Development of perturbations in plane shock waves

  • R. M. Zaidel


Investigation of the stability of plane shock waves as regards nonuniform perturbations was first performed by D'yakov [1]. He obtained criteria for stability, and showed that perturbations grow exponentially with time in the case of instability. Iordanskii [2] has shown that in the case of stability, the perturbations are attenuated according to a power law. However, the stability criteria of [2] do not agree with the results of [1], Kontorovich [3] has explained the cause of the apparent discrepancies, and asserts the correctness of the criteria of [2]. A power law for the attenuation of perturbations has also been obtained in [4,5] under a somewhat different formulation of the boundary conditions.

The Cauchy problem with perturbations is examined in §1 of this paper, results are obtained for cases of practical interest, and the asymptotic behavior is investigated.

In §2 the effect of a low viscosity on the development of perturbations is examined. It is shown that when t→∞ the amplitude of perturbations is attenuated mainly as exp(-αt), where α>0 does not depend on the form of the boundary conditions at the shock wave front. The results of §2 were used in processing the experimental data of [6], which made it possible to determine the viscosity of a number of substances at high pressure.


Viscosity Boundary Condition Experimental Data Mathematical Modeling Attenuation 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. P. D'yakov, “A note on stability of shock waves,” ZhETF, 27, no. 3 (9), 1954.Google Scholar
  2. 2.
    S. V. Iordanskii, “A note on the stability of a plane stationary Shock wave,” PMM, 21, no. 4, 1957.Google Scholar
  3. 3.
    V. M. Kontorovich, “Anote on stability of shock waves,” ZhETF, 33, no. 6(12), 1957.Google Scholar
  4. 4.
    N. C. Freeman, “Theory of stability of plane Shock waves,” Proc. Roy. Soc., A. vol. 228, p. 341, 1955.Google Scholar
  5. 5.
    R. M. Zaidel, “The Shock wave from a slightly distorted piston,” PMM, 24, no. 2, 1960.Google Scholar
  6. 6.
    A. D. Sakharov, R. M. Zaidel, V. N. Mineev, and A. G. Oleinik, “Experimental investigation of the stability of shock waves and of the mechanical properties of a material at high pressures and temperatures,” DAN SSSR, 159, no. 5, 1964.Google Scholar
  7. 7.
    M. A. Lavrent'ev and B. V. Shabat, Methods in the Theory of Functions of a Complex Variable, 2-nd ed. [in Russian], 1958.Google Scholar
  8. 8.
    A. G. Istratov and V. B. Librovich, “The influence of transfer processes on the stability of a plane flame front,” PMM, 30, no. 3, 1966.Google Scholar
  9. 9.
    Ya. B. Zel'dovich, S. B. Kormer, M. V. Sinitsyn, and K. B. Yusko, “Investigation of the optical properties of transparent materials at ultra-high pressure,” DAN SSSR, 138, no. 6, 1961.Google Scholar
  10. 10.
    L. D. Landau and E. M. Lifshits, Mechanics of Continuous Media [in Russian], 1953.Google Scholar

Copyright information

© Consultants Bureau 1971

Authors and Affiliations

  • R. M. Zaidel
    • 1
  1. 1.Moscow

Personalised recommendations