Stability of surfaces of strong discontinuity in gases

Fluid Dynamics

Volumn 31, Issue 2, 1996, Pages 163-177

  Barmin, A A ^a   Egorushkin, S A ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

FLOW STABILITY; GAS FLOWS;

EID: 0030464580     PISSN: 00154628     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02029675     Document Type: Article

References (105)

1. A. Jeffrey, Quasilinear Hyperbolic Systems and Waves, Pitman, London, (1978).
2. A. Majda, Compressible Fluid Flow and Systems of Conservation Laws in Several Space Variables, (Appl. Math. Sci., Vol. 53) Springer, New York, (1984).
3. A. Majda, "The existence and stability of multi-dimensional shock fronts," Bull. Amer. Math. Soc., 4, 342 (1981).
4. I. G. Petrovskii, "The Cauchy problem for a system of linear partial differential equations in the field of nonanalytic functions," Bul. MGU, Sec. A, Matematika i Mekhanika, 1, No. 1, 1 (1938).
5. I. M. Gel'fand, "Some problems of the theory of quasilinear equations," Usp. Mat. Nauk, 14, No. 2, 87 (1959).
6. B. L. Rozhdestvenskii and N. N. Yanenko, Systems of Quasilinear Equations and their Applications to Gas Dynamics [in Russian], Nauka, Moscow (1978).
7. S. K. Godunov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1979).
8. L. D. Landau and E. M. Lifshits, Theoretical Physics, Vol. 6, Hydrodynamics [in Russian], Nauka, Moscow (1986).
9. P. D. Lax, "Hyperbolic systems of conservation laws. II," Communs Pure and Appl. Math., 10, 537 (1957).
10. R. Courant and K. O. Friedrichs, Supersonic Flow and Shock Waves, Interscience, New York-London (1948).
11. G. Ya. Galin, "Shock wave theory", Dokl. Akad. Nauk SSSR, 127, 55 (1959).
12. R. G. Smith, "The Riemann problem in gas dynamics," Trans. Amer. Math. Soc., 249, 1 (1979).
13. L. I. Akhiezer, G. Ya. Lubarskii, and R V. Polovin, "Stability of shock waves in magnetohydrodynamics," Zh. Eksp. Teor. Fiz., 35, 731 (1958).
14. S. I. Syrovatskii, "Stability of shock waves in magnetohydrodynamics," Zh. Eksp. Teor. Fiz., 35, 1466 (1958).
15. A. G. Kulikovskii and E. I. Sveshnikova, "Certain properties of the shock adiabat of quasitransverse elastic waves," Prikl. Mat. Mekh., 48, 793 (1984).
16. A. G. Kulikovskii and G. A. Lyubimov, Magneto-Hydrodynamics, Addison-Wesley, Reading, Mass. (1965).
17. A. G. Kulikovskii, "Strong discontinuities in continuum flows and their structure," Tr. Matem. Inst. Akad Nauk SSSR im. V. A. Steklova, 182, 261 (1988).
18. A. G. Kulikovskii, "Surfaces of discontinuity separating ideal media with different properties: Recombination waves in magnetohydrodynamics," Prikl. Mat. Mekh., 32, 1125 (1968).
19. A. N. Kolmogorov, I. G. Petrovskii, and N. S. Piskunov, "Investigation of the diffusion equation associated with increase in the amount of matter and its application to a biological problem," Bul. MGU, Sec. A, 1, No. 6, 1 (1937).
20. S. S. Novikov and Yu. S. Ryazantsev, "Existence and uniqueness of the solution of a system of equations of thermal combustion theory," Zh. Prikl. Mekh. Tekh. Fiz., No. 4, 86 (1965).
21. M. Matalon and B. J. Matcowsky, "Flames as gasdynamic discontinuities," J. Fluid. Mech., 124, 239 (1982).
22. A. G. Kulikovskii and G. A. Lyubimov, "Magnetohydrodynamic shock waves ionizing a gas," Dokl. Akad. Nauk SSSR, 129, 52 (1959).
23. A. A. Barmin and A. G. Kulikovskii, "Shock waves ionizing a gas in the presence of an arbitrarily oriented magnetic field," in: Problems of Hydrodynamics and Continuum Mechanics [in Russian], Nauka, Moscow (1969), p.35.
24. A. G. Kulikovskii, "Shock wave structure", Prikl. Mat. Mekh., 26, 631 (1962).
25. S. P. D'yakov, "Shock wave stability," Zh. Eksp. Teor. Fiz., 27, 288 (1954).
26. K. V. Brushlinskii, "Instability of an imploding spherical shock wave," Zh. Vychisl. Mat. Matem. Fiz., 22, 1468 (1982).
27. S. V. Iordanskii, "Stability of a plane steady shock wave," Prikl. Mat. Mekh., 21, 465 (1957).
28. J. J. Erpenbeck, "Stability of step shocks," Phys. Fluids, 5, 1181 (1962).
