Geodesic
Linear problem of shock wave disturbance analysis. Part~3:~Refraction and reflection in the neutral stability case
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 493-510.

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The refraction and reflection in the neutral stability case, particularly the spontaneous emission, is investigated. The real agent (source) of spontaneous emission under the linear theory is indicated. The availability of infinite wave amplitudes at the plane waves refraction/reflection is disproved. The generalized generation and reflection coefficients for the appropriate description of refraction and reflection in the neutral stability case is proposed.
Keywords: shock wave, shock disturbance, entropy-vorticity wave, acoustic wave, incident wave, transmitted wave, reflection, reflected wave, stability, neutral stability, spontaneous emission
Mots-clés : refraction, Fourier transform. 
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     title = {Linear problem of shock wave disturbance analysis. {Part~3:~Refraction} and reflection in the neutral stability case},
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E. V. Semenko; T. I. Semenko. Linear problem of shock wave disturbance analysis. Part~3:~Refraction and reflection in the neutral stability case. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 493-510. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a89/

[1] L. D. Landau, E. M. Lifshitz, Course of Theoretical Physics, v. 6, Fluid Mechanics, 2nd edition, Elsevier, 1987 | MR

[2] S. P. D'yakov, “On the stability of shock waves”, Sov. Phys. JETP, 27 (1954), 288–295 | MR | Zbl

[3] S. P. D'yakov, “The interaction of shock waves with small perturbations”, Sov. Phys. JETP, 33 (1957), 948–974 | MR

[4] V. M. Kontorovitch, “Reflection and refraction of sound by shock waves”, Sov. Phys. JETP, 33 (1957), 1527–1528

[5] J. F. McKenzie, K. O. Westphal, “Interaction of linear waves with oblique shock waves”, Phys. Fluids, 11 (1968), 2350–2362 | DOI | Zbl

[6] W. R. Johnson, O. Laporte, “Interaction of Cylindrical Sound Waves with a Stationary Shock Wave”, Phys. Fluids, 1 (1958), 82–94 | DOI | MR | Zbl

[7] G. R. Fowles, G. W. Swan, “Stability of plane shock waves”, Phys. Rev. Lett., 30 (1973), 1023–1025 | DOI

[8] W. K. Van Moorhem, A. R. George, “On the stability of plane shocks”, Journal of Fluid Mechanics, 68 (1975), 97–108 | DOI | Zbl

[9] G. W. Swan, G. R. Fowles, “Shock wave stability”, Phys. Fluids, 18 (1975), 28–35 | DOI | Zbl

[10] G. R. Fowles, “Conditional stability of shock waves — a criterion for detonation”, Phys. Fluids, 19 (1976), 227–238 | DOI | Zbl

[11] G. R. Fowles, “Stimulated and spontaneous emission of acoustic waves from shock fronts”, Phys. Fluids, 24 (1981), 220–227 | DOI | Zbl

[12] M. Mond, I. M. Rutkevich, “Spontaneous acoustic emission from strong ionizing shocks”, Journal of Fluid Mechanics, 275 (1994), 121–146 | DOI | MR | Zbl

[13] J.-C. Robinet, G. Casalis, “Critical interaction of a shock wave with an acoustic wave”, Phys. Fluids, 13 (2001), 1047–1059 | DOI | MR

[14] I. Men'shov, Y. Nakamura, Abnormal amplification of sound waves refracted by an oblique shock wave, JAXA Special Publication, SP-03-002, 2004, 23–28

[15] S. V. Iordanski, “On stability of a plane shock wave”, Journal of Applied Mathematics and Mechanics, 21 (1957), 465–472 | MR

[16] J. J. Erpenbeck, “Stability of Steady-State Equilibrium Detonations”, Phys. Fluids, 5 (1962), 604–614 | DOI | MR

[17] J. J. Erpenbeck, “Stability of Step Shocks”, Phys. Fluids, 5 (1962), 1181–1187 | DOI | MR | Zbl

[18] R. M. Zaidel, “Shock wave from a slightly curved piston”, Journal of Applied Mathematics and Mechanics, 24 (1960), 316–320 | DOI | MR

[19] R. M. Zaidel, “The perturbations propagation in plane shock waves”, Journal of Applied Mechanics and Technical Physics, 4 (1967), 30–39

[20] J. W. Bates, “Initial-value-problem solution for isolated rippled shock fronts in arbitrary fluid media”, Phys. Rev. E, 69 (2004), 056313-1–056313-16 | DOI | MR

[21] J. W. Bates, “Instability of isolated planar shock waves”, Phys. Fluids, 19 (2007), 1–15

[22] A. Tumin, “Initial-value problem for small disturbances in an idealized one-dimensional detonation”, Phys. Fluids, 19 (2007), 106105-1–106105-12 | DOI

[23] G. R. Fowles, A. F. P. Houwing, “Instabilities of shock and detonation waves”, Phys. Fluids, 27 (1984), 1982–1990 | DOI | MR | Zbl

[24] N. M. Kuznetsov, “Contribution to shock-wave stability theory”, Zh. Eksp. Teor. Fiz., 88 (1985), 470–486

[25] N. M. Kuznetsov, “Stability of shock waves”, Usp. Fiz. Nauk, 159 (1989), 493–527 | DOI

[26] J. W. Bates, D. C. Montgomery, “The D'yakov–Kontorovich Instability of Shock Waves in Real Gases”, Phys. Rev. Lett., 84 (2000), 1180–1183 | DOI

[27] A. V. Konyukhov, A. P. Likhachev, V. E. Fortov, S. I. Anisimov, A. M. Oparin, “Stability and ambiguous representation of shock wave discontinuity in thermodynamically nonideal media”, Pis'ma Zh. Eksp. Teor. Fiz., 90 (2009), 28–34

[28] G. F. Carrier, M. Krook, C. E. Pearson, Functions of a complex variable, Hod Books, Ithaka, N. Y., 1983 | MR | Zbl

[29] E. Zauderer, Partial Differential Equations, 3rd edition, Wiley, 2006 | MR | Zbl