore, D. W. & Saffman, P. G. 1971 Structure of a line vortex in an imposed strain. In Aircraft Wake Turbulence (ed. J. H. Olsen, A. Goldburg & M. Rogers), pp. 339–353. Plenum.
Moore, D. W. & Saffman, P. G. 1975 The density of organized vortices in a turbulent mixing layer. J. Fluid Mech. 69, 465–473.Google Scholar
Pierrehumbert, R. T. 1980a A family of steady, translating vortex pairs with distributed vorticity. J. Fluid Mech. 99, 129–144.Google Scholar
Pierrehumbert, R. T. 1980b The structure and stability of large vortices in an inviscid flow. Ph.D. thesis, Massachusetts Institute of Technology.
Rayleigh, J. W. S. 1878 The Theory of Sound, vol. 2, p. 393 Dover.
Roshko, A. 1976 Structure of turbulent shear flows: a new look. A.I.A.A. J. 14, 1349–1357.Google Scholar
Saffman, P. G. & Baker, G. R. 1979 Vortex interactions. Ann. Rev. Fluid Mech. 11, 95–122.Google Scholar
Spreiter, J. R. & Sacks, A. H. 1951 The rolling up of the trailing vortex sheet and its effect on downwash behind wings. J. Aero. Sci. 18, 21–32.Google Scholar
Stuart, J. T. 1967 On finite amplitude oscillations in laminar mixing layers. J. Fluid Mech. 29, 417–440.Google Scholar
Winant, C. D. & Browand, F. K. 1974 Vortex pairing: the mechanism of turbulent mixing layer growth at moderate Reynolds number. J. Fluid Mech. 63, 237–255.Google Scholar