Fluid Dynamics

, Volume 22, Issue 6, pp 879–885 | Cite as

Nonlinear internal waves in a fluid of infinite depth in the presence of a horizontal magnetic field

  • M. S. Ruderman


An investigation is made into the propagation of long nonlinear weakly nonone-dimensional internal waves in an incompressible stratified fluid of infinite depth in the presence of a horizontal magnetic field. It is shown that such waves are described by an equation representing the extension of the Benjamin-Ono equation to the weakly nonone-dimensional case. The equation obtained differs from that obtained in [4], which is attributable to the anisotropy of the medium resulting from the presence of a magnetic field. The stability of a soliton with respect to flexural perturbations is investigated. A particular case of the variation of the density with height at constant Alfvén velocity is examined in detail.


Magnetic Field Anisotropy Soliton Internal Wave Stratify Fluid 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature cited

  1. 1.
    B. T. Benjamin, “Internal waves of permanent form in fluids of great depth,” J. Fluid Mech.,29, 559 (1967).Google Scholar
  2. 2.
    R. E. Davis and A. Acrivos, “Solitary internal waves in deep water,” J. Fluid Mech.,29, 593 (1967).Google Scholar
  3. 3.
    H. Ono, “Algebraic solitary waves in stratified fluids,” J. Phys. Soc. Jpn.,39, 1082 (1975).Google Scholar
  4. 4.
    M. J. Ablowitz and H. Segur, “Long internal waves in fluids of great depth,” Stud. Appl. Math.,62, 249 (1980).Google Scholar
  5. 5.
    B. B. Kadomtsev and V. I. Petviashvili, “Stability of solitary waves in weakly dispersive media,” Dokl. Akad. Nauk SSSR,192, 753 (1970).Google Scholar
  6. 6.
    D. J. Korteweg and G. de Vries, “On the change of form of long waves advancing in a rectangular channel, and on a new type of long stationary waves,” Philos. Mag.,39, 422 (1895).Google Scholar
  7. 7.
    R. G. Giovanelli, “Oscillations and waves in a sunspot,” Solar Phys.,27, 71 (1972).Google Scholar
  8. 8.
    P. S. Cally and J. A. Adam, “On photospheric and chromospheric penumbral waves,” Solar Phys.,85, 97 (1983).Google Scholar
  9. 9.
    K. D. Danov and M. S. Ruderman, “Nonlinear waves on shallow water in the presence of a horizontal magnetic field,” Izv. Akad. Nauk SSSR, Mekh. Zhidk. Gaza, No. 5, 110 (1983).Google Scholar
  10. 10.
    V. I. Yudovich, “Spectral properties of an oscillational differential operator on a straight line,” Usp. Mat. Nauk,38, 205 (1983).Google Scholar
  11. 11.
    L. A. Ostrovskii and V. I. Shrira, “Instability and self-refraction of solitons,” Zh. Eksp. Teor. Fiz.,71, 1412 (1976).Google Scholar

Copyright information

© Plenum Publishing Corporation 1988

Authors and Affiliations

  • M. S. Ruderman
    • 1
  1. 1.Moscow

Personalised recommendations