29. L. D. Landau, "Slow combustion theory," Zh. Eksp. Teor. Fiz., 14, 240 (1944).
30. C. S. Gardner and M. D. Kruskal, "Stability of magnetohydrodynamic shocks," Phys. Fluids, 7, 700 (1964).
31. O. A. Senkevich, "Stability of a plane ionizing shock wave," Dokl. Akad. Nauk SSSR, 199, 48 (1971).
32. S. A. Egorushkin and A. G. Kulikovskii, "Stability of solutions of certain boundary value problems for hyperbolic equations," Prikl. Mat. Mekh., 56, 40 (1992).
33. O. L. Filippova, "Stability of plane MHD shock waves," in: Sixth All-Union Congress on Theoretical and Applied Mechanics. Abstracts of Proceedings [in Russian], Fan, Tashkent (1986), p. 616.
34. O. L. Filippova, "Stability of plane MHD shock waves in an ideal perfect gas," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 128 (1991).
35. H.-O. Kreiss, "Initial boundary value problems for hyperbolic systems," Communs Pure and Appl. Math., 23, 277 (1970).
36. A. Majda and S. Oscher, "Initial-boundary value problems for hyperbolic equations with uniformly characteristic boundary," Communs Pure and Appl. Math., 28, 607 (1975).
37. A. M. Blokhin, Energy Integrals and their Applications to Gas Dynamic Problems [in Russian], Nauka, Novosibirsk (1986).
38. R. W. Griffiths, R. J. Sandeman, and H. G. Hornung, "The stability of shock waves in ionizing and dissociating gases," J. Phys. D: Appl. Physics, 9, 1681 (1976).
39. S. A. Egorushkin and V. S. Uspenskii, "Effect of leading radiation on stability of strong shock waves in gases with an arbitrary equation of state," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 125 (1990).
40. S. A. Egorushkin, M. L. Pekurovskii, and V. S. Uspenskii, "Instability of strong shock waves in monatomic gases," Dokl. Akad. Nauk SSSR, 313, 39 (1990).
41. S. A. Egorushkin and V. S. Uspenskii, "Properties of strong shock waves in monatomic gases," Khim. Fiz., 11, 1013 (1992).
42. I. I. Glass and W. S. Liu, "Effects of hydrogen impurities on shock structure and stability in ionizing monatomic gases," J. Fluid. Mech., 84, 55 (1978).
43. G. K. Tumakaev, V. G. Maslennikov, and B. V. Serova, "Instability of flow behind high-intensity shock waves in monatomic gases," Pis'ma Zh. Tekh. Fiz., 6, 354 (1980).
44. A. S. Baryshnikov, A. P. Bedin, V. G. Maslennikov, and G. I. Mishin, "Instability of bow shock wave front," Pis'ma Zh. Tekh. Fiz., 5, 281 (1979).
45. G. K. Tymakevich, "Systematization of anomalous phenomena in shock-heated monatomic gases. Nature of their onset and development," in: High-Temperature Gasdynamic Shock Tubes and Shock Waves: Proceedings of Intern. School-Seminar [in Russian], Minsk (1982), p. 154.
46. N. M. Kuznetsov and I. A. S. Alieva, "Stability of motion of a shock wave through channels," Khim. Fiz., 7, 377 (1988).
47. I. A. Alieva and E. A. Andreev, "Stability of shock waves in inert gases," Zh. Tekh. Fiz., 57, 1172 (1987).
48. P. Meier and R. J. Sandeman, "Interferometric studies of shock waves into argon up to 17 km/s in the free-piston double-diaphragm shock tube," in: Modern Developments Shock Tube Research, Proc. 10th Intern. Shock Tube Symp., Kyoto, (1975), p.328.
49. I. I. Glass, W. S. Liu, K. Takayama, and P. I. Brimelow, "Interaction of shock structure with shock-induced quasi-steady laminar sidewall and flat-plate boundary layer flows in ionizing argon," in: Shock Tubes and Waves, Proc. 12th Intern. Symp., Jerusalem, 1979, Magnes Press, Jerusalem, (1980), p.232.
50. J. J. Erpenbeck, "Stability of steady-state equilibrium detonations," Phys. Fluids, 5, 604 (1962).
51. A. Majda and R. Rosales, "A theory of spontaneous Mach stem formation in reacting shock fronts. I. The basic perturbation analysis," SIAM Journal Appl. Math., 43, 1310 (1983).
52. A. A. Vasil'ev, V. V. Mitrofanov, and M .E. Topchiyan, "Detonation waves in gases," Fiz. Goren. Vzryva, 23, No. 5, 109 (1987).
53. O. A. Sinkevich, "Stability of a plane ionizing shock wave in a magnetic field," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 122 (1972).
