The Influence of Surface-Tension Effects on Using Vortex Method in the Study of Rayleigh-Taylor Instability

  • Henryk Kudela
Conference paper
Part of the Notes on Numerical Fluid Mechanics (NNFM) book series (NNFM, volume 29)


The effect of surface-tension on the smoothing of irregular motion of vortices in the vortex simulation of Rayleigh-Taylor instability is shown. The irregular motion appears as an effect of short-wave disturbances the source of which is round-off error. Inclusion of surface tension allows the observation of the formation of singularities. The singularities make an infinite jump discontinuity in the curvature of vortex sheet. It is observed that for sufficiently small Atwood number and for initial amplitude perturbation large enough two singularities appear in a half period of the vortex sheet and that only one appears for greater Atwood numbers.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Aref H. “Finger, Bubble, Tendril, Spike”. Fluid Dynamics Transactions, vol.13(1987), PWN, Warsaw, pp. 25–54.ADSGoogle Scholar
  2. [2]
    Baker G. R., Merion D.I., Orszag S.A. “Vortex simulation of the Rayleigh-Taylor Instability”. Phys. Fluids, vol.23, (1980), pp. 1485–1490.ADSzbMATHCrossRefGoogle Scholar
  3. [3]
    Baker G. R., Merion D.I., Orszag S.A. “Generalized vortex methods for free surface flow problems”. J.Fluid Mech. vol.123, (1982), pp. 477–501.MathSciNetADSzbMATHCrossRefGoogle Scholar
  4. [4]
    Baker G. R. “Generalized vortex methods for free-surface flows.Proc. Wave on Fluid Interface”. Academic Press, (1983), pp. 53-81Google Scholar
  5. [5]
    Bellman R., Pennington R.H. “Effects of surface Tension and Viscosity on Taylor Instability”. Quart.Appl.Math., vol.12, (1954), pp. 151–162.MathSciNetzbMATHGoogle Scholar
  6. [6]
    Daly B.J. “Numerical Study of the Effect of Surface Tension on Interface Instability”, Phys.Fluids, vol. 12, (1969) pp. 1340–1354.ADSzbMATHCrossRefGoogle Scholar
  7. [7]
    Gahov F.G “Boundary problems” (in Russian), 1977, Moscow, ScienceGoogle Scholar
  8. [8]
    Kerr R.M. “Simulation of Rayleigh-Taylor Flows Using Vortex Blobs”, J.Comp.Phys. vol. 76 (1988) pp. 48–84.ADSzbMATHCrossRefGoogle Scholar
  9. [9]
    Krasny R. “A study of singularity formation in a vortex sheet by the point-vortex approximation”. J.Fluid Mech. vol.167, (1986) pp. 65–93.MathSciNetADSzbMATHCrossRefGoogle Scholar
  10. [10]
    Krasny R. “Desingularization of periodic vortex sheet roll-up”. J.Comp.Phys. vol. 65, (1986) pp. 292–313.ADSzbMATHCrossRefGoogle Scholar
  11. [11]
    Meiron D.I., Baker G.R., Orszag S.A. “Analytic structure of vortex sheet dynamics. Part 1. Kelvin-Helmholtz instability”. J.Fluid Mech. (1982), vol. 114, pp. 83–298.MathSciNetCrossRefGoogle Scholar
  12. [12]
    Moore D.W. “On the point vortex method”, SIAM J.SCI. STAT.COMPUT., vol.2 (1981) pp. 65–84.zbMATHCrossRefGoogle Scholar
  13. [13]
    Moore D.W. “Numerical and Analytical aspects of Helmholtz Instability”, 1985, Theoretical and Applied Mechanics, IUTAM, pp. 263-274.Google Scholar
  14. [14]
    Sharp D.H. “An overview of Rayleigh-Taylor Instability”. Physica 12D (1984) pp. 3–18.MathSciNetADSGoogle Scholar
  15. [15]
    Tryggvason G. “Numerical simulation of the Rayleigh-Taylor instability”, J.Comp.Phys., vol.75, (1988) pp. 253–282.ADSzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Fachmedien Wiesbaden 1990

Authors and Affiliations

  • Henryk Kudela
    • 1
  1. 1.Technical University of WroclawWroclawPoland

Personalised recommendations