Skip to main content
Log in

Nonlinear Kelvin-Helmholtz instability in hydromagnetics

  • Published:
Astrophysics and Space Science Aims and scope Submit manuscript

Abstract

By taking into account the temporal as well as the spatial effects, a weakly nonlinear theory of the propagation of wave packets in the Kelvin-Helmholtz instability problem in the presence of uniform magnetic fields, acting along the surface of separation of two moving superposed fluids, is presented. With the use of the method of multiple scaling, the evolution of the amplitude of the two-dimensional wave packets, which is governed by a nonlinear Klein-Gordon equation, is derived. The various stability criteria arising out of this equation are examined. The nonlinear cut-off wavenumber, which separates the region of stability from that of instability, is determined.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Briggs, R. J.: 1964,Electron-Stream Interactions with Plasmas, M.I.T. Press, Cambridge.

    Google Scholar 

  • Chandrasekhar, S.: 1961,Hydrodynamic and Hydromagnetic Stability, Clarendon Press, Oxford.

    Google Scholar 

  • Drazin, P. G.: 1970,J. Fluid Mech. 42, 321.

    Google Scholar 

  • Eckhaus, W.: 1965,Studies in Nonlinear Stability Theory, Springer Verlag, Heidelberg.

    Google Scholar 

  • Kant, R. and Malik, S. K.: 1982,Astrophys. Space Sci. 86, 345.

    Google Scholar 

  • Makhankov, V. G.: 1978,Phys. Reports 35C, 1.

    Google Scholar 

  • Nayfeh, A. H. and Saric, W. S.: 1971,J. Fluid Mech. 49, 209.

    Google Scholar 

  • Nayfeh, A. H. and Saric, W. S.: 1972,J. Fluid Mech. 55, 311.

    Google Scholar 

  • Newell, A. C.: 1974,Lect. Appl. Math. 15, 157.

    Google Scholar 

  • Stuart, J. T.: 1958,J. Fluid Mech. 4, 1.

    Google Scholar 

  • Weissman, M. A.: 1979,Phil. Trans. Roy. Soc. London 290, 58.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Malik, S.K., Singh, M. Nonlinear Kelvin-Helmholtz instability in hydromagnetics. Astrophys Space Sci 109, 231–239 (1985). https://doi.org/10.1007/BF00651269

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00651269

Keywords

Navigation