54. V. M. Zubtsov and O. A. Sinkevich, "Stability limits of a shock wave in a transverse magnetic field," Teplofiz. Vysok. Temp., 13, 1286 (1975).
55. V. M. Zubtsov and O. A. Sinkevich, "Stability of a plane ionizing shock wave in a longitudinal magnetic field," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 195 (1976).
56. A. G. Istratov and V. B. Librovich, "Effect of transport processes on stability of a plane flame front," Prikl. Mat. Mekh., 30, 451 (1966).
57. P. Germain and J. P. Guirand, "Conditions de choc et structure des ondes de choc dans un écoulement stationnaire de fluide dissipatif," Publ. O.N.E.R.A., No. 105, (1962).
58. R. M. Zaidel', "Perturbation development on plane shock waves," Zh. Prikl. Mekh. Tekh. Fiz., No. 4, 30 (1967).
59. A. G. Baryshnikov, "Surface properties and stability of shock waves in gases," Prikl. Mat. Mekh., 50, 748 (1986).
60. G. H. Markstein, "Experimental and theoretical studies of flame-front stability," J. Aeronaut. Sci., 18, 199 (1951).
61. Ya. B. Zel'dovich, G. I. Barenblatt, V. B. Librovich, and G. M. Makhviladze, Mathematical Theory of Combustion and Explosion [in Russian], Nauka, Moscow (1980).
62. G. H. Markstein (Ed.), Nonsteady Flame Propagation, Pergamon Press, London (1964).
63. G. B. Whitham, Linear and Nonlinear Waves, Wiley, New York (1974).
64. D. I. Blokhintsev, Acoustics of an Inhomogeneous Moving Medium [in Russian], Nauka, Moscow (1981).
65. S. E. Korshunov, "Stability of shock waves with a finite relaxation zone," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 176 (1982).
66. V. A. Levin, B. P. Solomakha, and S. P. Chikova, "Stability of a plane detonation wave," Tr. Inst. Mekhaniki MGU, No. 32, 44 (1974).
67. G. Ya. Galin and A. G. Kulikovskii, "Stability of flows developing in the breakdown of an arbitrary discontinuity," Prikl. Mat. Mekh., 39, 95 (1975).
68. A. A. Barmin and O. L. Gusarova, "Stability of flows with surfaces of discontinuity," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 10 (1982).
69. G. I. Mishin, A. P. Bedin, N. I. Yuschenkova et al., "Anomalous relaxation and instability of shock waves in gases," Zh. Tekh. Fiz., 51, 2315 (1981).
70. N. I. Yuschenkova, "A mechanism of relaxation instability in shock waves in inert gases," Pis'ma Zh. Tekh. Fiz., 6, 1283 (1980).
71. A. F. P. Houwing, T. J. McIntyre, P. A. Taloni, and R. J. Sandman, "On the population of the metastable atoms behind unstable shock wave in ionizing argon," J. Fluid Mech., 170, 319 (1986).
72. M. B. Zheleznyak and E. A. Filimonova, "Effect of associative ionization on relaxation behind a strong shock wave front in argon," Teplofiz. Vysok. Temp., 24, 1203 (1986).
73. R. I. Nigmatulin, Dynamics of Multiphase Media, Vol. 1 [in Russian], Nauka, Moscow (1987).
74. S. V. Iordanskii and A. G. Kulikovskii, "Motion of a fluid with fine particles," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 12 (1977).
75. G. I. Barenblatt and Ya. B. Zel'dovich, "Stability of flame propagation," Prikl. Mat. Mekh., 21, 856 (1959).
76. A. M. Zhilyaev and N. M. Kuznetsov, "Stability of shock waves in a chemically reacting gas," Mat. Modelirovanie, 3, No. 7, 71 (1991).
77. V. A. Vol'pert, "Nonlinear stability of combustion waves," in: Heat and Mass Transfer in Chemically Reacting Systems: Proceedings of Intern. School-Seminar, Vol. 1 [in Russian], Institute of Heat and Mass Transfer, Minsk (1988), p. 31.
78. G. I. Barenblatt, Ya. B. Zel'dovich, and A. G. Istratov "Diffusive-thermal stability of a laminar flame," Zh. Prikl. Mekh. Tekh. Fiz., No. 4, 21 (1962).
79. B. Lewis and G. Elbe, "On the theory of flame propagation," J. Chem. Phys., 2, 537 (1934).
80. V. V. Pukhnachev, "Stability of the Chapman-Jouguet detonation," Zh. Prikl. Mekh. Tekh. Fiz., No. 6, 66 (1963).
81. A. M. Blokhin and E. I. Romenskii, "Stability of the limiting steady-state solution in flow past a circular cone," Izv. SO Akad. Nauk SSSR, Ser. Tekh. Nauk, 13, No. 3, 87 (1978).
