Astrophysics and Space Science

, Volume 274, Issue 1–2, pp 327–341 | Cite as

Absolute and Convective Instability of Tangential Discontinuities in Viscous Fluids: Application to Heliopause

  • Michael S. Ruderman
Article

Abstract

The stability of the heliopause, which is a tangential discontinuity separating the flow of the solar wind plasma compressed at the termination shock, from the flow of the insterstellar plasma compressed at the bow shock, is discussed. A brief review of the normal mode analysis is given. The recent results of the study of the absolute and convective instability of a tangential discontinuity in an incompressible plasma, viscous at one side of the discontinuity, and ideal at the other side, are presented. This equilibrium configuration can be considered as a crude model of the flow near the heliopause in its near-flank regions, where the flow is essentially subsonic. The obtained results suggest that the near flanks of the heliopause are only convectively unstable. The relation of these results with results of recent numerical investigations of the absolute and convective instability of the heliopause are discussed.

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References

  1. Baranov, V.B.: 1990, Gas-dynamics of the solar-wind interaction with the interstellar-medium, Space Sci.Rev. 52, 89–120.CrossRefADSGoogle Scholar
  2. Baranov, V.B. and Malama, Y.G.: 1993, Model of the solar wind interaction with the local interstellar medium: Numerical solution of the self-consistent problem, J.Geophys.Res. 98 (A9), 15157–15163.ADSCrossRefGoogle Scholar
  3. Baranov, V.B., Ermakov, M.K. and Lebedev, M.G.: 1981, A three-component model of solar wind– interstellar medium interaction: Some numerical results, Sov.Astron.Lett. 7 (3), 206–209 (translated from Russian).ADSGoogle Scholar
  4. Baranov, V.B., Fahr, H.J. and Ruderman, M.S.: 1992, Investigation of macroscopic instabilities at the heliopause boundary surface, Astron Astrophys. 261, 341–347.ADSGoogle Scholar
  5. Baranov, V.B., Krasnobaev, K.V. and Kulikovski, A.G.: 1970, A model of the interaction of the solar wind with the interstellar medium, Sov.Phys.Dokl. 15, 791–793 (translated from Russian).ADSGoogle Scholar
  6. Baranov, V.B., Krasnobaev, K.V. and Ruderman, M.S.: 1976, On the model of the solar wind– interstellar medium interaction with two shock waves, Astrophys.Space Sci. 41, 481–490.CrossRefADSGoogle Scholar
  7. Baranov, V.B., Lebedev, M.G. and Ruderman, M.S.: 1979, The structure of the region of solar wind – interstellar medium interaction and its influence on H atom penetration in solar wind, Astrophys.Space Sci. 66, 441–451.CrossRefADSGoogle Scholar
  8. Belov, N.A.: 1997a, Instability of a tangential discontinuity in a plane flow with a stagnation point, Fluid Dyn. 32, 219–222 (translated from Russian).MATHMathSciNetGoogle Scholar
  9. Belov, N.A.: 1997b, Instability of a tangential discontinuity in an axisymmetric flow with a stagnation point, Fluid Dyn. 32, 780–783 (translated from Russian).MATHMathSciNetGoogle Scholar
  10. Belov, N.A. and Myasnikov, A.V.: 1999, Instability of a contact surface separating two hypersonic source flows, Fluid Dyn. 34, 379–387 (translated from Russian).MATHADSGoogle Scholar
  11. Bender, C.M. and Orszag, S.A.: 1987, Advanced Mathematical Methods for Scientists and Engineers, McGraw-Hill, Auckland.Google Scholar
