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A family of steady, translating vortex pairs with distributed vorticity

Published online by Cambridge University Press:  19 April 2006

R. T. Pierrehumbert
R. T. Pierrehumbert
Affiliation:
Department of Aeronautics and Astronautics, Massachusetts Institute of Technology, Cambridge, MA 02139
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Abstract

An efficient relaxation method is developed for computing the properties of a family of vortex pairs with distributed vorticity, propagating without change of shape through a homogeneous, inviscid fluid. The numerical results indicate that a steady state exists even when the gap between vortices is arbitrarily small, and that as the gap closes the steady state approaches a limiting vortex pair with a cusp on the axis of symmetry. Comparison is made with an approximate theory due to Saffman, and agreement is found to be good until the vortices are almost touching. The energy of members of the family is computed, and possible means of experimental production are discussed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 1 , 11 July 1980 , pp. 129 - 144
Copyright
© 1980 Cambridge University Press

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References

Ashley, H. & Landahl, M. 1965 Aerodynamics of Wings and Bodies, pp. 135–137. Addison-Wesley.
Batchelor, G. K. 1967 An Introduction to Fluid Dynamics, p. 534. Cambridge University Press.
Berger, M. S. 1977 Nonlinearity and Functional Analysis. Academic.
Deem, G. S. & Zabusky, N. 1978a Stationary ‘V-states’, interactions recurrence, and breaking. In Solitons in Action (eds K. Longren & A. Scott), pp. 277–293. Academic.
Deem, G. S. & Zabusky, N. 1978b Stationary ‘V-states’, interactions, recurrence and breaking. Phys. Rev. Lett. 40, 859–862.Google Scholar
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.
Norbury, J. 1973 A family of steady vortex rings. J. Fluid Mech. 57, 417–431.Google Scholar
Norbury, J. 1975 Steady planar vortex pairs in an ideal fluid. Comm. Pure Appl. Math. 28, 679–685.Google Scholar
Pierrehumbert, R. T. & Widnall, S. E. 1979 The structure of organized vortices in a free shear layer. A.I.A.A. Paper 79-1560.Google Scholar
Prandtl, L. 1922 Über die Entstehung von Wirbeln in der Idealen Flüssigkeit. In Gesammelte Abhandlungen, pp. 697–714. Springer.
Saffman, P. G. 1979 The approach of a vortex pair to a plane surface in inviscid fluid. J. Fluid Mech. 92, 497–503.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