Hostname: page-component-cd9895bd7-q99xh Total loading time: 0 Render date: 2024-12-26T07:41:12.516Z Has data issue: false hasContentIssue false
  • English
  • Français

Theory and observations of waves on hollow-core vortices

Published online by Cambridge University Press:  19 April 2006

Jakob J. Keller  and
M. P. Escudier
Jakob J. Keller
Affiliation:
Brown Boveri Research Centre, CH-5405 Baden-Dättwil, Switzerland
M. P. Escudier
Affiliation:
Brown Boveri Research Centre, CH-5405 Baden-Dättwil, Switzerland
Get access Rights & Permissions [Opens in a new window]

Abstract

A linear non-homogeneous analysis is presented for the standing waves produced on the hollow core of an irrotational vortex by an arbitrary obstacle on the wall of the tube containing the vortex. The group-velocity criterion based upon Kelvin's corresponding dispersion relation predicts whether a certain asymptotic wave pattern appears upstream or downstream of the obstacle. The analysis leads to amplitude singularities for the standing waves at certain critical radii of the core. The particularly interesting case of a counter-helix for which the wave energy is propagating upstream appears for a first-mode angular disturbance. For this situation it seems to be possible that the helix ends in a hydraulic jump and is continued by a counter-helix downstream, as the core size gradually diminishes due to the deceleration of the flow caused by viscous effects (not included in the analysis). The capillary-wave pattern produced by surface tension is also considered. A brief outline for the analogous wave problem is given for the case where the fluid rotates like a rigid body.

Photographic observations of hollow-core vortices in water flow are presented which confirm the qualitative predictions of the analysis, both for the response to an axisymmetric area contraction and also to a 90° bend at the downstream end of the vortex tube.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 99 , Issue 3 , 14 August 1980 , pp. 495 - 511
Copyright
© 1980 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

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.
Binnie, A. M. 1964 Annular Borda flow. J. Fluid Mech. 19, 187–192.Google Scholar
Escudier, M. P. 1979 Estimation of pressure loss in ring-type exit chambers. Trans. A.S.M.E. I, J. Fluids Engng 101, 511–516.Google Scholar
Escudier, M. P., Bornstein, J. & Zehnder, N. 1980 Observations and LDA measurements of confined turbulent vortex flow. J. Fluid Mech. 98, 49–63.Google Scholar
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Kelvin, Lord 1980 Vibrations of a columnar vortex. Phil. Mag. 10 (5), 155–168. (Math. and Phys. Papers 4, 152–171.)Google Scholar
Whitham, G. B. 1974 Linear and Nonlinear Waves. Wiley.