Skip to main content
SpringerLink
Log in

On the evolution of laminar vortex rings

  • Published:
Experiments in Fluids Aims and scope Submit manuscript

Abstract

Using Laser Doppler Anemometry (LDA) and Digital Particle Image Velocimetry (DPIV), the physical properties of laminar vortex rings are investigated in the Reynolds-number range 830 ≤ Re ≤ 1650. The measured initial circulations of the vortex rings are found to agree well with corrected versions of the vorticity-flux (slug-flow) model proposed by Didden and Pullin. The DPIV and LDA data show excellent agreement regarding local velocities and vortex-ring circulations. The DPIV data depict the distribution of the vorticity and circulation in the core regions, where the resulting vorticity distributions are found to be self-similar Gaussian profiles. The propagation velocity of the vortex rings is well approximated by an analytical model of Saffman for large core sizes. In the asymptotic limit t → ∞, the trajectories are in excellent agreement with the exact Stokes-dipole solution of Cantwell and Rott.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Batchelor GK (1967) An introduction to fluid dynamics. Cambridge: University Press

    MATH  Google Scholar 

  • Cantwell BJ; Rott N (1988) The decay of a viscous vortex pair, Phys Fluids 31: 3213–3224

    Article  MATH  Google Scholar 

  • Didden N (1979) On the formation of vortex rings: rolling-up and production of circulation, J Appl Math Phys 30: 101–116

    Article  Google Scholar 

  • Gharib M; Weigand A; Willert C; Liepmann D (1992) Experimental studies of vortex reconnection to a free surface: a physical flow model, In Proc 19th Symp on Naval Hydrodynamics, Seoul, Korea, National Academic Press, 507–520

    Google Scholar 

  • Gharib M; Weigand A (1996) Experimental studies of vortex disconnection and connection at a free surface, J Fluid Mech 321: 53–86

    Article  Google Scholar 

  • Glezer A; Coles D (1990) An experimental study of a turbulent vortex ring, J Fluid Mech 211: 243–283

    Article  Google Scholar 

  • Hicks (1885) Researches on the theory of vortex rings-Part II, Phil Trans A 176: 725–780

    Article  Google Scholar 

  • Kambe T; Oshima Y (1975) Generation and decay of viscous vortex rings, J Phys Soc Japan 38: 271–280

    Article  Google Scholar 

  • Lamb H (1932) Hydrodynamics, New York: Dover

  • Maxworthy T (1972) The structure and stability of vortex rings, J Fluid Mech 51: 15–32

    Article  Google Scholar 

  • Maxworthy T (1977) Some experimental studies of vortex rings, J Fluid Mech 81: 465–495

    Article  Google Scholar 

  • Nitsche M; Krasny R (1994) A numerical study of vortex ring formation at the edge of a circular tube, J Fluid Mech 276: 139–161

    Article  MATH  MathSciNet  Google Scholar 

  • Philips OM (1956) The final period of decay of nonhomogeneous turbulence, Proc Camb Phil Soc 52: 135–151

    Article  Google Scholar 

  • Pullin DI (1979) Vortex ring formation at tube and orifice openings, Phys Fluids 22: 401–403

    Article  Google Scholar 

  • Saffman PG (1970) The velocity of viscous vortex rings, Stud Appl Math 49: 371–380

    MATH  Google Scholar 

  • Saffman PG (1978) The number of waves on unstable vortex rings, J Fluid Mech 84: 625–639

    Article  MathSciNet  Google Scholar 

  • Saffman PG (1992) Vortex dynamics, University Press, Cambridge

    MATH  Google Scholar 

  • Sallet DW; Widmayer RS (1974) An experimental investigation of laminar and turbulent vortex rings in air, Z Flugwiss 22: 207–215

    Google Scholar 

  • Shariff K; Leonard A (1992) Vortex rings, Ann Rev Fluid Mech 24: 235–279

    Article  MathSciNet  Google Scholar 

  • Stanaway SK; Cantwell BJ; Spalart PR (1988) A numerical study of viscous vortex rings using a spectral method, NASA Tech Memo 101 041

  • Thomson W in p. 511 of Helmholtz H (1867) On integrals of the hydrodynamical equations, which express vortex-motion, Phil Mag 33 (Series 4): 485–512

    Google Scholar 

  • Tung C; Ting L (1967) Motion and decay of a viscous vortex ring, Phys Fluids 10: 901–910

    Article  Google Scholar 

  • Weigand A (1993) The response of a vortex ring to a transient spatial cut, Ph.D. Thesis, University of California, San Diego

    Google Scholar 

  • Widnall SE; Bliss DB; Tsai CY (1974) The instability of short waves on a vortex ring, J Fluid Mech 66: 35–47

    Article  MATH  MathSciNet  Google Scholar 

  • Willert CE; Gharib M (1991) Digital particle image velocimetry, Exp Fluids 10: 181–193

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. California Institute of Technology, Graduate Aeronautical Laboratories, 205-45 Pasadena, 91125, CA, USA

    A. Weigand & M. Gharib

Authors
  1. A. Weigand
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. Gharib
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

The support of the Office of Naval Research (ONR-URI grant N00014-92-J-1610) under the program management of Dr. Edwin Rood is gratefully acknowledged.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Weigand, A., Gharib, M. On the evolution of laminar vortex rings. Experiments in Fluids 22, 447–457 (1997). https://doi.org/10.1007/s003480050071

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s003480050071

Keywords

Search

Navigation