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Dynamics of thin vortex rings

Published online by Cambridge University Press:  31 July 2008

IAN S. SULLIVAN ,
JOSEPH J. NIEMELA ,
ROBERT E. HERSHBERGER ,
DIOGO BOLSTER  and
RUSSELL J. DONNELLY
IAN S. SULLIVAN
Affiliation:
Department of Physics, University of Oregon, Eugene, OR 97403, USA
JOSEPH J. NIEMELA
Affiliation:
Department of Physics, University of Oregon, Eugene, OR 97403, USA
ROBERT E. HERSHBERGER
Affiliation:
Department of Physics, University of Oregon, Eugene, OR 97403, USA
DIOGO BOLSTER
Affiliation:
Department of Physics, University of Oregon, Eugene, OR 97403, USA
RUSSELL J. DONNELLY
Affiliation:
Department of Physics, University of Oregon, Eugene, OR 97403, USA
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Abstract

As part of a long-range study of vortex rings, their dynamics, interactions with boundaries and with each other, we present the results of experiments on thin core rings generated by a piston gun in water. We characterize the dynamics of these rings by means of the traditional equations for such rings in an inviscid fluid suitably modifying them to be applicable to a viscous fluid. We develop expressions for the radius, core size, circulation and bubble dimensions of these rings. We report the direct measurement of the impulse of a vortex ring by means of a physical pendulum.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 609 , 25 August 2008 , pp. 319 - 347
Copyright
Copyright © Cambridge University Press 2008

