Hostname: page-component-78c5997874-lj6df Total loading time: 0 Render date: 2024-11-10T08:05:45.306Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamics of a vortex ring in a rotating fluid

Published online by Cambridge University Press:  26 April 2006

R. Verzicco ,
P. Orlandi ,
A. H. M. Eisenga ,
G. J. F. Van Heijst  and
G. F. Carnevale
R. Verzicco
Affiliation:
Universitá di Roma “La Sapienza” Dipartimento di Meccanica e Aeronautica, via Eudossiana n° 18 00184, Roma, Italy
P. Orlandi
Affiliation:
Universitá di Roma “La Sapienza” Dipartimento di Meccanica e Aeronautica, via Eudossiana n° 18 00184, Roma, Italy
A. H. M. Eisenga
Affiliation:
Fluid Dynamics Laboratory, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.
G. J. F. Van Heijst
Affiliation:
Fluid Dynamics Laboratory, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, The Netherlands.
G. F. Carnevale
Affiliation:
Scripps Institution of Oceanography, University of California, San Diego, La Jolla, CA 92093 USA.
Get access Rights & Permissions [Opens in a new window]

Abstract

The formation and the evolution of axisymmetric vortex rings in a uniformly rotating fluid, with the rotation axis orthogonal to the ring vorticity, have been investigated by numerical and laboratory experiments. The flow dynamics turned out to be strongly affected by the presence of the rotation. In particular, as the background rotation increases, the translation velocity of the ring decreases, a structure with opposite circulation forms ahead of the ring and an intense axial vortex is generated on the axis of symmetry in the tail of the ring. The occurrence of these structures has been explained by the presence of a self-induced swirl flow and by inspection of the extra terms in the Navier–Stokes equations due to rotation. Although in the present case the swirl was generated by the vortex ring itself, these results are in agreement with those of Virk et al. (1994) for polarized vortex rings, in which the swirl flow was initially assigned as a ‘degree of polarization’.

If the rotation rate is further increased beyond a certain value, the flow starts to be dominated by Coriolis forces. In this flow regime, the impulse imparted to the fluid no longer generates a vortex ring, but rather it excites inertial waves allowing the flow to radiate energy. Evidence of this phenomenon is shown.

Finally, some three-dimensional numerical results are discussed in order to justify some asymmetries observed in flow visualizations.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 317 , 25 June 1996 , pp. 215 - 239
Copyright
© 1996 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. 1964 Handbook of Mathematical functions with Formulas, Graphs and Mathematical Tables. National Bureau of Standards.
Ayotte, B. A. & Fernando, H. J. S. 1994 The motion of a turbulent thermal in the presence of background rotation. J. Atmos. Sci. 51, 1989–1994.Google Scholar
Dalziel, S. 1992 DigImage. Image Processing for Fluid Dynamics. Cambridge Environmental Research Consultants Ltd.
Greenspan, H. P. 1968 The Theory of Rotating Fluids. Cambridge University Press.
Helmholtz, H. 1858 On integrals of the hydrodynamical equations which express vortex motion. Translation by P. G. Tait in Phil. Mag. 33(4), 1867, 485–512.Google Scholar
Kelvin, Lord (Thomson, W.) 1867 A letter in the appendix to Helmholtz (1858) in the translation of P.G. Tait.
Métais, O., Flores, C., Yanase, S., Riley, J. J. & Lesieur, M. 1995 Rotating free-shear flows. Part 2. Numerical simulations. J. Fluid Mech. 293, 47–80.Google Scholar
Moffatt, H. K. 1988 Generalized vortex rings with and without swirl. Fluid Dyn. Res. 3, 22–30.Google Scholar
Orlandi, P. & Verzicco, R. 1993 Free vortex rings, analogies and differences between vorticity and passive scalar, In Vortex Flows and Related Numerical Methods, (ed. J.T. Beatle et al.) Kluwer.
Saffman P. G. 1975 On the formation of a vortex ring. Stud Appl. Maths 54, 261–268.Google Scholar
Saffman P. G. 1978 The number of waves on unstable vortex ring. J. Fluid Mech. 84, 625–639.Google Scholar
Sallet, D. W. & Widmayer, R. S. 1974 An experimental investigation of laminar and turbulent vortex rings in air. Z. Flugwiss. 22, 207–215.Google Scholar
Shariff, K., Verzicco, R. & Orlandi, P. 1994 A numerical study of three-dimensional vortex ring instabilities: viscous corrections and early non-linear stages J. Fluid Mech. 279, 351–375.Google Scholar
Stevenson, T. N. 1973 The phase configuration of internal waves around a body moving in a density stratified fluid. J. Fluid Mech. 60, 759–767.Google Scholar
Thomson, W. 1867 On vortex atoms. Phil. Mag. 34(4), 15–24.Google Scholar
Tritton, D. J. 1992 Stabilization and destabilization of turbulent shear flow in a rotating fluid. J. Fluid Mech. 241, 503–523.Google Scholar
Turkington, B. 1989 Vortex rings with swirl: axisymmetric solutions of the Euler equations with nonzero helicity. SIAM J. Math. Anal. 20, 57–73.Google Scholar
Verzicco, R., Jiménez, J. & Orlandi, P. 1995 On steady columnar vortices under local compression. J. Fluid Mech. 299, 367–388.Google Scholar
Verzicco, R. & Orlandi, P. 1995 Mixedness in the formation of a vortex ring. Phys. Fluids 7, 1513–1515.Google Scholar
Verzicco, R. & Orlandi, P. 1996 A finite–difference scheme for three–dimensional incompressible flows in cylindrical coordinates. J. Comput. Phys. 123, 402–414.Google Scholar
Virk, D., Melander, M. V. & Hussain, F. 1994 Dynamics of a polarized vortex ring. J. Fluid Mech. 260, 23–55.Google Scholar