Hostname: page-component-76fb5796d-qxdb6 Total loading time: 0 Render date: 2024-04-26T00:17:08.352Z Has data issue: false hasContentIssue false
  • English
  • Français

On a generalization of Kaden's problem

Published online by Cambridge University Press:  20 April 2006

D. I. Pullin  and
W. R. C. Phillips
D. I. Pullin
Affiliation:
Department of Mechanical Engineering, University of Melbourne, Parkville, Victoria 3052, Australia
W. R. C. Phillips
Affiliation:
Department of Mechanical and Production Engineering, University of Singapore, Kent Ridge, Singapore 0511
Get access Rights & Permissions [Opens in a new window]

Abstract

Kaden's problem of the roll-up of an initially planar semi-infinite vortex sheet with a parabolic distribution of circulation is extended to include vortex sheets exhibiting a general power law circulation distribution, resulting in the presence of a power law, and in one case a logarithmic-like, velocity-field singularity. Both semi-infinite and infinite initially plane sheets with this property are considered and the form of their roll-up in the similarity plane, into single and double-branched spirals respectively, is obtained numerically. Estimates of the Betz constant obtained from the solutions are found to be significantly different from values predicted by the Betz approximation.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 104 , March 1981 , pp. 45 - 53
Copyright
© 1981 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

Betz, A. 1919 Doctoral dissertation, Göttingen.
Betz, A. 1932 Z. angew. Math. Mech. 12, 164–174.
Graham, J. A. H., Newman, B. G. & Phillips, W. R. C. 1974 Proc. 9th Cong. Int. Counc. of Aeronautical Sciences, Haifa, Israel, 74–40.
Hoffman, E. R. & Joubert, P. N. 1963 J. Fluid Mech. 16, 395–411.
Jiminez, J. 1977 Structure and Mechanisms of Turbulence. I (ed. H. Fiedler), Lecture Notes in Physics, vol. 75, pp. 147–161. Springer.
Jiminez, J. 1980 J. Fluid Mech. 96, 447–460.
Kaden, H. 1931 Ing. Arch. 2, 140–68.
Küchemann, D. 1953 Aero. Quart. 4, 261–278.
Moore, D. W. 1975 Proc. Roy. Soc. A 345, 417–430.
Moore, D. W. 1979 Proc. Roy. Soc. A 365, 105–119.
Moore, D. W. & Saffman, P. G. 1973 Proc. Roy. Soc. A 333, 491–508.
Phillips, W. R. C. 1981 J. Fluid Mech. (to appear).
Poppleton, E. D. 1971 M.E.R.L., McGill Univ., T.N. 71–1.
Prandtl, L. & Tietjens, O. G. 1957 Applied Hydro and Aeromechanics (Dover).
Pullin, D. I. 1978 J. Fluid Mech. 88, 401–430.
Saffman, P. G. & Baker, G. R. 1979 Ann. Rev. Fluid Mech. 11, 95–122.
Smith, J. H. B. 1966 Proc. Roy. Soc. A 306, 67–90.