Hostname: page-component-848d4c4894-v5vhk Total loading time: 0 Render date: 2024-07-04T05:07:09.873Z Has data issue: false hasContentIssue false

Some experimental studies of vortex rings

Published online by Cambridge University Press:  12 April 2006

T. Maxworthy
Affiliation:
Departments of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles

Abstract

A series of experiments designed to reveal the properties of high Reynolds number vortex rings, using flow-visualization and laser-Doppler techniques, has uncovered several interesting and unexpected results. Starting at the beginning of the motion, at a nozzle, and proceeding downstream, these include the following.

  1. A formation process that is strongly Reynolds number dependent.

  2. The amount of vorticity that appears downstream is very close to that predicted by a simple ‘slug’ model. However flow-visualization studies show that such a model is an oversimplification and that an excess of ring vorticity is probably cancelled by the ingestion of vorticity of opposite sign at the nozzle lip.

  3. (iii) A new, bimodal form of vortex-core instability has been observed at moderate but not high Reynolds numbers.

  4. Azimuthal inhomogeneities in the breaking of these, and the normal instability waves, create an ‘axial’ flow along the vortex core in the turbulent ring. This axial flow takes the form of a propagating wave that has many characteristics of a solitary wave. It is hypothesized that this axial flow prevents further ring instability.

  5. The long-term behaviour of the turbulent ring is marked by dramatic changes in its growth rate, which are probably related to changes in the ‘organization’ of the vortex core. The descriptive turbulent-ring model developed in Maxworthy (1974) is substantially confirmed by these experiments and by observation of ring propagation through a stratified ambient fluid.

Type
Research Article
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

Arnold, O. 1974 Verhalten von Wirbelringen in turbulenzarmer und turbulenter Umgebung. Ph.D. dissertation, University of Karlsruhe, W. Germany.
Betz, A. 1932 N.A.C.A. Tech. Memo no. 713.
Crow, S. C. 1974 The motion of a vortex pair in a stratified fluid. Poseidon Res. Corp. Rep. no. 1.Google Scholar
Granger, R. A. 1968 Speed of a surge in a bathtub vortex. J. Fluid Mech. 34, 651656.Google Scholar
Krutzsch, C.-H. 1939 Über eine experimentelle beobachtete Erscheinung an Wirbelringen bei ihrer translatorischen Bewegung in wirklicher Flüssigkeit. Ann. Phys. 35, 497523.Google Scholar
Kulkarny, V. A. 1977 On vortex formation near sharp edges in impulsive flows. Submitted to J. Fluid Mech.Google Scholar
Lamb, H. 1932 Hydrodynamics, p. 241. Dover.
Leibovich, S. & Randall, J. D. 1972 Solitary waves in concentrated vortices. J. Fluid Mech. 51, 625635.Google Scholar
Liess, C. & Didden, N. 1975 Experimentelle Untersuchung von Ringwirbeln. 50 Jahre M. P. I. Strömungsforschung, Göttingen.
Liess, C. & Didden, N. 1976 Experimente zum Einfluss der Anfangsbedingungen auf die Instabilität von Ringwirbeln. Z. angew. Math. Mech. 56, T206T208.Google Scholar
Linden, P. F. 1973 The interaction of a vortex ring with a sharp density interface: a model for turbulent entrainment. J. Fluid Mech. 60, 467480.Google Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51, 1532.Google Scholar
Maxworthy, T. 1974 Turbulent vortex rings. J. Fluid Mech. 64, 227239.Google Scholar
Moore, D. W. 1974 A numerical study of the roll-up of a finite vortex sheet. J. Fluid Mech. 63, 225235.Google Scholar
Moore, D. W. & Saffman, P. G. 1973 Axial flow in laminar trailing vortices. Proc. Roy. Soc. A 333, 491508.Google Scholar
Moore, D. W. & Saffman, P. G. 1975 The instability of a straight vortex filament in a strain field. Proc. Roy. Soc. A 346, 413425.Google Scholar
Oster, G. 1965 Density gradients. Sci. Am. 213 (2), 7076.Google Scholar
Prandtl, L. 1961 Gesammelte Abhandlungen zur angewandten Mechanik, Hydro- und Aerodynamik, 2nd edn, pp. 697713. Springer.
Saffman, P. G. 1976 On the formation of vortex rings. Stud. Appl. Math. 51, 261268.Google Scholar
Sallet, R. S. & Widmeyer, D. W. 1974 An experimental investigation of laminar and turbulent vortex rings in air. Z. Flugwiss. 22, 207215.Google Scholar
Scorer, R. S. & Davenport, L. J. 1970 Contrails and aircraft downwash. J. Fluid Mech. 43, 451464.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, 3547.Google Scholar
Widnall, S. E. & Sullivan, J. P. 1973 On the stability of vortex rings. Proc. Roy. Soc. A 332, 335353.Google Scholar
Yuen, H. C. 1973 Waves on vortex filaments. Ph.D. dissertation, California Institute of Technology.