Skip to main content
SpringerLink
Log in

Nonlinear waves in superposed fluids

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

Abstract

A weakly nonlinear theory of wave propagation in superposed fluids in the presence of magnetic fields is presented in this paper. We derive the equations governing the evolution of the amplitude of the progressive as well as the standing waves. It is demonstrated that the waves can be unstable against modulation in the presence of the magnetic fields. We also obtain the nonlinear cut off wave number which separates the region of stability from instability.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

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

    Google Scholar 

  • Gater, R. L. and L'Eouyer, M. R.: 1969, ‘A Fundamental Investigation of the Phenomena that Characterize Liquid Film Cooling’, Purdue University Rep. No. Tm-69-1.

  • Gold, H., Otis, J. H., and Schlier, R. E.: 1971, ‘Surface Liquid Film Characteristics: An Experimental Paper’, AIAA Paper No. 71-623.

  • Hasegawa, A.: 1974,Plasma Instabilities and Nonlinear Effects, Springer-Verlag.

  • Helmholtz, H.: 1882, ‘Über discontinuierliche Flüssikeitsbewegungen’, inWissenschaftliche Abhandlungen 146, J. A. Barth, Leipzig.

    Google Scholar 

  • Karpman, V. I.: 1975,Nonlinear Waves in Dispersive Media, Pergamon Press.

  • Lighthill, M. J.: 1965,J. Inst. Math. Appl. 1, 269.

    Google Scholar 

  • Lord Kelvin: 1910,Hydrodynamics and General Dynamics, Cambridge, England.

  • Maslowe, S. A. and Kelly, R. E.: 1970,Int. J. Non-Linear Mech. 5, 427.

    Google Scholar 

  • Michael, D. H.: 1955,Proc. Camb. Phil. Soc. 51, 528.

    Google Scholar 

  • Nayfeh A. H. and Saric, W. S.: 1972,J. Fluid Mech. 50, 311.

    Google Scholar 

  • Ong, R. S. B. and Roderick, N.: 1972,Planetary Space Sci. 20, 1.

    Google Scholar 

  • Saric, W. S. and Marshall, B. W.: 1971,AIAA J. 9, 1946.

    Google Scholar 

  • Southwood, D. J.: 1968,Planetary Space Sci. 16, 587.

    Google Scholar 

  • Whitham, G. B.: 1974,Linear and Nonlinear Waves, John Wiley, New York.

    Google Scholar 

  • Zakharov, V. E. and Shabat, A. B.: 1972,Soviet Phys. JETP 34, 62.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Panjab University, Chandigarh, India

    R. Kant & S. K. Malik

Authors
  1. R. Kant
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. K. Malik
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kant, R., Malik, S.K. Nonlinear waves in superposed fluids. Astrophys Space Sci 86, 345–360 (1982). https://doi.org/10.1007/BF00683341

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00683341

Keywords

Search

Navigation