Geodesic
Linear problem of shock wave disturbance analysis. Part~2:~Refraction and reflection of plane waves in the stability case
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 473-492

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This part is devoted to the propagation of plane waves in the stability case. First the fact that each post-shock plane wave is accompanied with damped wave, and so the plane waves refraction/reflection quantity characteristics are determined up to the damped waves, is established. The correspondence between angles of incidence and angles of refraction/reflection, i.e. Snell's laws, is obtained. The matrix of generation coefficients as a whole is calculated. Its behaviour for an ideal gas when the pre-shock Mach number tends to infinity, i.e. coefficients' amplification, is investigated. The degree of amplification for different kinds of incident waves is found. Furthermore, numerical calculations of generation coefficients for an ideal gas are performed, in particular, the coefficients' amplification is investigated numerically and the results are found to confirm analytical conclusions. For reflection, all four reflection coefficients are calculated and some of their properties are established. In particular, vanishing of the reflected entropy-vorticity plane waves and mutual suppression of the incident and reflected acoustic plane waves at critical angles of incidence are established. The numerical calculations of reflection coefficients are also performed. A comparison is carried out between the obtained results and the already-known ones. It is found that the known formulas for the refraction/reflection angles and for the generation/reflection coefficients should be specified and corrected. In particular, the existence of so-called abnormal amplification is disproved.
Keywords: shock wave, shock disturbance, entropy-vorticity wave, acoustic wave, incident wave, refraction, transmitted wave, reflection, reflected wave, stability, neutral stability, spontaneous emission
Mots-clés : Fourier transform. 
@article{SEMR_2017_14_a88,
     author = {E. V. Semenko and T. I. Semenko},
     title = {Linear problem of shock wave disturbance analysis. {Part~2:~Refraction} and reflection of plane waves in the stability case},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {473--492},
     publisher = {mathdoc},
     volume = {14},
     year = {2017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2017_14_a88/}
}
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E. V. Semenko; T. I. Semenko. Linear problem of shock wave disturbance analysis. Part~2:~Refraction and reflection of plane waves in the stability case. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 14 (2017), pp. 473-492. http://geodesic.mathdoc.fr/item/SEMR_2017_14_a88/