Skip to main content
SpringerLink
Log in

On the neutral stability of a shock wave in real media

  • Plasma, Gases
  • Published:
JETP Letters Aims and scope Submit manuscript

Abstract

The results of the theoretical analysis and computer simulation of the behavior of neutrally stable shock waves with real (van der Waals gas, magnesium) equations of state are presented. An approach is developed in which the region of the neutral stability of a shock wave for each pressure value in front of the wave is determined from the analysis of the equation of state. A simple algorithm is developed to determine the cause of acoustic perturbations (a shock front or an external source) immediately from the flow pattern. In contrast to the predictions of the linear theory, the amplitude of the perturbations of the neutrally stable shock wave decreases with time, although this process is noticeably slower than in the case of an absolutely stable shock wave.

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

  1. S. P. D”yakov, Zh. Eksp. Teor. Fiz. 27, 288 (1954).

    MathSciNet  Google Scholar 

  2. V. M. Kontorovich, Zh. Eksp. Teor. Fiz. 33, 1525 (1957) [Sov. Phys. JETP 6, 1179 (1957)].

    Google Scholar 

  3. S. V. Iordanskii, Prikl. Mat. Mekh. 21, 465 (1957).

    MathSciNet  Google Scholar 

  4. G. Ya. Galin, Dokl. Akad. Nauk SSSR 120, 730 (1958) [Sov. Phys. Dokl. 3, 503 (1958)].

    MathSciNet  Google Scholar 

  5. J. J. Erpenbeck, Phys. Fluids 5, 1181 (1962).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  6. G. W. Swan and G. R. Fowles, Phys. Fluids 18, 28 (1975).

    Article  MATH  ADS  Google Scholar 

  7. A. L. Ni, S. G. Sugak, and V. E. Fortov, Teplofiz. Vys. Temp. 24, 564 (1986).

    Google Scholar 

  8. N. M. Kuznetsov and O. N. Davydova, Teplofiz. Vys. Temp. 26, 567 (1988).

    ADS  Google Scholar 

  9. A. V. Bushman, in Proc. of the All-Union Symp. on Pulse Pressures (VNIIFTRI, Moscow, 1976), p. 613.

    Google Scholar 

  10. I. V. Lomonosov, V. E. Fortov, K. V. Khischenko, and P. R. Levashov, in Proc. Shock Compression of Condensed Matter-2002 (AIP, New York, 2003), p. 91.

    Google Scholar 

  11. I. Rutkevich, E. Zaretsky, and M. J. Mond, Appl. Phys. 81, 7228 (1997).

    Article  Google Scholar 

  12. M. Mond and I. M. Rutkevich, J. Fluid Mech. 275, 121 (1994).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  13. S. A. Egorushkin, Izv. AN SSSR, Ser. Mekh. Zhidk. Gasa, No. 6, 147 (1982).

  14. S. A. Egorushkin, Izv. AN SSSR, Ser. Mekh. Zhidk. Gasa, No. 3, 110 (1984).

  15. N. M. Kuznetsov, Usp. Fiz. Nauk 159, 493 (1989) [Sov. Phys. Usp. 32, 993 (1989)].

    Google Scholar 

  16. J. W. Bates and D. C. Montgomery, Phys. Rev. Lett. 84, 1180 (2000).

    Article  ADS  Google Scholar 

  17. A. V. Konyukhov, A. P. Likhachev, A. M. Oparin,, et al., Zh. Eksp. Teor. Fiz. 131, 761 (2007) [JETP 104, 670 (2007)].

    Google Scholar 

  18. R. L. Fogelson and E. R. Likhachev, Zh. Tekh. Fiz. 74, 129 (2004) [Tech. Phys. 49, 935 (2004)].

    Google Scholar 

  19. L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 6: Fluid Mechanics (Nauka, Moscow, 1986; Pergamon, Oxford, 1987).

    Google Scholar 

  20. J. Y. Yang and C. A. Hsu, AIAA J. 30, 1570 (1992).

    Article  MATH  ADS  Google Scholar 

  21. P. L. Roe, J. Comput. Phys. 43, 357 (1981).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  22. P. Glaister, J. Comput. Phys. 74, 382 (1988).

    Article  MATH  ADS  Google Scholar 

  23. A. Harten, J. Comput. Phys. 49, 357 (1983).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  24. C.-W. Shu and S. Osher, J. Comput. Phys. 77, 439 (1988).

    Article  MATH  ADS  MathSciNet  Google Scholar 

  25. I. V. Lomonosov, V. E. Fortov, K. V. Khishchenko, and P. R. Levashov, in Proc. Shock Compression of Condensed Matter-2001 (AIP, New York, 2002), p. 111.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Joint Institute for High Temperatures, Russian Academy of Sciences, ul. Izhorskaya 13 str. 2, Moscow, 125412, Russia

    A. V. Konyukhov, A. P. Likhachev, V. E. Fortov & K. V. Khishchenko

  2. Landau Institute for Theoretical Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432, Russia

    S. I. Anisimov

  3. Institute for Computer Aided Design, Russian Academy of Sciences, Vtoraya Brestskaya ul. 19/18, Moscow, 123056, Russia

    A. M. Oparin

  4. Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, Moscow region, 142432, Russia

    I. V. Lomonosov

Authors
  1. A. V. Konyukhov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. P. Likhachev
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. V. E. Fortov
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. K. V. Khishchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. S. I. Anisimov
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. A. M. Oparin
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. I. V. Lomonosov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. P. Likhachev.

Additional information

Original Russian Text © A.V. Konyukhov, A.P. Likhachev, V.E. Fortov, K.V. Khishchenko, S.I. Anisimov, A.M. Oparin, I.V. Lomonosov, 2009, published in Pis’ma v Zhurnal Éksperimental’noĭ i Teoreticheskoĭ Fiziki, 2009, Vol. 90, No. 1, pp. 21–27.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Konyukhov, A.V., Likhachev, A.P., Fortov, V.E. et al. On the neutral stability of a shock wave in real media. Jetp Lett. 90, 18–24 (2009). https://doi.org/10.1134/S0021364009130050

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0021364009130050

PACS numbers

Search

Navigation