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Two-Frequency Rayleigh-Taylor and Richtmyer-Meshkov Instabilities

  • G. R. Baker
Conference paper
Part of the The IMA Volumes in Mathematics and Its Applications book series (IMA, volume 12)

Abstract

When a flat interface between an incompressible, inviscid fluid and vacuum is driven by a pressure gradient in the direction opposite to that of the density gradient, it is linearly unstable to any sinusoidal perturbation. The nonlinear evolution of a single frequency has been studied in the past using boundary integral methods. In practice, the interface is usually randomly perturbed, but this case presents great difficulty to numerical studies because the interface soon becomes severely distorted. However, it is possible to study the evolution of two modes long enough to gain some understanding of their interaction in the nonlinear regime. The behavior is different depending on whether the pressure gradient is externally imposed (Rayleigh-Taylor instability) or internally present (Richtmyer-Meshkov instability).

Keywords

High Mode Vortex Core Curvature Singularity Singularity Time Vortex Sheet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    G. Fraley, W. Gupta, D. Henderson, R. McCrory, R. Malone, R. Mason and R. Morse, in Proc Intern. Conf. on Plasma Physics and Controlled Nuclear Fusion Research. Tokyo, Japan, p. (1974).Google Scholar
  2. 2.
    D. H. Sharp, Physica 12D, p. 3, (1984).MathSciNetADSGoogle Scholar
  3. 3.
    H. W. Emmons, C. T. Chang and B. C. Watson, J. Fluid Mech. 7, p.177, (1960).ADSzbMATHCrossRefGoogle Scholar
  4. 4.
    K. I. Read, Physica 12D, p. 45, (1984).ADSGoogle Scholar
  5. 5.
    G. R. Baker, D. I. Meiron and S. A. Orszag, Phys. Fluids 23, p.1485, (1980).ADSzbMATHCrossRefGoogle Scholar
  6. 6.
    R. Menikoff and C. Zemach, J. Comp. Phys. 51, p.28, (1983).MathSciNetADSzbMATHCrossRefGoogle Scholar
  7. 7.
    D. I. Pullin, J. Fluid Mech. 119, p.507, (1982).ADSzbMATHCrossRefGoogle Scholar
  8. 8.
    G. Dagan, J. Fluid Mech. 67, p.113, (1975).MathSciNetADSzbMATHCrossRefGoogle Scholar
  9. 9.
    D. W. Moore and R. Griffith-Jones, Mathematika 21, p.128, (1974).zbMATHCrossRefGoogle Scholar
  10. 10.
    D. W. Moore, private communication.Google Scholar
  11. 11.
    D. W. Moore, Proc. R. Soc. Lond. A365, p.105, (1979).ADSGoogle Scholar
  12. 12.
    D. I. Meiron, G. R. Baker and S. A. Orszag, J. Fluid Mech. 114, p.283, (1982).MathSciNetADSzbMATHCrossRefGoogle Scholar
  13. 13.
    R. Krasny, J. Fluid Mech. 167, p.65, (1986).MathSciNetADSzbMATHCrossRefGoogle Scholar
  14. 14.
    R. Krasny, J. Comp. Phys. 65, p.292, (1986).ADSzbMATHCrossRefGoogle Scholar
  15. 15.
    G. Trygvason, submitted to J. Comp. Phys.Google Scholar
  16. 16.
    R. Kerr, Lawrence Livermore National Laboratory Report No. UCID-20915, (1986).Google Scholar
  17. 17.
    N. J. Zabusky, M. H. Hughes and K. V. Roberts, J. Comp. Phys. 30, p.96, (1979).MathSciNetADSzbMATHCrossRefGoogle Scholar
  18. 18.
    D. W. Moore, Stud. Appl. Math. 58, p.119, (1978).ADSGoogle Scholar
  19. 19.
    C. Pozrikidas and J. J. L. Higdon, J. Fluid Mech. 157, p.225, (1985).ADSCrossRefGoogle Scholar
  20. 20.
    G. R. Baker and M. J. Shelley, J. Comp. Phys. 64, p.112, (1986).MathSciNetADSzbMATHCrossRefGoogle Scholar
  21. 21.
    A. E. Overman and N. J. Zabusky, Phys. Fluids 25, p.1297, (1982).MathSciNetADSzbMATHCrossRefGoogle Scholar
  22. 22.
    V. I. Yudovich, Zh. Vych. Mat. 3, p.1032, (1963).zbMATHGoogle Scholar

Copyright information

© Springer-Verlag New York Inc. 1988

Authors and Affiliations

  • G. R. Baker
    • 1
  1. 1.Exxon Research and Engineering CompanyAnnandaleUSA

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