Skip to main content
SpringerLink
Log in

Propagation of surface gravity waves in a layer of electrically conducting liquid

  • Published:
Fluid Dynamics Aims and scope Submit manuscript

Abstract

The wave motion of a weakly conducting incompressible liquid in a transverse magnetic field is investigated within the framework of the nonlinear theory of magnetohydrodynamics. The influence of MHD interaction effects on harmonic perturbations of infinitesimal amplitude is analyzed and a long-wave equation of the Kortewegde Vries-Burgers type describing the evolution of weakly nonlinear perturbations of the free surface is derived. It is shown that the influence of the electrical conductivity leads to a change in both the dissipative and the dispersive properties of the system.

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

Literature cited

  1. L. E. Fraenkel, “A shallow-liquid theory in magnetohydrodynamics,” J. Fluid Mech.,7, 81 (1960).

    Google Scholar 

  2. J. A. Shercliff, “Anisotropic surface waves under a vertical magnetic force,” J. Fluid Mech.,38, 353 (1969).

    Google Scholar 

  3. M. Hofman, “Nonlinear waves on the free surface of an electrically conducting liquid,” Wave Motion, No. 5, 115 (1983).

    Google Scholar 

  4. T. N. Aitov, A. V. Ivanov, and A. V. Tananaev, “Trough flow of liquid metal in a coplanar magnetic field,” Magn. Gidrodin., No. 1, 91 (1987).

    Google Scholar 

  5. I. T. Selezov, “Some approximate forms of the equations of motion of magnetoelastic media,” Izv. Akad. Nauk SSSR, Mekh. Tverd. Tela, No. 5, 86 (1975).

    Google Scholar 

  6. G. B. Whitham, Linear and Nonlinear Waves, Wiley-Interscience, New York (1974).

    Google Scholar 

  7. E. Ott and R. N. Sudan, “Damping of solitary waves, Phys. Fluids,13, 1432 (1970).

    Google Scholar 

  8. V. N. Karpman, Nonlinear Waves in Dispersive Media [in Russian], Nauka, Moscow (1973).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kiev

    S. V. Korsunskii

Authors
  1. S. V. Korsunskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 4, pp. 173–175, July–August, 1989.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Korsunskii, S.V. Propagation of surface gravity waves in a layer of electrically conducting liquid. Fluid Dyn 24, 637–639 (1989). https://doi.org/10.1007/BF01052433

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01052433

Keywords

Search

Navigation