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References

REFERENCES

Auerbach, D. 1988 Some open questions on the flow of circular vortex rings. Fluid Dyn. Res. 2, 209–213.CrossRefGoogle Scholar
Baird, M. H. I., Wairegi, T. & Loo, H. J. 1977 Velocity and momentum of vortex rings in relation to formation parameters. Can. J. Chem. Engng 55, 19–26.CrossRefGoogle Scholar
Baker, D. J. 1966 A technique for the precise measurement of small fluid velocities. J. Fluid Mech. 26, 573–575.CrossRefGoogle Scholar
Barenghi, C. F., Donnelly, R. J. & Vinen, W. F. 1983 Friction on quantized vortices in helium II. J. Low Temp. Phys. 52, 189–247.CrossRefGoogle Scholar
Barenghi, C. F., Hänninen, R. & Tsubota, M. 2006 Anomalous translational velocity of a vortex ring with finite-amplitude Kelvin waves. Phys. Rev. E 74, 046303.Google ScholarPubMed
Dabiri, J. O. & Gharib, M. 2004 Fluid entrainment by isolated vortex rings. J. Fluid Mech. 511, 311–331.CrossRefGoogle Scholar
Didden, N. 1979 On the formation of vortex rings: rolling-up and production of circulation. J. Appl. Maths Phys. 30, 101–116.Google Scholar
Donnelly, R. J. 1991 Quantized Vortices in Helium II. Cambridge University Press.Google Scholar
Fetter, A. L. & Donnelly, R. J. 1966 On the equivalence of vortices and current filaments. Phys. Fluids 9, 619–620.CrossRefGoogle Scholar
Fraenkel, L. E. 1972 Examples of steady vortex rings of small cross-section in an ideal fluid. J. Fluid Mech. 51, 119–135.CrossRefGoogle Scholar
Fukumoto, Y. & Moffatt, H. K. 2000 Motion and expansion of a viscous vortex ring. J. Fluid Mech. 417, 1–45.CrossRefGoogle Scholar
Gauthier, G., Gondoret, P. & Rabaud, M. 1998 Motion of anisotropic particles: application to visualization of three dimensional flows. Phys. Fluids 10, 2147–2154.CrossRefGoogle Scholar
Gharib, M., Rambod, E. & Shariff, K. 1998 A universal time scale for vortex ring formation. J. Fluid Mech. 360, 121–140.CrossRefGoogle Scholar
Goldstein, S. 1938 Modern Developments in Fluid Dynamics, vols. 1 and 2. Oxford University Press.Google Scholar
Hollerbach, R., Wiener, R. J., Sullivan, I. S. & Donnelly, R. J. 2002 The flow about a torsionally oscillating sphere. Phys. Fluids 14, 4192–4205.CrossRefGoogle Scholar
Kiknadze, L. & Mamaladze, Y. 2002 The waves on the vortex ring in H II. J. Low Temp. Phys. 126, 321–326.CrossRefGoogle Scholar
Krueger, P. S. 2005 An over-pressure correction to the slug model for vortex ring circulation. J. Fluid Mech. 545, 427–443.CrossRefGoogle Scholar
Krutzsch, C. H. 1939 Uber eine experimentell beobachtete erscheinung an wirbelringen bei ihrer translatorischen bewegung in wirklichen flussigkeiten. Annln Phys. 35, 497–523.CrossRefGoogle Scholar
Lamb, H. 1945 Hydrodynamics. Dover.Google Scholar
Lim, T. T. & Nickels, T. B. 1995 Vortex rings. In Fluid Vortices (ed. Green, S. I.). Kluwer.Google Scholar
Loitsyanskii, L. G. 1966 Mechanics of Liquids and Gases. Pergamon.Google Scholar
Matisse, P. & Gorman, M. 1984 Neutrally bouyant anisotropic particles for flow visualization. Phys. Fluids 27, 759–760.CrossRefGoogle Scholar
Maxworthy, T. 1972 The structure and stability of vortex rings. J. Fluid Mech. 51, 15–32.CrossRefGoogle Scholar
Maxworthy, T. 1974 Turbulent vortex rings. J. Fluid Mech. 64, 227–239.CrossRefGoogle Scholar
Mazo, R. M., Hershberger, R. E. & Donnelly, R. J. 2008 Observations of flow patterns by electrochemical means. Exps. Fluids 44, 49–57.CrossRefGoogle Scholar
Park, K., Barenghi, C. F. & Donnelly, R. J. 1980 Subharmonic destabilization of Taylor vortices near an oscillating cylinder. Phys. Lett. 78 A, 152–154.CrossRefGoogle Scholar
Rayfield, G. & Reif, F. 1964 Quantized vortex rings in superfluid helium. Phys. Rev. 136, A1194–1208.CrossRefGoogle Scholar
Reynolds, O. 1876 On the resistance encountered by vortex rings, and the relation between the vortex rings and streamlines of a disk. Nature 14, 477–579.Google Scholar
Roberts, P. H. & Donnelly, R. J. 1970 Dynamics of vortex rings. Phys. Lett. 31 A, 137–138.CrossRefGoogle Scholar
Roberts, P. H. & Grant, J. 1971 Motions in a bose condensate I. the structure of the large circular vortex. J. Phys. A 4, 55–72.Google Scholar
Rogers, W. B. 1858 On the formation of rotating rings by air and liquids under certain conditions of discharge. Am. J. Sci. (ser. 2) 26, 246–268.Google Scholar
Saffman, P. G. 1970 The velocity of viscous vortex rings. Stud. Appl. Maths. 49, 371–380.CrossRefGoogle Scholar
Saffman, P. G. 1978 The number of waves on unstable vortex rings. J. Fluid Mech. 84, 625–639.CrossRefGoogle Scholar
Saffman, P. G. 1981 Dynamics of vorticity. J. Fluid Mech. 106, 49–58.CrossRefGoogle Scholar
Savas, O. 1985 On flow visualization using reflective flakes. J. Fluid Mech. 152, 235–248.CrossRefGoogle Scholar
Scase, M. M. & Dalziel, S. B. 2006 An experimental study of the bulk properties of vortex rings translating through a stratified fluid. Euro. J. Fluid Mech. 25, 302–320.CrossRefGoogle Scholar
Shariff, K. & Leonard, A. 1992 Vortex rings. Annu. Rev. Fluid Mech. 24, 235–279.CrossRefGoogle Scholar
Shusser, M. & Gharib, M. 2000 Energe and velocity of a forming vortex ring. Phys. Fluids 12, 618–621.CrossRefGoogle Scholar
Stanaway, S. K., Cantwell, B. J. & Spalart, P. R. 1988 Navier–Stokes simulations of axisymmetric vortex rings. In AIAA 26th Aerospace Sciences Meeting, Reno, Nevada pp. 1–14.Google Scholar
Weigand, A. & Gharib, M. 1997 On the evolution of laminar vortex rings. Exps. Fluids 22, 447–457.CrossRefGoogle Scholar