  12. Braginskii, S.I.: 1965, Transport processes in plasmas, in: M.A. Leontovich (ed.), Reviews of Plasma Physics 1, 205–309, Consultant Bureau, New York.Google Scholar
  13. Briggs, R.J.: 1964, Electron-stream interaction with plasmas, MIT Press.Google Scholar
  14. Chalov, S.V.: 1996, On the Kelvin-Helmholtz instability of the nose part of the heliopause. 1. Axisymmetric disturbances, Astron Astrophys. 308, 995–1000.ADSGoogle Scholar
  15. Chandrasekhar, S.: 1961, Hydrodynamic and Hydromagnetic Stability, Clarendon, Oxford.Google Scholar
  16. Fahr, H.J., Neutsch, W., Grzedzielski, S., Macek, W. and Ratkiewicz, R.: 1986, Plasma transport across the heliopause, Space Sci.Rev. 43, 329–381.CrossRefADSGoogle Scholar
  17. Fejer, J.A.: 1964, Hydromagnetic stability at a fluid velocity discontinuity between compressible fluids, Phys.Fluids 7, 499–503.MATHMathSciNetCrossRefADSGoogle Scholar
  18. Kikina, N.G.: 1967, Effect of viscosity on the instability of tangential disturbances in an incompressible medium, Sov.Phys.– Acoustics 13, 184–187 (translated from Russian).Google Scholar
  19. Landau, L.D.: 1944, Ob ustoichivosti tangentsial'nyh razryvov v szhimaemoi zhidkosti, Dokl.Akad.Nauk USSR 44, 151–153 (in Russian).Google Scholar
  20. Myasnikov, A.V. and Belov, N.A.: 2000, On the stability of contact discontinuity separating two hypersonic sources, this issue.Google Scholar
  21. Myasnikov, A.V. and Zhekov, S.A.: 1991, Colliding stellar winds in WR+O binary systems, Astrophys.Space Sci. 184, 287–295.MATHCrossRefADSGoogle Scholar
  22. Myasnikov, A.V. and Zhekov, S.A.: 1993, Modelling of X-ray emission fromWR+O binary systems, Mon.Not.R.Astron.Soc. 260, 221–240.ADSGoogle Scholar
  23. Myasnikov, A.V. and Zhekov, S.A.: 1998, Dissipative models of colliding stellar winds – I. Effects of thermal conduction in wide binary systems, Mon.Not.R.Astron.Soc. 300, 686–694.ADSGoogle Scholar
  24. Nerney, S., Suess, S.T. and Schmall, E.J.: 1991, Flow downstream of the heliospheric terminal shock – magnetic-field kinematics, Astron.Astrophys. 250, 556–564.ADSGoogle Scholar
  25. Ruderman, M.S. and Fahr, H.J.: 1993, The effect of magnetic field on the macroscopic instability of the heliopause. I. Parallel interstellar magnetic fields, Astron.Astrophys. 275, 635–644.ADSGoogle Scholar
  26. Ruderman, M.S. and Fahr, H.J.: 1995, The effect of magnetic field on the macroscopic instability of the heliopause. II. Inclusion of solar wind magnetic fields, Astron.Astrophys. 299, 258–266.ADSGoogle Scholar
  27. Syrovastskii, S.I.: 1954, Neustoichivost' tangentsial'nyh razryvov v szhimaemoi zhidkosti, J.Exp.Theor.Phys. 27, 121–123 (in Russian).Google Scholar
  28. Syrovastskii, S.I.: 1957, Magnitnaya gidrodynamika, Usp.Fiz.Nauk 62, 247–303 (in Russian).Google Scholar
  29. Wang, C. and Belcher, J.W.: 1998, Numerical investigation of hydrodynamic instabilities of the heliopause, J.Geophys.Res. 103 (A1), 247–256.CrossRefADSGoogle Scholar
  30. Zhekov, S.A., Palla, F. and Myasnikov, A.V.: 1994, X-ray emission from colliding winds in pre-mainsequence binary-systems, Mon.Not.R.Astron.Soc. 271, 667–675.ADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Michael S. Ruderman
    • 1
    • 2
  1. 1.School of Mathematical and Computational SciencesSt Andrews UniversitySt Andrews, FifeUnited Kingdom
  2. 2.Institute for Problems in Mechanics RASMoscowRussia

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