Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-18T20:28:44.625Z Has data issue: false hasContentIssue false
  • English
  • Français

The observation of the simultaneous development of a long- and a short-wave instability mode on a vortex pair

Published online by Cambridge University Press:  26 April 2006

P. J. Thomas  and
D. Auerbach
P. J. Thomas
Affiliation:
Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge, CB3 9EW, UK
D. Auerbach
Affiliation:
Max-Planck-Institut für Strömungsforschung, Bunsenstr. 10, D-37073 Göttigen, Germany
Get access Rights & Permissions [Opens in a new window]

Abstract

Experiments on the stability of vortex pairs are described. The vortices (ratio of length to core diameter L/c of up to 300) were generated at the edge of a flat plate rotating about a horizontal axis in water. The vortex pairs were found to be unstable, displaying two distinct modes of instability. For the first time, as far as it is known to the authors, a long-wave as well as a short-wave mode of instability were observed to develop simultaneously on such a vortex pair. Experiments involving single vortices show that these do not develop any instability whatsoever. The wavelengths of the developing instability modes on the investigated vortex pairs are compared to theoretical predictions. Observed long wavelengths are in good agreement with the classic symmetric long-wave bending mode identified by Crow (1970). The developing short waves, on the other hand, appear to be less accurately described by the theoretical results predicted, for example, by Windnall, Bliss & Tsai (1974).

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 265 , 25 April 1994 , pp. 289 - 302
Copyright
© 1994 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

Barker, S. J. & Crow, S. C. 1977 The motion of two-dimensional vortex paris in a ground effect. J. Fluid Mech. 82, 659–671.Google Scholar
Crow, S. C. 1970 Stability theory for a pair of trailing vortices. AIAA J. 8, 2172–2179.Google Scholar
Didden, N. 1977 Untersuchung laminarer, instabiler Ringwirbel mittels Laser-Doppler-Anemometrie. Mitt. aus dem MPI für Strömungsforschung und der AV A, Nr. 64, Göttingen, Germany.
Fukumoto, Y. & Miyazaki, T. 1991 Three-dimensional distortions of a vortex filament with axial velocity. J. Fluid Mech. 222, 369–416.Google Scholar
Klein, R., Majda, A. J. & McLaughlin, R. M. 1992 Asymptotic equations for the stretching of vortex filaments in a background flow field. Phys. Fluids A 4, 2271–2281.Google Scholar
Krutzsch, C. H. 1939 Über eine experimentell beobachtete Erscheinung an Wirbelringen bei ihrer translatorischen Bewegung in wirklichen Flüssigkeiten. Ann. Phys. 5, 497–523.Google Scholar
Landman, M. J. & Saffman, P. G. 1987 The three-dimensional instability of strained vortices in a viscous fluid. Phys. Fluids A 30, 2339–2342.Google Scholar
Marshall, J. S. 1992 The effect of axial stretching on the three-dimensional stability of a vortex pair. J. Fluid Mech. 241, 403–419.Google Scholar
Marshall, J. S. 1993 The effect of axial pressure gradient on axisymmetrical and helical vortex waves. Phys. Fluids A 5 588–599. (see also erratum, Phys. Fluids A 5, 1857).Google Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51, 15–36.Google Scholar
Maxworthy, T. 1974 Turbulent vortex rings. J. Fluid Mech. 64, 227–239.Google Scholar
Maxworthy, T. 1977 Some experimental studies of vortex rings. J. Fluid Mech. 81, 465–495.Google Scholar
Saffman, P. G. 1992 Vortex Dynamics. Cambridge University Press.
Smith, T. B. & Beesmer, K. M. 1959 Contrail studies of Jet Aircraft. ASTIA AD 217 188, April. Meteorology Research Inc. Pasadena, California, USA.
Spreiter, J. R. & Sacks, A. H. 1951 The rolling up of the trailing vortex sheet and its effect on downwash behind wings. J. Aeronaut. Sci. 18, 21–32.Google Scholar
Thomas, P. 1988 Experimentelle Untersuchung von Stabwirbeln in Wasser. Rep. 15/1988. Max-Planck-Institut für Strömungsforschung, Göttingen, Germany.
Tsai, C.-Y. & Widnall, S. E. 1976 The stability of short waves on a straight vortex filament in a weak externally imposed strain field. J. Fluid Mech. 73, 721–733.Google Scholar
Van Dyke, M. 1982 An Album of Fluid Motion. Stanford: Parabolic Press.
Windnall, S. E. 1975 The structure and dynamics of vortex filaments. Ann. Rev. Fluid Mech. 7, 141–165.Google Scholar
Widnall, S. E., Bliss, D. B. & Tsai, C.-Y. 1974 The instability of short waves on a vortex ring. J. Fluid Mech. 66, 35–47.Google Scholar
Windnall, S. E. & Tsai, C.-Y. 1977 The instability of the thin vortex ring of constant vorticity. Phil. Trans. R. Soc. Lond. A 287, 273–305.Google Scholar