Abstract
The structure and stability of quasiparallel magnetohydrodynamic shock waves of small but finite amplitude are investigated. Only those waves whose propagation velocities are close to the Alfvén velocity are considered, i.e., fast shock waves in a medium in which the Alfvén velocity is greater than the speed of sound and slow shock waves in a medium in which the Alfvén velocity is less than the speed of sound and, moreover, intermediate (nonevolutionary) shock waves.
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Literature cited
M. S. Ruderman, “Stability of quasilongitudinally propagating solitons in a plasma with Hall dispersion,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 2, 159 (1987).
A. G. Kulikovskii and G. A. Lyubimov, Magnetohydrodynamics [in Russian], Fizmatgiz, Moscow (1962).
A. A. Barmin, “Investigation of surfaces of discontinuity with release (absorption) of energy in magnetohydrodynamics,” Prikl. Mat. Mekh.,26, 801 (1962).
A. A. Barmin and A. G. Kulikovskii, “Gas-ionizing shock waves in the presence of an arbitrarily oriented magnetic field,” in: Problems of Hydrodynamics and Continuum Mechanics [in Russian], Nauka, Moscow (1969), p. 35.
E. P. Zhidkov, I. D. Iliev, and K. P. Kirchev, “Stability of a solution of the solitary wave type for the nonlinear modified complex Korteweg-de Vries equation,” Sib. Mat. Zh.,26, 39 (1985).
T. Cazenave and P. I. Lions, “Orbital stability of standing waves for some nonlinear Schrödinger equations,” Commun. Math. Phys.,85, 549 (1982).
L. Todd, “The evolution of trans-Alfvénic shocks in gases in finite electrical conductivity,” J. Fluid Mech.,21, 193 (1965).
C. C. Wu, “The MHD intermediate shock interaction with an intermediate wave: are intermediate shocks physical?” J. Geophys. Res.,93, 987 (1988).
C. C. Wu, “Effects of dissipation on rotational discontinuities,” J. Geophys. Res.,95, 3969 (1988).
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In conclusion, the author wishes to thank A. A. Barmin for discussing his results and offering useful comments.
Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 153–160, July–August, 1989.
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Ruderman, M.S. Structure and stability of quasiparallel small-amplitude magnetohydrodynamic shocks. Fluid Dyn 24, 618–625 (1989). https://doi.org/10.1007/BF01052428
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DOI: https://doi.org/10.1007/BF01052428