Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-20T08:46:55.918Z Has data issue: false hasContentIssue false
  • English
  • Français

The number of waves on unstable vortex rings

Published online by Cambridge University Press:  12 April 2006

P. G. Saffman
P. G. Saffman
Affiliation:
Applied Mathematics, California Institute of Technology, Pasadena
Get access Rights & Permissions [Opens in a new window]

Abstract

An explanation is proposed for the dependence on Reynolds number and other parameters of the number of waves which appear on vortex rings formed by pushing fluid out of a tube. It is shown that the number of waves can be sensitive to the vorticity distribution in the core of the ring. The process of ring formation is discussed and it is concluded that peaked vorticity distributions, limited by viscosity, will occur. Quantitative estimates of the number of waves are made. Agreement with observation is satisfactory.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 84 , Issue 4 , 27 February 1978 , pp. 625 - 639
Copyright
© 1978 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

Abramowitz, M. & Stegun, I. A. 1965 Handbook of Mathematical Functions. Washington: Nat. Bur. Stand.
Anton, L. 1939 Ing. Arch. 10, 411.
Dyson, F. W. 1893 Phil. Trans. Roy. Soc. A 184, 1041.
Fraenkel, L. E. 1970 Proc. Roy. Soc. A 316, 29.
Kaden, H. 1931 Ing. Arch. 2, 140.
Kirde, K. 1962 Ing. Arch. 31, 385.
Krutzsch, C. H. 1939 Ann. Phys. 35, 497.
Kulkarny, V. A. 1977 On vortex formation near sharp edges in impulsive flows. To appear.
Liess, C. & Didden, N. 1976 Z. angew. Math. Mech. 56, T206.
Maxworthy, T. 1972 J. Fluid Mech. 51, 15.
Maxworthy, T. 1974 J. Fluid Mech. 64, 227.
Maxworthy, T. 1977 J. Fluid Mech. 81, 465.
Moore, D. W. & Saffman, P. G. 1971 In Aircraft Wake Turbulence (ed. Olsen, Goldburg & Rogers), p. 339. Plenum.
Moore, D. W. & Saffman, P. G. 1973 Proc. Roy. Soc. A 333, 491.
Moore, D. W. & Saffman, P. G. 1974 Proc. Roy. Soc. A 338, 535.
Moore, D. W. & Saffman, P. G. 1975 Proc. Roy. Soc. A 346, 413.
Saffman, P. G. 1970 Stud. Appl. Math. 49, 371.
Saffman, P. G. 1975 Stud. Appl. Math. 54, 261.
Sallet, D. W. & Widmayer, R. S. 1974 Z. Flugwiss 22, 207.
Sheffield, J. S. 1977a Phys. Fluids 20, 543.
Sheffield, J. S. 1977b Ph.D. thesis, California Institute of Technology.
Tsai, C.-Y. & Widnall, S. E. 1976 J. Fluid Mech. 73, 721.
Wedermeyer, E. 1961 Ing. Arch. 30, 187.
Widnall, S. E., Bliss, D. B. & Tsai, C.-Y. 1974 J. Fluid Mech. 66, 35.
Widnall, S. E. & Sullivan, J. P. 1973 Proc. Roy. Soc. A 332, 335.
Widnall, S. E. & Tsai, C.-Y. 1977 The instability of the thin vortex ring of constant vorticity. To appear.