On the neutral stability of a shock wave in real media

Konyukhov, A. V.; Лихачев, А. П.; Фортов, В. Е.; Khishchenko, K. V.; Анисимов, С. И.; Oparin, A. M.; Ломоносов, И. В.

doi:10.1134/s0021364009130050

Cited by 17 publications

(9 citation statements)

References 11 publications

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“…In [20] the results of numerical study of shock waves stability are given (see chap. 12 in [20] and [21,22]). It is shown that on the nonlinear stage the increasing of disturbances amplitude which occurs in a situation when in classical theory [8][9][10] only neutral stability (with constant amplitude of oscillations) is realizing under the following condition:…”

Section: Comparison To the Numerical Simulation Resultsmentioning

confidence: 99%

“…h and condition (1.3) herein are carried out for shock waves in fluids and gases through the use of known from experiment representations for the Huganiot curve (in the form of a linear dependence of the shock wave velocity on medium velocity behind the front [17][18][19]). In this connection, the results [7,[20][21][22] of numerical simulation of the shock wave instability are also considered.…”

Section: Concretization Formentioning

confidence: 99%

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Dissipative Instability of Shock Waves

Chefranov

2020

J. Exp. Theor. Phys.

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A new condition for the linear dissipative instability of the strong plane shock wave in an arbitrary medium is obtained. The instability of the shock is realized due to the flow instability behind its front, which is similar to the known dissipative instability in the boundary layer for the Tollmien-Schlichting waves. It is found that within the limit of low viscosity the one-dimensional longitudinal disturbances grow much faster than the two-dimensional corrugation ones. It points to a better correspondence to experiment of the new condition for the absolute instability of the shock in comparison with the S.P. D'yakov classical theory (1954), which does not take viscosity into account.

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Section: Comparison To the Numerical Simulation Resultsmentioning

confidence: 99%

Section: Concretization Formentioning

confidence: 99%

Dissipative Instability of Shock Waves

Chefranov

2020

J. Exp. Theor. Phys.

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“…Distinguished regimes for isolated planar shocks ((a) known results) and expanding accretion shocks ((b) new findings) along the variable h. (Bates & Montgomery 2000), and magnesium (Lomonosov et al 2000;Konyukhov et al 2009); for ionizing shock waves in inert gases (Mond & Rutkevich 1994;Mond, Rutkevich & Toffin 1997); for shock waves dissociating hydrogen molecules (Bates & Montgomery 1999); for Gbar-and Tbar-pressure range shocks in solid metals, where the shell ionization affects the shapes of Hugoniot curves (Rutkevich, Zaretsky & Mond 1997;Das, Bhattacharya & Menon 2011;Wetta, Pain & Heuzé 2018); for shock fronts producing exothermic reactions, such as detonation (Huete & Vera 2019;Huete et al 2020). Other examples include EoS constructed ad-hoc specifically for analytical and numerical studies of shock instabilities: (Ni, Sugak & Fortov 1986;Konyukhov, Levashov & Likhachev 2020;Kulikovskii et al 2020).…”

Section: Introductionmentioning

confidence: 91%

Stability of expanding accretion shocks for an arbitrary equation of state

et al. 2021

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We present a theoretical stability analysis for an expanding accretion shock that does not involve a rarefaction wave behind it. The dispersion equation that determines the eigenvalues of the problem and the explicit formulae for the corresponding eigenfunction profiles are presented for an arbitrary equation of state and finite-strength shocks. For spherically and cylindrically expanding steady shock waves, we demonstrate the possibility of instability in a literal sense, a power-law growth of shock-front perturbations with time, in the range of $h_c< h<1+2 {\mathcal {M}}_2$ , where $h$ is the D'yakov-Kontorovich parameter, $h_c$ is its critical value corresponding to the onset of the instability and ${\mathcal {M}}_2$ is the downstream Mach number. Shock divergence is a stabilizing factor and, therefore, instability is found for high angular mode numbers. As the parameter $h$ increases from $h_c$ to $1+2 {\mathcal {M}}_2$ , the instability power index grows from zero to infinity. This result contrasts with the classic theory applicable to planar isolated shocks, which predicts spontaneous acoustic emission associated with constant-amplitude oscillations of the perturbed shock in the range $h_c< h<1+2 {\mathcal {M}}_2$ . Examples are given for three different equations of state: ideal gas, van der Waals gas and three-terms constitutive equation for simple metals.

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“…Mond et al [26] studied shock waves propagating in room-temperature argon, with post-shock temperatures not exceeding several eV. Konyukhov et al who approximated a realistic EOS for magnesium with a van der Waals model, found the D'yakov-Kontorovich unstable regions at plasma temperatures below 20 eV [35]. At such low temperatures, one can safely neglect the energy density and pressure of the plasma radiation.…”

Section: Radiative Pressure and Internal Energymentioning

confidence: 99%

“…To our knowledge, the D'yakov-Kontorovich instability has never been observed experimentally. Some numerical modelings have been performed [21][22][23]34]; for instance, Konyukhov et al [35] carried out hydrodynamic simulations. In a previous paper Konyukhov et al [36] had presented a numerical analysis of the nonlinear instability of shock waves for solid deuterium and for a model medium described by a properly constructed equation of state.…”

Section: Introductionmentioning

confidence: 99%

D'yakov-Kontorovitch instability of shock waves in hot plasmas

2018

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The D'yakov-Kontorovich stability criterion for spontaneous emission of acoustic waves behind shock fronts is investigated for high-temperature carbon, aluminum, silicon and niobium plasmas. The D'yakov and critical stability parameters are calculated along the principal Rankine-Hugoniot curve with an equation-of-state model in which the contribution of bound and free electrons is calculated through a relativistic quantum average-atom model, solving the Dirac equation. The pressure is determined using the stress-tensor formula in the relativistic framework. We find that the instability occurs at the end of the ionization of electronic shells, when the Hugoniot curve departs from the ρ/ρ0=4 asymptote to tend to the ρ/ρ0=7 limit. In such conditions, if the plasma is optically thick, the contribution of blackbody radiation to the EOS is dominant, and the system becomes always stable. Our results indicate that the conditions in which the instability takes place are different from previously published estimates, due to assumptions made in the corresponding equation-ofstate models, especially as concerns the relativistic effects, and depend on the radiative opacity of the material.

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On the neutral stability of a shock wave in real media

Cited by 17 publications

References 11 publications

Dissipative Instability of Shock Waves

Dissipative Instability of Shock Waves

Stability of expanding accretion shocks for an arbitrary equation of state

D'yakov-Kontorovitch instability of shock waves in hot plasmas

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