82. V. V. Rusanov and A. A. Sharakshane, "Investigation of a linearized unsteady model of flow past an infinite wedge," [in Russian], Preprint No. 103, Institute of Applied Mathematics of the USSR Academy of Sciences, Moscow (1980).
83. A. A. Barmin and A. G. Kulikovskii, "Change in gas velocity in ionizing shock waves. The problem of a conducting piston," Prikl. Mat. Mekh., 32, 495 (1968).
84. A. A. Barmin and V. S. Uspenskii, "Development of pulsatory regimes in one-dimensional unsteady MHD-flows with switching-off of electrical conductivity," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 4, 115 (1986).
85. S. A. Egorushkin, "Breakdown of a plane shock wave in a two-parameter medium with an arbitrary equation of state," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 6, 147 (1982).
86. G. R. Fowles and A. F. P. Houwing, "Instabilities of shock and detonation waves," Phys. Fluids, 27, 1982 (1984).
87. N. M. Kuznetsov, "On the theory of shock wave stability," Zh. Eksp. Tekh. Fiz., 88, 470 (1985).
88. C. S. Gordner, "Comment on 'Stability of step shocks'", Phys. Fluids, 6, 1366 (1963).
89. G. R. Fowles, "Conditional stability of shock waves - a criterion for detonation," Phys. Fluids, 19, 227 (1976).
90. N. M. Kuznetsov, "Criterion of instability for a shock wave sustained by a piston," Dokl. Akad. Nauk SSSR, 277, 65 (1984).
91. A. Majda and R. Rosales, "A theory for spontaneous Mach-stern formation in reacting shock fronts. II. Steady-wave bifurcations and evidence for breakdown," Stud. Appl. Math., 71, 117 (1984).
92. S. A. Egorushkin, "Nonlinear stability of a spontaneously radiating shock wave," Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 3, 110 (1984).
93. A. A. Borisov and O. V. Sharypov, "Modeling of autowave processes in chemically nonequilibrium media," in: Hydrodynamics of Turbulent Flows [in Russian], Institute of Thermal Physics, Siberian Branch of the USSR Academy of Sciences (1989), p. 5.
94. Yu. N. Denisov, Gas Dynamics of Detonation Structures [in Russian], Mashinostroenie, Moscow (1989).
95. A. A. Vasil'ev and Yu. A. Nikolaev, "A model of a multifront gas detonation cell," Fiz Goren. Vzryva, 12, No. 5, 744 (1976).
96. A. M. Anile and G. Russo, "Corrugation stability for plane relativistic shock waves," Phys. Fluids, 19, 2847 (1986).
97. Fujuwara Kuzuhito, Matsuo Hideo, and Hiroe Tetsuyuki, "Stability of imploding shocks," J. Japan. Soc. Aeronaut, and Space Sci., 39, No. 445, 81 (1991).
98. A. S. Baryshnikov and N. Yu. Vasil'ev, "Evolution of nonlinear perturbations of a shock front and stability of an imploding shock wave in real media," [in Russian], Preprint No. 1517, Physico-Technical Institute, Leningrad (1991).
99. R. Guirguis, E. S. Oran, and K. Kailasanath, "Numerical simulations of the cellular structure of detonations in liquid nitromethane. Regularity of the cell structure," Combust. and Flame, 65, No. 3, 339 (1986).
100. K. Kailasanath, E. S. Oran, J. P. Boris, and T. R. Young, "Determination of detonation cell size and role of transverse waves in two-dimensional detonations," Combust. and Flame, 61, No. 3, 199 (1985).
101. E. S. Oran, T. R. Young, J. P. Boris et al., "A study of detonation structure: the formation of unreacted gas pockets," in: Proc. 19th Sympos. (Intern.) on Combustion. Combust. Inst., Pittsburgh (1982), p.573.
102. Sugimura Tadagoshi, Fujiwara Toshitaka, and J. M. Lee, "Cellular detonation - instability and sub-structure," Mem. Fac. Eng. Nagoya Univ., 42, 360 (1990).
103. P. A. Voinovich, N. V. Evtyukhin, A. I. Zhmakin et al., "Stratification of shock waves in inhomogeneous media," Fiz. Goren. Vzryva, 23, No. 1, 77 (1987).
104. S. M. Ignat'ev and Yu. I. Petukhov, "Nonlinear analysis of the cellular structure of the flame front with allowance for hydrodynamic and diffusive-thermal processes," Fiz. Goren. Vzryva, 25, No. 5, 58 (1989).
105. G. A. Zulinyan, G. M. Makhviladze, and V. I. Melikhov, "Effect of the Lewis number on the laws of flame propagation," Fiz. Goren. Vzryva. 28, No. 6, 58 (1992).