THERMODYNAMIC CRITERION OF NEUTRAL STABILITY OF SHOCK WAVES IN HYDRODYNAMICS AND ITS IMPLICATIONS

Cover Page

Cite item

Full Text

Abstract

It is shown that the Kontorovich criterion for neutral stability of relativistic shock waves (the relativistic analog of the Dyakov-Kontorovich criterion in classical hydrodynamics), after eliminating the derivative along the Taub-Hugoniot shock adiabat using relations at the relativistic shock-wave discontinuity, reduces to a constraint on the isenthalpic derivative of internal energy with respect to specific volume in the rest frame: p>-∂ϵ∂vω>p0. The obtained formulation is also valid in classical hydrodynamics. The implications of this formulation for shock waves with single-phase and two-phase final states in a medium with first-order phase transition are derived. The influence of the Riedel parameter and isochoric heat capacity on the realizability of neutrally stable shock waves is shown. In a model problem formulation, the effect of local thermodynamic non-equilibrium on the damping of perturbations of a neutrally stable shock wave is investigated.

About the authors

A. V. Konyukhov

Joint Institute for High Temperatures of the Russian Academy of Sciences

Author for correspondence.
Email: konyukhov_av@mail.ru
Russian Federation, 125412, Moscow

References

  1. S. P. D’yakov, The Stability of Shockwaves: Investigation of the Problem of Stability of Shock Waves in Arbitrary Media, Zh. Eksp. Teor. Fiz. 27, 288 (1954).
  2. V. M. Kontorovich, Concerning the Stability of Shock Waves, Zh. Eksp. Teor. Fiz. 33, 1525 (1957).
  3. J. J. Erpenbeck, Stability of Step Shocks, Phys. Fluids 5, 1181 (1962); doi: 10.1063/1.1706503.
  4. V. M. Kontorovich, Stability of Shock Waves in Relativistic Hydrodynamics, Zh. Eksp. Teor. Fiz. 34, 186 (1958).
  5. P. V. Tytarenko and V. I. Zhdanov, Existence and Stability of Shock Waves in Relativistic Hydrodynamics with General Equation of State, Phys. Lett. A 240, 295 (1998); doi: 10.1016/S0375-9601(97)00973-0.
  6. I. V. Lomonosov, V. E. Fortov, K. V. Khishchenko, and P. R. Levashov, Shock Wave Stability in Metals, AIP Conf. Proc. 505, 85 (2000); doi: 10.1063/1.1303427.
  7. I. V. Lomonosov, V. E. Fortov, K. V. Khishchenko, and P. R. Levashov, Theoretical Investigation of Shock Wave Stability in Metals, AIP Conf. Proc. 706, 91 (2004); doi: 10.1063/1.1780191.
  8. I. V. Lomonosov and N. A. Tahir, Theoretical Investigation of Shock Wave Stability in Metals, Appl. Phys. Lett. 92, 101905 (2008).
  9. M. Mond and I. M. Rutkevich, Spontaneous Acoustic Emission from Strong Ionizing Shocks, J. Fluid Mech. 275, 121 (1994).
  10. M. Mond and I. M. Rutkevich, Spontaneous Acoustic Emission from Strong Shocks in Diatomic Gases, J. Fluid Mech. 14, 1468 (2002); doi: 10.1063/1.1458005.
  11. G. Russo, Some Remarks on the Stability of Shock Waves, Meccanica 25, 83 (1990); doi: 10.1007/BF01566206.
  12. J. Bates and D. Montgomery, The D’yakov–Kontorovich Instability of Shock Waves in Real Gases, Phys. Rev. Lett. 84, 1180 (2000); doi: 10.1103/PhysRevLett.84.1180.
  13. A. V. Konyukhov, A. P. Likhachev, V. E. Fortov, S. I. Anisimov, and A. M. Oparin, On the Neutral Stability of a Shock Wave in Real Media, JETP Lett. 90, 18 (2009); doi: 10.1134/S0021364009130050.
  14. N. Wetta, J.-C. Pain, and O. Heuz´e, D’yakov–Kontorovitch Instability of Shock Waves in Hot Plasmas, Phys. Rev. E 98 , 033205 (2018); doi: 10.1103/PhysRevE.98.033205.
