Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-27T13:34:25.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Nonlinear hydrodynamic Rayleigh—Taylor instability of viscous magnetic fluids: effect of a tangential magnetic field

Published online by Cambridge University Press:  13 March 2009

Yusry O. El-Dib
Yusry O. El-Dib
Affiliation:
Department of Mathematics, Faculty of Education, Ain Shams Unviersity, Heliopolis, Cairo, Egypt
Get access Rights & Permissions [Opens in a new window]

Abstract

The nonlinear Rayleigh—Taylor instability of viscous magnetic fluids is considered under the influence of gravity and surface tension in the presence of a constant tangential magnetic field. The method of multiple-scales expansion is employed. A nonlinear Schrödinger equation with complex coefficients is imposed from the solvability conditions and used to analyse the stability of the system. A quadratic dispersion relation with complex coefficients is obtained. The Hurwitz criterion for a quadratic polynomial with complex coefficients is used to control the stability of the system. It is found that an increase in the viscosity increases the extent of the stable region in the presence of a magnetic field. Finally it is shown that the magnetic permeability of the fluid affects the stability conditions.

Type
Research Article
Information
Journal of Plasma Physics , Volume 51 , Issue 1 , February 1994 , pp. 1 - 11
Copyright
Copyright © Cambridge University Press 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Bashtovoy, V. G., Berkovsky, B. M. & Vislovich, A. N. 1988 Introduction to Thermomechaics of Magnetic Fluids. Hemisphere.Google Scholar
Bellman, R. & Pennington, R. H. 1954 Q. Appl. Maths 12, 151.Google Scholar
Bernhardt, P. A., Roussnl-Dupré, R. A., Pongratz, M. B., Haerendel, G., Valenzuela, A., Gurnett, D. & Anderson, R. R. 1987 J. Geophys. Res. 92, 5777.Google Scholar
Chandrashekhar, S. 1961 Hydrodynamic and Hydrornagnetic Stability. Oxford University Press.Google Scholar
Cowley, M. D. & Rosensweig, R. E. 1967 J. Fluid Mech. 30, 671.Google Scholar
El-Dib, Y. O. 1993 J. Plasma Phys. 49, 317.Google Scholar
Elhefnawy, A. R. F. 1992 Int. J. Theor. Phys. 31, 1505.Google Scholar
Emmons, H. W., Chang, C. T. & Watson, B. C. 1960 J. Fluid Mech. 7, 177.Google Scholar
Gailitis, A. 1977 J. Fluid Mech. 82, 401.Google Scholar
Kant, R. & Malik, S. K. 1985 Phys. Fluids 28, 3534.Google Scholar
Lewis, D. J. 1950 Proc. B. Soc. Lond. A 202, 81.Google Scholar
Lizuka, T. & Wadati, M. 1990 J. Phys. Soc. Japan 59, 3182.Google Scholar
Malik, S. K. & Singh, M. 1985 Q. Appl. Maths 43, 57.Google Scholar
Malik, S. K. & Singh, M. 1989a Phys. Rev. Lett. 26, 1724.Google Scholar
Malik, S. K. & Singh, M. 1989b Q. Appl. Maths. 47, 59.CrossRefGoogle Scholar
Nayfeh, A. H. 1976 J. Appl. Mech. 98, 584.Google Scholar
Newhouse, L. A. & Pozrikidis, C. 1990 J. Fluid Mech. 217, 615.Google Scholar
Obted, Allah M. H. & Yahia, A. A. 1991 Astrophys. Space Sci. 181, 183.Google Scholar
Rayleigh, Lord 1900 Scientific Papers, vol. II. Cambridge University Press.Google Scholar
Rosensweig, R. E. 1985 Ferrohydrodynamics. Cambridge University Press.Google Scholar
Taylor, G. I. 1950 Proc. R. Soc. Lond. A 201, 192.Google Scholar
Zahreddine, Z. & Elshehawey, E. F. 1988 Indian J. Pure Appl. Maths 19, 963.Google Scholar
Zelazo, R. E. & Melcher, J. R. 1969 J. Fluid Mech. 39, 1.Google Scholar