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This article is cited in 3 scientific papers (total in 3 papers)
Differentical equations, dynamical systems and optimal control
Linear problem of shock wave disturbance analysis. Part 2: Refraction and reflection of plane waves in the stability case
E. V. Semenko, T. I. Semenko Novosibirsk State Technical University,
Prospekt K. Marksa 20,
630073, Novosibirsk, Russia
Abstract:
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, Fourier transform.
Received December 13, 2016, published May 23, 2017
Citation:
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”, Sib. Èlektron. Mat. Izv., 14 (2017), 473–492
Linking options:
https://www.mathnet.ru/eng/semr799 https://www.mathnet.ru/eng/semr/v14/p473
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