Hostname: page-component-8448b6f56d-t5pn6 Total loading time: 0 Render date: 2024-04-19T16:17:50.547Z Has data issue: false hasContentIssue false
  • English
  • Français

Hydromagnetic stability of a compressible jet

Published online by Cambridge University Press:  13 March 2009

B. B. Chakraborty  and
H. K. S. Iyengar
B. B. Chakraborty
Affiliation:
Mathematics Section, Department of Chemical Technology, Bombay University, Matunga, Bombay 400 019
H. K. S. Iyengar
Affiliation:
Mathematics Section, Department of Chemical Technology, Bombay University, Matunga, Bombay 400 019
Get access Rights & Permissions [Opens in a new window]

Abstract

This paper studies the hydromagnetic stability of a cylindrical jet of a perfectly-conducting, inviscid and compressible fluid. The fluid velocities and magnetic fields, inside and outside the jet, are uniform and in the axial direction, with possible discontinuities in their values across the jet surface. For large wavelength disturbances, the jet behaves as though it were incompressible. Numerical evaluation of the roots of the dispersion relation for a number of different magnetic-field strengths and jet velocities, but for disturbances of finite ranges of wavenumbers, indicates that the jet is stable against axisymmetric disturbances, but instability is present for asymmetric disturbances when the magnetic fields are sufficiently small. The magnetic field is found to have a stabilizinginfluence when compressibility is not very large; for high compressibility, it may have even a destabilizing effect. The paper explains physically the roles of compressibility and the magnetic field in bringing about the stability of the jet. When the wavelengths of disturbances are small, the dispersion relation reduces to that for a two-dimensional jet and a vortex sheet; and the results for these cases are known from earlier studies.

Type
Research Article
Information
Journal of Plasma Physics , Volume 14 , Issue 3 , December 1975 , pp. 443 - 448
Copyright
Copyright © Cambridge University Press 1975

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

Batchelor, G. K. & Gill, A. E. 1962 J. Fluid Mech. 14, 529.Google Scholar
Chakraborty, B. B. 1968 a Phys. Fluids 11, 2402.Google Scholar
Chakraborty, B. B. 1968 Prog. Theor. Phys. (Kyoto) 40, 210.Google Scholar
Cowling, T. G. 1957 Magnetohydrodynamics. Interscience.Google Scholar
Fejer, J. A. 1964 Phys. Fluids 7, 499.Google Scholar
Fejer, J. A. & Miles, J. W. 1963 J. Fluid Mesh. 15, 335.Google Scholar
Landau, L. D. & Lifshitz, E. M. 1960 Electrodynamics of Continuous Media. Pergamon.Google Scholar
Lessen, M., Fox, J. A. & Zien, H. M. 1965 J. Fluid Mech. 21, 129.CrossRefGoogle Scholar
Lessen, M., Zien, H. M. & Leibovich, S. 1966 J. Fluid Mech. 24, 335.Google Scholar
Michael, D. H. 1953 Proc. Camb. Phil. Soc. 49, 166.Google Scholar
Michael, D. H. 1955 Proc. Camb. Phil. Soc. 51, 528.Google Scholar
Squire, H. B. 1933 Proc. Roy. Soc. A 142, 621.Google Scholar
Unsöld, A. 1969 The New Cosmos. Longmans.Google Scholar
Watson, G. N. 1952 A Treatise on the Theory of Bessel Functions. Cambridge University Press.Google Scholar