  15. C. Huete and M. Vera, D’Yakov–Kontorovich Instability in Planar Reactive Shocks, J. Fluid Mech. 879, 54 (2019); doi: 10.1017/jfm.2019.942.
  16. C. Huete, F. Cobos-Campos, E. Abdikamalov, and S. Bouquet, Acoustic Stability of Nonadiabatic HighEnergy-Density Shocks, Phys. Rev. Fluids 5, 113403 (2020); doi: 10.1103/PhysRevFluids.5.113403.
  17. G. R. Fowles, Stimulated and Spontaneous Emission of Acoustic Waves from Shock Fronts, Phys. Fluids 24, 220 (1981); doi: 10.1063/1.863369.
  18. A. M. Anile and G. Russo, Linear Stability for Plane Relativistic Shock Waves, Phys. Fluids 30, 1045 (1987); doi: 10.1063/1.866302.
  19. G. Russo and A. M. Anile, Stability Properties of Relativistic Shock Waves: Basic Results, Phys. Fluids 30, 2406 (1987).
  20. G. Russo, Stability Properties of Relativistic Shock Waves: Applications, Astrophys. J. 334, 707 (1988); doi: 10.1086/166872.
  21. A. H. Taub, Relativistic Rankine–Hugoniot Equations, Phys. Rev. 74, 328 (1948); doi: 10.1103/PhysRev.74.328.
  22. J. L. Synge, The Relativistic Gas, Series in Physics, North-Holland Publ. Comp. (1957).
  23. K. A. Bugaev and M. I. Gorenstein, Relativistic Shocks in Baryonic Matter, J. Phys. G: Nucl. Phys. 13, 1231 (1987).
  24. K. A. Bugaev, M. I. Gorenstein, B. K¨ampfer, and V. I. Zhdanov, Generalized Shock Adiabatics and Relativistic Nuclear Collisions, Phys. Rev. D 40, 2903 (1989); doi: 10.1103/PhysRevD.40.2903.
  25. A. V. Konyukhov, A. P. Likhachev, and V. E. Fortov, Behavior of Relativistic Shock Waves in Nuclear Matter, High. Temp. 53, 622 (2015); doi: 10.1134/S0018151X15050181.
  26. J. Cleymans, R. V. Gavai, and E. Suhonen, Quarks and Gluons at High Temperatures and Densities, Phys. Rep. 130, 217 (1986); doi: 10.1016/0370-1573(86)90169-9.
  27. B. E. Poling, J. M. Prausnitz, and J. P. O’Connell, Properties of Gases and Liquids, McGraw-Hill Education (2001).
  28. М. Д. Вайсман, Термодинамика парожидкостных потоков, Энергия. Ленинградское отделение, Москва (1977).
  29. A. G. Kulikovskii, A. T. Il’ichev, A. P. Chugainova, and V. A. Shargatov, On the Structure Stability of a Neutrally Stable Shock Wave in a Gas and on Spontaneous Emission of Perturbations, J. Exp. Theor. Phys. 131, 481 (2020); doi: 10.1134/s1063776120090186.
  30. A. G. Kulikovskii, A. T. Il’ichev, A. P. Chugainova, and V. A. Shargatov, Spontaneously Radiating Shock Waves, Doklady Physics 64, 293 (2019); doi: 10.1134/s1028335819070036.
  31. C. S. Gardner, Comment on Stability of Step Shocks, Phys. Fluids 6, 1366 (1963); doi: 10.1063/1.1706917.
  32. N. M. Kuznetsov, The Theory of Shock-Wave Stability, Zh. Eksp. Teor. Fiz. 88, 470 (1985).
  33. N. M. Kuznetsov, Stability of Shock Waves, Sov. Phys. Usp. 32, 993 (1989); doi: 10.1070/PU1989v032n11ABEH002777.
  34. G. R. Fowles and A. F. P. Houwing, Instabilities of Shock and Detonation Waves, Phys. Fluids 27, 1982 (1984); doi: 10.1063/1.864853.
  35. A. V. Konyukhov, A. P. Likhachev, V. E. Fortov, S. I. Anisimov, and A. M. Oparin, Stability and Ambiguous Representation of Shock Wave Discontinuity in Thermodynamically Nonideal Media, JETP Lett. 90, 25 (2009); doi: 10.1063/1.3295149.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download

Copyright (c) 2024 Russian Academy of Sciences

Согласие на обработку персональных данных

 

Используя сайт https://journals.rcsi.science, я (далее – «Пользователь» или «Субъект персональных данных») даю согласие на обработку персональных данных на этом сайте (текст Согласия) и на обработку персональных данных с помощью сервиса «Яндекс.Метрика» (текст Согласия).