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Two-Frequency Rayleigh-Taylor and Richtmyer-Meshkov Instabilities

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Computational Fluid Dynamics and Reacting Gas Flows

Part of the book series: The IMA Volumes in Mathematics and Its Applications ((IMA,volume 12))

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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).

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References

  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. D. H. Sharp, Physica 12D, p. 3, (1984).

    MathSciNet  ADS  Google Scholar 

  3. H. W. Emmons, C. T. Chang and B. C. Watson, J. Fluid Mech. 7, p.177, (1960).

    Article  ADS  MATH  Google Scholar 

  4. K. I. Read, Physica 12D, p. 45, (1984).

    ADS  Google Scholar 

  5. G. R. Baker, D. I. Meiron and S. A. Orszag, Phys. Fluids 23, p.1485, (1980).

    Article  ADS  MATH  Google Scholar 

  6. R. Menikoff and C. Zemach, J. Comp. Phys. 51, p.28, (1983).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  7. D. I. Pullin, J. Fluid Mech. 119, p.507, (1982).

    Article  ADS  MATH  Google Scholar 

  8. G. Dagan, J. Fluid Mech. 67, p.113, (1975).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  9. D. W. Moore and R. Griffith-Jones, Mathematika 21, p.128, (1974).

    Article  MATH  Google Scholar 

  10. D. W. Moore, private communication.

    Google Scholar 

  11. D. W. Moore, Proc. R. Soc. Lond. A365, p.105, (1979).

    ADS  Google Scholar 

  12. D. I. Meiron, G. R. Baker and S. A. Orszag, J. Fluid Mech. 114, p.283, (1982).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  13. R. Krasny, J. Fluid Mech. 167, p.65, (1986).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  14. R. Krasny, J. Comp. Phys. 65, p.292, (1986).

    Article  ADS  MATH  Google Scholar 

  15. G. Trygvason, submitted to J. Comp. Phys.

    Google Scholar 

  16. R. Kerr, Lawrence Livermore National Laboratory Report No. UCID-20915, (1986).

    Google Scholar 

  17. N. J. Zabusky, M. H. Hughes and K. V. Roberts, J. Comp. Phys. 30, p.96, (1979).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  18. D. W. Moore, Stud. Appl. Math. 58, p.119, (1978).

    ADS  Google Scholar 

  19. C. Pozrikidas and J. J. L. Higdon, J. Fluid Mech. 157, p.225, (1985).

    Article  ADS  Google Scholar 

  20. G. R. Baker and M. J. Shelley, J. Comp. Phys. 64, p.112, (1986).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  21. A. E. Overman and N. J. Zabusky, Phys. Fluids 25, p.1297, (1982).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  22. V. I. Yudovich, Zh. Vych. Mat. 3, p.1032, (1963).

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Exxon Research and Engineering Company, Route 22 East, Annandale, NJ, 08801, USA

    G. R. Baker

Authors
  1. G. R. Baker
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of California, Los Angeles, CA, 90024, USA

    Bjorn Engquist

  2. Department of Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Andrew Majda

  3. School of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Mitchell Luskin

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© 1988 Springer-Verlag New York Inc.

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Baker, G.R. (1988). Two-Frequency Rayleigh-Taylor and Richtmyer-Meshkov Instabilities. In: Engquist, B., Majda, A., Luskin, M. (eds) Computational Fluid Dynamics and Reacting Gas Flows. The IMA Volumes in Mathematics and Its Applications, vol 12. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3882-9_1

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  • DOI: https://doi.org/10.1007/978-1-4612-3882-9_1

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-8388-1

  • Online ISBN: 978-1-4612-3882-9

  • eBook Packages: Springer Book Archive

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