Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-14T21:54:28.858Z Has data issue: false hasContentIssue false
  • English
  • Français

Parameter regimes for slow, intermediate and fast MHD shocks

Published online by Cambridge University Press:  08 March 2010

P. DELMONT and
R. KEPPENS
P. DELMONT
Affiliation:
Centre for Plasma Astrophysics, K.U. Leuven, Belgium (peter.delmont@wis.kuleuven.be)Leuven Mathematical Modeling and Computational Science Centre, K.U. Leuven, Belgium
R. KEPPENS
Affiliation:
Centre for Plasma Astrophysics, K.U. Leuven, Belgium (peter.delmont@wis.kuleuven.be)Leuven Mathematical Modeling and Computational Science Centre, K.U. Leuven, BelgiumAstronomical Institute, Utrecht University, The NetherlandsFOM Institute for Plasma Physics Rijnhuizen, Nieuwegein, The Netherlands
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the 'Save PDF' action button.

We investigate under which parameter regimes the magnetohydrodynamic (MHD) Rankine–Hugoniot conditions, which describe discontinuous solutions to the MHD equations, allow for slow, intermediate and fast shocks. We derive limiting values for the upstream and downstream shock parameters for which shocks of a given shock-type can occur. We revisit this classical topic in nonlinear MHD dynamics, augmenting the recent time reversal duality finding by in the usual shock frame parametrization.

Information

Type
Papers
Information
Journal of Plasma Physics , Volume 77 , Issue 2 , April 2011, pp. 207 - 229
Copyright
Copyright © Cambridge University Press 2010

References

Akhiezer, A. I., Lyubarskii, G. Ya. and Polovin, R. V. 1959 On the stability of shock waves in magnetohydrodynamics. Soviet Phys. -JETP 8, 507–511.Google Scholar
Anderson, J. E. 1963 Magnetohydrodynamical Shock Waves. Cambridge, MT: MIT Press.CrossRefGoogle Scholar
Barmin, A. A., Kulikovskiy, A. G. and Pogorelov, N. V. 1996 Shock-capturing approach and nonevolutionary solutions in magnetohydrodynamics. J. Comp. Phys. 126, 77–90.CrossRefGoogle Scholar
Brio, M. and Wu, C. C. 1988 An upwind differencing scheme for the equations of ideal magnetohydrodynamics. J. Comp. Phys. 75, 400–422.Google Scholar
Chao, J. K., Lyu, L. H., Wu, B. H., Lazarus, A. J., Chang, T. S. and Lepping, R. P. 1993 Observation of an intermediate shock in interplanetary space. J. Geophys. Res. 98, 17443–17450.Google Scholar
Chu, C. K. and Taussig, R. T. 1967 Numerical experiments of magnetohydrodynamic shocks and the stability of switch-on shocks. Phys. Fluids 10, 249–256.CrossRefGoogle Scholar
Coppi, P. S., Blandford, R. D. and Kennel, C. F. 1988 On the existence and stability of intermediate shocks. ESA SP 285 381–384.Google Scholar
De Hoffmann, F. and Teller, E. 1950 Magneto-hydrodynamic shocks. Phys. Rev. 80, 692–703.CrossRefGoogle Scholar
De Sterck, H., Low, B. C. and Poedts, S. 1998 Complex magnetohydrodynamic bow shock topology in field-aligned low-β flow around a perfectly conducting cylinder. Phys. of Plasmas 11, 4015–4027.CrossRefGoogle Scholar
De Sterck, H. and Poedts, S. 2000 Intermediate shocks in three-dimensional magnetohydrodynamic bow-shock flows with multiple interacting shock fronts Phys. Rev. Lett. 84, 5524–5527.Google Scholar
Falle, S. A. E. G. and Komissarov, S. S. 1997 On the existence of intermediate shocks. Mon. Not. R. Astron. Soc. 123, 265–277.Google Scholar
Falle, S. A. E. G. and Komissarov, S. S. 2001 On the inadmissibility of non-evolutionary shocks. J. Plasma Phys. 65, 29–58.Google Scholar
Feng, H. and Wang, J. M. 2008 Observations of a 2 → 3 type interplanetary intermediate shock. Solar Phys. 247, 195–201.CrossRefGoogle Scholar
Germain, P. 1960 Shock waves and shock-wave structure in magneto-fluid dynamics. Rev. Mod. Phys. 32, 951–958.CrossRefGoogle Scholar
Glimm, J. 1965 Solutions in the large for nonlinear hyperbolic systems of equations. Comm. Pure Appl. Math. 41, 569–590.CrossRefGoogle Scholar
Goedbloed, J. P. 2008 Time reversal duality of magnetohydrodynamical shocks. Phys. Plasmas 15, 062101.Google Scholar
Goedbloed, H. and Poedts, S. 2004 Principles of Magnetohydrodynamics With Applications to Laboratory and Astrophysical Plasmas. Cambridge, UK: Cambridge University Press.CrossRefGoogle Scholar
Gombosi, T. I. 1998 Physics of the Space Environment. Cambridge, UK: Cambridge University Press.Google Scholar
Jeffrey, A. and Taniuti, T. 1964 Nonlinear Wave Propagation. New York: Academic Press.Google Scholar
Kennel, C. F., Blanford, R. D. and Coppi, P. 1989 MHD intermediate shock discontinuities. I - Rankine–Hugoniot conditions. J. Plasma Phys. 42, 219–319.CrossRefGoogle Scholar
Lax, P. D. 1957 Hyperbolic system of conservation laws II. Comm. Pure Appl. Math. 10, 537–566.CrossRefGoogle Scholar
Liberman, M. A. and Velikhovich, A. L. 1986 Physics of Shock Waves in Gases and Plasmas. New York: Springer.Google Scholar
Myong, R. S. and Roe, P. L. 1997a Shock waves and rarefaction waves in magnetohydrodynamics. Part 1. A model system. J. Plasma. Phys. 58, 485.CrossRefGoogle Scholar
Myong, R. S. and Roe, P. L. 1997 Shock waves and rarefaction waves in magnetohydrodynamics. Part 2. The MHD system. J. Plasma. Phys. 58, 521.Google Scholar
Sturtevant, B. 1987 Shock Tubes and Waves. Berlin: VCH Verlag.Google Scholar
Todd, L. 1965 Evolution of switch-on and switch-off shocks in a gas of finite electrical conductivity. J. Fluid Mech. 24, 597–608.Google Scholar
Whang, Y. C., Zhou, J., Lepping, R. P., Szabo, A., Fairfield, D., Kukobun, S., Ogilvie, K. W. and Fitzenreiter, R. 1998 Double discontinuity: A compound structure of slow shock and rotational discontinuity. J. Geophys. Res. 103, 6513–6520.Google Scholar
Wu, C. C. 1987 On MHD intermediate shocks. Geophys. Res. Lett. 14, 668–671.CrossRefGoogle Scholar
Wu, C. C. 1988 The MHD intermediate shock interaction with an intermediate wave: Are intermediate shocks physical? J. Geophys. Res. 93 (A2), 987–990.Google Scholar
Wu, C. C. 1990 Formation, structure, and stability of MHD intermediate shocks. J. Geophys. Res. 95 (A6), 8149–8175.Google Scholar